University of Genoa
Ph.D. Program in Space Science and Engineering
CYCLE XXVI
Doctor of Philosophy Thesis
Opportunistic Spectrum Access
in Wide-band Cognitive Radios
via Compressive Sensing
SSD: ING-INF 03
Author:
Supervisor:
Chairperson:
Sk. Shariful Alam
Prof. Carlo S. Regazzoni
Prof. Silvano Cincotti
April 2014
Design is not just what it looks like
and feels like - Design is how it works
( Steve Jobs)
Abstract
With the increasing emergence of new wireless systems and
the explosive development of mobile internet applications, the demands on Radio Frequency spectrum have been constantly increasing, and therefore, the related demands for bandwidth, wireless communication technology is facing a potentially scarcity of
radio spectrum resources. However, spectrum measurement campaigns have shown that the shortage of radio spectrum is due to
inefficient usage and static spectrum allocation policies. Thus, to
be able to meet the requirements of bandwidth and spectrum utilization, spectrum underlay access, one of the techniques in Cognitive Radio Networks, has been proposed as a frontier solution
to deal with this problem.
Nowadays, cognitive radio is one of the most promising paradigms
in the arena of wireless radio communications, as it provides the
proficient use of radio resources. In the Cognitive Radio networks,
the Cognitive Radio (CR) can dynamically regulate its transmission parameters. Proper utilization of the radio spectrum can be
performed by the scheme of dynamic spectrum accessing which
is undoubtedly necessary. To regulate its Radio Frequency (RF)
transmission properties, the CRs are required to sense the radio
spectrum periodically for being aware of the licensed users. The
enhancement of the spectrum efficiency can opportunistically be
iii
iv
achieved by dynamic spectrum management schemes
The thesis is divided into an introduction part and five parts
based on peer-reviewed international research publications. The
introduction part provides the reader with an overview and background on Cognitive Radio Networks. In this thesis work, we
wish to present various approaches for Dynamic Spectrum Access
schemes and a survey of spectrum sensing methodologies for cognitive radio networks. Also, the challenges associated with spectrum
sensing and dynamic spectrum access techniques are analyzed.
Wideband spectrum sensing is a challenging task due to the
constraints of Digital Signal Processing) unit using in extant wireless systems. Compressive Sensing is a new paradigm in signal
processing, chosen for sparse wideband spectrum estimation with
compressive measurements, thus provides relief of high-speed Digital Signal Processing (DSP) requirements of CR receivers. In CS,
whole wideband spectrum is estimated to find an opportunity for
a CR usage requiring significant computation as well as sensing
time, hence shrinkage the achievable throughput of CRs. In this
paper, a novel model-based CR receiver wideband sensing unit is
addressed where a significant portion of the wideband spectrum
is approximated through compressed sensing rather than recovering the entire wideband spectrum. This model necessitates lesser
sensing time and lower computational burden to detect a signal
and as a result a level up of throughput is obtained.
University of Genova – DITEN
Contents
Abstract . . . . .
List of Figures .
List of Tables . .
List of Acronyms
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. iii
. viii
. xi
. xiii
1 Introduction
1.1 Motivations: Spectrum Sensing for Dynamic Spectrum Access . . . . . . . . . . . . . . . . . . . . . .
1.2 Preliminaries of Cognitive Radio Networks . . . . .
1.2.1 Spectrum holes . . . . . . . . . . . . . . . .
1.2.2 Cognitive radio features . . . . . . . . . . .
1.3 Challenges of Dynamic Spectrum Access in Cognitive Radio Networks . . . . . . . . . . . . . . . . .
1.4 Objectives and Research Contributions . . . . . . .
1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . .
8
10
12
2 State of the Art and Literature Reviews
2.1 Introduction . . . . . . . . . . . . . . . . . .
2.2 Dynamic Spectrum Access in CR Networks
2.2.1 Hierarchical access model . . . . . .
2.2.2 Dynamic exclusive use model . . . .
2.2.3 Open sharing model . . . . . . . . .
15
16
18
19
21
23
v
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
3
4
5
6
vi
CONTENTS
2.3
.
.
.
.
.
.
.
.
.
26
27
32
40
41
41
42
42
43
Overview of the Proposed Approach
3.1 Introduction . . . . . . . . . . . . . . . . . . . . .
3.2 Measurement Matrix of Compressive Sensing (CS)
Recovery . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Sparsity Level Detection . . . . . . . . . . . . . . .
3.4 Signal Reconstruction Algorithm . . . . . . . . . .
3.4.1 Discrete Walsh-Hadamard transform coding
3.4.2 Discrete cosine transform . . . . . . . . . .
3.4.3 Discrete Fourier transform (DFT) . . . . .
3.5 Different Schemes of CS Recovery . . . . . . . . . .
3.5.1 Basis pursuit . . . . . . . . . . . . . . . . .
3.5.2 Orthogonal Matching Pursuit . . . . . . . .
3.6 Simulations and Analytic Results . . . . . . . . . .
3.6.1 Normalized Mean Squared Error (MSE) performance . . . . . . . . . . . . . . . . . . .
3.6.2 Average execution time comparisons: . . . .
3.6.3 Detection performance versus compression
ratio . . . . . . . . . . . . . . . . . . . . . .
45
45
2.4
2.5
2.6
2.7
3
Spectrum Sensing Techniques . . .
2.3.1 Narrowband sensing . . . .
2.3.2 Wideband sensing . . . . .
Cooperative Spectrum Sensing . .
Signal Estimation Schemes . . . .
2.5.1 Parametric methods . . . .
2.5.2 Nonparametric methods . .
MIMO Scheme in Cognitive Radios
Summary . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
46
48
49
50
51
53
54
56
57
59
60
61
62
4 Compressive Sensing for Wideband Cognitive Radios
65
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 66
University of Genova – DITEN
CONTENTS
vii
4.2
Signal model . . . . . . . . . . . . . . . . . . . . .
70
4.3
System Model and Problem Formulation . . . . . .
72
4.4
Computational Complexity of the Proposed Method 73
4.5
Performance Analysis and Simulation Results . . .
76
4.6
Achievable Throughput of a Stand-Alone CR Terminal . . . . . . . . . . . . . . . . . . . . . . . . .
81
Summary . . . . . . . . . . . . . . . . . . . . . . .
85
4.7
5 Cooperative Compressive Sensing for Wideband Cognitive Radios
87
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . .
87
5.2
System Model . . . . . . . . . . . . . . . . . . . . .
88
5.3
Decision Fusion . . . . . . . . . . . . . . . . . . . .
90
5.4
Performance Comparison and Simulation Results .
91
5.5
Practical Implementation Challenges . . . . . . . .
95
5.5.1
Degrees of freedom to enhance detection performance . . . . . . . . . . . . . . . . . . .
96
5.5.2
Detection without estimation . . . . . . . .
97
5.5.3
Shortcomings in signal detection . . . . . .
98
5.5.4
Random Demodulator (RD)/ Analog-to-Information
Converter (AIC) implementation issues . . 102
5.5.5
Summary . . . . . . . . . . . . . . . . . . . 103
6 MIMO Scheme for Opportunistic Radio Systems 105
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . 106
6.2
Problem Definition . . . . . . . . . . . . . . . . . . 109
6.3
Transmit Beamforming . . . . . . . . . . . . . . . . 113
6.4
6.3.1
Channel model . . . . . . . . . . . . . . . . 114
6.3.2
Derivation of the achievable rates . . . . . . 116
6.3.3
Computation of matrix A . . . . . . . . . . 118
Explicit ZF-BF Scheme for a CR System . . . . . . 118
University of Genova – DITEN
viii
6.5
6.6
6.7
CONTENTS
Linear Pre and Post Processing Requirements to
Exploit Unique Degree of Freedom . . . . . . . . . 121
Computational Load Required at the CR Nodes . . 125
Summary . . . . . . . . . . . . . . . . . . . . . . . 136
Conclusions and Future Work
136
Bibliography
143
University of Genova – DITEN
List of Figures
1.1
Spectrum used by Primary Users (PUs) . . . . . .
4
2.1
Fundamental classification of dynamic spectrum access . . . . . . . . . . . . . . . . . . . . . . . . . .
19
(a) Spectrum Underlay, (b) Spectrum Overlay (e.g.
Spectrum Pooling or OSA) . . . . . . . . . . . . .
20
2.3
Hierarchy of spectrum sensing in cognitive radio .
28
3.1
Normalized MSE performance versus compression
rate, M
N (setting SNR = 20 dB) . . . . . . . . . . .
61
2.2
3.2
3.3
3.4
4.1
4.2
M
N
Execution time versus compression rate,
(setting
SNR = 20 dB). . . . . . . . . . . . . . . . . . . . .
62
rate, M
N .(setting
Detection probability versus compression
SNR = 20 dB) . . . . . . . . . . . . . . . . . . . .
63
Influence of compression ratio on the detection performance. . . . . . . . . . . . . . . . . . . . . . . .
64
Schemetic block to detect the sparse wideband segment. . . . . . . . . . . . . . . . . . . . . . . . . .
73
Influence of compression ratio on the detection performance. . . . . . . . . . . . . . . . . . . . . . . .
77
ix
x
LIST OF FIGURES
4.3
Detection performance as a function of compression
ratio M
N . . . . . . . . . . . . . . . . . . . . . . . .
78
Order of computational burden needed with the influence of no. of filters. . . . . . . . . . . . . . . . .
79
4.5
Order of memory space requirement with the influence of no. of filters. . . . . . . . . . . . . . . . .
80
4.6
Graphical structure of a typical frame of a CR data
transmission. . . . . . . . . . . . . . . . . . . . . .
81
Simulation of achievable rate against sensing time
for a fixed frame length . . . . . . . . . . . . . . .
83
Illustration of the achievable rate against Frame
length for a fixed sensing time . . . . . . . . . . . .
84
Influence of the CR Achievable rate on the sensing
time . . . . . . . . . . . . . . . . . . . . . . . . . .
84
5.1
Detection probability as a function of sparsity. . .
93
5.2
ROC performance of stand-alone and cooperative
narrowband CR nodes. . . . . . . . . . . . . . . . .
94
ROC performance of stand-alone and cooperative
wideband CR nodes. . . . . . . . . . . . . . . . . .
95
4.4
4.7
4.8
4.9
5.3
6.1
The considered Multiple Input Multiple Output (MIMO)
interference channel model. In the same region
three primary systems, having overall M1 = 3 transmitting and N1 = 4 receiving antennas, operate in
a given frequency band. The primary systems are
thought as half-duplex systems but for full duplex
systems an analogous scheme applies. A MIMO
secondary system with M2 transmitting and N2 receiving antennas would like to reliably communicate in the same band without affecting the transmissions of primary systems. . . . . . . . . . . . . 111
University of Genova – DITEN
LIST OF FIGURES
6.2
6.3
6.4
6.5
Processing chain for the secondary transmitter and
receiver when just one degree of freedom is available
to the secondary system. . . . . . . . . . . . . . . .
Processing chain for the secondary transmitter and
receiver according to [17], independently of the number of degrees of freedom of the secondary system
(the case it is equal to one being included). . . . .
Computational load expressed in flops required by
the secondary transmitter and receiver proposed in
Fig. 6.2, when M1 = N1 . This load is compared
with some meaningful approximation of the flops
required by the secondary transmitter and receiver
shown in Fig. 6.3, under the same condition. . . .
Computational load expressed in flops required by
the secondary transmitter and receiver proposed in
Fig. 6.2, when M1 = N1 +1. This load is compared
with some meaningful approximation of the flops
required by the secondary transmitter and receiver
shown in Fig. 6.3, under the same condition. . . .
University of Genova – DITEN
xi
124
127
134
135
xii
LIST OF FIGURES
University of Genova – DITEN
List of Tables
2.1
Comparison of different spectrum sensing schemes
[73]. . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
33
xiv
LIST OF TABLES
University of Genova – DITEN
List of Acronyms
AWGN
Additive White Gaussian Noise
AIC
Analog-to-Information Converter
ADC
Analog-to-Digital Converter
AR
Auto-Regressive
ARMA
Auto-Regressive Moving Average
BP
Basis Pursuit
BPF
Band-Pass Filter
CR
Cognitive Radio
CM
Cognitive Manager
CRN
Cognitive Radio Network
CS
Compressive Sensing
CSI
Channel State Information
CoSaMP Compressive Sampling Orthogonal Matching Pursuit
DWHT
Discrete Walsh Hadamard Transform
xv
xvi
LIST OF TABLES
DFT
Discrete Fourier Transform
DCT
Discrete Cosine Transform
DoF
Degree of Freedom
DSA
Dynamic Spectrum Access
DSP
Digital Signal Processing
DM
Decision Maker
DVB-T
Digital Video Broadcasting-Terrestrial
FCC
Federal Communications Commission
GLRT
General Likelihood Ratio Test
iid
independent and identically distributed
KLT
KarhunenLove Transform
MA
Moving Average
MAC
Medium Access Control
MASS
Multi-rate Asynchronous wideband Sub-Nyquist
Sampling
MP
Matching Pursuit
MSE
Mean Squared Error
MWC
Modulated Wideband Converter
MIMO
Multiple Input Multiple Output
NP
Neyman-Pearson
NNZ
Number of Non-Zero
University of Genova – DITEN
LIST OF TABLES
OSA
Opportunistic Spectrum Access
OMP
Orthogonal Matching Pursuit
OSGA
One-Step Greedy Algorithm
OFDM
Orthogonal Frequency Division Multiplexing
PSD
Power Spectral Density
PU
Primary User
QoS
Quality of Service
RAN
Radio Access Network
RD
Random Demodulator
ROC
Receiver Operating Characteristics
RF
Radio Frequency
RIP
Restricted Isometry Property
SCF
Spectral Correlation Function
SDR
Software-defined Radio
SVD
Singular Value Decomposition
UR
Underlay Radio
VHF
Very High Frequency
WSS
Wide-Sense Stationary
WHT
Walsh Hadamard Transform
ZFBF
Zero-Forcing Beam-Forming
DBN
Dynamic Bayesian Network
University of Genova – DITEN
xvii
xviii
LIST OF TABLES
University of Genova – DITEN
Chapter 1
Introduction
The strategy of static spectrum allocation policies leads spectral underutilization, an innovative technology named Cognitive
Radio (CR), has been designed to exploit spectrum white spaces.
Spectrum sensing is the most crucial part upon which the full
operation of CR relies.
In particular, a CR should explore the information about spectrum white spaces and geographical location which is then opportunistically utilized by the CRs, thus leads enhanced spectrum
efficiency. Several narrowband spectrum sensing algorithms have
been studied in the literature [34], [10] [32] [82] [73] and references therein, including matched-filtering, energy detection, and
cyclostationary feature detection.
To obtain higher opportunistic throughput for different multimedia data services wideband spectrum sensing [25] [69] [61]
is necessary for future interoperable wireless networks as Shannons formula says that, under certain conditions, the maximum
theoretically throughput is directly proportional to the spectral
bandwidth. However, conventional wideband spectrum sensing
1
2
Chapter 1 : Introduction
techniques becomes challenging due to high sampling frequency
functioning at or above Nyquist rates could lead implementation complexity [53]. There are several wideband sensing approaches exploiting sub-Nyquist sampling commonly known as
Compressive Sensing (CS), thus employs relief of high-speed Digital Signal Processing (DSP)) units and is elaborately illustrated
in [53] [23] [15] [72] [19].Wideband spectrum sensing is the key
technology that enables the efficient operation of both the primary user and the CR networks. However, wideband spectrum
sensing systems are difficult to design, due to either high implementation complexity or high energy consumption from high-rate
analog-to-digital converter (ADC).
This thesis points out the issues of wideband spectrum sensing in CR networks. It is proposed an efficient way for wideband
cognitive receiver sensing unit that estimate the highly sparse segment of wideband through compressed sensing rather than entire
wideband signal and then discover spectral opportunity for a cognitive user. The proposed model deals with the highly-sparse signal segment which provides better spectral estimation and hence
improves the detection performance, demonstrated by the simulation. Eventually, reduction of computational complexity as well
as a level up of detection performance of the proposed method
has sorted out compared to a single Radio Frequency (RF) chain
followed by compressed sensing. Therefore, a reduction of computational complexity is addressed without interfering with the
detection performances, evaluated after spectrum estimation of a
preferred band of interest by means of a well-known energy detector.
University of Genova – DITEN
1.1 Motivations: Spectrum Sensing for Dynamic
Spectrum Access
1.1
3
Motivations: Spectrum Sensing for
Dynamic Spectrum Access
The radio frequency (RF) spectrum is a limited natural resource regulated by government agencies, such as the federal communications commission (FCC) [2] in the United States. Under
current policy, all frequency bands are exclusively and statistically
licensed to wireless networks on a particular time period for a specific geographical location, and every system has assigned a fixed
frequency band. In recent years, due to the support of huge number of wireless systems and wireless multimedia services, it has become evident that there will not be enough spectrum exclusively
available for all wireless systems currently under development.
Interestingly, the spectrum policy task force (SPTF) within the
FCC has reported that localized temporal and geographic spectrum utilization efficiency ranges from 15% to 85% [2].
Therefore, the most crucial task of unlicensed radio (also termed
as simply Cognitive Radio in literature) is to reliably identify
available frequency bands across multiple dimensions like time,
space, frequency, angle and code etc., and efficiently exploit them
by dynamically updating its transmission parameters under the
stringent requirement of avoiding interference to the Primary User
(PU)s of that spectrum. To accomplish this, the CRs rely on robust and efficient spectrum sensing to identify vacant frequency
bands under uncertain RF environment and to detect PUs with
high probability of detection, as soon as the incumbents become
active in the band of interest [73]. If the spectrum hole is reacquired by a PU, the CR should vacate the band or adjust its
transmission parameters to accommodate the PU or , if available/possible, shift to another spectrum hole. Many extensive
studies have been carried out to develop efficient and reliable specUniversity of Genova – DITEN
4
Chapter 1 : Introduction
trum sensing methods. Despite numerous spectrum sensing algorithms being reported in the literature [69] [15] [64] [53], few of
them are effective for wideband spectrum sensing due to energy
and hardware constraints.
Power
Frequency
Spectrum
used by PUs
Opportunistic
access
Spectrum
white space
Time
Figure 1.1: Spectrum used by Primary Users (PUs)
1.2
Preliminaries of Cognitive Radio Networks
In this section, we would like to address some basic features
which relate to Cognitive Radio. Cognitive radio is essentially
an evolution of Software-defined Radio which is formally defined
by Federal Communications Commission [2] as A Cognitive Radio is a radio that can change its transmitter parameters based
on interaction with the environment in which it operates. The ulUniversity of Genova – DITEN
1.2 Preliminaries of Cognitive Radio Networks
5
timate objective of CR is to utilize the underutilized spectrum.
In essence, this means that CR introduces intelligence to conventional radio such that it searches for a vacant spectrum spaces or
a spectrum hole [73].
1.2.1
Spectrum holes
A spectrum hole is originally defined as a band of frequencies
which are readily assigned to a PU, however, it may not be always
used by the PU at a specific time or a geographic area [41]. Depending on the communication environment, the spectrum holes
can be identified following frequency and time (Fig. 1.1):
• Spectrum hole in time domain: This is defined as a frequency band that is not currently being occupied by a PU
for a certain period of time. By using advanced spectrum
sensing techniques, a CR can detect spectrum holes and opportunistically access it without degrading any Quality of
Service (QoS) of the licensed user or the PU.
• Spectrum hole in frequency domain: It is a contiguous frequency band in which activities of the CR do not cause any
harmful interference to the PUs.
• Spectrum hole in spatial domain: This is a frequency band
in a specific geographic location area where the PU transmission is being occupied. The CR can utilize this empty
band opportunistically if it is outside this location (see 1.1).
Additionally, spectrum holes may also be categorized into socalled spaces as follows [41]
• White spaces: In spectrum white spaces, license bands
are no more exist at that time, only natural noises such as
broadband thermal noise and impulsive noise are present.
University of Genova – DITEN
6
Chapter 1 : Introduction
• Gray spaces: In gray spaces which partially filled by low
power interferers.
• Black spaces: Those places are occupied by the high priority licensed users which is also called as PUs.
According to the space classification, a CR node can transmit
in the gray and white spaces, but it is prohibited to operate in
the black space once the PU is active. On the basis of spectrum
hole concepts, an important definition of CR, which is generally
accepted by the research community, has been given in [41]: is an
intelligent wireless communication system that is aware of its surrounding environment (i.e., outside world), and uses the methodology of understanding-by-building to learn from the environment
and adapt its internal states to statistical variations in the incoming RF stimuli by making corresponding changes in certain
operating parameters (e.g.,transmit-power, carrier-frequency, and
modulation strategy) in real-time, with two primary objectives in
mind :
1. Highly reliable communications whenever and wherever needed;
2. Efficient utilization of the radio spectrum.
Clearly, the awareness and adjustment according to the fluctuations of the radio environment to create reliable communications
and efficient spectrum utilization are the most important criteria
in a Cognitive Radio Network (CRN).
1.2.2
Cognitive radio features
Cognitive capabilities are the most different characteristics of
a CRN from traditional wireless communication networks. These
capabilities allow an CR to observe the surrounding radio environment such as available frequency, interference temperature, noise
University of Genova – DITEN
1.2 Preliminaries of Cognitive Radio Networks
7
power, distance, and so on. Depending on the collected information, the CRs will make decisions about the selected frequency,
transmit power level, or modulation scheme, to achieve an optimal performance. In fact, to implement the CRN in practice, it
should have main characteristics as follows [48]
• A CR should take advantage of efficient spectrum sensing
and analysis techniques so that the CR can maintain continuous spectrum and keep a reliable communication.
• A CR should utilize dynamic spectrum access approaches
which can adapt to the fluctuating nature of the CRN.
• A CR should be equipped with a unified cross-layer architecture in order to meet different QoS demands.
• A CR should share the spectrum information with other
users and coordinate communication to cause minimal interference or no collisions to the PUs occupying the same
frequency bands.
Another key feature of CR is reconfigurability. In order to
adapt with the RF environment, the CR should have the capability of changing its operational parameters [5]
• The CR is capable of changing its operating frequency in
order to avoid the PU or to share spectrum with other users.
• The CR should adaptively reconfigure the modulation scheme,
according to the user requirements and the channel conditions.
• Within the power constraints, transmission power can be reconfigured in order to mitigate interference or improve spectral efficiency.
University of Genova – DITEN
8
Chapter 1 : Introduction
• The CR can also be used to provide interoperability among
different communication systems by changing modulation
scheme etc.
Spectrum sensing is the foundation of all other cognitive radio
functions. The other functionalities of the CR can be spectrum
sharing, spectrum management and spectrum mobility. The first
functionality (spectrum sharing) are related to coordination and
reconfiguration among cognitive radio terminals. However, the
last two functionalities require interactions with all other layers
for exchanging information about QoS requirements, application
control, routing, reconfiguration, and scheduling.
1.3
Challenges of Dynamic Spectrum Access in Cognitive Radio Networks
Overall, the benefits of the CRN are obvious. However, there
are many challenging problems that need to be solved before
CRNs can be implemented in practice such as [6]
1. Common control channel: A common control channel
supports many functionalities of a CRN. It is an efficient
approach to exchange information during spectrum sensing
and communication of the CR. However, this channel is
not always available due to the randomness appearance of
the PU. It can be occupied by the PU at an unpredictable
time. In this context, a fixed common control channel implemented for the CRN is in-feasible. In order to properly
operate in a CRN, the common control channel setup and
its maintenance mechanism are expected to need more advanced investigations.
University of Genova – DITEN
1.3 Challenges of Dynamic Spectrum Access in
Cognitive Radio Networks
9
2. Channel estimation: To protect the communication among
the PUs and enhance the performance of the CRNs, channel
information between the cognitive and the primary terminals are very important. Though,in real radio environment,
it is difficult to obtain the exact Channel State Information (CSI) due to fading, path loss, delay, and so on.
3. Common control channel: A common control channel
supports many functionalities of a CRN. It provides an efficient way to exchange information during spectrum sensing
and communication of the CRs. However, control channel is
not always available due to the randomness appearance of
the PU. It can be occupied by the PU at an unpredictable
time. In this context, a fixed common control channel implemented for the Cognitive Radio Network is in-feasible.
In order to properly operate in a CRN, the common control
channel setup and its maintenance mechanism are expected
to need more advanced investigations.
4. Joint sensing and access: The sensing and accessing
of spectrum are usually designed separately. Though their
should be a trade-off to optimize the Cognitive Radio sensing time and power allocation in multiband CRNs [63]. One
of the most concerned problems in CRNs is how to sense
multiple channels and utilize these multiple random channels efficiently.
5. Location information: Knowing distances between the
PU and the CR are crucial in a CRN. Based on the distance among users, the CR can regulate its communication
parameters to cancel interference and enhance system performance. Existing works often assume that the information about distance and PU transmit power are available
University of Genova – DITEN
10
Chapter 1 : Introduction
for simple investigation. However, this assumption may not
be always true in a practical CRN.
6. CRN architectures: To implement a CRN with full characteristics of CRN prototypes, a cross-layer architecture of
the CRs is essential. An expected cross-layer architecture
for the CR should be flexible to meet different QoS requirements. This is a complicated problem and desires more investigations.
1.4
Objectives and Research Contributions
The aim of this thesis is to study the performance of wideband spectrum sensing algorithms, and develop efficient wideband
spectrum sensing techniques which provides more opportunistic
access to the CRs, less computational burden that can be used in
distributed and cooperative cognitive radio networks. The main
contributions from the research activities are divided in:
• Opportunistic Spectrum Access: (the following contributions have been published in [10]. In this chapter, various
aspects of Dynamic Spectrum Access schemes are presented,
together with a brief discussion of the pros and cons of each
algorithm of spectrum sensing methodologies from CR perspective. Additionally, the future challenges are investigated
that are associated with Dynamic Spectrum Access (DSA)
and spectrum sensing techniques. Moreover, special attention is paid to the challenges associated with wideband sensing.
• Enhanced Performance in Wideband CS: A novel
wideband CR receiver sensing module has been proposed
University of Genova – DITEN
1.4 Objectives and Research Contributions
11
which estimates a highly-sparse part of the whole wideband
to find an opportunistic access to a CR (the following contributions have been published in [8] [11] [9]. Refer to chapter
4)
1. As this approach deals with a portion of the whole
wideband, thus requires less computational complexity and less physical memory [11].
2. Again, to estimate a portion of the wideband requires
less execution time for spectrum sensing which means
a CR may get more time for data transmission. Hence,
higher achievable rate is possible for the CR network
[9].
3. The theory of CS tells us that the more the sparsity
present in the signal, the better the signal reconstruction leading to better detection performance. As a result, our scheme provides better probability of detection, published in [8]
• Cooperative Compressed Sensing: Refer to Chapter 5
1. A cooperative Cognitive Radio Network is formed exploiting proposed cognitive radio receiver and analyze
the detection performance.
• Multiple Input Multiple Output scheme for Opportunistic Radio Systems We propose here a simple transceiver
for Multiple Input Multiple Output (MIMO) employing opportunistic radio systems having just a single degree of freedom. The proposed scheme requires less computational burden than the traditional approach under the same hypothesis resulting less power consumption of a Cognitive Radio.
University of Genova – DITEN
12
1.5
Chapter 1 : Introduction
Thesis Outline
This thesis has aimed at investigating CR opportunistic spectrum access in which the CR transmit power is subject to practical
constraints such as interference power and outage constraint of the
PU, and peak transmit power constraint of the CR.
The thesis consists of seven chapters based on a number of
peer-reviewed conference papers, and one published book chapter
as follows.
In Chapter 1, an introduction to the topics discussed in this
work is presented. In particular, Chapter 1 details the context of
this thesis and emphasizes the main contribution of the research
activities.
In Chapter 2, the state of art schemes of CR systems are described. In particular, state of art of dynamic spectrum access in
CR networks and the spectrum sensing techniques are presented
which are essential for understanding the rest of the chapters.
In section 3.4 of Chapter 3, we illustrate the overview of several
signal acquisition techniques which deals with sparse signals. Furthermore in section 3.6 of Chapter 3, we provide comparisons of
performance study of a well known signal acquisition study while
exploiting different transform coding in measurement matrix.
Chapter 4 describes the problems associated with the traditional wideband Compressive Sensing schemes and we have proposed an innovative CR receiver sensing module which could provides several advantages such as higher probability of detection,
less computational burden and higher achievable rate to the Cognitive Radio Networks.
While Chapter 4 presents an algorithm that extends the single
CR from Chapter 5 in order to deal with multiple CRs to support
a cooperative radio environment.
In Chapter 6, we propose a simple linear transceiver for MulUniversity of Genova – DITEN
1.5 Thesis Outline
13
tiple Input Multiple Output cognitive radio systems while the degree of freedom is considered one. By employing the proposed
approach, the computational burden is significantly reduced comparing with the conventional algorithms achieving the same results
under the same hypothesis.
Last but not least, Chapter 6.7 provides some recommendations and possible future direction of research in CR network.
University of Genova – DITEN
14
Chapter 1 : Introduction
University of Genova – DITEN
Chapter 2
State of the Art and
Literature Reviews
1
Radio spectrum is a precious resource which is shrinking progressively due to inventions of several multimedia applications incorporating in wireless communication systems. Cognitive Radio
is considered as a promising solution to the spectrum scarcity
problems that allows proficient use of radio resources through accessing radio spectrums opportunistically. In order to support
spectrum accessing functionality, the Cognitive Radio (CR) nodes
have the duty to sense the radio environment dynamically for being aware of the highly prioritized licensee while spectrum sensing
is one of the most challenging tasks in the promising CR networks.
1 Contents
of the current chapter have been published in [10]
15
16 Chapter 2 : State of the Art and Literature Reviews
2.1
Introduction
Spectrum scarcity problems occur due to the proliferation of
various wireless devices and services employing static frequency
access schemes and to cope up with this demand, CR is a solution of huge prospect. In the emerging paradigm of opportunistic
radio networks, unlicensed radio users are allowed to transmit opportunistically on a temporarily empty frequency band that is not
currently being accessed by the licensee. The CR can be described
as an intelligent and dynamically reconfigurable radio which itself
can regulate its radio parameters in temporal and spatial domain
according to the requirements of surrounding environment. As
the CR technology allows flexible and agile access to the spectrum, thus improves spectrum efficiency substantially [5]. It has
been reported by the Federal Communications Commission (FCC)
that localized temporal and spatial spectrum utilization is very
poor [2].
Currently, new spectrum policies are being developed by the
FCC that will allow CRs to opportunistically access a licensed
Primary User (PU) band, when the PU does not occupy a frequency band. The growing interest of Dynamic Spectrum Access (DSA) in CR is specially related to the fact that it is considered as a possible solution of the static spectrum allocation
policies and a number of DSA models are proposed in open literatures [5] [34] [86] [21] [10]. In order to dig up the benefit from
DSA, knowledge about the PU vacant bands are necessary and
CRs should be able to independently detect spectral opportunities
without any assistance from PUs; this ability is called spectrum
sensing, which is considered as one of the most challenging tasks
in CR networks [32]. In particular, a CR should explore the information about inactive PU bands and geographical location which
is then opportunistically utilized by the CRs, thus leads enhanced
University of Genova – DITEN
2.1 Introduction
17
spectrum efficiency.
Several narrowband spectrum sensing algorithms have been
studied in the literature [34], [10] [32] [82] [73] and references
therein, including matched-filtering, energy detection, and cyclostationary feature detection. To obtain higher opportunistic
throughput for different multimedia data services wideband spectrum sensing [25] [69] [69] is necessary for future wireless networks as Shannons formula says that, under certain conditions,
the maximum theoretically throughput is directly proportional to
the spectral bandwidth. However, conventional wideband spectrum sensing techniques becomes challenging due to high sampling
frequency functioning at or above Nyquist rates could lead implementation complexity [53]. There are several wideband sensing
approaches exploiting sub-Nyquist sampling commonly known as
Compressive Sensing (CS), thus employs relief of high-speed Digital Signal Processing (DSP) units and is elaborately illustrated
in [53] [23] [15] [72] [44].
This chapter presents an introductory tutorial on DSA schemes
and spectrum sensing for CR viewpoint featuring both non-cooperative
and cooperative sensing strategies and provides comparative analysis among various detection techniques. We begin with a short
review of DSA management methodologies and point out the characteristic features of DSA in Section 2.2. In Section 2.3, we would
like to deliver a comprehensive classification of narrowband and
wideband spectrum sensing schemes. A variety of conventional
and emerging wideband spectrum sensing techniques based on recent advances in detection of narrowband and wideband signal
at CR nodes are illustrated as long as performance comparisons
provided of few schemes. Moreover, the challenges are analyzed
that are associated with spectrum sensing and dynamic spectrum
access techniques. Sensing beacon transmitted from different cogUniversity of Genova – DITEN
18 Chapter 2 : State of the Art and Literature Reviews
nitive terminals creates significant interference to the primary
users if proper precautions have not be not taken into consideration.This is followed by a detailed discussion on the limitations
associated with spectrum sensing at individual CR terminal. Section 2.5 presents signal estimation techniques which is useful to
detect and distinguish of different radio signals( e.g., the PU status). Incorporating multiple antennas in CR improves achievable
capacity that is supporting for different wireless multimedia applications. Therefore, in Section 2.6, we discuss about different
Multiple Input Multiple Output (MIMO) schemes in Cognitive
Radio Network (CRN)s. Lastly, we have drawn some conclusions
in Section 2.7.
2.2
Dynamic Spectrum Access in CR
Networks
Nowadays, wireless communication is suffered from spectrum
scarcity due to newly developed various wireless applications of
them most of which are multimedia applications. The FCC disclosed that the licensed frequency bands are poorly utilized most
of the time and a particular geographic location mainly due to
the conventional command and control type spectrum regulation (i.e., static spectrum allocation) policy that has prevailed
for decades [2], [10]. In order to use the unused licensed spectrum
holes or white spaces, effort is put on achieving DSA. CR can
manage in order to mitigate the spectrum scarcity problem by enabling DSA scheme, which allows CRs to identify the unemployed
portions of licensed band and utilize them opportunistically as
long as the CRs do not interfere with the PUs communication.
A taxonomy of the DSA scheme [10] and references therein is illustrated in the following figure (Fig.2.1). In order to meet the
University of Genova – DITEN
2.2 Dynamic Spectrum Access in CR Networks
19
massive demand of radio spectrum, the CR network has opened
up flexible and agile access to the wireless radio resources, which
in turn, improve spectrum utilization efficiency [5]. The CR is a
dynamically reconfigurable radio which can adjust its radio parameters in response to the surrounding environment. The state
of art of DSA schemes will be discussed in this section.
Figure 2.1: Fundamental classification of dynamic spectrum access
2.2.1
Hierarchical access model
In this model, a hierarchical access pattern for the PUs and
CRs have been discussed. The fundamental concept is to open licensed spectrum to CRs while limiting the interference perceived
by the PUs. This model can be categorized as two different approaches for sharing the spectrum, i.e., spectrum underlay and
spectrum overlay. Spectrum underlay (Fig. 2.2 a) exploits the
spectrum by using it despite of a PU transmission, but by controlling the interference within a prescribed limits. This can be
obtained by using spread spectrum techniques, resulting in a signal with large bandwidth but having low Power Spectral Density (PSD), which can coexist with PUs. In an underlay sysUniversity of Genova – DITEN
20 Chapter 2 : State of the Art and Literature Reviews
tem, regulated spectral masks impose stringent limits on radiated
power as a function of frequency, and perhaps location [86]. Due to
power limitation, Underlay Radio (UR)s must spread their signals
across large bandwidths with lower energy, and/or operate at relatively low rates. An advantage of such a system is that radios can
be dumb, they do not need to sense the channel in order to defer
to PUs. The underlying principle is that the PUs are either sufficiently narrowband or sufficiently high-powered or the URs are
sufficiently fast frequency hopping with relatively narrow bandwidth usage in each dwell, so that there is little interference from
the URs. As the signal is spread out over a large bandwidth, URs
can use spread spectrum signaling systems, wideband Orthogonal Frequency Division Multiplexing (OFDM) or impulse radio.
Because of the large front-end bandwidth, URs are susceptible to
interference from a sort of co-existing sources, including relatively
narrowband signals from PUs. In summary, URs tend to be complex in terms of hardware implementation, front-end interference
suppression, high-fidelity low-power high-rate Analog-to-Digital
Converter (ADC) circuit design, and estimation and equalization
of long delay-spread channels. An UR could sense the spectrum
as to shape its transmitted signal to avoid band congestion which
requires reliable spectrum sensing like spectrum overlay systems.
Spectrum overlay intends to use empty PU bands in an oppor-
Figure 2.2: (a) Spectrum Underlay, (b) Spectrum Overlay (e.g.
Spectrum Pooling or OSA)
University of Genova – DITEN
2.2 Dynamic Spectrum Access in CR Networks
21
tunistic way without interfering PUs, indicating that the spectrum
should be monitored periodically by the CRs and seeking absence
of PUs to utilize the unoccupied band. Opportunistic Spectrum
Access (OSA) can be applied in either temporal or spatial domain.
For the first case, CRs exploit temporal spectrum opportunities
resulting from the bursty trafc of PUs and in latter case, CRs
aim to exploit frequency bands that are not being occupied by
the PUs in a specific geographic location [86], e.g., the reuse of
various TV white spaces that are very often used for TV broadcasting (e.g., digital TV transmission) in a particular geographic
location. In the TV broadcasting system, TV-bands assigned to
adjacent regions are different to avoid co-site interference. This
results in unused frequency bands varying over space. Spectrum
overlay mechanism is shown in 2.2b. OSA is also termed as interweaving of frequencies, is therefore done by doing some pre-coding
at the transmitter to lessen the interference at the receiver. This
technique is also known as dirty paper coding [21] and references
therein. The majority of existing work on OSA focuses on the spatial domain where spectrum opportunities are considered static or
slowly varying in time. As a consequence, real-time opportunity
identification is not as critical a component in this class of applications, and the prevailing approach tackles network design in
two separate steps: (i) opportunity identification considering continuous full spectrum sensing (ii) opportunity allocation among
CRs assuming perfect knowledge of spectrum opportunities at any
location over the entire spectrum.
2.2.2
Dynamic exclusive use model
In this model, the radio spectrum is licensed to a user or a
service for exclusive usage under an agreement to enhance the
spectrum efficiency and this model maintains the basic structure
University of Genova – DITEN
22 Chapter 2 : State of the Art and Literature Reviews
of spectrum regulation policy. Two schemes like spectrum property rights and dynamic spectrum allocation have been proposed
under this model [86].
2.2.2.1
Spectrum property rights
Generally, when PUs do not utilize their spectrum the PUs can
sub-lease those underutilized spectrum to third party thus can do
spectrum trading. This type of spectrum trading can be given the
right to exclusively use those resources without being mandated by
a regulation authority. This approach is called spectrum property
rights, as the license or the right is based on the three spectrum
properties as fixed frequency band, time and a geographic location
and detailed can be found in [10]. One of the most important
difficulties in applying this scheme lies in the unpredictability of
radio wave propagation in both frequency and space. Spectral and
spatial spillover is unavoidable, unpredictable, and depending on
the characteristics of both transmitters and receivers.
2.2.2.2
Dynamic spectrum allocation
The temporal and spatial traffic statistics are explored, which
is valuable for sub-leasing long-period of applications. Sub-leasing
based on traffic statistics leads to a much more exible spectrum
allocation than in the previous fixed spectrum allocation scheme.
As an example, the spectrum assigned to UMTS and Digital Video
Broadcasting-Terrestrial (DVB-T) can differ over temporal basis
and geographic location. DSA opens new possibilities of multiple
radio communications infrastructures when optimized interworking is considered. Firstly, to access every service operators can
allocate spectrums inside a radio network according to local and
temporal needs. Secondly, users on the move are provided with
the benefit of accessing enhanced internet protocol (IP) based moUniversity of Genova – DITEN
2.2 Dynamic Spectrum Access in CR Networks
23
bile services on the fly and wherever they are in a cost efficient
way [34]. Multiple networks regulation policy and issues in the
context of temporal and spatial DSA algorithms are pointed out
in [34]. The typical operational steps in temporal DSA algorithm
include:
1. Periodic triggering of DSA algorithm,
2. Management of the traffic on the carriers,
3. Prediction of the loads on the networks and
4. Access decision while the goal of spatial DSA is to allocate
spectrum to Radio Access Network (RAN)s according to the
traffic requirements in each location using DSA scheme.
Still, the spectrum allocations of different RANs belong to adjacent DSA areas should not overlap in the same portion of spectrum
to avoid interference. A guard band of suitable size guarantees
the coexistence of the different radio systems. The structure of
an usual spatial DSA scheme can be summarized in three main
steps:
1. Calculating the spectrum overlap,
2. Performing initial assignment and
3. Optimize the spectrum usage.
2.2.3
Open sharing model
The two models addressed in dynamic exclusive model deals
with the opportunistic usage of the license band, while open sharing model accepts an empty band focused only peer users. Mostly,
technical features of this model are close to the traditional Medium
Access Control (MAC) issues and this model can be categorized as
University of Genova – DITEN
24 Chapter 2 : State of the Art and Literature Reviews
centralized and distributed modes. In a centralized model, there
is one Cognitive Manager (CM) presents controlling the entire
CM environment. The CM can be an intelligent system and the
problem can be seen as an optimization problem. The centralized
approach considers that there is a reliable pilot channel connecting
each CRs to the CM. In fact, the CM has great influence on the
proficient spectrum usage, as well as reconfigure other transmission parameters e.g., transmit-power, signal-to-noise ratio(SNR),
modulation scheme, etc. In this model, coordination between
pairs or coalitions of pairs can facilitate the spectrum sensing,
competent use of radio resources and enhance the quality of the
information by which the pairs can rely to make their decisions.
Centralized dynamic spectrum access can be studied in two ways
as optimization approach and auction-based approach [32]. With
an optimization-based approach, different types of optimization
problems can be formulated (e.g., convex optimization, assignment problem, linear programming, and graph theory). While
auction based spectrum access mainly states the spectrum trading in a business oriented viewpoint. Here, every CR offers price
for a specific band of interest to the spectrum owner or broker and
the highest bidder will then get access to utilize it for a certain
time period. Though, in most of practical scenarios e.g., in adhoc CR networks, incorporating a CM is problematic [32] while
distributed DSA suits well in such networks. As there is no CM
present, every CR user has to gather, exchange, and process the
information about the surrounding environment independently.
Further, independent decisions would be taken by the CRs based
on available radio environment information thus, the CRs obtain
its performance objective under interference constraints. In the
following we will present methodologies where a CM is absent in
the collaborative environment and how the learning capability can
University of Genova – DITEN
2.2 Dynamic Spectrum Access in CR Networks
25
be employed in such cooperative scenario.
2.2.3.1
Cooperative or non-cooperative behavior
Due to the absence of a CM, a CR user can adopt either cooperative or non-cooperative behavior. When a CR operating in
cooperative mode will make a decision on spectrum access concerning the performance of the overall network (i.e., a collective
objective), however, this decision may not result in the highest
individual benefit of individual CR user. On the other hand, a
CR user with non-cooperative behavior will make a decision that
is opposite to cooperative behavior i.e. it wants to maximize the
individual performance while without concerning about the network performance. This behavior is also known as selfish behavior
of a CR terminal. In [21], it is discussed that game theory and
iterative water filling approach can be used for the distributed
DSA. To pertain game theory to the process of decision making
in a CR, the decision making process needs to be modelled as a
game. First of all, it should be checked whether it is a centralized or a distributed DSA model (i.e., the centralized or the distributed open sharing model). Secondly, it must be decided which
performance metric (i.e., the throughput or the latency) is to be
optimized. Thirdly, all information about any CR in the environment of the decision maker needs to be collected (i.e., the possible
actions and the preferred strategy). With non-collaborative behavior, all network information is gathered and processed locally
by each CR nodes while without interactions among the CRs. In
contrary to collaborative behavior, the CR users can exchange network information with each other. Typically, collaboration among
CR users to exchange network information is required to achieve
collective goal. In fact, if the CRs are collaborative, they could
be either cooperative or non-cooperative as the CRs may agree
University of Genova – DITEN
26 Chapter 2 : State of the Art and Literature Reviews
to reveal some information (e.g., the chosen spectrum access action), but they make a decision to achieve their own objectives
(non-cooperative), rather than a group objective (cooperative).
A protocol will be needed to exchange network information for
the collaboration among CRs. However, when a CR node possesses non-cooperative behavior, the network information has to
be observed and learned individually. Therefore, learning ability
plays an important role for sorting out intelligent decisions concerning radio parameters in the CR distributed DSA management
systems. The learning process can be either non-collaborative or
collaborative. In the case of non-collaborative learning, the knowledge about the system is produced by each individual CRs without interaction with other nodes. On the other hand, the CRs can
exchange network information as well as to process and produce
overall system knowledge and based on this a CR can make the
decision whether to achieve the group objective or its individual
objective.
2.3
Spectrum Sensing Techniques
Radio spectrum is classified as black spaces, grey spaces and
white spaces based on the usage of it [34]. CRs take the advantages from grey and white spaces by opportunistic use. To
reuse the spectrum, spectrum sensing is necessary and there are
different approaches for CR to grasp the spectrum sensing issues.
Based on the band of interest, spectrum sensing techniques can be
classified as narrowband and wideband. The CR is liable to identify the presence of PU transmission hence it is called transmitter
based detection or stand-alone detection [34] which is addressed
for military and many civilian applications for signal detection,
automatic modulation classification, to locate radio source and to
University of Genova – DITEN
2.3 Spectrum Sensing Techniques
27
perform the jamming activities in communication networks. As,
no collaboration is apparent among the CRs hence this method
cannot identify hidden PUs. In this section, some of the most
common transmitter based sensing schemes are addressed.
2.3.1
Narrowband sensing
The most efficient way to sense spectral opportunities is to
detect active primary transmitters in the vicinity of CRs. Here,
the term narrowband implies that the bandwidth of interest is less
than the coherence bandwidth of the channel. We would like to
address a number of narrowband spectrum sensing methods (Fig.
2.3) in the following:
2.3.1.1
Energy detection
A well-known method for spectrum sensing is based on energy
detection (ED) where received PU signal energy is measured in
a specific time period of a particular frequency band of interest.
This technique comprises low computational and implementation
complexities, thus leads to its popularity. In addition, the notable
advantage of this scheme is that it does not require any prior
information about the PUs transmission [82]. While the signal
received at CR node, the PU status is determined by comparing
the output of the ED with a threshold which depends on the
noise floor. The performance of the detection algorithm can be
determined by two probabilities as the probability of detection
Pd and probability of false alarm Pf . ED is considered a noncoherent detection method where knowledge of noise variance is
adequate for choosing threshold to obtain a predetermined false
alarm rate. Meanwhile, to design a standard CR system higher
value of detection probability Pd as well as lower value of false
alarm probability Pf is anticipated. The decision threshold E
University of Genova – DITEN
28 Chapter 2 : State of the Art and Literature Reviews
can be selected for finding an optimum balance between Pd and
Pf however this requires knowledge of noise and detected signal
powers. The noise power can be estimated, while the signal power
is difficult to predict as it changes depending on the transmission
characteristics and the distance between the CR and PU [82]. A
major drawback is that it has poor detection performance under
low SNR scenarios and cannot differentiate between the signals
from PUs and the interference from other cognitive radios.
Figure 2.3: Hierarchy of spectrum sensing in cognitive radio
2.3.1.2
Feature detection
Another promising spectrum sensing technique is based on feature detection. A feature is unique and inherent characteristics
of the PUs signal and it is drawn as pilot signal, segment sync,
University of Genova – DITEN
2.3 Spectrum Sensing Techniques
29
field sync, and also the instantaneous amplitude, phase and frequency [73]. In practice, these features are commonly perceived
many signals employed in wireless communication and radar systems [82]. Cyclostationary feature detection method detects and
distinguishes between different types of PU signals by exploiting
their cyclostationary features. Nowadays, analog to digital conversion has made the use of signal transformation practical in
order to discover a specific feature. The fundamental and promising feature detection technique is based on the cyclic feature [82].
Cyclic-feature detection approaches are based on the fact that
modulated signal are usually coupled with sinusoidal carriers, hopping sequences, cyclic prefixes, spreading codes, or pulse trains,
which result in a built-in periodicity [73]. Cyclostationary features are originated by the periodicity in the signal in statistical
manner like mean and autocorrelation or they can be intentionally used in order to sustain the spectrum sensing by analyzing
a Spectral Correlation Function (SCF) or cyclic spectrum [73].
This detection algorithms can differentiate noise from the signals
as the noise is Wide-Sense Stationary (WSS) with no correlation
while modulated signals are cyclostationary with spectral correlation due to the redundancy of signal periodicities. Cyclostationary feature detector can overcome the energy detector limits in
detecting signals in low SNR environments [86]. In fact, signals
with overlapping features in the power spectrum, can have nonoverlapping features in the cyclic spectrum [82]. Waveform based
or coherent sensing is another promising feature detection scheme
which uses patterns like preambles, repeatedly transmitted pilot
patterns, spreading sequences, etc. in wireless systems. In the
presence of a known pattern, sensing can be performed by correlating the received PU signal with a known copy of itself [82]
which provides a barrier of this type of sensing. It is shown that
University of Genova – DITEN
30 Chapter 2 : State of the Art and Literature Reviews
waveform based sensing outperforms energy detector based sensing in terms of reliability and convergence time. Likewise, the
performance of the sensing algorithm increases if the length of the
known signal pattern increases. The OFDM waveform is altered
before transmission to generate cycle-frequencies at different frequencies which is effective to categorize the signals [82]. Again if
the number of features generated in the signal is increased, the
robustness against multipath fading is improved considerably at a
cost of bigger overhead and bandwidth loss. The main advantage
of the feature detection is easily distinguishable the signals from
the noise (even under low SNR value). In contrast, feature detection requires long observation time and higher computationally
complexity as it requires to calculate a two-dimensional function
dependent on both frequency and cyclic frequency and also this
scheme needs a-priori information of the PUs.
2.3.1.3
Matched filtering
The advantage is achieved by correlating the received signal
with a template for detecting the presence of a known signal in
the received signal. However, it requires a-priori knowledge of
the PUs and requires CRs to be equipped with carrier synchronization and timing devices that leads enhanced implementation
complexity. At a CR node, to maximize the output SNR for a
certain input signal a matched filter is designed which belongs
to the linear filter [10]. Matched filter detection is applied if a
CR has a-priori knowledge of PUs transmitted signal. Therefore,
matched-filtering is known as the optimal strategy for detection
of PUs in the presence of stationary Gaussian noise. The main
advantage of matched filtering is the short time as it requires
only O(1/SNR) samples to meet a given probability of detection
constraint as compared to other detection schemes. As matched
University of Genova – DITEN
2.3 Spectrum Sensing Techniques
31
filtering requires a CR node to demodulate received PU signals
and thus, it requires a-priori information of the PUs transmission features such as bandwidth, operating frequency, modulation
type and order, pulse shaping, and frame format [73]. Further,
if the CRs want to process a variety of signals, the implementation complexity of sensing unit is impractically large. In addition,
this scheme consumes large power as various receiver algorithms
require to be executed for detection and a-priori knowledge requirement of PU signals place it in challenging to implement in
CR networks [10].
2.3.1.4
Covariance based detection
Another narrowband spectrum sensing is based on covariance
based detection which exploits the inherent correlation in received
signals at the CR terminal ensuing from the time dispersive nature
of wireless channel and oversampling of received signal [73]. Usually covariance based detection does not require any prior information about the PU signal or noise. Conversely, if some a-priori
knowledge concerning the correlation of PU signal becomes available, this helps to develop sample covariance matrix making the
decision test statistic more reliable. In particular, received PU signal samples in MIMO-CR systems are spatially correlated as they
originated from the same PU signals. Another significant feature
of this detection scheme is that the noise power estimation is not a
requisite here as the threshold is related to false alarm probability
and number of samples of the received signal at CR. The better
performance would possibly be achieved for highly correlated PU
signals while the performance of this detection degrades with the
uncorrelated PU signal. In multi-antenna CR systems, multiple
copies of the received PU signal can be coherently combined to
maximize the SNR of received signal. The diversity combining apUniversity of Genova – DITEN
32 Chapter 2 : State of the Art and Literature Reviews
proaches of maximum ratio combining (MRC) and selection combining (SC) are analyzed for ED in [57] and the references therein.
Although, MRC gives optimal detection performance but is difficult to implement as it necessitates a-priori knowledge of PU
signal and channel in the form of eigen vector corresponding to
maximum eigenvalue of the received PU signal covariance matrix
and the eigen vector can be estimated using the received PU signal
samples.
2.3.1.5
Eigenvalue based detection (EBD)
If the received signals exhibit time correlation as well, the concept of EBD can be extended to incorporate joint spacetime processing [73]. This approach is generally known as covariance based
detection, EBD being its one special case where the eigenvalues of
received signal sample covariance matrix are used for PU signal
detection. In [73], authors have indicated that number of significant eigenvalues is directly related to presence/absence of data
in received PU signal and may be exploited to identify the PU
occupancy status.
2.3.2
Wideband sensing
Wideband spectrum sensing techniques aim to sense a frequency bandwidth that exceeds the coherence bandwidth of the
channel (e.g., 300 MHz - 3 GHz). In the wideband regime, traditional narrowband sensing methods cannot be casted off directly
for performing wideband spectrum sensing, as of making a single binary decision (PU present or absent) in the entire wideband
signal, thus cannot locate individual spectral opportunities that
lie within the wideband spectrum. As shown in Fig. 2.3, wideband spectrum sensing can be broadly categorized into two types;
University of Genova – DITEN
2.3 Spectrum Sensing Techniques
33
Table 2.1: Comparison of different spectrum sensing schemes [73].
SS
Advantages
Disadvantages
Comments
scheme
Energy
Detection
+ Implementation simplicity.
+ Low computational
complexity.
Feature
Detection
+ Robust to
Noise
uncertainty.
+ High reliability.
+ Less complex
than cyclostationary feature
detection.
+ Less susceptible
to
hidden terminal
problems.
Matchedfilter
Detection
Covariance- + High Accubased
racy, blind.
Detection + Low computational
complexity.
− Threshold strongly
depends on Noise uncertainties.
− Non Robust and
Low accuracy.
− More susceptible to
hidden terminal problem.
−
Implementation
complexity and nonblind.
− Non-blind.
− High complexity and
high sensitivity to PU
signals information.
− Performance degrades for uncorrelated
PU signals.
University of Genova – DITEN
Advanced power
estimation techniques become
feasible
wideband spectrum
sensing
such
as Compressive
Sensing [69].
Hybrid schemes
using
coarse
detection using
ED and feature
detection.
Provides all advantages of feature detection
at
reasonable
complexity cost
but
susceptible to errors
in
a-priori
information.
Computational
complexity
depends
on
blind detection
algorithm.
34 Chapter 2 : State of the Art and Literature Reviews
Nyquist rate wideband sensing and sub-Nyquist wideband sensing. The former type processes digital signals taken at or above
the Nyquist rate, while the latter acquires signals using sampling
rate lower than the Nyquist rate. In the rest of this paper, an
overview of the state-of-the-art wideband spectrum sensing algorithms will be provided.
2.3.2.1
Nyquist rate wideband sensing
A conventional approach of wideband multi-carrier signal sensing is to directly acquire the entire signal using a standard ADC
and then use DSP algorithms to detect spectral opportunities to
CRs. A promising solution for the multicarrier wideband sensing
would be the filter bank schemes as presented in [25]. A special
class of filter banks (prototype filters) was proposed to detect the
opportunity in the wideband spectrum. Besides, those filter banks
can be used for the multicarrier communications for the CR nodes.
The baseband can be directly estimated through using a prototype filter, and other bands can be obtained through modulating
the prototype filter [25]. From a filter-bank point of view, in each
subcarrier, the corresponding portion of the input wideband signal was down-converted to base-band, low-pass filtered, and then
decimated. Later, this technique finds the correlation properties
of the low rate samples comes from each sub-carrier band. Therefore, the same filter bank can be used demodulation as well as
signal analysis. In fact, this scheme offers parallel arrangement
of the filter banks demanding a large number of RF modules,
which put limit to implement it in economy CR systems design.
Moreover, a wavelet approach to efficient spectrum sensing algorithm is proposed by using a standard ADC in [69]. There, the
wideband spectrum has decomposed into a train of consecutive
subbands, where the power spectral property is regular within
University of Genova – DITEN
2.3 Spectrum Sensing Techniques
35
each subband but exhibits discontinuities and irregularities between adjacent subbands. In order to locate the singularities and
irregular structures of the wideband PSD, the wavelet transform
is an attractive mathematical tool, chosen for this scheme. This
algorithm works well for the wide range of bandwidth to simultaneously identify all piecewise smooth subbands, without having
prior information about the number of subbands within the band
of interest. Furthermore, it leads more benefit than multiple narrowband band-pass filters, in terms of implementation costs and
flexibility in adapting to dynamic PSD structures. Furthermore, a
novel multiband joint spectrum detection was introduced in [61],
which jointly detects the PU occupancy status over multiple frequency bands rather than over one band at a time where the
spectrum sensing problem was considered as a class of optimization problems. Here, the wideband signal was firstly sampled at
Nyquist rate, after which a serial to parallel conversion circuit
was introduced to divide sampled data into parallel data streams.
Time domain wideband signal was converted to frequency domain
spectrum by using standard Fourier transformation. The whole
wideband spectrum was then divided into successive sequences of
narrowband spectra. Lastly, binary hypotheses tests was been
performed at the bank of multiple narrowband detectors to find
the empty PU bands for opportunistic usage by the CRs. By using
proper optimization technique the detection threshold was chosen
mutually as to maximize the aggregate opportunistic throughput
in an interference-limited CR network. This strategy allows CRs
to take maximum advantage of the unused spectra and limit the
subsequent interference.
University of Genova – DITEN
36 Chapter 2 : State of the Art and Literature Reviews
2.3.2.2
Sub-Nyquist rate wideband sensing
The high sampling rate as well as obligation of diverge DSP
utensils in Nyquist systems set limit to explore in wideband sensing hence, sub-Nyquist approaches are drawing more and more
attention in both academia and industry [53] [23] [15] [72] [44].
Sub-Nyquist wideband sensing refers to the procedure of acquiring
wideband signals/spectrums using sampling rates lower than the
Nyquist rate and detecting spectral opportunities in the wideband.
Two important types of sub-Nyquist wideband sensing are illustrated so far in the open literatures; wideband CS and wideband
multi-channel sub-Nyquist sensing. In the subsequent paragraphs,
we will deliver some discussions and comparisons regarding these
wideband sensing algorithms.
a) Compressive sensing
As wideband spectrum is inherently sparse due to its low utilization and capitalizing the sparseness, CS becomes a promising
approach to recover the wideband signal (or data) expending only
partial measurements. In the CS framework [23] a real-valued,
finite-length, one-dimensional time-variant signal x(t), 0 ≤ t ≤ x,
can be denoted as a finite weighted sum of orthonormal basis functions (e.g., Discrete Cosine Transform (DCT), Discrete Fourier
Transform (DFT), etc.) as follows:
x(t) =
N
X
bi ψi (t) = ψb
(2.1)
i=1
where only a small number of basis coefficientsbi signifying the
sparsity of wideband signal x(t). Let the acquisition of an N × 1
vector x = ψb whereψ is the sparsity basis matrix of size N × N
and b an M × 1 vector with S, the number non-zero entries in
bi . In case of sparse signals, an S-sparse depiction of x can be
University of Genova – DITEN
2.3 Spectrum Sensing Techniques
37
realized as a linear combination of S orthonormal basis functions,
with S N and it can be obtained by considering only S of
the bi coefficients in (2.1) those are significant Number of NonZero (NNZ) elements, while the rest (N −S) of values representing
less significant elements or zeros leads to the basis of the transform
coding [15]. It is confirmed that the original signal x can be reconstructed by using M = SO(logN ) non-adaptive linear projection
measurements against a measurement matrix φ of size M × N
which is incoherent with sparsifying basis, ψ [15]. The formation
of measurement matrix φ is given by choosing elements that are
drawn independently from a random distribution functions, e.g.
Bernoulli, Gaussian, etc. thus the measuring expression, y can be
written as
y = Φx = ΦΨb = Θb
(2.2)
where Θ= ΦΨ is a matrix of size M × N . As M N , the the
dimension of y in (2.2) is much lower than that of x, thus there
are theoretically infinite solutions to the equation. However, if the
condition that x is S-sparse is satisfied and with a proper condition
of measurement matrix, Φ and the recovery of x can be achieved
with only y measurements by solving the l1 -norm minimization
problem [23] [15] as follows
b̂ = arg minkbk1 suchthatΘb = y
(2.3)
b
This is a convex optimization problem solved as a linear program
celebrated as Basis Pursuit (BP)), iterative greedy algorithms,
etc. Though, the CS scheme has concentrated on finite-length
and discrete-time signals and to acquire sparse, band limited signals an Analog-to-Information Converter (AIC) was introduced
in [16] which is also entitled as Random Demodulator (RD). An
AIC is theoretically similar to an ADC operating at Nyquist rate
followed by the above mentioned CS procedure. The AIC-based
University of Genova – DITEN
38 Chapter 2 : State of the Art and Literature Reviews
model consists of a pseudo-random number generator, a mixer,
an accumulator, and a low-rate sampler. To decline design time,
behavioral models of AIC yield the same results as the costly
circuit models, but reduce the complexity of simulation [72]. Usually, sub-Nyquist rate samples are employed for wideband spectral
reconstruction and classify the frequency bands via PSD, waveletbased edge detector tailored to the coarse sensing task of vacant
spectrum identification. The advantage of this scheme is robust
to noise and can afford less number of samples.
b) Multi-channel sub-Nyquist wideband sensing
Conventional CS scheme for analog signals require prior information about the signal sparsity pattern. The spectral estimation
becomes more challenging without having the spectral support
i.e., blind sub-Nyquist sampling of multiband signals. The authors in [53] presented a mixed analog-digital spectrum sensing
method also known as Modulated Wideband Converter (MWC)
that has multiple sampling channels, with the accumulator in each
channel replaced by a general low-pass filter. A unified digital
architecture for spectrum-blind reconstruction was introduced in
that scheme and the architecture consists of an analog back-end
and digital support recovery, the crucial part in this technique.
Very few number of measurements are required for the digital operations in support recovery, thus introducing a short delay and
making computationally efficient. When the signal support set
is identified, numerous real-time computations are possible with
this scheme. The multi-channel structure in MWC provides robustness against the noise. Another multi-channel sub-Nyquist
sampling approach employs multi-coset (MC) sampling which incorporates the advantages of CS when the frequency power distribution is sparse, but applies to both sparse and non-sparse power
University of Genova – DITEN
2.3 Spectrum Sensing Techniques
39
spectra [44]. An innovative PSD estimator was presented in their
works for continuous WSS random processes producing both compressive and non-compressive estimates at finite resolutions. The
method estimates the average PSD within specific sub-bands of
a WSS random process. Hence, it produces piece-wise constant
estimates that are in contrast to those supported on a discrete
frequency grid, while the DFT has been employed to sort the periodogram. Through proper estimating the PSD, the estimator
minimized the spectral aliasing effects that occurs in each channel to underpin the formation of a linear system of equations.
Therefore, MC sampling is often implemented by using multiple
channels with different sub-sampling rates while each sampling
channels having unlike time offsets. In order to obtain a unique solution for the WSS random process from the compressive measurements, the sampling pattern should be carefully designed in [44]
as a result multi-coset sampling approach requires the channel
synchronization for a robust spectral reconstruction. An alternative sub-Nyquist sampling scheme also accredited as Multi-rate
Asynchronous wideband Sub-Nyquist Sampling (MASS) scheme
was presented in [64] to perform wideband spectrum sensing. In
that scheme, the sampling of the wideband signals were performed
by the parallel low-rate samples. Consequently, spectral aliasing
generated by the sub-Nyquist samples is persuaded in each sampling branch to wrap the sparse spectrum occupancy map onto
itself, as of the low utilization factor of the spectrum. Specifically,
in the same observation time, the numbers of samples in multiple sampling channels are selected as different consecutive prime
numbers [64]. Additionally, this scheme only acknowledge the amplitudes of sub-Nyquist spectra are of interest, such a multi-rate
wideband sensing approach was perceived robust against lack of
time synchronization between multiple sampling channels, lead-
University of Genova – DITEN
40 Chapter 2 : State of the Art and Literature Reviews
ing to lower implementation complexity, better data compression
capability, to have excellent performance in realistic wireless channels, and is more suitable to implement in CR networks.
2.4
Cooperative Spectrum Sensing
Spectrum sensing by a stand-alone CR is a challenging task
due to shadowing, fading, and time-varying natures of wireless
channels. In CR systems, cooperative spectrum sensing has been
widely used to detect the PUs with a high agility and accuracy
and certainly enhanced detection performance has been obtained
exploiting cooperative scheme [26]. To combat these impacts, cooperative spectrum sensing schemes have been proposed to obtain
the spatial diversity in multiuser CRN [26], [38], [43].In order to
improve the detection performance, various cognitive users to collaborate by sharing their sensing information.
In a CRN, every cognitive node performs individual spectrum
sensing employing some detection scheme and then sends local decision (binary or decision statistic) through control channel to the
common receiver called CM. Usually, the local decision is made
by comparing the observation with a preset threshold value [43].
In order to minimize the control channel overhead, CRs only share
their final 1-bit hard decisions (H0 or H1 ) rather than their decision statistics [26]. A CM is responsible to collect the local sensing
decisions from all the member nodes present in a CRN and then
fusing the local decisions by employing different fusion rules [75].
In the following chapter, we will show the enhanced detection
performance in a cooperative CRN by exploiting compressive detection performance.
University of Genova – DITEN
2.5 Signal Estimation Schemes
2.5
41
Signal Estimation Schemes
The spectral estimation illustrates the distribution of the power
contained in a signal over the frequency band, based on a finite
set of data. Estimation of power spectra is useful in a variety of
applications, including the detection of signals buried in wideband
noise. The PSD of a stationary random process x(n) is mathematically related to the correlation sequence rx (n) by the discrete
time Fourier transform. This is given by
Sx (ejω ) =
+∞
X
rx (n)ejωn
− π < ω < +π
(2.4)
n=−∞
with
rx (n) = E[x∗ (m)x(m + n)].
(2.5)
The average power of a signal over a particular frequency band
[ω1 , ω2 ], 0 ≤ ω1 ≤ ω2 ≤ π, can be found by integrating the PSD
over that band
We can see from the above expression that Sx (ejω ) represents
the power content of a signal in an infinitesimal frequency band,
which is why it is called the power spectral density. The main
methods for wideband spectrum estimation can be divided into
non-parametric and parametric methods, described in the following [31].
2.5.1
Parametric methods
Parametric methods Parametric methods are those in which
the PSD is estimated from a signal that is assumed to be the output of a linear system driven by white noise. Examples can be
provided of this type are the Yule-Walker auto-regressive (AR)
method and the Burg method. These methods estimate the PSD
University of Genova – DITEN
42 Chapter 2 : State of the Art and Literature Reviews
by first estimating the parameters (coefficients) of the linear system that hypothetically generates the signal. They tend to produce better results than classical non-parametric methods while
dealing with relatively short signal length.
This selection may be based on a-priori knowledge about how
the process is generated or, perhaps on experimental results indicating that a particular model matches well. Models that are commonly used include Auto-Regressive (AR), moving average Moving Average (MA), and autoregressive moving average (ARMA).
2.5.2
Nonparametric methods
Non-parametric methods are those in which the PSD is estimated directly from the signal itself. The simplest of such methods
is the periodogram. An improved version of the periodogram is
Welch’s method. A more modern non-parametric technique is the
multi-taper method.
2.6
MIMO Scheme in Cognitive Radios
OSA leads to a dynamic and effective management of the spectrum, many problems arise since PUs should be protected from
detrimental interference while assuring an acceptable Quality of
Service (QoS) to the cognitive radio nodes [58]. The CRNs operate in a heavy interference corrupted environment and effective
interference management has to be addressed to permit the coexistence among primary and CR networks [33]. Most of prior
research about OSA and interference mitigation for CRNs focuses
on the detection of PUs activity in frequency, time or spatial domain considering single antenna at both primary and cognitive
transceivers [85].Though, it is well known that the introducing
multiple antennas at the transmitting and/or receiving end can
University of Genova – DITEN
2.7 Summary
43
provide many desirable advantages, such as capacity enhancement, effective co-channel interference mitigation, spatial division
multiple access, etc [85].
In spite of the introduction of multiple antennas in CR networks has gained attention from theoretical and practical perspectives, only few researches have been carried out and some
open issues persist [85]. In the open literature, in order to face
the complex problem of the coexistence among PU and CR networks, some simplifying hypotheses are considered. As an example, in [35] [36] it is assumed that a cognitive system, equipped
with multiple antennas, are provided with the message sent by
the primary transmitter. Under this assumption the capacity of
the cognitive system is evaluated and it is shown that significant
improvements can be obtained with respect to traditional single antenna system [16]. However, such an approach suffers in
practical opportunistic scenarios where PUs are unaware of the
presence of the cognitive system and cooperation (i.e. sharing of
the transmitted message) cannot be assumed. In [49], although
the secondary system does not know the primary message and an
interference free CR networks is obtained by implementing properly designed filters at both primary and secondary transceivers,
it is required some modifications to the legacy terminals which is
unpractical in real environment.
2.7
Summary
In this chapter, various aspects and issues of Dynamic Spectrum Access and spectrum sensing in CR networks have presented.
A variety of detection techniques have been briefly studied, compared and classified in this section. We found that spectrum blind
detection methods are most generic in their application and are
University of Genova – DITEN
44 Chapter 2 : State of the Art and Literature Reviews
robust to all kinds of channel uncertainties. Moreover, they provide highly accurate results at reliable complexity. However, if a
CR functions independently leads to drastic sensing performance
degradation in multipath fading or shadowing environment which
is more likely happening in practical wireless networks. Hence,
cooperative spectrum sensing could provide a mature solution of
this type of problems. In summary, future research is envisioned
to be focused more on implementation-friendly, low-complexity
sensing algorithms that are robust enough to timely provide requisite sensing performance with demanded reliability.
University of Genova – DITEN
Chapter 3
Overview of the
Proposed Approach
3.1
Introduction
Wideband spectrum sensing plays a significant role to Cognitive Radio cognitive radio systems as a means of identifying
spectrum holes or characterizing interference. Measurement matrix plays an important role to reconstruct the sparse signal. The
fact that compressible signals are well approximated by S-sparse
representations forms the foundation of transform coding [15]. As
for example, In data acquisition systems (i.e., digital cameras)
transform coding plays a central role. In this chapter, we would
like to focus on different signal acquisition schemes based on
Compressive Sensing (CS). Later, we provide some simulations
and analytic results based on a comparative study of the effect of
transform coding in signal acquisition schemes.
45
46
Chapter 3 :
3.2
Overview of the Proposed Approach
Measurement Matrix of CS Recovery
The goal is to make M measurements from which the length-N
signal x could be reconstructed, or equivalently its sparse coefficient vector s in the basis Ψ. Clearly reconstruction will not be
possible if the measurement process damages the information in x.
Hence, the measurement process is linear and defined in terms of
the matrices Φ and Ψ, solving for s given y in (2.9) is a linear algebra problem, with M < N , i.e., fewer equations than unknowns,
resulting in an infinite number of solutions (ill-posed). However
the S-sparsity of s comes to the rescue and an intuitive approach
to ensure the solution is that the measurement matrix Φ should
be incoherent with the sparsifying basis Ψ [18] in the sense that
M
N
the vectors {Φj }j=1 cannot sparsely represent the vectors {Ψi }i=1
and vice versa. Some favorable distributions to represent Φ are:
1
• Gaussian: Φi,j ∼ N 0, M
(
+ √1M with probability 0.5
• The Bernouilli/Rademacher: Φi,j =
− √1M with probability 0.5
 1
1

+ √M with probability 6
• Database-friendly: Φi,j =
0
with probability 23

 √1
− M with probability 61
• Random orthoprojection to RM
A Gaussian measurement matrix has an important and useful
property: the matrix Θ = ΦΨ is also independent and identically
distributed (i.i.d) Gaussian regardless of the choice of the sparsifying basis matrix Ψ. Thus, random Gaussian measurements are
universal in the sense that Φ is incoherent with Ψ for every possible Ψ making the reconstruction possible with high probability
University of Genova – DITEN
3.2 Measurement Matrix of CS Recovery
47
if M > cK log(N ), with c a small constant. In order to study the
general robustness of the CS measurement matrix, the so-called
Restricted Isometry Property (RIP) has been proposed in the paper [18]. For each integer S = 1, 2, · · · , they define the isometry
constant δs of a matrix Θ = ΦΨ as the smallest number such
that
(1 − δs )ksk22 ≤ kΘs k22 ≤ (1 + δs )ksk22
(3.1)
holds for all S-sparse vectors s. A matrix Θ is said to obey the
RIP of order S if δs is not too close to one. When this property
holds, Θ approximately preserves the Euclidean length of S-sparse
signals. An equivalent description of the RIP is to say that all
subsets of S columns taken from Θ are in fact nearly orthogonal.
Therefore, the mutual coherence parameter µ represents as well a
good measure of robustness
√
µ(Φ, Ψ) =
N·
max |< Φk , Ψj >|
s≤Mj ≤N
√ µ(Φ, Ψ) ∈ 1, N (3.2)
(3.3)
µ is defined as a measure of the incoherence between the matrices involved in CS and it is proportional to the minimum number
of measurements which are needed to perfectly or near perfectly
reconstruct the sparse vector. Therefore, it is possible to define a
universal measurement process, based on projections over a random matrix in which the signal is not sparse. This is possible
because even if the projection Φ does not have full rank (M < N )
and loses information in general, it preserves structure and information in sparse signal models with high probability and it is
University of Genova – DITEN
48
Chapter 3 :
Overview of the Proposed Approach
invertible also for sparse models with high probability solving the
ill-posed inverse problem.
3.3
Sparsity Level Detection
Mostly all sub-Nyquist wideband sensing techniques require
that the wideband signal should be sparse in a suitable basis [65].
Given the low spectrum utilization, most of existing wideband
sensing techniques assumed that the wideband signal is sparse in
the frequency domain, i.e., the sparsity basis is a Fourier matrix.
However, as the spectrum utilization improves, e.g., due to the use
of Cognitive Radio (CR) techniques in future cellular networks,
the wideband signal may not be sparse in the frequency domain
any more. Thus, a significant challenge in future cognitive radio
networks is how to perform wideband sensing using partial measurements, if the wideband signal is not sparse in the frequency
domain. It will be essential to study appropriate wideband sensing
techniques that are capable of exploiting sparsity in any known
sparsity basis. Furthermore, in practice, it may be difficult to acquire sufficient knowledge about the sparsity basis in cognitive radio networks, e.g., when we cannot obtain enough prior knowledge
about the primary signals. Hence, future Cognitive Radio Network (CRN)s will be required to perform wideband sensing when
the sparsity basis is not known. In this context, a more challenging issue have to be studied named blind sub-Nyquist wideband
sensing algorithms (e.g., Modulated Wideband Converter (MWC)
proposed in [53], where prior knowledge regarding sparsity of the
signal has not been required for the sub-Nyquist sampling or the
spectral reconstruction.
University of Genova – DITEN
3.4 Signal Reconstruction Algorithm
3.4
49
Signal Reconstruction Algorithm
The recovery of a signal deeply influenced by the class of signals
which is responsible to fix the number of needed measurements
depending on different factors:
• The sparsity level S of the signals.
• The length of the signal N .
• The coherence between the measurement matrix Φ and the
sparsity basis Ψ.
To sum up, some important CS features are as follows:
1. Stable: Signal acquisition/reconstruction process is numerically stable .
2. Universal: the same random projections/hardware can be
used for any compressible signal class.
3. Asymmetrical: most of the signal processing carried out at
the receiver end.
4. Equal distribution: Each measurement carries the same amount
of information which makes it robust to measurement loss.
5. Weak encryption of the random projections.
In this chapter, we would like to illustrate some typical CS
schemes for signal acquisition which gives relief from the conventional high sampling rates needed for wideband spectrum sensing
in CR networks. In the following chapter, we shall provide a novel
wideband sensing approach to lessen the computational complexity, to improve the detection performance as well as to enhance
the achievable data rate to the CR nodes.
University of Genova – DITEN
50
Chapter 3 :
3.4.1
Overview of the Proposed Approach
Discrete Walsh-Hadamard transform coding
In mathematics, a Walsh matrix is a specific square matrix,
with dimensions a power of 2, the entries of which are +1 or 1,
and the property that the dot product of any two distinct rows
(or columns) is zero. Each row of a Walsh matrix corresponds to a
Walsh function. The natural ordered Hadamard matrix is defined
by the recursive formula, and the sequential ordered Hadamard
matrix is formed by rearranging the rows so that the number of
sign-changes in a row is in increasing order. Confusingly, different
sources refer to either matrix as the Walsh matrix. The Walsh
matrix (and Walsh functions) are used in computing the Walsh
transform and have applications in the efficient implementation of
certain signal processing operations.
Hadamard is a computationally simpler substitute than the
Fourier transform, since it requires no multiplication or division
operations (all factors are plus or minus one). Multiply and divide
operations were extremely time intensive on the small computers
used on board those spacecraft, so avoiding them was beneficial
both in terms of computing time and energy consumption. The
coefficients of the Hadamard transform are all +1 or −1. The
Fast Hadamard Transform can therefore be reduced to addition
and subtraction operations (no division or multiply). This allows
the use of simpler hardware to calculate the transform [59].
The basis vectors of the discrete Hadamard and the discrete
Walsh-Hadamard transforms consist of the values ±1; just like
the Walsh functions. Both transforms are unitary. Basically they
differ only in the order of the basis vectors.
We have
University of Genova – DITEN
3.4 Signal Reconstruction Algorithm
y = Hx,
51
(3.4)
x = Hy,
where x denotes the signal, y the representation, and H the
transform matrix of the Hadamard transform. H is symmetric
and self-inverse:
H T = H = H −1 .
(3.5)
The transform matrix of the 2 × 2-Hadamard transform is given
by
H
(2)
"
1 Hn
=√
2 Hn
#
Hn
.
−H n
(3.6)
The Walsh-Hadamard transform is obtained by taking the
Hadamard transform and rearranging the basis vectors according to the number of zero crossings [51]. Somehow, this yields an
order of the basis vectors with respect to their spectral properties.
3.4.2
Discrete cosine transform
A Discrete Cosine Transform (DCT) expresses a finite sequence
of data points in terms of a sum of cosine functions oscillating at
different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio
(e.g., MP3) and images (e.g., JPEG) (where small high-frequency
components can be discarded), to spectral methods for the numerical solution of partial differential equations. It is expressed
the following four types of DCTs [51]:
DCT-I:
knπ
2
, k, n = 0, 1, · · · N.
(3.7)
CkI (n) = √ γk γn cos
N
N
University of Genova – DITEN
52
Chapter 3 :
Overview of the Proposed Approach
DCT-II:
2
CkII (n) = √ γk cos
N
k(n + 12 )π
N
, k, n = 0, 1, · · · N.
(3.8)
DCT-III:
2
CkIII (n) = √ γn cos
N
(k + 12 )nπ
N
, k, n = 0, 1, · · · N.
(3.9)
DCT-IV:
CkIV
2
(n) = √ cos
N
(k + 12 )(n + 12 )π
N
, k, n = 0, 1, · · · N.
(3.10)
The constants γj in 3.7-3.9 are given by
(
γj =
√1
2
for j = 0 or j = 1
1
otherwise
(3.11)
The coefficients ck (n) are the elements of the orthonormal basis
vectors ck (n) = [ck (0), ck (1), · · · ]T .
In order to point out clearly how 3.7-3.10 are to be understood,
let us consider the forward and inverse DCT-II:
XCII (k)
=
N
−1
X
x(n)cII
k (n)
n=0
r
= γk
2
N
N
−1
X
x(n) cos
n=0
k(n + 12 )π
N
(3.12)
,
and
x(n) =
n−1
X
XCII (k)cII
k (n)
k=0
r
=
2
N
N
−1
X
k=0
XCII (k)γk
cos
k(n + 12 )π
N
University of Genova – DITEN
(3.13)
.
3.4 Signal Reconstruction Algorithm
53
Especially the DCT-II is of major importance in signal coding
because it is close to the KarhunenLove Transform (KLT) for firstorder autoregressive processes with a correlation coefficient that
is close to one.
3.4.3
Discrete Fourier transform (DFT)
The transform pair of the Discrete Fourier Transform (DFT)
is defined as [51]
X(k) =
N
−1
X
x(n)WNnk ,
n=0
1
x(n) =
N
N
−1
X
(3.14)
X(k)WN−nk ,
k=0
where
WN = e−j2π/N ,
(3.15)
Due to the periodicity of the basis functions, the DFT can be
seen as the discrete-time Fourier transform of a periodic signal
with period N . With




x(0))
X(0))




 x(1) 
 X(1) 



,
x=
..
..
,X = 





.
.
x(N − 1)
X(N − 1)
(3.16)
and

1

1
W = [WNkn ] = 
 ..
.
1
1
WN
..
.
N −1
WN
···
···
···
1

WNN −1
..
.





(N −1)(N −1)
WN
the above relationships can also be expressed as
University of Genova – DITEN
(3.17)
54
Chapter 3 :
Overview of the Proposed Approach
X = Wx ↔ x =
1
W HX
N
(3.18)
It is observed from the above equation that W is orthogonal,
but not orthonormal.
The DFT can be normalized as follows:
where
α = ΦH x ↔ x = Φα,
(3.19)
1
Φ = √ W H.
N
(3.20)
−(n−1
The columns of Φ, can be represented as ψk = √1N [1, WN−k , WN−2k , · · · , WN
0, 1, · · · N − 1 which is then form an orthonormal basis.
3.5
Different Schemes of CS Recovery
In this section, we will outline several well-known formulation
for CS recovery schemes which can be used for spectral estimation.
Over the last decades, there has been an explosion of interest in
alternatives to traditional signal representations [20]. Instead of
just representing signals as superpositions of sinusoids (the traditional Fourier representation) we now have available alternate
dictionaries - collections of parameterized waveforms - of which the
Wavelets dictionary is only the best known. Wavelets, Steerable
Wavelets, Segmented Wavelets, Gabor dictionaries, Multi-scale
Gabor Dictionaries, Wavelet Packets, Cosine Packets, Chirplets,
Warplets, and a wide range of other dictionaries are now available.
Each such dictionary D is a collection of waveforms (Φγ )γ∈Γ with
γ a parameter, and we envision a decomposition of a signal s as
X
s=
αγ φγ ,
(3.21)
γ∈Γ
University of Genova – DITEN
3.5 Different Schemes of CS Recovery
55
or an approximate decomposition
s=
m
X
αγ i φγ i + R(m) ,
(3.22)
i=1
where R(m) is a residual. Depending on the dictionary, such a
representation decomposes the signal into pure tones (Fourier dictionary), bumps (wavelet dictionary),chirps (chirplet dictionary),
etc.
Most of the new dictionaries are over-complete, either because
they start out that way, or merging various complete dictionaries,
obtaining a huge dictionary containing numerous types of waveforms (e.g., Fourier and wavelet dictionaries). The decomposition
3.21 is then non-unique, because some elements can be represented
in terms of other elements in the dictionary.
3.5.0.1
Goals of adaptive representation
: Non-uniqueness gives the possibility of adaptation, i.e., from
many representations, one that is most suited to a specific problem
and motivated to achieve the following goals simultaneously:
• Speed: It should be possible to obtain a representation in
the order of O(n) or O(n) log(n) time.
• Sparsity: It is possible to obtain the sparsest possible representation of a signal - i.e., the one with fewer significant
elements.
• Perfect separation: When the signal is made up of a superposition of a few very disparate phenomena (e.g., impulses and
sinusoids), those should be clearly separated and marked.
• Superresolution: We should obtain a resolution of sparse
objects that is much higher-resolution than that possible
with traditional non-adaptive approaches.
University of Genova – DITEN
56
Chapter 3 :
Overview of the Proposed Approach
• Stability: Small perturbations of the signal s should not
seriously degrade the results.
3.5.1
Basis pursuit
The Time-Frequency and Time-Scale communities have recently developed a large number of overcomplete waveform dictionaries i.e., stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into
over-complete systems is not unique, and several methods for decomposition have been proposed, including the Method of Frames
(MOF), Matching Pursuit (MP), and for special dictionaries, the
Best Orthogonal Basis (BOB). Basis Pursuit (BP) is a principle
for decomposing a signal into an optimal superposition of dictionary elements, where optimal means having the smallest l1 norm
of coefficients among all such decompositions [20]. BP has interesting relations to ideas in areas as diverse as ill-posed problems, in
abstract harmonic analysis, total variation denoising, and multiscale edge denoising [20].
BP in highly over-complete dictionaries leads to large-scale optimization problems. Such problems can be attacked successfully
only because of recent advances in linear programming by interiorpoint methods. We obtain reasonable success with a primal-dual
logarithmic barrier method and conjugate-gradient solver.
BP finds signal representations in over-complete dictionaries
by convex optimization: it obtains the decomposition that minimizes the l1 norm of the coefficients occurring in the representation. Because of the non-diffierentiability of the l1 norm, this
optimization principle leads to decompositions that can have very
different properties from the Method of Frames - specifically, they
can be much sparser. Because it is based on global optimization,
it can stably super-resolve the problems in ways that Matching
University of Genova – DITEN
3.5 Different Schemes of CS Recovery
57
Pursuit can not. BP can be used with noisy data by solving an optimization problem trading off a quadratic misfit measure with an
l1 norm of coefficients. Examples show that it can stably suppress
noise while preserving structure that is well-expressed in the dictionary under consideration. BP is closely connected with linear
programming. Recent advances in large-scale linear programming
- associated with interior-point methods - can be applied to BP,
and make it possible, with certain dictionaries, to nearly-solve the
BP optimization problem in nearly-linear time [20]. Among the
many possible solutions to Φα = s, they pick one whose coefficients have minimum l1 norm.
min kαk1 subject to Φα = s
(3.23)
To deal with the signal at the noise level σ > 0, it is proposed an
approximate decomposition as in 3.22, solving
2
min kΦα − sk2 + λn kαk1
(3.24)
p
with λn = σ 2 log(#D) depending on the number of #D of
distinct vectors in the dictionary.
3.5.2
Orthogonal Matching Pursuit
Let s be a d-dimensional real signal with at most nonzero components. This type of signal is called s-sparse. Let {x1 , · · · , xN }
be a sequence of measurement vectors in Rd that does not depend on the signal s. Those vectors can be used to collect N
linear measurements of the signal
hs, x1 i, hs, x2 i, · · · , hs, xN i
where h·, ·i denotes the usual inner product. The problem of
signal recovery depends mainly two distinct factors: number of
University of Genova – DITEN
58
Chapter 3 :
Overview of the Proposed Approach
measurements are necessary to recover the signal and the algorithm which can perform the recovery job. The algorithm of
Orthogonal Matching Pursuit (OMP) for signal recovery can be
illustrated as follows [71]: The input for this approach should be:
• An N -dimensional signal ν
• An N × d measurement matrix Φ
• The sparsity level s of the ideal signal.
While the output of this approach will be
• An estimate x̂ in Rd for the ideal signal
• A set Λm containing m-elements from {1, · · · , d}
• An N -dimensional approximation am of the data ν.
• An N -dimensional residual r m = ν − am
The procedure of this scheme is
1. Initialize the residual r 0 = ν, the index set Λ0 = 0, and the
iteration counter t = 1.
2. Find the index λt that solves the easy optimization problem
λt = arg maxj=1,··· ,d hr t−1 , ϕj i.
If the maximum occurs for multiple indices, break the tie
deterministically.
3. Augment the index set and the matrix of chosen atoms:Λt =
Λt−1 ∪ {λt } and Φt = [Φt−1 ϕλt ]. Here, Φ0 is an empty
matrix.
4. Solve a least squares problem to obtain a new signal estimate: xt = arg minx kν − Φt xk2 .
University of Genova – DITEN
3.6 Simulations and Analytic Results
59
5. Calculate the new approximation of the data and the new
residual at = Φt xt
r t = ν − at .
6. Increment t, and return to Step 2 if t < m.
7. The estimate ŝ for the ideal signal has nonzero indices at
the components listed in Λm . The value of the estimate ŝ
in component Λj equals the jth component of xt .
3.6
Simulations and Analytic Results
So far, we have discussed different CS schemes for sparse signal acquisition in an efficient way. Most of the CS based signal
acquisition scheme requires a measurement matrix based on specific mathematical basis: sparsity, which pertains to the signals
of interest, and incoherence, which pertains to the sensing modality [19]. Hence, the formation of measurement matrix plays an
important role for signal/data acquisition schemes. In this chapter, we would like to compare the performance of Walsh Hadamard
Transform (WHT) and DCT transform coding employed in measurement matrix, Φ of the sparse signal acquisition system. Usually, DFT and DCT transform coded measurement matrix provide the similar results which is less significant in our discussion
while the comparison between WHT and DCT transform coded
measurement matrix illustrates very significant in wideband sensing algorithm. Therefore, in this section, we compare the performance of the WHT and DCT transform coding employed in
measurement matrix, Φ in order to recover the wideband signal
at a single CR node. We consider, at baseband, a wideband spectrum range [0M Hz − 60M Hz] containing 30 channels of 2 MHz
each and encode it as c = {c1 , c2 , · · · , cn } where n = 30. Every
University of Genova – DITEN
60
Chapter 3 :
Overview of the Proposed Approach
channel is possible occupied by a Primary User (PU) using digital modulation scheme either 16-PSK or 16-QAM. So, the symbol
rate is 2 MHz and number of samples per symbol is 16 and number
of symbols in a frame is chosen 512. In a single attempt there are
three PUs communicating with the center frequency of 20.7 MHz,
45.3 MHz, 59.5 MHz respectively while their individual bandwidth
is 2 MHz each. Here, we have considered the Nyquist sampling
frequency,fs = 128 MHz and the sampling number, N = 8192.
We also consider, the received signal at the cognitive terminal is
corrupted by the Additive White Gaussian Noise (AWGN). The
received SNR of the active channels is considered 20dB. For CS
reconstruction, the chosen compression ratio, M
N is varying from
2.5% to 60%. The entries of the compressed measurement ma1
trix Φ be Gaussian distributed with zero mean and variance M
and this random matrices allow sparse recovery using l1 minimization. The DCT and the WHT coding is selected to form the
measurement matrix, Φ and then compare the normalized Mean
Squared Error (MSE) w.r.t. Power Spectral Density (PSD), detection performance and average execution time. The statistical
average of normalized MSE and execution time have set after 500
experimental realizations were taken into consideration.
3.6.1
Normalized MSE performance
we compute the normalized MSE of the PSD obtained from
Welch periodogram which is defined by:

2 



Ŝx − Sx 
2
M SE = E
(3.25)
2

 kSx k2 

where Sx denotes the average of the PSD estimates based
on Welch power periodogram, where the original signal sampled
University of Genova – DITEN
3.6 Simulations and Analytic Results
61
Performance test of the compressive sampling scheme
1
Normalized MSE
0.9
0.8
0.7
PSK-WHT: 20dB
0.6
PSK-DCT : 20dB
QAM-WHT: 20dB
0.5
QAM-DCT : 20dB
0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
Compression rate, M/N
Figure 3.1: Normalized MSE performance versus compression
rate, M
N (setting SNR = 20 dB)
at Nyquist rate and Ŝx is the average PSD estimate from periodogram of same type of the reconstructed signal through compressed sampling. It is obvious from the Fig. 3.1 that the higher
the compression ratio, M
N the better the signal reconstruction
quality.
3.6.2
Average execution time comparisons:
In order to compare the execution time for two types (DCT
and WHT) of transformed measurement matrix, Φ, we consider
the compression rate M
N of interest in the range of 2.50%−60%. It
is clearly shown in Fig. 3.2 that WHT matrix executes 30% faster
than its DCT counterparts while their detection probability (as
shown in Fig. 3.3 is comparable.
University of Genova – DITEN
62
Chapter 3 :
Overview of the Proposed Approach
Execution time comparison Vs. compression rate
200
Average execution time
180
160
140
120
PSK-WHT: 20dB
PSK-DCT : 20dB
100
QAM-WHT: 20dB
QAM-DCT : 20dB
80
60
0
0.1
0.2
0.3
0.4
0.5
0.6
Compression rate, M/N
Figure 3.2: Execution time versus compression rate,
SNR = 20 dB).
3.6.3
M
N
(setting
Detection performance versus compression
ratio
We evaluate detection probability, based on the averaged PSD
estimate. The decision of the presence of a licensed transmission
signal in a certain channel is made by an energy detector used in
paper [76].
Q
N = Ŝx (k) =
1 X
2
|Xq (K))|
Q q=1
(3.26)
where Xq (K) is the Fourier transform of the q-th block of the
received time-domain signal xq (n), n denoting the sampling index,
each block contains 8 PSD samples and the total number of blocks,
Q = 1028 . The probability of detection, Pd is calculated as:
pd = P r(N > (γ | H1 ))
University of Genova – DITEN
(3.27)
3.6 Simulations and Analytic Results
63
Performance test of the compressive sampling scheme
1
Detection probability
0.95
0.9
0.85
0.8
PSK-WHT: 20dB
PSK-DCT : 20dB
0.75
QAM-WHT: 20dB
QAM-DCT : 20dB
0.7
0.65
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
Compression rate, M/N
Figure 3.3:
Detection probability
M
rate, N .(setting SNR = 20 dB)
versus
compression
where γ is the decision threshold and is centralized chi-square
distributed function which is found by fixing the probability of
false alarm, Pf = 0.05 and H1 represents the presence of PUs. Fig.
3.3 describes the Pd with different values of compression ratios, M
N.
From simulation results (Fig. 3.3) it is seen that the detection
probability of two types of transform coding is comparable with
respect to the two considered types of digital modulation schemes.
University of Genova – DITEN
64
Chapter 3 :
Overview of the Proposed Approach
Simulated Throughput (bits/Sec/Hz)
Influence of the Throughput on τ: T=50 msec.
8
7
WHT: 20dB
6
DCT: 20dB
5
WHT:10dB
4
DCT: 10dB
WHT: 5dB
3
DCT: 5dB
2
1
0
5
10
15
20
25
Sensing Time (msec.)
Figure 3.4: Influence of compression ratio on the detection performance.
University of Genova – DITEN
Chapter 4
Compressive Sensing
for Wideband
Cognitive Radios
1
Radio spectrum is an expensive resource and only licensed
users have the right to use it. In the emerging paradigm of interoperable radio networks, the unlicensed users are allowed to use
the radio frequency that is unoccupied by the licensed users in
temporal and spatial manner. To support this spectrum optimization functionality, the unlicensed users are required to sense the
radio environment periodically for being aware of the high-priority
licensed users. Wideband spectrum sensing is a challenging task
for the present analog-to-digital converters used in wireless systems due to the constraints of digital signal processing unit. Exploiting on the sparseness of the wideband signal, the spectrum
1 Contents
of the current chapter have been published in [11] [8] [9]
65
66
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
can be recovered with only few compressive measurements, consequently employs relief of high-speed signal processing units. This
paper presents a novel wideband sensing approach where a significant portion of wideband spectrum is approximated via compressive sensing rather than entire wideband spectrum estimation,
thus reducing computational complexity for the cognitive radios.
Detection performances are evaluated through spectrum estimation of the desired frequency band by means of a well-known energy detection method. Finally, reduction of computational burden and memory spaces obligation are described compared to the
conventional Compressive Sensing (CS) preceded over a single RF
chain, without interfering with the detection performances.
4.1
Introduction
With the rapid growth of mobile wireless services and systems,
the scarcity of the Radio Frequency (RF) spectrum is starting to
represent an important issue. Recent research shows that at any
particular spatial region and time, spectrum might not be fully occupied by the licensed or Primary User (PU)s). In particular, the
spectrum is often poorly utilized in television broadcasting has
licensed under very high frequency (VHF) bands [2, 32]. Those
unused spectrums can opportunistically be accessed by Cognitive
Radio (CR), thus improving overall spectrum efficiency. The enhancement of the spectrum usage can be speculatively achieved by
means of automatic frequency switching techniques [55]. Unfortunately, wideband spectrum sensing for CRs is a challenging task
and there are mostly two conventional ways to perform this operation [60, 67]. Firstly, wideband spectrum sensing is performed
by using a bank of tunable narrowband Band-Pass Filter (BPF)s
at the RF front-end to scan one narrowband frequency for every
University of Genova – DITEN
4.1 Introduction
67
sensing interval. The BPFs involve with a variable number of RF
components and the tuning range of each BPF is pre-selected.
Secondly, a single wideband RF front-end followed by high-speed
Digital Signal Processing (DSP) unit can be used to flexibly search
over multiple frequency bands simultaneously. In the later option,
high-speed Analog-to-Digital Converter (ADC) is required to cope
up with extremely high sampling rates. Nyquist rate sampling
requires high-rate ADCs and the ability for processing devices
to handle a huge number of samples resulting in excessive memory occupation and energy consumption requirements. Therefore,
lower computational complexity and reduced power consumption
is desired for wideband sensing algorithms [60]. CS can overcome
those difficulties effectively [15, 18, 19, 23]. CS is a method of acquisition of sparse signals considering very few samples which are
significantly lower than the Nyquist sampling rate. The problem of signal reconstruction can be solved by convex optimization
problem, called l1 -norm regularization, that uses the Basis Pursuit (BP) [20] or some other greedy pursuits such as Orthogonal
Matching Pursuit (OMP) [71] or compressed sensing orthogonal
matching pursuit [56]. All these schemes provide an effective way
to sense the discrete-time sparse (sparsity in frequency domain)
signals and perfectly (or near perfectly) reconstruct by using a
few number of random projections. CS relies on the empirical
observation that many types of signals or images can be wellapproximated by sparse representation in terms of a suitable basis functions, i.e., considering only a few significant coecients or
Number of Non-Zero (NNZ) elements in the signal vector. When
reconstructing the signal, the non-stored coecients are simply set
to zero. This is obviously a reasonable strategy when full information of the signal is unavailable or difficult to obtain. In
order to deal with wideband signal acquisition from compress-
University of Genova – DITEN
68
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
ible signals which enables sub-Nyquist data acquisition via an
Analog-to-Information Converter (AIC) or a Random Demodulator (RD) [?,40]. An AIC directly relates to the idea of sampling at
the information rate of the signal. The CR with a wider spectral
awareness could potentially exploit more spectral opportunities
and obtain greater achievable rates. Therefore, wide band spectrum sensing techniques have attracted much attention among
researchers [64]. In [25], a traditional filter-bank based approach
was presented for wideband spectrum sensing in a multi-carrier
communication environment. It has been shown to have a higher
spectral dynamic range than conventional power spectrum estimation approach. Another filter-based method has been discussed
for wideband spectrum sensing in [30] and here the filter outputs
has been considered for channel energy vector recovery via a CS
scheme. In [61], the authors proposed a multiband joint detection
scheme in order to detect the active PUs over multiple frequency
bands. Also, the authors have claimed this scheme outperforms in
some practical conditions. Compressed samples subsequent to a
wavelet based approach were employed to detect and classify the
wideband RF signals [69]. In [77], an estimation of the RF spectrum based on CS scheme was proposed for wideband spectrum
sensing in CR networks. In particular, authors in [77] introduced
the auto-correlation of the compressed signal to estimate the spectrum of the sparse signal. In most of the papers, the authors are
devoted to estimate the whole wideband spectrum to find a spectrum hole for opportunistic access of CRs [30,64]. To estimate the
whole wideband in CS domain implies computational burden as
well as it requires more memory space to store signal vector and
hence prohibitive energy cost.
To avoid the estimation of wideband spectrum, our emphasis is to reconstruct a significant portion (which is more sparse
University of Genova – DITEN
4.1 Introduction
69
than the other part of spectrum) of it, as a result of making computational complexity significantly lower. As soon as the wideband signal undergoes at different BPFs, it selects the RF band
of interest and divide the whole wideband spectrum into several
frequency bins (FBs). Sparsity is one of the fundamental requirements for spectral recovery that has already been proposed in
CS theory [19, 23]. Primarily, this paper aims to discover the
highly-sparse frequency bin (HSFB) by average energy comparison of each FB. The energy estimation of every FB has performed
by taking random sub-Nyquist rate samples coming out from the
RD. The HSFB exploits several indications; first, it ensures of
having minimum number of PUs active which substantially exploit maximum opportunistic accessibility for a CR user. Second,
the more the sparsity, the better would be the spectral estimation
which contributes better detection performance. Third, spectral
estimation of a single HSFB rather than entire wideband would
ask minor computational complexity. Now we give emphasis on
spectral estimation of the HSFB via a convex optimization approach called l1 -norm minimization. Later, we pay attention to
check the spectrum occupancy status of a PU by using the energy
detector (ED) [22]. The proposed approach outperforms existing
wideband spectrum sensing methods, in terms of lower computational burden, lower memory requirements as well as progressive
achievable throughputs for CR networks [9].
The remainder of this chapter is organized as follows. In section 4.3, compressive sampling basics are discussed and section 4.4
briefly describes compressed spectrum sensing from a single CR
node. Signal and system model for the problem is proposed in section IV and V, respectively. In section VI, performance analysis
and computational complexity are carried out through simulations
and analysis, respectively. Also, some advantages of the proposed
University of Genova – DITEN
70
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
model are highlighted in this section. Finally, some conclusions
are drawn in section VII.
4.2
Signal model
Our objective is to decide the primary signal occupancy state
of a specific frequency band within a frequency bin(FB) and the
band is denoted by l(l = 1, 2, · · · , L). To do so, the hypothesis
test for detecting the occupancy status of PU in a band of interest
is measured as H0,l (absences of a PU and H1,l (presence of a PU).
That is, we test the following binary hypotheses:
(
X̂[l] =
W [l]
H0,l
Hl S[l] + W [l] H1,l
(4.1)
where X is the spectrum of the band of interest estimated
through the promising l1 -minimization scheme, discussed in [6-7].
Hl stands for the discrete frequency response between the PU and
the CR, S[l] is the primary signal transmitted within a PU band
n along with complex Additive White Gaussian Noise (AWGN)
W [l] of zero mean and unity variance. For simplicity, we note
that the CRs keep quiet during every detection period while the
PU signals with background noises are in the environment which
is secured by the higher layer protocols e.g., medium access control schemes. Since the performance of an ED does not require
a-priori information of the PU network and less complex to implement [65] which make it popular to the designer in practical
cases. Therefore, the signal energy is calculated over an interval
of J samples by
E[l] =
J−1
X
2
X̂j [l] , l = 1, 2, · · · , L
j=0
University of Genova – DITEN
(4.2)
4.2 Signal model
71
where X̂j [l] indicates the spectral estimation of the j-th subchannel under concerning to CR and the decision parameter of
the ED is given by
H1,l
E[l]
≥
<
λl , l = 1, 2, · · · L
(4.3)
H0,l
where λl is the decision threshold of a PU sub-channel of interest
inside a FB xk . Following [65], the signal energy can be described
as
(
E[l] ∼
χ22j ,
2
χ2j (2γ[l]),
H0,l
H1,l
(4.4)
where γ[l] denotes the signal-to-noise ratio (SNR) at the CR
of a frequency band, and χ22j and χ22j (2γ[l]) denote central and
non-central chi-square distributions, respectively. Both those distributions have degrees of freedom of 2j. For simplicity, we assume that the primary radios deploy uniform power transmission
strategy. Both distributions have degrees of freedom of 2j. We assume for simplicity that the primary radios deploy uniform power
transmission strategy. The probability of detection, Pd and the
probability of false alarm, Pf a can be calculated as offered in [22].
Pf,l = P r(E[l] > λl | H0,l ) =
Pd,l = P r(E[l] > λl | H1,l ) = QJ
p
Γ(J, λ2l )
Γ(J)
(4.5)
√ 2γ[l], γl
(4.6)
where, Γ(u) is the gamma function, Γ(u, x) is the incomplete
gamma function, and Qj (u, x) denotes the generalized Marcum
Q-function.
University of Genova – DITEN
72
4.3
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
System Model and Problem Formulation
Suppose that a CR receiver has employed with a band-pass
filter bank as depicted in Fig. 4.1. Let the PUs of a radio network mutually share the wideband signal xc (t) of bandwidth W
Hz and the bandwidth of every non-overlapped PU is B Hz which
could potentially serve the demand of a CR node. In addition,
the signal xc (t) is comprised of a maximum of W
B PU bands as
depicted in Fig. 4.1 where a few bands are always randomly available for opportunistic accessing to CRs. Here, K number of idenK
tical BPFs {Hk (f )}k=1 (where Hk (f ) denotes transfer function
of the k-th BPF) divide the signal in K different frequency bins
(FBs), are denoted as xk of equal bandwidth wk = W
K Hz where
k = 1, 2, · · · , K. At any particular time each xk is accommodated
with different number of active PUs randomly from a maximum
of wBk bands. For simplicity, assume that at least one PU subband exists in a FB xk at a certain time. The energy estimation
of every FB has performed by taking random compressed samples
Mk derived from the RD. Those Mk samples are intended for calculating the average energy Ek of a single FB and compare those
K
average energies {Ek }k=1 at the energy estimate and compare
block. It is important to note that the comparator should restore
the sample values while comparing the values of Ek of various
FBs. Meanwhile, the HSFB of having minimum average energy,
Ek(min) is detected by the comparator along with the samples
which is then considered for approximating the spectral magni 2
tude X̂k via a well-known l1 -minimization algorithm [23]. The
HSFB indicates minimum number of PUs actively present which
substantially provides maximum opportunistic accessibility to a
CR user. Besides, the theory of CS tells that the more the sparUniversity of Genova – DITEN
4.4 Computational Complexity of the Proposed Method
73
sity, the better would be the spectral estimation which contributes
better detection performance. Moreover, spectral estimation of a
single HSFB rather than entire wideband require less computational burden. With HSFB spectrum, we proceed to look for a
vacant PU sub-band for opportunistic usage to a stand-alone CR
by exploiting a well-known ED approach proposed in [22]. Later,
to improve the reliability of sensing performance, a cooperative
CR network is set where each CR has the capability of wideband
sensing exploiting the schematic in Fig. 4.1.
Figure 4.1:
ment.
4.4
Schemetic block to detect the sparse wideband seg-
Computational Complexity of the
Proposed Method
Now we try to compute the computational complexity of this
CR receiver block expressed in Fig. 4.1. As the subsampled
Fourier matrix (it is customized by pooling of m rows selected
uniformly at random from the Discrete Fourier Transform (DFT)
matrix) is applied to the signal recovery hence it necessitates
O(N logN ) operation (in particular, the computational burden
= numberof iterations × N × logN , where number of iterations is
University of Genova – DITEN
74
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
not usually easy to bound, but in worst-case, it can be bounded
by N ). By using K number of filters, the computational complexN
N
ity is reduced in the order of O(KlogK) and it requires O K
log K
.
In addition, in a static manner, the floating point computation
needed to estimate the average energy of each FB by applying
linear algebra which in the order of O(2n − 1) ≈ O(2n) where n is
the percentage of random samples that considered for estimating
the average energy. Furthermore, large value of n (energy estimate block in Fig.4.1 gives the better estimate of choosing the
most suitable FB and let, O(2n) = O(P ). There is one additional
item of computation that is used for comparison of the average
energies of every FB that depends on the number of BPFs. So,
O(K) computation is needed for energy comparison of each FB.
Therefore, the total computational burden is the added form of
all those three items discussed above
Ω = O(
N
N
log + P + K)
K
K
(4.7)
As K P and K N , the 4.7 can be re-written in the following
form
Ω = O(
N
N
log + P )
K
K
(4.8)
Another important entity is to notice the memory space needed
for the proposed CR receiver system as well as convex optimization process. There are two terms to consider; firstly O(N ) bits of
memory spaces are to be required for the recovered spectrum of
length N and the later is O(M × N ) for the measurement matrix
N
to store [15]. In the proposed method, we require only O( K
) memory spaces to store the estimated spectrum as K numbers of filters
are used. Besides, memory space requirement is greatly reduced
by the measurement matrix as the space requirement is divided
University of Genova – DITEN
4.4 Computational Complexity of the Proposed Method
75
N
M ×N
by the K-th square of O(M × N ) i.e. O( M
K × K ) = O( K 2 ). Furthermore, we have to spend some static memory spaces for storing
the random samples comes out from the RD which is in the order
of O( 12 P ). The storing of the random samples is a prerequisite due
to average energy estimation of each FBs. Therefore, the expression of the total memory spaces required for the proposed method
is
Υ = O(
N
M ×N
1
+
+ P)
2
K
K
2
(4.9)
which is greatly influenced by the number of BPFs, K. As computational burden decreases with the increasing number of filters, K
and so this does not necessarily mean that high number of filters
K always increases the sparsity in some basis functions. If K is
too large, the sparsity is reduced in substantial order and hence
spectral recovery would be ambiguous to resolve. Therefore, selection of higher values of BPF, K have two complications; one is
budget constraints for designing such type of CR receiver sensing
block and later, too high value of K does not convey suitable sparsity S. Therefore, there should be a trade-off to choose the value
K in which sparsity and cost is bounded in a best possible way.
If all the PU sub-channels are empty of a FB, xk then the spectral estimation of that FB is based on only the background noise
(i.e. absent of NNZ values and the FB is no more sparse in arithmetic viewpoint) and spectral estimation via the l1 -minimization
methodology could give incorrect result that might mislead detection performance in wideband spectrum sensing.
University of Genova – DITEN
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
76
4.5
Performance Analysis and Simulation Results
We consider, at baseband, the wideband signal xc (t) falling in
the range of [1 ∼ 64]∆ Hz can accommodate a maximum of 32
32
non-overlapping PU bands of [1 ∼ 2]∆ Hz and encoded as {chl }l=1
, where ∆ is the frequency resolution. The received signal xc (t)
at the CR node is as follows [64]
xc (t) =
N p
X
(En Bn ). sinc(Bn (t − δ)). cos(2πfn (t − δ)) + z(t)
n=1
(4.10)
where sinc(x) = sin(πx)
πx , δ denotes a random time offset within
sampling branches, z(t) is the Additive White Gaussian Noise of
unit variance. In simulations, the number of BPFs are considered
as K = 4 so the bandwidth of each xk is wk = 16∆ Hz, i.e., a
single FB can comprise a maximum of wBk = 8 PUs having no
sparsity. A total of 15 PU bands with different carrier frequen15
cies {fn }n=1 present inside the wideband W when probing the
burst of transmissions. The distribution of active PUs in various
4
FBs are {xk }k=1 = {4, 5, 4, 2} with dissimilar sparsity levels. The
number of Nyquist rate samples N are taken from HSFB for an
observation time T . The average energy estimation of various FBs
are performed by reflecting a fixed compression ratio M
N = 40%
and from those FBs, the energy comparator selects x4 (t) as HSFB
(having average sparsity of 75%) tailored for spectral estimation.
DFT is selected as the sparsifying basis to form the measurement
matrix, and is used to solve the l1 -minimization scheme leading
to HSFB spectrum estimation. Centered on the HSFB spectrum,
the detection performance is tested of a band of interest of PU by
varying the compression ratio M
N from 1% to 40%. For comparUniversity of Genova – DITEN
4.5 Performance Analysis and Simulation Results
77
ison, detection performance of the same PU band is considered
after spectral estimation of the full wideband signal xc (t) preceded over a single radio block (with average sparsity of 53%).
Consequently, number of samples N changes accordingly to fix
the sampling time T = 32s.
Pd of a PU band with the influence of Compression Ratio
Simulated Detection Probability,Pd
1
SNR:10dB
SNR: 5dB
SNR: 0dB
0.8
0.6
0.4
0.2
0
0
10
20
30
40
Compression Ratio, M/N (%)
Figure 4.2: Influence of compression ratio on the detection performance.
Fig. 4.2 illustrates the influence of the compression ratio M
N on
the PU detection performance by setting Pf a = 0.01 and received
SNR of the active channels are set to 0 dB,5 dB and 10 dB which
also illustrates the detection performance is a function of signal
sparsity (shown in Fig. 4.3); the proposed block selects HSFB
which provides improved detection performance. The Fig. 4.3
satisfies the theory of compressed sensing as highly sparse signals
provides better spectral estimation and hence the probability of
detection.
To make simulation environment relaxed, we consider frequency
University of Genova – DITEN
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
78
Pd of a PU band with the influence of Compression Ratio
Simulated Detection Probability,Pd
1
0.8
0.6
Proposed method:10dB
traditional method:10dB
Proposed method: 5dB
traditional method: 5dB
0.4
0.2
0
0
10
20
30
40
Compression Ratio, M/N (%)
Figure 4.3: Detection performance as a function of compression
ratio M
N
resolution ∆ is 1 MHz so the signal has a global bandwidth of
W = 64 MHz. In this setting, the number of Nyquist samples,
N = 4096 if the band was sampled at Nyquist rate for T = 32µs.
For energy estimation inside each FB we chose a compression raM
tio, M
N of 40% while the compression ratio, N has varied from
1% to 40% for spectral estimation. Fig. 4.3 presents the trade-off
between performance and processing time for different values of
S which is the number of particles in the proposal and the only
additional parameter in the presented method. For a number of
particles S = 1000 one can obtain a good trade-off between relative increase in performance (Aprox. 75% decrease in error) while
having a low relative increase in processing time (Aprox. 25%).
In simulation, probability of detection Pd is chosen by statistical
averaging of 2000 experimental results.
There are several obtainable advantages of the proposed comUniversity of Genova – DITEN
4.5 Performance Analysis and Simulation Results
79
Complexity order with the influence of no. of filters
1
0.9
Complexity order
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
No. of filters
Figure 4.4:
Order of computational burden needed with the
influence of no. of filters.
pressed sensing approach with the proposed CR receiver sensing
block. First, with l1 -minimization, the desired spectrum is estimated considering only a few (M ) number of random samples of
the designated FB, xk . In Fig. 4.4, it is analytically computed
the order of computational burden by using (4.7) which enables
to perform wideband spectrum sensing with fewer computational
complexity. Here, the number of samples are decreased by the
influence of the number of BPFs, K. Therefore, in the proposed
system saves arithmetic computations in the order of O(K log K).
As a rough estimate, the proposed approach saves computational
burden of 45% while using K = 4 (Fig. 4.4).
Moreover, this approach of wideband sensing saves the memory storage of bits in the order of O(K) according to 4.9. The
consequence of number of BPFs on the memory space requisite is
plotted in Fig. 4.5. It displays the proposed technique of wideUniversity of Genova – DITEN
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
80
Order of memory space required
Memory space required as a function of no. of filters
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
No. of filters
6
7
8
Figure 4.5: Order of memory space requirement with the influence of no. of filters.
band sensing involves only 10% of physical memory spaces than
that followed by a single RF chain.
Besides, the K-th number of filters introduced in the proposed
method are wideband BPF having much smaller impulse response
which make the filter less complex to be constructed. As the Kth filter having the bandwidth, wk larger than a single PU can
occupy, give the indications that the filtering complexity of the
proposed method is reduced by a factor of w1k × wK2 = wK2 over the
k
k
conventional channel-by-channel scanning [30].
The FB comprising minimum energy Ek(min) has two significant meaning; firstly, within this frequency bin xk , minimum
number of PU bands are possibly active at that time. Secondly,
Ek(min) suggests the enhanced sparsity level in the frequency domain of that FB which is one of the fundamental requirements
of signal recovery in CS from partial non-adaptive measurements.
University of Genova – DITEN
4.6 Achievable Throughput of a Stand-Alone CR
Terminal
81
As this method estimate the spectrum of a single FB which is
highly-sparse in frequency domain than the complete spectrum estimation, thus dry up computational burden as well sensing time.
Considering those issues in future, we will find improved detection
performance and enhanced achievable capacity [9] of the proposed
CR receiver sensing module.
4.6
Achievable Throughput of a StandAlone CR Terminal
To compute the achievable throughput for CR network we consider a simple problem which is collision free (as PU is absent and
so no false alarm is caused by the CR) achievable throughput for
CR network. Let us consider, τ is the time slot reserved for sensing operation and (T −τ ) is the data transmission slot duration as
shown in Fig. 4.6 [68]. Also, denote C0 as the achievable capacity
of a CR network considering PU data transmission off and C0 can
be written
Figure 4.6: Graphical structure of a typical frame of a CR data
transmission.
as C0 = log2 (1 + SN Rs ), where SN Rs denote the signal-toUniversity of Genova – DITEN
82
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
noise ratio (SNR) of a CR link. Inside an interoperable network,
we also consider PU data transmission, CR data transmission and
reception are Gaussian, white in nature and independent to each
other. For a particular band of interest, P (H0 ) signifies the probability for which the PU data transmission is absent. Therefore,
we recall the optimal achievable rate R(τ ) from [45] is
√
τ
R(τ ) = C0 P (H0 )(1 − )(1 − Q(α + N γ))
(4.11)
T
p
where α = 2γ + 1Q−1 Pd . From equation 4.11, it has been
noticed that the achievable rate of a CR node varies with the sensing slot duration as well as frame duration e.g., the throughput
is greater for shorter sensing time period τ with a fixed frame
length T . Hence, we try to sort out a trade-off between the sensing length and frame length. As the miss detection probability,
Pm can obligate with the possibility of data collision (a collapse
of achievable throughput) with the PU transmission while the
probability of false alarm Pf a recommends the CR to stop packet
transmission during the frame interval though PU channel is idle
at that instant which also decrease the throughput performance.
We assume Medium Access Control (MAC) layer of CR network
guarantees that only one CR can have the accessibility of a PU
sub-channel at a particular time to avoid the collisions among the
CR nodes inside the network [45]. Therefore, collisions can only
be possible between the CR and the PU.
Later, to testify the achievable rate of the proposed CR system, the throughput performance is investigated. To make easily
understandable, we choose low regime SNR value of the PU system, e.g., SNR= −10 dB, probability of detection Pd = 0.90 and
probability of PU transmission is absent, P (H0 ) = 0.90 when a
CR node wishes to transmit. Intuitively, the sensing time, τ engaged for the proposed approach and the full spectrum estimation
University of Genova – DITEN
4.6 Achievable Throughput of a Stand-Alone CR
Terminal
83
Simulated Throughput (bits/Sec/Hz)
Influence of the Throughput on τ: Frame=50 msec.
7
6
SNR:
SNR:
SNR:
SNR:
SNR:
SNR:
5
4
3
20dB-p.
20dB
10dB-p.
10dB
5dB-p.
5dB
2
1
0
2
4
6
8
10
12
Sensing Time, τ (msec)
Figure 4.7: Simulation of achievable rate against sensing time for
a fixed frame length
with a single RF chain followed by promising CS method is considered during simulation operation. Meanwhile, this sensing time, τ
is applied in equation 4.11 to find the optimum throughput for a
fixed frame length of 50 ms and different SNR values as illustrated
in Fig. 4.7. To proceed further, we again investigate (Fig. 4.8 and
4.9) the optimum throughput of the same arrangement but this
time a variation of the frame length is used with a fixed sensing
time, = 4.7 ms and = 11 ms. Both plots (Fig. 4.8 and Fig. 4.9)
demonstrate that the proposed method outperforms with respect
to a conventional CS based spectrum estimation. Inside the legends of the figures the notation · · · p. have marked ( Fig. 4.7, Fig.
4.8 and Fig. 4.9) our proposed approach.
University of Genova – DITEN
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
84
Achievable Throughput vs. varying T: τ=4.7 msec.
Simulated Throughput (bits/Sec/Hz)
6
5
SNR:
SNR:
SNR:
SNR:
SNR:
SNR:
4
3
5dB-p.
5dB
10dB-p.
10dB
20dB-p.
20dB
2
1
0
0
20
40
60
80
100
Frame Length, T (msec.)
Figure 4.8: Illustration of the achievable rate against Frame length
for a fixed sensing time
Throughput vs. variable Frame Length: τ=11.6msec.
Simulated Throughput (bits/Sec/Hz)
5.5
5
SNR:20dB
SNR:20dB-p.
SNR:15dB
SNR:15dB-p.
SNR:10dB
SNR:10dB-p.
4.5
4
3.5
3
2.5
2
0
0.1
0.2
0.3
0.4
0.5
Frame Length (sec.)
Figure 4.9: Influence of the CR Achievable rate on the sensing
time
University of Genova – DITEN
4.7 Summary
4.7
85
Summary
This chapter describes an innovative block of CR receiver module for wideband spectrum sensing by exploiting Compressive Sensing. Starting with a time domain signal, a single FB is estimated
and detection performance has been explored through simulations
to a band of interest of a CR. Finally, achievable throughput performance of a static frame duration as well as static sensing length
are compared to a traditional spectrum sensing methodology subsequent to a single RF chain with CS method. Corroborating simulation outcomes guarantee the worth of the proposed approach.
University of Genova – DITEN
86
Chapter 4 : Compressive Sensing for Wideband
Cognitive Radios
University of Genova – DITEN
Chapter 5
Cooperative
Compressive Sensing
for Wideband
Cognitive Radios
5.1
Introduction
Recent research claims that spectrum is heavily underutilized
( [10] [32] [43] [64]) most of the times by the Primary User (PU)s)
at any particular time and geographic location, thus degrades
spectrum utilization efficiency. To improve the efficiency, opportunistic spectrum access is employed by Cognitive Radio (CR)s;
a new paradigm of spectrum agile wireless networks. while the
CR searches opportunity in the wideband, it could potentially exploit more spectral opportunities and obtain greater data rates
for various mobile applications [64]. As sparsity plays a key role
87
88
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
in Compressive Sensing (CS) [23], the previous chapter [4] introduces a novel schematic block of spectrum sensing incorporated
in stand-alone wideband CR receiver which aims to discover the
highly-sparse frequency bin (HSFB) by compairing the average energies among the different frequency bins (FBs) come out from the
entire wideband. The spectrum of HSFB is then approximated via
a convex optimization approach [23] called l1 -norm minimization
and the detection performance of a Primary User band remains
in HSFB is identified by using an energy detector (ED) [22] and
compared it with the detection performance of the same band of
the entire wideband in terms of sparsity. In fact, the proposed
scheme provides better detection performance since the presence
of higher sparsity in HSFB. Besides, this scheme requires lower
computational burden and lower memory requirements.
Spectrum sensing performed by a stand-alone CR is critical
while dealing with multipath fading and hidden node problems
[43], [75] and reliability of performance is questionable. Thus,
cooperative spectrum sensing (COSS) is introduced to get reliable
detection performance as well as to minimize the interference to
PUs and in consequence, the false alarm probability is reduced.
We compare different fusion rules in COSS environment in terms
of detection performance, control channel capacities, etc. and
in consequence the detection performance is again improved in
terms of number of CRs. In the later section 5.5, we discuss some
practical implementation issues related to wideband CR exploiting
compressed sensing.
5.2
System Model
Let the PUs of a radio network mutually share the wideband
signal xc (t) of bandwidth W Hz and the bandwidth of every nonUniversity of Genova – DITEN
5.2 System Model
89
overlapped PU is B Hz which could potentially serve the demand
of a CR node. In addition, the signal xc (t) is comprised of a maximum of W
B PU bands as depicted in Fig. 4.1 where a few bands
are always randomly available for opportunistic accessing to CRs.
K
Here, K number of identical BPFs {Hk (f )}k=1 (where Hk (f ) denotes transfer function of the k-th Band-Pass Filter (BPF)) divide
the signal in K different frequency bins (FBs), are denoted as xk
of equal bandwidth wk = W
K Hz where k = 1, 2, · · · , K. At any
particular time each xk is accommodated with different number of
active PUs randomly from a maximum of wBk bands. For simplicity, assume that at least one PU sub-band exists in a FB xk at a
certain time. The energy estimation of every FB has performed by
taking random compressed samples Mk derived from the Random
Demodulator (RD). Those Mk samples are intended for calculating the average energy Ek of a single FB and compare those
K
average energies {Ek }k=1 at the energy estimate and compare
block. It is important to note that the comparator should restore
the sample values while comparing the values of Ek of various
FBs. Meanwhile, the HSFB of having minimum average energy,
Ek(min) is detected by the comparator along with the samples
which is then considered for approximating the spectral magni 2
tude X̂k via a well-known l1 -minimization algorithm [23]. The
HSFB indicates minimum number of PUs actively present which
substantially provides maximum opportunistic accessibility to a
CR user. Besides, the theory of CS tells that the more the sparsity, the better would be the spectral estimation which contributes
better detection performance. Moreover, spectral estimation of a
single HSFB rather than entire wideband require less computational burden. With HSFB spectrum, we proceed to look for a
vacant PU sub-band for opportunistic usage to a stand-alone CR
by exploiting a well-known ED approach proposed in [22]. Later,
University of Genova – DITEN
90
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
to improve the reliability of sensing performance, a cooperative
CR network is set where each CR has the capability of wideband
sensing exploiting the schematic discussed in Chapter 4 in Fig.
4.1.
5.3
Decision Fusion
In COSS, all the member CRs take part independently in local spectrum sensing and based on this detection performance a
binary decision of a chosen PU band status is made. Now, all CRs
forward their local decisions ui ∈ {0, 1} to a Decision Maker (DM)
and it is responsible to find the global decision U of a chosen PU
band by combining the local hard decisions [75].
(
U =0
ui
F =
U =1
i=1
n
X
if F < J
otherwise
(5.1)
where U = 1 indicates that the PU is present whereas U = 0
indicates opposite to it. Note that the fusion rule reported in
(5.1) represents the J-out-of-N fusion rule and indicates global
decision U = 1 if at least J number of CR nodes over N decide
for the presence of the PU [75]. In fact, if J = 1 the fusion
rule in (5.1) coincides with logic-OR (LO) fusion rule, while logicAND (LA) fusion rule occurs when J = N , where both rules
represent the special cases of (5.1). Intuitively, the LO rule is
much conservative than the LA fusion rule while accessing PU
bands as LO fusion rule does not allow CR transmissions even if
a single CR detects the presence of PUs in COSS network [43]
whereas the LA rule stops CR transmission only if all the CR
nodes in the network detect the presence of PUs. Those logical
rules can provide a satisfactory performance in many practical
scenario while the optimality of the fusion is not guaranteed, hence
University of Genova – DITEN
5.4 Performance Comparison and Simulation Results 91
optimal fusion (OF) rule comes out which is employed by the
following likelihood ratio test [75]:
Λ0 =
n X
Pdi
1 − Pdi
P (H1 )
ui log
+ (1 − ui ) log
+ log
(5.2)
P
1
−
P
P (H0 )
f
f
i
i
i=1
When Λ0 ≥ 0, then the PU is present; otherwise, DM decides
the absence of PUs. The OF rule presented in (5.2) is monotonic assuming Pdi ≥ Pf i and can be implemented by adopting
a weighted sum of the incoming local decisions then, comparing
it with a threshold which also depends on prior probabilities and
cost [75]. Usually, the weights represent the reliability of the local
decisions in terms of the probability of detection and the probability of false alarm and OF rule tries to minimize the average cost
of making decisions. As OF scheme requires the local decision ui ,
along with the probability of false alarm Pf i , and the the probability of detection Pdi of the i-th CR node, thus, higher processing
and control channel capacities are required than the logical fusion
rules in (5.1).
5.4
Performance Comparison and Simulation Results
At baseband, the wideband signal xc (t) falling in the range of
[1 ∼ 64]∆ Hz can accommodate a maximum of 32 non-overlapping
32
PU bands of [1 ∼ 2]∆ Hz and encoded as {chl }l=1 , where ∆ is the
frequency resolution. The received signal xc (t) at the CR node is
as follows [64]
xc (t) =
N p
X
(En Bn ). sinc(Bn (t − δ)). cos(2πfn (t − δ)) + z(t)
n=1
(5.3)
University of Genova – DITEN
92
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
where sinc(x) = sin(πx)
πx , δ denotes a random time offset within
sampling branches, z(t) is the Additive White Gaussian Noise
(AWGN) of unit variance. In simulations, the number of BPFs
are considered as K = 4 so the bandwidth of each xk is wk = 16∆
Hz, i.e. a single FB can comprise a maximum of wBk = 8 PUs
having no sparsity. A total of 15 PU bands with different carrier
15
frequencies {fn }n=1 present inside the wideband W when probing the burst of transmissions. The distribution of active PUs in
4
various FBs are {xk }k=1 = {4, 5, 4, 2} with dissimilar sparsity levels. The number of Nyquist rate samples N are taken from HSFB
for an observation time T (e.g., the chosen frequency resolution
∆ = 1 MHZ and N = 1024 samples to satisfy T = 32µs). The average energy estimation of various FBs are performed by reflecting
a fixed compression ratio M
N = 40% and from those FBs, the energy comparator selects x4 (t) as HSFB (having average sparsity of
75%) tailored for spectral estimation. The Discrete Fourier Transform (DFT) is selected as the sparsifying basis to form the measurement matrix, and is used to solve the l1 -minimization scheme
leading to HSFB spectrum estimation. Centered on the HSFB
spectrum, the detection performance is tested of a band of interest of PU by varying the compression ratio M
N from 1% to 40%.
For comparison, detection performance of the same PU band is
considered after spectral estimation of the full wideband signal
xc (t) preceded over a single radio block (with average sparsity of
53%). Consequently, number of samples N changes accordingly
to fix the sampling time T = 32s. Fig. 5.1 illustrates the influence
of the compression ratio M
N on the PU detection performance by
setting Pf a = 0.01 and received SNR of the active channels are
set to 5 dB and 10 dB which also illustrates the detection performance is a function of signal sparsity; the proposed block selects
HSFB which provides improved detection performance. In simu-
University of Genova – DITEN
5.4 Performance Comparison and Simulation Results 93
lation, Pd is selected by statistical averaging of 2000 experimental
results.
Pd of a PU band with the influence of Compression Ratio
Simulated Detection Probability,Pd
1
0.8
0.6
Sparsity
Sparsity
Sparsity
Sparsity
0.4
S=75%
S=53%
S=75%
S=53%
&
&
&
&
SNR=
SNR=
SNR=
SNR=
10dB
10dB
5dB
5dB
0.2
0
0
5
10
15
20
25
30
35
40
Compression Ratio, M/N (%)
Figure 5.1: Detection probability as a function of sparsity.
Again, in COSS scenario, we assume two and threes identical
CRs, successively. The receiver operating characteristic (ROC)
is obtained in Fig. 5.3 by CRs which incorporate the receiver
block of Fig. 4.1 in Chapter 4 and forward the sensing decisions
to the DM which combines according to fusion rules. Fig. 5.2
demonstrates the optimal fusion rule of sensing decisions which
employs narrowband signal in CR while Fig. 5.3 represents the
fusion rules of sensing decisions that employs wideband signal in
CR systems. The curves in Fig. 5.2 and Fig. 5.3 illustrate the
superiority of different fusion rules in different regions and it illustrates the monotonic OF rule has overall better performances
than the considered logical fusion schemes. In addition, by using
COSS in a highly noisy case, the performance is much better than
the high SNR values used by a single CR node. Besides, the detecUniversity of Genova – DITEN
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
94
tion performance improves with the number of cooperative CRs
which is examined by considering three CRs in COSS setting.
ROC curves after applying different fusion rules
Probability of detection
1
0.8
OR Rule
AND Rule
0.6
OR3 Rule
AND3 Rule
0.4
ROC
CVfusion3node
0.2
0
0
0.2
0.4
0.6
0.8
1
Probability of false alarm
Figure 5.2: ROC performance of stand-alone and cooperative narrowband CR nodes.
The performance improvement is achieved with the optimal
fusion (OF) rule at the expense of the processing capabilities of
DM, CRs and control channel. In fact, the OF rule requires the
knowledge of the local decisions ui with the associated Pd and
Pf which must be obtained at the CRs to forward to the DM.
Moreover, the combining decisions at the DM is more complex
to apply OF rule, reported in (5.2), than its logical counterparts,
reported in (5.1). In the presence of channel fading, the detection performance and Receiver Operating Characteristics (ROC)
curves provided in [64] having similar characteristics except degraded detection performance with respect to AWGN channel.
Therefore, the fusion rule is proposed here to improve reliability in PU detection would also applicable for CR network which
University of Genova – DITEN
5.5 Practical Implementation Challenges
95
experiences the problem of multipaths and channel fading.
1
ROC curves in cooperative wideband CRNs
0.9
Detection probability
0.8
ROC-SNR5dB
0.7
CV-Fusion2Node
0.6
LO-Fusion2Node
0.5
LA-Fusion2Node
CV-Fusion3Node
0.4
LO-Fusion3Node
0.3
LA-Fusion3Node
0.2
ROC-SNR10dB
0.1
0
0
0.2
0.4
0.6
0.8
1
Probability of False Alarm
Figure 5.3: ROC performance of stand-alone and cooperative
wideband CR nodes.
5.5
Practical Implementation Challenges
In this section, we would like to point out some major practical
performance issues related with the proposed wideband spectrum
sensing module. We start with a a description of the influence of
the main parameters governing the scheme performance. Second,
we point out the shortcomings arise for this detector (for simplicity
we consider the linear and known noise variance which is not the
case in practice, also local channels of the distributed network is
considered as independent and identically distributed (iid). Then
we describe the main architectures which have already been proposed in the literature to implement the Analog-to-Information
Converter (AIC) and we finally conclude the chapter with a low
University of Genova – DITEN
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
96
complexity distributed compressive reconstruction algorithm to
perform the detection without going into the intermediate stage
of estimating the Power Spectral Density (PSD).
5.5.1
Degrees of freedom to enhance detection
performance
All simulations that have been performed throughout the thesis considering the preset value of the parameters. The influence
of the parameters are illustrated in the following:
• Spectral estimaion block size (N ): this parameter is related
to the bandwidth resolution of CR receiver, referred to as
the ability to distinguish the spectral features.
• Number of compressive measurements (M): the applied compression in the scheme influences the error in the formation
of PSD estimate. it has been shown from simulations that
a compression rate of 5% incurs a very similar performance
as the classic full rate Nyquist samples.
• Measurement Matrix (Φ): In the earlier section, we have introduced several possible measurement matrices. The main
significant issue of the measurement matrix is to provide the
incohorency with the sparsifying basis. The more the incoherency is, the less measurements are needed by the compressive edge optimization algorithm to converge. Owing to
the universal incoherency of the Gaussian matrix, we have
chosen this type of matrix to run the simulations all along
the thesis.
• Wavelet smoothing function (W): The matrix W introduced
in [ZTian:2006] to calculate the edge transform domain matrix G represents the discrete time wavelet smoothing funcUniversity of Genova – DITEN
5.5 Practical Implementation Challenges
97
tion. Due to the inversion involved when obtaining G, the
wavelet function can not be freely dilated. In fact, our
method is not eligible to perform a multiscale or multiresolution wavelet transform. The interest of a multi-resolution
transform comes from the fact that the edges of interest
would show up always at the same positions. On the contrary, noise-induced spurious edges are random at each scale
and thus tend not propagate through all scales; hence, if
a multiscale wavelet transform has been provided, an enhanced PSD estimation would be possible as well as improved detection performance of the CR networks.
5.5.2
Detection without estimation
A joint recovery algorithm has been proposed in [24], named as
One-Step Greedy Algorithm which is intended to recover the joint
common sparse support of a wideband signal ensemble with fewer
than O(K log N ) measurements per CR. Of course this approach
does not recover the coefficients for each signal but it provides a
sufficient statistic to perform detection at lower complexity, i.e.
theorem 1 in [24] claims that with M ≥ 1 measurements per signal, One-Step Greedy Algorithm (OSGA) recovers the common
sparse support with probability approaching 1 as J → ∞. We
next show from simulations that OSGA may be utilized as a recovery algorithm for the architecture shown in Figure 5.4 under
the same assumption of joint sparsity concerning the case of multiple sparse signals that share common sparse components, but
with different coefficients. The measurements can be obtained
following any of the acquisition schemes described in Chapter 3.
Again, for simplicity we shall develop the equations for our proposed architecture (Section 3.3). We assume that an equal number
of measurements is taken per CR and we write Θj in terms of its
University of Genova – DITEN
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
98
columns
Θj = [θj,1 , θj,2 , · · · θj,N ]
j = 1, 2, · · · J,
(5.4)
where Θj is given by
Θj = ΦII,j F where j = 1, 2, · · · J,
(5.5)
with ΦII,j denoting the 2M ×2N compressive sampling matrix
as defined in (3.14) at the j-th CR and F standing for the 2N ×2N
discrete Fourier matrix. The measurements obtained under the
architecture proposed in [76]
ry,j = ΦII,j FSx,j where j = 1, 2, · · · J,
(5.6)
with Sx,j denoting the PSD of the sought signal xj (t) at the
j-th CR. After gathering all of the measurements the following
statistic is computed
J
ξn =
1 X T
hr , θj,n i2 where n = 1, 2, · · · 2N,
Jχ j=1 y,j
(5.7)
where χ denotes the mean of the test statistic ξn in the absence
of the PU signal.
5.5.3
Shortcomings in signal detection
We have proposed signal detection algorithms are based on
some considerations which are common in literature. In the following, we illustrate them further [76]:
• We considered that noise variance is precisely known at the
receiver terminal, so that the threshold can be set accordingly. In contrary, this is impossible in practice, as noise
University of Genova – DITEN
5.5 Practical Implementation Challenges
99
could vary over time due to different parameters (e.g., temperature change, ambient interference, filtering, etc). The
deviation of the variance from the assumed known value becomes important when the signal strength is below the error
of the noise variance. In that case, the detection threshold,
which is set based on the known variance, should be changed
accordingly.
• It is assumed that the noise is a white, additive and Gaussian
Wide-Sense Stationary (WSS) process, with zero mean, and
known variance. Though, noise is an aggregation of various
sources including not only thermal noise at the receiver and
underlined circuits, but also interference due to the emissions from neighbor radio terminals, transmitters at very
far distance, etc [1].
• In modeling the channels we assumed that they are independent and identically distributed(iid). As a result, the
diversity gains that we obtained are maximized. However,
channel coefficients resulting of superposition of different parameters (e.g., path loss, shadowing, and multipath) that do
not necessarily need to be iid for all radios. While path loss
for small to medium networks can be assumed equal for all
radios, the other two effects could have quite different characteristics. For example, shadowing can exhibit high correlation if two radios are blocked by the same obstacle [1].
• Lastly, we consider equal distribution of noise and local interference across all radio nodes. Consequently, every CR
could apply the same detection threshold and obtain identical Pf a . However, in practice, these two assumptions do
not serve the purposes. First, due to circuits variability or
temperature difference, each radio node has a different agUniversity of Genova – DITEN
100
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
gregate local noise.
In a time-variant environment, a fixed threshold Neyman-Pearson
(NP) detector cannot be used, because, as the background conditions vary, the resulting value of pf a may be too high (i.e., decreasing the reuse of the unused spectrum) or the value of pd may be
too low (i.e., increasing the interference to the PU systems). This
suggests to exploit cognitive threshold schemes based on the estimate of mean power of the background noise. Several approaches
may be reused from the noise estimation literature to solve the
practical spectrum sensing problem: how can we set the threshold based on a real time estimation of the noise power, so that
a fixed probability of detection, pd or a fixed probability of false
alarm, pf a is ensured? A simple but reasonable method is to treat
the estimate of noise power as the true noise power and calculate
the threshold used in energy detection accordingly. In [54], the
practicality of performing real time noise estimation was justified
with two examples:
1. Assume the spectrum regulators still want to reserve certain
channels for special applications, and CRs are never allowed
to access this channel. In addition, this special channel is
rarely used and therefore can serve the purpose of noise estimation, e.g., in the United States, channel 37 (from 608
to 614 MHz) is reserved for radio astronomy and is used in
very few occasions.
2. Detecting pilot signals which are distinct narrowband spectral features. After performing the PSD estimation on the
received signal, the noise variance can be estimated from
some frequency bin not corresponding to the pilot frequency.
Intuitively, this approach may incur in an inherent loss of detection probability since the threshold is chosen while considering
University of Genova – DITEN
5.5 Practical Implementation Challenges
101
the total noise power from only a finite number of observed noise
samples. In [80], a method is proposed to determine the threshold
considering real time noise variance estimation which may provide
the desired probability of detection and probability of false alarm.
The previous approach relies on a noise variance estimated
from a possibly vacant channel. In [50], the authors presented a
new method of estimating noise power. The method is applicable
for ID and 2D signal processing. The essence of this method is estimation of the scatter of normally distributed data with high level
of outliers. The method is applicable to data with the majority
of the data points having no signal present. The method is based
on the shortest half sample method. The assumption is quite reasonable, since the current dynamic spectrum sharing research is
motivated by the fact that many parts of the spectrum are underutilized most of the times. This makes the concept of spectrum
sharing to be attractive. Therefore, one can estimate the noise
power without doing any explicit separation of the noise from the
noisy signal. In [66] a wideband detector for single CRs or multiple collaborative CRs which does not require the noise variance
is proposed based on the General Likelihood Ratio Test (GLRT).
They assume that among the sub-bands there is some minimum
number of vacant sub-bands. Basically, the estimate of the noise
variance in [66] is based on the average of the least energies of the
sub-bands when sorted in an ascending order. This approach is
intuitively justified, since it is more likely for the subbands with
lower energies to be vacant rather than the higher energy ones.
Most of the fusion approaches in the literature have focused on
the cases with conditionally iid observations. The correlated case
where it is assumed that each CR knows the geographic locations
of the other users and hence the correlation between the observations is studied in [74].
University of Genova – DITEN
102
5.5.4
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
RD/ AIC implementation issues
A significant part of the Compressive Sensing research has focused on advanced devices for AIC of large-bandwidth signals [40]
[?]. The goal as introduced in this thesis is to alleviate the pressure on conventional Analog-to-Digital Converter (ADC) technology, which is currently limited to sampling rates on the order
of 1 GHz. There are two contributions in the paper [40], the
first contribution is to provide a new framework for wideband signal acquisition purpose-built for compressible signals that enables
sub-Nyquist data acquisition via an AIC. The framework is based
on the recently developed theory of CS [23] in which a few number of non-adaptive, randomized measurements are sufficient to
reconstruct compressible signals. The second contribution of this
paper is to introduce an AIC implementation design and study of
the tradeoffs and non-idealities introduced by real hardware. The
goal is to identify and optimize the parameters that dominate the
overall system performance. In [?], the authors suggested a new
type of data acquisition system, called a RD, that is constructed
from robust, readily available components. Let L denote the total
number of frequencies in the signal, and let W denote its bandlimit in Hz. Simulations suggest that the random demodulator
requires just O(L log( W
L )) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than
the Nyquist rate of W Hz. The AIC bridges the gap between the
CS theory, which is based on discrete-time signals, and the needs
of real data acquisition devices, which deal with continuous-time
signals. The construction and behavioral models of AIC have
been provided in [40] which enabled to study the design space for
the four key building blocks in order to optimize the end-to-end
performance. The authors in [40] have studied the non-idealities
introduced by actual circuit implementations suggests that the
University of Genova – DITEN
5.5 Practical Implementation Challenges
103
mixer non-linearity dominates over the effects of clock jitter in
the chipping sequence generator and the non-ideal transfer function of the integrator. To obtain expected performance from AIC,
we need to enhance the performance of the following equipments:
• To enhance the mixer linearity
• To increase the number of quantization bits
• To enhance the integrator performance, and
• To improve the clock jitter.
5.5.5
Summary
In this chapter, we have proposed a schematic block of CR
receiver to distinguish HSFB in the wideband and estimates the
spectrum following a CS approach which indicates better detection performance than that achieved in full wideband estimation
which is investigated through simulations. Later, we have introduced this scheme in COSS scenario to have the reliable detection
performance and several fusion rules are compared in terms of detection performance, control channel capabilities and processing
capacities.
University of Genova – DITEN
104
Chapter 5 : Cooperative Compressive Sensing for
Wideband Cognitive Radios
University of Genova – DITEN
Chapter 6
MIMO Scheme for
Opportunistic Radio
Systems
1
As the growing number of multimedia applications introduced
in mobile radio devices, hence the achievable capacity of the radio
terminals should be improved. There are several ways to improve
the achievable capacity of the cognitive radio terminals. First,
when dealing with the highly sparse frequency segment of the
sparse wideband signal, the detection performance and the achievable capacity are improved which is drawn in Chapter 4. Second,
to form a cooperative environment of the Cognitive Radio (CR)s
could also improve the detection performance (as shown in Chapter 5) and the achievable capacity [45]. Third, exploiting multiple
antennas in Multiple Input Multiple Output (MIMO) systems can
1 Contents
of the current chapter are part of [7] [16]
105
106
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
increase the achievable capacity discussed in [16] [17] [7] [84].
In this chapter we would like to illustrate a simple linear
transceiver for MIMO cognitive radio systems having just one
degree of freedom. The computational burden required to implement our algorithm, which guarantees the decoupling of the
primary and secondary channels under perfect channel state information, is significantly reduced with respect to the conventional
algorithms achieving the same results under the same hypothesis.
This reduction is verified by a detailed evaluation of the floating
point operations required to implement the proposed algorithm.
This result could be of interest in order to reduce the power consumption of cognitive radio terminals.
6.1
Introduction
In the last few years several research studies have been focused
on the so-called MIMO) systems because wireless communications
can obtain many important benefits, like capacity enhancements
and interference reductions, from the use of multiple transmit and
multiple receive antennas [81], [35], [36], [28], [85]. For example,
the mitigation of the interference and the enhancement of the
channel capacity which can be obtained by using a Zero-Forcing
Beam-Forming (ZFBF)) algorithm is discussed in [81] while the
achievable rate which can be obtained by using the same algorithm for the two-user case is analyzed in [46]. Another algorithm, based on a combination of ZFBF and orthogonal BF, is
proposed in [83]. Other important studies are aimed at determining the degrees of freedom [35], [36] for different types of
MIMO interference channels (X-channel, Z-channel, etc.) or the
transmission strategies to achieve the Pareto optimal operating
points [54] (see also [37]). MIMO systems have also been considUniversity of Genova – DITEN
6.1 Introduction
107
ered for opportunistic (or secondary or even cognitive) communication systems [28], [85], [27], [84], [17], since their properties
are very useful to this kind of systems, which have to communicate without creating any significant interference to licensed (or
primary) users [27], [17]. Moreover, in the context of wireless communication systems and for cognitive radios and mobile devices
in particular [4], [62], [29], a special attention is dedicated to the
technological developments or to the studies which could allow a
reduction of the power consumption of the radio terminals. Needless to say, any algorithm allowing a significant reduction of the
computational load required to the terminals could be of help for
this target. Moreover, systems exploiting the minimum number of
antennas at the transmitting and receiving terminals could have
some advantages in this sense.
In this study we present an architecture which could be of
interest for MIMO opportunistic systems and for the minimization of the power consumption of these systems. The definition
of simple algorithms designed for simple architectures is, for the
reasons indicated above, the main target of our work. The general approach to these topics is very similar to the one we adopted
in [17]. In that paper, in particular, it is presented a closed form
expression for a linear precoding and linear reception scheme for
the secondary system, which allowed to obtain the achievable rate
and no mutual interference between primary and cognitive terminals. This result were obtained under the assumptions that just
one primary transmitter-receiver pair was present, that the link
between them was half-duplex, that both these terminals were
provided with just one antenna, that both sides of the secondary
system had two antennas and that the cognitive terminals had a
perfect knowledge of the channel matrices (perfect channel state
information [27], [79], [42]). The explicit form of the matrices
University of Genova – DITEN
108
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
defining the linear precoding and reception scheme deduced in [17]
was of fundamental importance to reduce the computational effort
required at the cognitive terminals to implement the algorithm
there presented. In this paper, we extend our previous work [17]
by removing many of the hypotheses which were there assumed.
In particular, we deduce, as before, a closed form expression for
a linear precoding and linear reception scheme for the secondary
system, which allows to obtain the achievable rate and no mutual
interference between primary and cognitive terminals, with no restrictions on the number of transmitting and receiving terminals,
on the type of link (half duplex or full duplex) and on the number
of antennas which are present on these terminals. Since we are
particularly interested in simple and energy-efficient terminals, we
perform this task by considering secondary terminals having the
smallest numbers of antennas which allow the opportunistic radio
to retain one degree of freedom. As a by-product of this analysis,
we deduce an algorithm which is much simpler and more general
than the one defined in [17]. A comparison of the computational
load required at the cognitive terminals between the algorithm
defined in [17] and the one we define in this work show that the
possible reduction of floating point operations for any secondary
system symbol time is bigger than two and could be included in
the range {2.5, 6}. It is important to notice that this analysis
is theoretical in nature and that in this work we do not analyze
the effects of imperfect channel knowledge [81], [79], [42] at the
secondary terminals.
For this topic the reader is referred, for example, to [81], [79],
[17], [42]. In particular, the same analysis carried out in [17] could
be repeated in the more general cases here considered. However,
it could be important to notice that the simplified algorithm here
defined allows to obtain an important by-product for this kind of
University of Genova – DITEN
6.2 Problem Definition
109
analysis, too. As a matter of fact, while the algorithm in [17] requires the knowledge or the estimation of three matrices (the ones
related to the secondary to primary, to the primary to secondary
and to the secondary to secondary links), the new algorithm requires the knowledge or the estimation of two matrices (the ones
related to the secondary to primary and to the primary to secondary).
This chapter is organized as follows. In Section ?? the general
setting of our study in defined. Section 6.4 is dedicated to the
explicit definition of the matrices allowing to decouple the secondary communication from those of the primary systems. Some
additional linear preprocessing and postprocessing techniques of
the secondary signals are discussed in Section 6.5. Finally, before the conclusions, we deeply analyze the computational load
(in section 6.6) required to the secondary terminals to implement
the new algorithm.
6.2
Problem Definition
In this paper we consider a set of primary systems working in
the same frequency band and having overall M1 transmitting and
N1 receiving antennas. In the same region and in the same band a
secondary system having M2 transmitting and N2 receiving antennas would like to operate without causing any interference on and
without suffering any interference from the primary systems. One
possible configuration involving different primary systems and a
secondary system is shown in Fig. 6.1. In black we have indicated
the possible primary links; the green arrow indicates the secondary
link of interest whereas the unwanted links between the M1 primary transmitters and the secondary receiver and between the
secondary transmitter and the N1 primary receivers are in red.
University of Genova – DITEN
110
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
In practice, different numbers of transmitting and receiving
antennas on the primary systems are required to take account of,
for example, broadcast or multicast communications. It could be
important to notice that our general setting allows to consider not
only half-duplex primary systems (as those considered in [17]) but
also full duplex ones, with transmitter and receiver operating on
the same frequency band. As a matter of fact, if a given antenna
works as a transmitting and as a receiving one, then it can be
considered twice, once in the M1 transmitting and once in the N1
receiving antennas, since in our model transmitters and receivers
can be spatially overlapped. Finally, this setting can also be of
interest for military applications, for example when a soldiers of
a squad would like to communicate with its squad head and vice
versa and the communication is disturbed by a set of jammers. In
this context, the soldier and the squad head are considered as the
secondary system which needs to avoid the intentional disturbing
interference of the jammers, considered, in this case, as primary
systems (with M1 given by the number of antennas of the jammers
and N1 = 0).
Remark 1. It could be interesting to observe that in our model
primary systems placed in the far-field region [14] (p. 33) of all the
antennas of the secondary system can be considered as having a
single antenna even if they are actually equipped with an antenna
array. This fact could be useful to simplify the model of interest
for civil or military applications.
In this configuration we can define two complex vectors xp ∈
C
and yp ∈ CN1 having as components the complex baseband
signals generated by the primary transmitters or arriving to the
primary receivers. The link between these two vectors is provided
by the primary to primary channel matrix Hpp ∈ CN1 M1 . The
signals received by the primary terminals are affected by zeroM1
University of Genova – DITEN
6.2 Problem Definition
primary receiver
with 1 antenna
primary transmitter
with 1 antenna
111
primary receiver
with 1 antenna
MIMO cognitive
receiver with N2
antennas
primary transmitter
with 1 antenna
primary receiver
with 1 antenna
Primary receiver
with 1 antenna
primary transmitter
with 1 antenna
MIMO cognitive
transmitter with M2
antennas
Figure 6.1: The considered MIMO interference channel model. In
the same region three primary systems, having overall M1 = 3
transmitting and N1 = 4 receiving antennas, operate in a given
frequency band. The primary systems are thought as half-duplex
systems but for full duplex systems an analogous scheme applies.
A MIMO secondary system with M2 transmitting and N2 receiving antennas would like to reliably communicate in the same band
without affecting the transmissions of primary systems.
University of Genova – DITEN
112
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
mean complex Gaussian noise signals, defining np ∈ CN1 . The
secondary system is described in terms of a transmitted complex
baseband signal vector xs ∈ CM2 and of a received complex baseband signal vector ys ∈ CN2 . The secondary transmitter is
coupled to the primary receivers by the secondary to primary
channel matrix Hsp ∈ CN1 ×M2 and to the secondary receiver by
the secondary to secondary channel matrix Hss ∈ CN2 ×M2 . Of
course, also a zero-mean complex Gaussian noise ns ∈ CN2 and the
primary transmitters could affect the signals arriving at the secondary receiver. The latter is taken into account by the primary
to secondary channel matrix Hps ∈ CN2 ×M1 . All these considerations determine the following input-output relationships [35]
(
yp = Hpp xp + Hsp xs + np
ys = Hps xp + Hss xs + ns .
(6.1)
These relationships assume that all signals are narrowband,
since all entries in Hpp , Hsp , Hps and Hss are frequency independent. However, we can extend our developments to multicarrier systems by applying it on a subcarrier basis, so extending
in a significant way the importance of our analysis [17]. In this
study, as we did in [17], we assume a zero mean complex Gaussian noise ns having [79] E {ns ns } = σs2 IN1+1 , where E {} is
the expectation operator [17] and IN1+1 is the identity matrix of
dimensions (N1 + 1) × (N1 + 1). According to [35] we will assume, moreover, that all channel matrices are full rank. In this
paper we are interested in the simplest, cheapest and, possibly,
low-power-consumption hardware set up for the secondary system allowing the secondary system itself to communicate without
causing any interference on the primary receivers and, at the same
time, without suffering interference from the primary transmitters [17]. With these constraints, in order to retain at least one
degree of freedom for the secondary radio link the secondary terUniversity of Genova – DITEN
6.3 Transmit Beamforming
113
minals have to be equipped with at least M2 = N1 +1 transmitting
and N2 = M1 +1 receiving antennas [35], [79]. We do not consider
secondary terminals with more antennas because this choice would
imply an increase of complexity, cost and power-consumption. In
order to decouple the N1 ×M1 MIMO channels of the primary systems from the N2 × M2 MIMO channel of the secondary one we
proceed as in [17] (see also [79]). In particular, we introduce a precoding matrix A ∈ CM2 ×M2 and a postcoding matrix B ∈ CN2 ×N2
, such that xs = Ax˜s and y˜s = Bys . With these additional linear
preprocessing and post processing operations we determine the
following input-output relationships:
(
yp = Hpp xp + Hsp Ax˜s + np
y˜s = Bys = BHps xp + BHss Ax˜s + Bns .
(6.2)
The indicated decoupling is achieved by requiring that, during any
symbol time of the secondary system, the following coexistence
conditions hold true [17], [79]:
(
Hsp A = 0
BHps = 0.
(6.3)
In the following we define an explicit algorithm for calculating
the matrices A and B. It is important to point out that we will
assume that the matrices Hsp and Hps are stable during the secondary system symbol time. Moreover, it will be assumed that the
secondary transmitter knows Hsp and that the secondary receiver
knows Hps .
6.3
Transmit Beamforming
Generally speaking, the simplest CR problem can be represented by a communication scenario in which a couple of primary
University of Genova – DITEN
114
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
terminals and a couple of cognitive radios wish to communicate
over the same resource [37], [27].
As remarked in section 6.2, in spite of the simplicity of the
model, few algorithms have been proposed. In this section, the
benefits coming from the introduction of multiple antennas at the
cognitive terminals is analyzed. In particular a transmit beamforming scheme is introduced to satisfy the constraint imposed by
the CR communications. For the sake of simplicity, the primary
terminals are equipped with a single antenna system, while the
cognitive terminals are equipped with two antennas, but the analysis can be easily extended to a high number of antennas, both at
the primary and cognitive systems.
6.3.1
Channel model
Transmit beamforming can be used by a CR system to steer
the power towards the direction of interest (i.e. secondary receivers) while minimizing the interference to primary receivers
[33]. In particular, this technique, employed by different approaches [58], [39], allows minimizing the interference caused to
primary users while maximizing the SINR for the cognitive users.
In the proposed approach transmit beamforming is implemented,
by introducing a linear pre-processing scheme which guarantee,
under specific conditions, to perform complete interference cancellation at the primary receiver.
The equations which describe the channel of interest, known
in the open literature as the MIMO Z channel [36] and usually
assumed for treating the problem of interest [85], [39] shown in
Fig. 1, are the following
yp = gtr xc + hxp + np
University of Genova – DITEN
(6.4)
6.3 Transmit Beamforming
yc = Hxc + nc
115
(6.5)
in which yp ∈ C and xp ∈ C are respectively the received and
transmitted complex baseband signals of the primary terminals,
yc ∈ C 2 and xc ∈ C 2 are respectively the received and transmitted complex baseband signal vectors (represented in bold, in the
entire paper) of the cognitive terminals, H ∈ C 2×2 is the complex
channel matrix between the cognitive terminals, h ∈ C is the complex channel coefficient between the primary terminals, gr ∈ C 2
is the complex channel vector between the cognitive transmitter
and the primary receiver (·T stands for transpose), and np ∈ C
and nc ∈ C 2 are the zero-mean complex Gaussian noise quantities [12] respectively for the primary and the cognitive receivers.
In the following,
E np n∗p = ηp2
E nc n⊥
= ηp2 I2
c
will be assumed [62] where ·⊥ stands for transpose and complex
conjugate, I2 is an 2×2 identity matrix and E (·) is the expectation
operator.
It is important to note that, in this case, the interference
caused by primary users is included in the additive noise term.
Moreover, although the channel model in equations 6.4 and 6.5
refers to the narrowband case (all channel coefficients are frequency independent), it can be easily extended to multi-carrier
systems by applying it on a sub-carrier basis [29]. To perform
the transmit beamforming, let us introduce a transmit precoding
matrix A ∈ C 2×2 such that xc = Axa . By substituting it in the
channel model expressed by 6.4 and 6.5, one can obtain
yp = gTr xc + hxp + np = gTr Axa + hxp + np
University of Genova – DITEN
(6.6)
116
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
yc = HAxa + nc
(6.7)
To guarantee that the cognitive transmitter causes no interference
to the primary receiver
gTr A = 0
(6.8)
has to be enforced, together with kAk2 = 1, where the symbol
k·k2 stands for 2-norm, in order to avoid signal amplification or
reduction, to obtain
yp = hxp + np
(6.9)
e a + nc
yc = Hx
(6.10)
e = HA. Such a process allows an effective decoupling
in which H
of the scalar Additive White Gaussian Noise (AWGN) channel of
the primary users 6.9 from that one of the cognitive users 6.10.
6.3.2
Derivation of the achievable rates
As suggested by the large amount of literature dedicated to
MIMO transmissions [12], [29], [79] the 2 × 2 channel expressed by
6.10 can be exploited through the Singular Value Decomposition
e = U P V ⊥ , with P diagonal matrix
(SVD). Hence by writing H
and U and V unitary matrices, and by introducing x = V ⊥ xa and
y = U ⊥ yc , from 6.10
e x + U ⊥ nc =
y = U ⊥ yc = U ⊥ HV
X
x + U ⊥ nc
(6.11)
can be obtained. Equation 6.11 represents two parallel Gaussian
channels
University of Genova – DITEN
6.3 Transmit Beamforming
y=z+n
117
(6.12)
P
with input z = x and complex Gaussian noise n = U ⊥ nc . The
noise has zero-mean and covariance matrix ηc2 I2 , since the multiplication by a unitary matrix does not change the distribution of
P
the noise [29], while the input has covariance E zz⊥ =
Kx
⊥
where Kx = E xx .
The obtained linear processing scheme, shown in Fig. 6.2,
allows, under the hypotheses of a perfect knowledge of the Channel State Information (CSI) between cognitive terminals and the
channel from cognitive transmitter to primary receiver, to exploit
the degrees of freedom of the 2 × 2 MIMO channel for the transmission of the cognitive users, and, at the same time, to cancel
the interference to the primary receiver. It is important to note
that, in order perform such a cancelation, the available degrees of
freedom of the MIMO Z-channel which models the CR problem,
expressed by the equations 6.4 and 6.5, are reduced. In particular,
since the number of Degree of Freedom (DoF)s of the considered
MIMO Z-channel is 2 [17] and the number of DoFs of the primary
link is 1, one can deduce that the number of DoFs available for
the cognitive link is 1 and for this reason Σ will have at most one
non-trivial diagonal entry.
This property allows simplifying the computation of the achievable rates of the proposed processing scheme. From [16] and by
taking into account the statistical variations of the channel, the
achievable rats of the cognitive link is expressed as
1
Φ
C = EH,gr max log 1 + 2
A,Φ 2
ηc
University of Genova – DITEN
(6.13)
118
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
6.3.3
Computation of matrix A
In order to complete the analysis, an explicit expression for C
has to be found. To this end, the expression of matrix A (and
consequently ε) which guarantees the maximum achievable rate
has to be computed. By assuming that gr,i 6= 0 (i = 1, 2, ...) (otherwise, a partial spatial orthogonalization is already performed by
the channel) and by enforcing (5), one can obtain
6.4
Explicit ZF-BF Scheme for a CR
System
In this section we would like to discuss about a special case
of CR system where the CRs are equipped with a fixed number
of antennas (e.g., number of transmit antennas M2 = N1 + 1 and
number of receive antennas N2 = M1 + 1). With the indicated
number of antennas on the secondary terminals we deduce that the
matrices Hsp and Hps are rectangular, of dimension respectively
N1 × (N1 + 1) and (M1 + 1) × M1 .
Let us firstly analyze the effects of the constraint in Fig. 6.31 .
Since, according to our hypotheses, the rank of Hsp is N1 , we
can find one and only one [52] (pp. 57-61) non-trivial solution
v ∈ CN1 +1 of
Hsp v = 0
(6.14)
having euclidean norm [52] (p. 270) kvk2 = 1 (uniqueness is
achieved apart from a possible complex scalar factor of absolute
value 1). Now, since the constraint 6.3 can be equivalently written
as
Hsp Ax = 0 ∀x ∈ CN1 + 1
University of Genova – DITEN
(6.15)
6.4 Explicit ZF-BF Scheme for a CR System
119
it is immediate to understand that any column of the matrix A
should necessarily be equal to v multiplied by an arbitrary complex coefficient. This means that in order to satisfy the constraint
6.3 matrix A should necessarily have the following form
A = [b1 v|b2 v| . . . |bN1 +1 v] = vbT
(6.16)
where bi , i = 1, · · · , N1 + 1, are arbitrary complex coefficients
T
defining the entries of the column vector b ∈ CN1 +1 and (·)
denotes the transpose (row) vector. If the precoding matrix A has
to avoid any signal amplification we have to enforce kAk2 = 1 [17],
being k k2 the so called matrix 2-norm induced by the euclidean
vector norm, that is [52] (p. 281)
kAk2 = max kAxk2 .
(6.17)
kxk2 =1
If we denote by xi one of the N1 + 1 coefficients of the generic
column vector x ∈ CN1 +1 , from (6.16) we deduce
kAxk2 = NX
1 +1
i=1
N +1
N +1
! 1
1
X
X
bi xi v = bi xi kvk2 = bi x i .
2
i=1
i=1
(6.18)
We have to enforce
N +1
1
X
1 = kAk2 = max kAxk2 = max bi x i kxk2 =1
kxk2 =1 (6.19)
i=1
and a trivial application of the Cauchy-Schwarz inequality [52]
(p. 271) implies that this constraint is enforced if and only if the
euclidean norm of the vector b ∈ CN1 +1 is equal to 1. No other
constraints have to be enforced on b, which, as a consequence, is
highly undetermined. In summary, we satisfy constraint 6.3 and
University of Genova – DITEN
120
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
avoid any signal amplification or attenuation by the precoding
whenever the matrix A is determined by:
A = vbT
(6.20)
for any b ∈ CN1 +1 such that kbk2 = 1. It could be useful to
observe that in order to define the matrix A just the knowledge
of Hsp is necessary. Let us now consider the constraint in Fig.
6.3. It is important to observe that B Hps = 0 if and only if
∗
Hps
B ∗ = 0, where ∗ denotes the conjugate transpose (matrix or
vector). The latter condition has the same form as of Fig. 6.3.
∗
and B ∗ are, respectively, M1 × (M1 + 1) and (M1 +
Moreover, Hps
1) × (M1 + 1), whereas Hsp and A are of dimensions N1 × (N1 + 1)
and (N1 + 1) × (N1 + 1), respectively. Thus, if we define w from
∗
by using the same procedure adopted to definevfrom Hsp ,
Hps
by using6.16 we deduce that the postcoding matrix B should be
such that B ∗ = wcT , where c is an arbitrary column vector
belonging to CM1 +1 . Contrary to what is stated in [17], there is
no need to enforce a constraint on the 2-norm on the matrix B
since any signal amplification or reduction is present in all addends
appearing in equation (2)2. Since kBk2 = kB ∗ k2 [52] (p. 283) we
conclude that on c no restriction is required and that
∗ B = cT w∗ , dw∗
(6.21)
being d the column vector having the ith entry equal to the
complex conjugate of the ith entry of c, i = 1, . . . , M1 + 1.
The determination of the infinite many matrices A and B satisfying the constraint of interest for this analysis is now complete.
It remains to define in which way we can exploit the unique degree
of freedom we have on the secondary system.
Remark 2. The matrices Hps and Hsp are managed as indicated above and no limitation can arise due to the presence of priUniversity of Genova – DITEN
6.5 Linear Pre and Post Processing Requirements to
Exploit Unique Degree of Freedom
121
mary antennas working, at the same time, as transmitting (considered in Hps ) and as receiving (considered in Hsp ). Thus, full
duplex primary systems need not be avoided as in [17].
6.5
Linear Pre and Post Processing Requirements to Exploit Unique Degree of Freedom
By using one of the infinite many precoding and postcoding
matrices A and B defined in the previous section, system 6.2 becomes
(
yp = Hpp xp + np
ỹs = Bys = BHss Ax̃s + Bns
(6.22)
and, of course, the primary transmissions are completely decoupled from the secondary ones. We now focus our attention on
the secondary channel, governed by equation 6.222 . As we have
already pointed out we have only one degree of freedom on this
channel. In general the available degrees of freedom can be exploited by using aSVD of the channel matrix BHss A [17], but
in this case this exploitation is particularly simple as it will be
pointed out in the following. In particular, these considerations
will allow a significant reduction of the information necessary and
of the algebraic operations required to the secondary transmitter
and receiver with respect to those required according to [17] when
M1 = N1 = 1. For this reason, these considerations are provided
in full details. From 6.20 and 6.21 we deduce
BHss A = (dw∗ )Hss (vbT ) = d(w∗ Hssv )bT
University of Genova – DITEN
(6.23)
122
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
the last equality being a direct consequence of the associative property of matrix multiplication [52](p. 105). It is important to notice that w∗ Hss v is a complex number and that
b ∈ CN1 +1 and d ∈ CM1 +1 are completely arbitrary apart from
the requirementkbk2 = 1. In particular, w∗ Hssv depends just on
Hps , Hss and Hsp . It is equal to zero if and only if it is not
possible to transmit from the secondary transmitter to the secondary receiver in an orthogonal way with respect to the primary
transmissions.
If we substitute 6.23 into 6.5 we obtain for the secondary system
ỹs = d(w∗ Hss v)bT x˜s + Bns .
(6.24)
Let us denote by e1 ∈ CN1 +1 the column vector whose entries
are the complex conjugate of those of b. It is a vector, actually,
since ke1 k2 = kbk2 = 1. We can define an orthonormal basis
{e1 , e2 , . . . , eN1 +1 } for CN1 +1 . It is clear that, if we denote by
a∗ b the standard scalar product in CN1 +1 [70] (p. 12),
x̃s =
NX
1 +1
(e∗i x˜s ) ei
(6.25)
i=1
However, by definition we have bT e1 = 1 and bT ei = 0 for
i = 2, · · · , N1 + 1, so that from 6.33 and 6.25 we obtain
∗
T
ỹs = d(w Hss v)b
NX
1 +1
!
(e∗i x˜s ) ei
+ Bns .
(6.26)
i=1
which can also be expressed as in simplified form
ỹs = d(w∗ Hss v)(bT e1 ) (e∗i x˜s )+dw∗ ns = d ((w∗ Hss v) (e∗i x˜s ) + w∗ ns ) .
(6.27)
University of Genova – DITEN
6.5 Linear Pre and Post Processing Requirements to
Exploit Unique Degree of Freedom
123
For the Cauchy-Schwarz inequality it is now evident that, in
order to maximize the information transfer on the secondary system, at the secondary transmitter we should generate
x̃s = ei xss
(6.28)
and at the secondary receiver we should perform
yss = d∗ ỹs
(6.29)
so that the best input-output relationship at the secondary
system can be finally written as
yss = d∗ ỹs = (d∗ d) ((w∗ Hss v) (e∗i x˜s ) + w∗ ns )
(6.30)
Therefore, 6.30 can be expressed as
2
yss = kdk2 ((w∗ Hss v) xss + w∗ ns )
(6.31)
2
Since d is arbitrary, we can choose it in such a way that kdk2 =
1 and we finally obtain
yss = (w∗ Hss v) xss + w∗ ns
(6.32)
In 6.2 we show the processing chain for a secondary system
which operates as indicated in equation 6.32.
Thus, we deduce that the achievable rate for the secondary
system, under the hypotheses considered in [7], is
1
C = EHps ,Hsp ,Hss
2
(
2
|w∗ Hss v|
log 1 + P
σs2
!)
(6.33)
which simplify and extend the covering of eq. (13) of [17].
Now we could proceed as in [17] the evaluate the performances of
University of Genova – DITEN
124
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
for each T
estimate Hsp
find
v
1
xss
multiply v vx ss transmitter
by x ss
M2= N1+1
1
N2 =M1+1
receiver
Hssvx ss
for each T
estimate Hps
multiply by w*
yss
find
w
Figure 6.2: Processing chain for the secondary transmitter and
receiver when just one degree of freedom is available to the secondary system.
University of Genova – DITEN
6.6 Computational Load Required at the CR Nodes 125
the proposed secondary system in practical scenarios. However,
there would be nothing new in this analysis since, for example, all
considerations reported in [17] on this aspect apply in this case,
too. The only significant novelty of this paper is related to the
possibility of implementing by using much simpler algorithms the
processing required to a secondary system with one degree of freedom in order to be able to avoid disturbing primary ones without
suffering, at the same time, any interference from the primary
systems. For this reason, in the following we focus our analysis
on the computational load required to implement the proposed
algorithm.
6.6
Computational Load Required at the
CR Nodes
As the reader may have noticed from Fig.6.2 the processing
chain indicated in Fig. 6.2 of [17] can be significantly simplified,
without any reduction of the performances and under more general conditions, without any limitation on M1 and N1 (as already
pointed out, in [17] we had M1 = N1 = 1), provided that we assume the secondary system to be the simplest one (that is, having
just one degree of freedom). In order to ease the reading we report
in Fig. 6.3 in more details the processing chain required to implement the secondary system proposed in 6.2 of [17], independently
of the number of degrees of freedom of the secondary system and
then also in the case it is equal to one. This processing chain
should be compared with the one shown in 6.2. In particular, one
can notice that with the new algorithm it is not necessary anymore
to compute the matrices A and V at the secondary transmitter
and that it is not necessary anymore to compute the matrices B
and U at the secondary receiver. The only operations required for
University of Genova – DITEN
126
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
the new algorithm to be implemented are those which allow the
calculation of v at the secondary transmitter and of w at the secondary receiver. As another important by-product, one can notice
that, moreover, the transmitter and the receiver implementing the
new algorithm have just to know or estimate, respectively, Hsp or
Hps . With the standard algorithm both transmitter and receiver
have to know or estimate Hsp , Hps and Hss , in order to be able to
carry out the singular value decomposition of the matrix BHss A.
This is an additional simplification allowing an additional reduction of the computational load for the secondary terminals. The
problem of the estimation of the channel matrices and of the effects of the errors of these estimations is not developed in this
paper. Some considerations on these important and widely analyzed topics can be found, for example, in [17], [81], [79] and [42].
For this reason we do not analyze the reduction of the computational load due to the reduced requirements on the estimation of
the channel matrices of the new algorithm. Moreover, we observe
that the transmitter and the receiver blocks shown in Fig. 6.2 and
Fig. 6.3 could be the same. Thus, we focus our attention on the
different computational load required to implement the processing chains shown in Fig.6.2 and Fig. 6.3, without considering the
blocks related to the estimation of the channel matrices, to the
transmitter and to the receiver. In order to develop this analysis,
we observe that we can calculate v by solving the homogeneous
linear system (4), having N1 equations and N1 + 1 unknowns.
By using, as suggested in [52] (p. 57), Gaussian elimination and
back substitution [52] (pp. 3-10), [70] (pp. 147-154), a vector
proportional to the vector v appearing in equation (4) can be calculated after 13 N1 3 + N1 2 − 13 N1 multiplications or divisions and
3
2
1
1
5
3 N1 + 2 N1 − 6 N1 additions or subtractions.
Remark 3. According to [52] (p. 57) Gaussian elimination
University of Genova – DITEN
6.6 Computational Load Required at the CR Nodes 127
1
N2+1
Hssv xss
multiply byw1*
receiver
multiply by w2*
for each T
estimate Hps
w1* Hss v x ss
w2*Hssv x ss
multiply by d1
multiply by d2
1
2
find w1 and w2
for each T
define d1 and d2
1
2
d1(w1*Hssv xss )
BH ssAVx
multiply by u*1
yss
d2(w2*Hssv xss)
find u1
Figure 6.3: Processing chain for the secondary transmitter and
receiver according to [17], independently of the number of degrees
of freedom of the secondary system (the case it is equal to one
being included).
University of Genova – DITEN
128
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
for homogeneous systems is applied just to the coefficient matrix.
In particular, if the homogeneous system has n equations and n+1
unknowns the coefficient matrix has n rows and n + 1 columns.
Moreover, according to [52] (p. 8), Gaussian elimination should
be executed on the associated augmented matrix [A|b] for nonhomogeneous systems of the form [Ax = b]. This matrix has n
rows and n + 1 columns if the non-homogeneous system has n
equations and n unknowns. Finally, the indicated expressions for
the number of multiplications or divisions and for the number of
additions or subtractions are provided in [52] (p. 10) for Gaussian
elimination with back substitution when it is applied to an n × n
non-homogeneous system.
Then, N1 + 1 multiplications and N1 additions are required
to find the square of the euclidean norm of the solution. Moreover, one square root and one division is necessary to normalize the solution and find v. This completes the operation count
implemented by the find v block. Finally, we need N1 + 1 multiplication to implement the multiply v by xss block and find
vxss . In summary, the secondary transmitter shown in Fig. 6.2
requires 13 N1 3 + N1 2 + 53 N1 + 3 multiplications or divisions and
3
2
1
1
1
3 N1 + 2 N1 + 6 N1 additions or subtractions and one square root.
All these operations are floating point operations, the so-called
flops [70] (pp. 58-59). Even if in some cases different floating
point operations are considered separately [52] (p. 10), in order
to simplify the following analysis we use the approach proposed
in [70] (pp. 58-59) and avoid any distinction among addition, subtraction, multiplication, division or square root operations involving floating point numbers.With this simplification we conclude
that the secondary transmitter shown in Fig. 6.2 requires overall
ftxnew (N1 ) =
2 3 3 2 11
N1 + N1 + N1 + 4
3
2
6
flops.
University of Genova – DITEN
(6.34)
6.6 Computational Load Required at the CR Nodes 129
Analogously, the secondary receiver shown in Fig.6.2 requires
the calculation of w, resulting in the same expressions as before
with N1 replaced by M1 for the implementation of the find w
block. However, in this case the following multiply w by xss block
of Fig. 6.2 is replaced by a multiply by w∗ block. In this case
the multiplication of a vector by a scalar is replaces by the scalar
multiplication of two vectors and this requires not only multiplications but also additions. Precisely, M1 + 1 multiplications and
M1 additions are required to finally obtain yss . In summary, the
secondary receiver shown in Fig. 6.2 requires overall
ftxnew (M1 ) =
2
3
17
M1 3 + M 1 2 + M 1 + 4
3
2
6
(6.35)
flops.
This completes the operation count required to implements the
blocks of interest in Fig. 6.2. Now we try to do the same for the
blocks of interest in Fig. 6.3. The find A and find B blocks of Fig.
6.3 could be implemented in several ways. However, to carry out
the comparison of interest, we assume that they can be calculated
as indicated in equations (10) and (11), with generic vectors or
vectors b and d. Thus, the operations of the find v and find
w block are required in this case too and we have, moreover, to
perform the column vector by a row vector multiplications shown
in (10) and (11). We conclude that we should be fair if we assume
that the find A (find B) blocks of Fig. 6.3 requires the same flops
required by the find v and multiply v by xss (find w and multiply
by w∗ ) blocks of the secondary transmitter (receiver) shown in
Fig. 6.2. The operation count required by the blocks multiply by
V , multiply by A, multiply by B and multiply by U ∗ in Fig. 6.3
is easy, since just multiplications of square matrices by column
vectors are involved. This means that each of the blocks multiply
by V and multiply by A requires (N1 + 1)2 multiplications and
University of Genova – DITEN
130
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
N1 (N1 + 1) additions, that is, with the indicated simplification,
gmul (N1 ) = 2N1 2 + 3N1 + 1
(6.36)
flops. Analogously, each of the blocks multiply by B and multiply by U ∗ requires at least gmul (M1 ) flops. It remains to consider
the block find U − V in Fig. 6.3, related to the singular value
decomposition of the matrix BHss A ∈ C(M1 +1)×(N1 +1) .
Remark 4. It is important to point out that all the indicated
floating point operations relative to the blocks find A, find B and
find U − V , appearing in Fig. 6.3, should be performed by both the
secondary transmitter and receiver, if the matrices B and U are
not being transmitted from one side to the other of the secondary
system. On the contrary, the secondary transmitter and receiver
of Fig. 6.2 does not need to share the same calculations.
It is not easy to deduce how many flops are necessary to compute this singular value decomposition. The difficulties are related
to the fact that any single algorithm which permits this calculation
is not simple and to the fact that several algorithms are present
in the open literature [70] (pp. 234-240). For this reason this
flop count is taken from [70] (pp. 234-240), where the estimates
provided express the computational load for large values of the
number of rows and columns. This is not the case of greatest
interest but we think it provides in any case a significant information. In particular, it is shown that the different algorithms which
can be considered to compute the singular value decomposition
require a number of flops larger than
2
gsvd (M1 , N1 ) = 2(M1 + 1)(N1 + 1)2 + (N1 + 1)3 .
3
(6.37)
Remark 5. The above asymptotic count refers to a matrix
with a number of rows larger than or equal to the number of
University of Genova – DITEN
6.6 Computational Load Required at the CR Nodes 131
columns [70] (p. 234). In our case BHss A has M1 + 1 rows
and N1 + 1 columns and in practical applications we can have
M1 < N1 . In these cases, the above estimate is correct if the role
of M1 and N1 is exchanged (corresponding to the singular value
decomposition of (BHss A)∗ .
With these considerations we can easily deduce the behaviors
of the leading terms of the flop counts for the transmitters and
receivers considered in Fig. 6.2 and Fig. 6.3. We have that:
• the secondary transmitter in Fig. 6.2 asymptotically requires 32 N1 3 flops,
• the secondary receiver in Fig. 6.2 asymptotically requires
3
2
3 M1 flops,
• both the secondary transmitter and receiver in Fig. 6.3
asymptotically requires at least 23 N1 3 + 23 M1 3 + 2(M1 +
1)(N1 + 1)2 + 23 (N1 + 1)3 ' 43 N1 3 + 23 M1 3 + 2M1 N1 2 flops
(if M1 < N1 replace M1 with N1 and vice-versa in the last
addend of the right-hand member).
For example, if M1 = N1 the new algorithm (the one of Fig.
6.2) asymptotically requires 23 N1 3 flops at the transmitter and at
the receiver while the older one (of Fig. 6.3) asymptotically requires 43 N1 3 + 23 N1 3 + 2N1 3 = 4N1 3 flops on both sides. This
means that there is a reduction of a factor equal to six in the
number of flops required at both the transmitter and the receiver.
It is now important to recall that these calculations have, in general, to be performed once for any ∆T (secondary system symbol
time) in narrowband systems. This effect is then repeated for
all sub-carriers in the case of a multi-carrier system. In practice,
as already pointed out, we could be interested in calculating the
number of flops in cases involving primary systems with small values of M1 and N1 . In these cases all terms should be retained,
University of Genova – DITEN
132
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
since the leading terms are not guaranteed to be dominant, and
we obtain that
• the secondary transmitter in Fig. 6.2 requires at most ftxnew N1
flops,
• the secondary transmitter in Fig. 6.2 requires at most ftxnew M1
flops,
• the secondary transmitter in Fig. 6.3 requires ftxnew (N1 ) +
frxnew (M1 ) + 2gmul (N1 ) flops plus those required by the
block calculating the singular value decomposition).
• the secondary receiver in Fig. 6.3 requires ftxnew (N1 ) +
frxnew (M1 ) + 2gmul (M1 ) flops plus those required by the
block calculating the singular value decomposition.
For the block relative to the singular value decomposition we
have just an asymptotic estimate. For this reason, in order to
give an idea of what can happen and of the possible advantages
which can be obtained when M1 and N1 are small, in the following figures we compare the behavior of the flops required by
the secondary transmitter and receiver proposed in Fig. 6.2 with
the underestimates, obtained neglecting the computational load
due to the singular value decomposition, of the numbers of flops
required by the older release of the secondary transmitter or receiver. In the same figures we provide also another kind of estimate of the numbers of flops required by the old transmitter
and receiver. The one obtained by taking account of the computational cost of the singular value decomposition, assumed to
be given by the available asymptotic expression. In Fig. 6.4 we
show the results obtained when M1 = N1 . The flops required by
the the new secondary transmitter and receiver are added to show
a cumulative result for the secondary system. The same is done
University of Genova – DITEN
6.6 Computational Load Required at the CR Nodes 133
for the two estimates of the flops required by the two terminals
of the old secondary system. On the one hand it is interesting to
observe that, for M1 = N1 = 10 the three curve assume the values
' 11398.67, 4300 and 1688. As indicated in Fig. 4, these three results refer, respectively,to the secondary system of Fig. 6.3, when
the flops required by the singular value decomposition are deduced
from the asymptotic estimate, to the secondary system of Fig. 6.3,
when the flops required by the singular value decomposition are
neglected, and to the secondary system of Fig. 6.2. If we divide
the first two values by the last one we obtain ' 6.75 and ' 2.55.
This could be an indication that for M1 = N1 = 10 in practice we
can already obtain a reduction of flops similar to what we obtain
asymptotically. Moreover, for M1 = N1 = 10 we have the smallest
difference between the flops required by the secondary system of
Fig. 6.3, when the singular value decomposition is neglected, and
the flops required by the secondary system of Fig. 6.2. Since we
plot these quantities by using a logarithmic scale on the vertical
axis this difference actually refers to a factor of proportionality between them. From these considerations we conclude, in particular,
that the new algorithm allows a reduction of the computational
load with respect to an underestimate of the computational load
required by the older algorithm by a factor bigger than or equal
to 2.55, at least for the small values of M1 = N1 considered. On
the other hand, for M1 = N1 = 1 the three curves assume the
values ' 100.67, 58 and 17. In this case, if we consider the contribution of the asymptotic estimate of the flops required by the
singular value decomposition we obtain that the factor giving the
reduction of the computational load is ' 5.92, whereas the underestimate of this factor, obtained by neglecting the load due to the
singular value decomposition, is ' 3.41.
It could be interesting to notice that both these values are
University of Genova – DITEN
134
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
12000
Computational Load [flops]
10000
8000
New secondary tx and rx
Old secondary tx and rx: neglecting SVD
Old secondary tx and rx: asymptotic
6000
4000
2000
0
1
2
3
4
5
6
7
8
9
10
M1 =N1
Figure 6.4: Computational load expressed in flops required by
the secondary transmitter and receiver proposed in Fig. 6.2, when
M1 = N1 . This load is compared with some meaningful approximation of the flops required by the secondary transmitter and
receiver shown in Fig. 6.3, under the same condition.
relatively stable: the first has a value of about 5.92 for M1 =
N1 = 1, of about 6.75 for M1 = N1 = 10 and of 6 for M1 =
N1 → ∞; the second is equal to ' 3.41 for M1 = N1 = 1, to
' 2.55 for M1 = N1 = 10, and to 2 for M1 = N1 → +∞. In
order to give an indication of what can happen when for a given
N1 we have M1 > N1 (but the reader can obtain similar results
when M1 < N1 , provided the roles of M1 and N1 are exchanged;
see Remark 5), let us consider the case in which M1 = N1 + 1.
The cumulative results are shown in Fig. 6.5. As the reader can
easily check, the behavior of the plots is similar to the one of the
plots reported in Fig. 6.4. In order to check that the reduction
of the computational load is significant in this case, too, let us
consider that, for example, for N1 = 1 (respectively, N1 = 10)
the obtained values are (the same order as before is used, as can
be easily checked from Fig. 6.4): 158.67, 100 and 29 (respectively,
University of Genova – DITEN
6.6 Computational Load Required at the CR Nodes 135
12482.67, 4900 and 1943). One can observe that the underestimate
of the factor giving the reduction of the computational load for
N1 = 1 (respectively, N1 = 10) and M1 = N1 + 1 is equal to
4900
' 100
29 ' 3.45 (respectively, ' 1943 ' 2.52), which is almost equal
to value of ' 3.41 (respectively, ' 2.55 ) we obtained in the case
M1 = N1 = 1 (respectively, M1 = N1 = 10).
14000
Computational Load [flops]
12000
new secondary tx and rx
old secondary tx and rx (neglecting SVD)
old secondary tx and rx:asymptotic
10000
8000
6000
4000
2000
0
1
2
3
4
5
6
7
8
9
10
N1 (M1=N1+1)
Figure 6.5: Computational load expressed in flops required by the
secondary transmitter and receiver proposed in Fig. 6.2, when
M1 = N1 + 1. This load is compared with some meaningful approximation of the flops required by the secondary transmitter
and receiver shown in Fig. 6.3, under the same condition.
Similar analysis can be easily performed for different values of
M1 and N1 . For example, in the case we have M1 = N1 + 2 the
results for N1 = 1 (respectively, N1 = 10) are: 246.67, 172 and 52
(respectively, 13668.67, 5602 and 2245) and the corresponding underestimate of the reduction of the computational load becomes
' 3.31 (' 2.50). The results are not shown in an independent
figure since it would be very similar to 6.4 and 6.5. From these
results we are able to deduce that the new algorithm provides
significant reductions of the computational load required to the
University of Genova – DITEN
136
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
secondary system in some important cases for practical applications (M1 = N1 , M1 = N1 + 1 and M1 = N1 + 2). Finally, from all
these considerations we infer that the reduction of the number of
floating point operations the secondary system has to perform is
in any case given by a factor larger than 2.5. In many significant
cases, this factor can be much larger.
6.7
Summary
The focus of this chapter is on the possibility of designing
simple and power efficient radio terminals for opportunistic communications. For this reason we consider only radio terminals
which has the minimum number of antennas allowing a secondary
communication to be established. For the same reason we define
a very simple linear transceiver with respect to other algorithms
giving the decoupling of the primary and secondary channels under perfect CSI, permits a significant reduction of the number
of floating point operations. This result could have a significant
impact on the choices of a designer of secondary terminals, for
example in terms of reduced computational power required to the
hardware or reduced battery capacity.
University of Genova – DITEN
Conclusions and
Future Work
With the rapid growth in wireless applications, spectrum resource becomes scarce. Although the current static spectrum
management avoids interference effectively, this comes with the
price of very low spectrum utilization. Cognitive Radio (CR)
promises to increase the spectrum utilization factor employing
several Dynamic Spectrum Access schemes. The under-utilization
in most of assigned spectrum bands results in signals that are
sparse in frequency domain. Such sparsity has motivated the use
of Compressive Sensing in reconstructing the frequency representation of the signal with far-less time samples than their Nyquist
counterpart. By exploiting wide-band spectrum sensing techniques, CR nodes can scan the whole spectrum or a large portion
of the spectrum at once and avoid the delay and complexity of
channel-by-channel scanning. Besides, wideband spectrum sensing provides higher possibility of opportunistic access to a Cognitive Radio. Several architectures and algorithms were provided
depending on whether or not there was coordination between different CRs in the CR network. Due to the low implementation
complexity, energy detection is commonly used for spectrum sens137
138
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
ing in a cognitive radio network.
The work presented in this thesis provides practical solutions
to important problems exploiting several Compressive Sensing
methods for wideband Cognitive Radio systems and presented
three main objectives:
The first one was finding efficient methods for a CR to detect
the spectrum holes in a wide-band radio signal. The proposed
scheme was described in Chapter 4 where we figure out a CR
receiver module for wideband sensing. The proposed module deals
with a highly sparse segment of a wideband signal and finds a
spectrum opportunity to a CR. Simulation results have shown the
higher detection performance, lower computational burden and
enhanced achievable rate which satisfies to the theoretical concept.
The second objective employs the proposed technique in a cooperative CR atmosphere to overcome the hidden node problems
and improve the reliability in detection performance. In this context, several well-known fusion rules have been studied and simulated results have shown in Chapter 5.
In addition, the third objective has to propose a simple linear
transceiver for Multiple Input Multiple Output (MIMO) cognitive
radio systems which has a single Degree of Freedom. This approach requires less computational burden than the conventional
algorithms under the same hypothesis. This approach illustrates
in Chapter 6 and added a new dimension to the MIMOCognitive
Radio Networks
Future Works and Recommendations
In this section, we would like to focus some research challenges
that outstretched while implementing the CR scenario in practical
cases. Especially, attention is paid to the issues related to the
University of Genova – DITEN
6.7 Summary
139
wideband spectrum sensing in heterogeneous radio environment
as it gives more opportunistic access to the future CR networks.
Since Compressive Sensing (CS) scheme has lot of prospers and
applications, hence in future, the possible research include that
could extend the contents of this thesis:
Spectrum blind detection
It will open a new domain for possible future approach [53] [3]
[47] [13]. To date, recovery methods for multi-coset sampling [44]
strategy ensure perfect reconstruction either when the band locations are known, or under strict restrictions on the possible
spectral supports. In [53], only the number of bands and their
widths are considered without any other limitations on the support. To estimate the signal, the continuous reconstruction is
replaced by a single finite-dimensional problem without the need
for discretization. Numerical experiments are presented in [53]
demonstrating blind sampling and reconstruction with minimal
sampling rate while this approach ensures perfect reconstruction
for a wide class of signals sampled at the minimal rate, and provides a first systematic study of CS in a real analog set up.
Cooperative wideband sensing
Research is still carried out for deploying the dynamic spectrum management; the received Primary User (PU) signal (either narrowband or wideband) at a single CR terminal may be
severely degraded, basically due to hidden terminal problems,
multipath fading or shadowing problems, lead to sensing performances in a challenge. Such a scenario can be employed with
cooperative sensing strategies to obtain highly reliable detection
performance while the computational complexity and hardware
University of Genova – DITEN
140
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
constraints push those schemes into challenge. Cooperative spectrum sensing is considered as a solution to some common problems. Several approaches of this kind was proposed in [26] [28] and
the references therein. Usually, control channels can be employed
using suitable methodologies schemes to share common spectrum
sensing outcomes. When considering centralized and distributed
sensing, optimization technique could be a good choice to implement in both data and decision fusion. There are several fusion
schemes presented in [75] with their performances wireless network which could be explored in cooperative CR environment. In
fact, in a distributed CR network, the wideband signal is observed
by different CRs, while each CRs sense a precise spectral components with compressive measurements. Those compressed data
from different CR nodes are fused together at the fusion center
and exploit the spectral opportunities in entire wideband in order
to save the total number of measurements at CR node leads to
computationally efficient. As the data transmission burden is too
high for control channels in such a data fusion method, thus, to
lessen the data load, decision fusioning is introduced when each
CR is able to detect wideband spectrum independently and at
the global decision is originated from fusing the local decisions.
When the CR nodes perceive fading or shadowing independently,
in such a scenario cooperative sensing performs better. Flexible
radio, will possibility be employed for future wireless network;
which will be increasingly complex and certainly heterogeneous in
nature and the idea of flexible radio will play a vital role in the
future wireless communications that must satisfy the scalability,
adaptability, reconfigurability, modularity, and many more.
University of Genova – DITEN
6.7 Summary
141
Direct detection from compressive measurements
Most of the research try to figure out the reconstructs or estimates of the Power Spectral Density (PSD) (relying on the assumption of sparsity) prior detecting a PU band presence. However, to reduce the complexity of the algorithms involved, we must
not forget that the fundamental task is not estimating the PSD
but detecting the presence of the primary users, subsequently, the
full reconstruction of the signal should not be required. In [76],
it is described an approach meeting this goal, without going into
the intermediate stage of estimating the PSD.
Sparsity basis and level selection
Practically most of the CS techniques assume that the signal
is sparse in some suitable basis functions (frequency domain) i.e.,
the sparsity basis is a Fourier matrix while estimating wideband
spectrum. The theory of CS states that the more the sparsity the
better would be the signal estimation which directs to better detection performance [8] [65] at the CR node as shown in Fig. 5.1.
In future, the spectrum usage improves in cellular networks and
the sparsity in Fourier domain shrinks while sparsity may exist
in other domain (e.g., sparsity based on mathematical functions).
Therefore, forthcoming CR receiver exploiting CS will have the
capability to find the effective basis functions which will computationally efficient to estimate dynamic sparse spectrum and thus
minimizes prohibitive energy cost.
Hence, one possibility for future CR would be to perform the
sparsity pattern recovery based on the PU received signal. The
authors in [78] addressed the problem of collaborative sparsity
pattern recovery of a sparse signal with multiple measurement
data in a distributed network. In that paper, it is considered that
University of Genova – DITEN
142
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
every node in the network takes measurements via random projections while considering the same sparse signal. For this reason,
the authors proposed a distributed greedy algorithm based on
Orthogonal Matching Pursuit (OMP) in which the locations of
non zero coefficients of the sparse signal are estimated iteratively
while performing fusion of estimates at distributed nodes to get
a global estimate. Another promising candidate will be exploiting spectrum blind sub-Nyquist wideband sensing, where a-priori
information of sparsity pattern is insignificant for the spectral
estimation. In most of CS schemes, the required number of compressive measurements will proportionally varies with the sparsity
level of wideband signal. Therefore, to calculate the exact number
of compressive measurement for doing wideband spectral estimation sparsity level estimation is often required. Yet, due to the
dynamic behavior of the PUs and time variant fading channels,
the sparsity level of wideband signal is often time-varying and difficult to estimate. This type of uncertainty in sparsity level will
be studied in future CR networks for the minimum number of
compressive measurements which will also be energy efficient.
Sequential compressed sensing
Existing analytical results on CS provide guidelines on how
many measurements are needed to ensure exact recovery with
high probability, but these are often seen to be pessimistic and
rely on a-priori knowledge about the sparsity of the unknown signal. A more suitable scenario would then be to get observations
in sequence, and perform computations in between observations
to decide whether enough samples have been obtained. Exact
recovery would be in that case, possible from the smallest possible number of observations, and without any a-priori knowledge
about how sparse the underlying wideband signal is.
University of Genova – DITEN
6.7 Summary
143
CS recovery algorithm
When the wavelet transform is involved, a multi-resolution solution may be available by dilating the wavelet basis function.
The interest in a multi-resolution transform comes from the fact
that the edges of interest would show up always at the same positions for different scaling, however, noise-induced spurious edges
are random at each scale and thus tend not to propagate through
all scales; hence, if a multiscale wavelet transform was available,
an improved recovery could be applied.
Decentralized computation
When performing joint recovery in a distributed wireless network under the assumption of common sparse support set when no
Channel State Information (CSI) is available, reliability depends
on the fusion center. It could be interesting if a detection consensus has to be acquired to completely distribute the computation
of compressive measurements to different radio users.
University of Genova – DITEN
144
Chapter 6 : MIMO Scheme for Opportunistic Radio
Systems
University of Genova – DITEN
Bibliography
[1] “Distributed compressive wide-band spectrum sensing,” in
Cognitive Wireless Networks:Concepts, Methodologies and
Visions Inspiring the Age of Enlightenment of Wireless Communications, F. H. P. Fitzek and M. D. Katz, Eds., 2007.
[2] “Federal communications commission - first report and order
and further notice of proposed rulemaking, unlicensed operation in the tv broadcast bands,,” FCC 06-156,, Tech. Rep.,
Oct. 2006.
[3] A. and A. Coulson, “Blind wideband spectrum sensing using cluster analysis,” in Communications Theory Workshop
(AusCTW), 2010 Australian, Feb 2010, pp. 133–138.
[4] A. Abidi, G. Pottie, and W. Kaiser, “Power-conscious design
of wireless circuits and systems,” Proceedings of the IEEE,
vol. 88, no. 10, pp. 1528–1545, 2000.
[5] I. F. Akyildiz, W. Lee, M. C. Vuran, and S. Mohanty,
“Next generation/dynamic spectrum access/cognitive radio
wireless networks: a survey,” Comput. Netw., vol. 50,
no. 13, pp. 2127–2159, Sept. 2006. [Online]. Available:
http://dx.doi.org/10.1016/j.comnet.2006.05.001
145
146
BIBLIOGRAPHY
[6] I. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, “A survey on spectrum management in cognitive radio networks,”
Communications Magazine, IEEE, vol. 46, no. 4, pp. 40–48,
2008.
[7] S. S. Alam, L. Bixio, M. Ottonello, M. Raffetto, and
C. S. Regazzoni, “An explicit zero forcing beamforming
algorithm for simple and low-power-consumption opportunistic systems,” Department of Biophysical and Electronic
Engineering, University of Genoa, Via Opera Pia 11a,
I16145, Genoa, Italy, Tech. Rep. Cognitive Radio Laboratory: report no. 1.22.2.2012, February 2012. [Online].
Available:
http://www.aem.dibe.unige.it/RAFFETTO/
JOURNAL PAPERS/cr mimo simpleandefficient.pdf
[8] S. S. Alam, L. Marcenaro, and C. S. Regazzoni, “Enhanced
performance in wideband cognitive radios via compressive
sensing,” in in Proc. of 1st IEEE Global Conference on Signal and Information Processing (GlobalSIP), Texas, U.S.A.,
Dec. 2013.
[9] ——, “Improved throughput performance in wideband cognitive radios via compressive sensing,” in in Proc. of 8th
EUROSIM Congress on Modeling and Simulation, Cardiff,
Wales, United Kingdom, Sept. 2013, pp. 585–590.
[10] ——, “Opportunistic spectrum sensing and transmissions,
cognitive radio and interference management: Technology
and strategy,” Book chapter, pp. 1–28, 2013.
[11] S. S. Alam, M. O. Mughal, L. Marcenaro, and C. S. Regazzoni, “Computationally efficient compressive sensing in wideband cognitive radios,” in Seventh International Conference
University of Genova – DITEN
BIBLIOGRAPHY
147
on Next Generation Mobile Apps, Services and Technologies
(NGMAST), 2013, Sept 2013, pp. 226–231.
[12] E. T. Ar and I. E. Telatar, “Capacity of multi-antenna gaussian channels,” European Transactions on Telecommunications, vol. 10, pp. 585–595, 1999.
[13] D. Ariananda and G. Leus, “Compressive wideband power
spectrum estimation,” Signal Processing, IEEE Transactions
on, vol. 60, no. 9, pp. 4775–4789, Sept 2012.
[14] C. A. Balanis., ANTENNA THEORY: ANALYSIS
AND DESIGN, 2ND ED. Wiley India Pvt. Limited,
2007. [Online]. Available: http://books.google.it/books?id=
3qOrxC8IGNMC
[15] R. G. Baraniuk, “Compressive sensing [lecture notes],” Signal
Processing Magazine, IEEE, vol. 24, no. 4, pp. 118–121, 2007.
[16] L. Bixio, L. Ciardelli, M. Ottonello, M. Raffetto, C. S. Regazzoni, S. S. Alam, and C. Armani, “A transmit beamforming technique for mimo cognitive radios,” in Wireless Innovation Forum Conference on Communications Technologies
and Software Defined Radio, SDR’11 - WInnComm- Europe,
Brussels, Belgium, June 22-24,2011.
[17] L. Bixio, G. Oliveri, M. Ottonello, M. Raffetto, and C. Regazzoni, “Cognitive radios with multiple antennas exploiting
spatial opportunities,” Signal Processing, IEEE Transactions
on, vol. 58, no. 8, pp. 4453–4459, 2010.
[18] E. Candes, J. Romberg, and T. Tao, “Robust uncertainty
principles: exact signal reconstruction from highly incomplete frequency information,” Information Theory, IEEE
Transactions on, vol. 52, no. 2, pp. 489–509, 2006.
University of Genova – DITEN
148
BIBLIOGRAPHY
[19] E. Candes and M. Wakin, “An introduction to compressive
sampling,” Signal Processing Magazine, IEEE, vol. 25, no. 2,
pp. 21–30, 2008.
[20] S. S. Chen, D. L. Donoho, Michael, and A. Saunders, “Atomic
decomposition by basis pursuit,” SIAM Journal on Scientific
Computing, vol. 20, pp. 33–61, 1998.
[21] S. Couturier and B. Scheers, “The state of the art
of dynamic spectrum access,” Military Communication
and Information Systems Conference (MCC 2009),Prague,
Czech Republic,, no. 0, pp. –, September 29-30, 2009.
[Online]. Available: http://www.sciencedirect.com/science/
article/pii/S1874490712000687
[22] F. F. Digham, M. S. Alouini, and M. K. Simon, “On the
energy detection of unknown signals over fading channels,”
Proc. IEEE International Conference on Communications,
no. 64, pp. 3575–3579, 2003.
[23] D. L. Donoho, “Compressed sensing,” Information Theory,
IEEE Transactions on, vol. 52, no. 4, pp. 1289–1306, 2006.
[24] M. Duarte, S. Sarvotham, D. Baron, M. Wakin, and R. Baraniuk, “Distributed compressed sensing of jointly sparse signals,” in Signals, Systems and Computers, 2005. Conference
Record of the Thirty-Ninth Asilomar Conference on, 2005,
pp. 1537–1541.
[25] B. Farhang-Boroujeny, “Filter bank spectrum sensing for
cognitive radios,” Signal Processing, IEEE Transactions on,
vol. 56, no. 5, pp. 1801–1811, 2008.
[26] A. Ghasemi and E. S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in New
University of Genova – DITEN
BIBLIOGRAPHY
149
Frontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005. 2005 First IEEE International Symposium on,
2005, pp. 131–136.
[27] A. Goldsmith, S. Jafar, I. Maric, and S. Srinivasa, “Breaking
spectrum gridlock with cognitive radios: An information theoretic perspective,” Proceedings of the IEEE, vol. 97, no. 5,
pp. 894–914, 2009.
[28] K. Hamdi, W. Zhang, and K. Letaief, “Opportunistic spectrum sharing in cognitive mimo wireless networks,” Wireless
Communications, IEEE Transactions on, vol. 8, no. 8, pp.
4098–4109, 2009.
[29] C. Han, T. Harrold, S. Armour, I. Krikidis, S. Videv, P. M.
Grant, H. Haas, J. Thompson, I. Ku, C.-X. Wang, T. A.
Le, M. Nakhai, J. Zhang, and L. Hanzo, “Green radio: radio techniques to enable energy-efficient wireless networks,”
Communications Magazine, IEEE, vol. 49, no. 6, pp. 46–54,
2011.
[30] V. Havary-Nassab, S. Hassan, and S. Valaee, “Compressive detection for wide-band spectrum sensing,” in Acoustics
Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on, 2010, pp. 3094–3097.
[31] M. H. Hayes., Statistical digital signal processing
and modelling. John Wiley and Sons., 1996. [Online]. Available:
http://books.google.com.bd/books/
about/Statistical Digital Signal Processing An.html?id=
z0GqhOe9GNQC&redir esc=y
[32] S. Haykin, D. Thomson, and J. H. Reed, “Spectrum sensing
for cognitive radio,” Proceedings of the IEEE, vol. 97, no. 5,
pp. 849–877, 2009.
University of Genova – DITEN
150
BIBLIOGRAPHY
[33] X. Hong, Z. Chen, C. Wang, S. Vorobyoyv, and J. Thompson, “Interference cancellation for cognitive radio networks,”
IEEE Vehicular Technology Magazine, vol. 4/4, pp. 76–84,
2009.
[34] E. Hossain, D. Niyato, and Z. Han, “Dynamic spectrum access and management in cognitive radio networks,” Cambridge University Press, Tech. Rep., July 2009.
[35] S. Jafar and M. Fakhereddin, “Degrees of freedom for
the mimo interference channel,” Information Theory, IEEE
Transactions on, vol. 53, no. 7, pp. 2637–2642, 2007.
[36] S. Jafar and S. Shamai, “Degrees of freedom region of the
mimo x channel,” Information Theory, IEEE Transactions
on, vol. 54, no. 1, pp. 151–170, 2008.
[37] E. Jorswieck and E. Larsson, “Monotonic optimization framework for the two-user miso interference channel,” Communications, IEEE Transactions on, vol. 58, no. 7, pp. 2159–2168,
2010.
[38] M. Jun, Z. Guodong, and L. Ye, “Soft combination and detection for cooperative spectrum sensing in cognitive radio networks,” Wireless Communications, IEEE Transactions on,
vol. 7, no. 11, pp. 4502–4507, 2008.
[39] M. S. Kang, B. C. Jung, D. K. Sung, and W. Choi, “A prewhitening scheme in a mimo-based spectrum-sharing environment,” Communications Letters, IEEE, vol. 12, no. 11,
pp. 831–833, 2008.
[40] S. Kirolos, T. Ragheb, J. Laska, M. Duarte, Y. Massoud,
and R. Baraniuk, “Practical issues in implementing analogto-information converters,” in System-on-Chip for Real-Time
University of Genova – DITEN
BIBLIOGRAPHY
151
Applications, The 6th International Workshop on, 2006, pp.
141–146.
[41] L. Le and E. Hossain, “Qos-aware spectrum sharing in cognitive wireless networks,” in Global Telecommunications Conference, 2007. GLOBECOM ’07. IEEE, 2007, pp. 3563–3567.
[42] K. Lee, C.-B. Chae, R. Heath, and J. Kang, “Mimo
transceiver designs for spatial sensing in cognitive radio networks,” Wireless Communications, IEEE Transactions on,
vol. 10, no. 11, pp. 3570–3576, 2011.
[43] K. B. Letaief and W. Zhang, “Cooperative communications for cognitive radio networks,” Proceedings of the IEEE,
no. 97, pp. 878–893, 2009.
[44] M. A. Lexa, M. Davies, J. Thompson, and J. Nikolic, “Compressive power spectral density estimation,” in Acoustics,
Speech and Signal Processing (ICASSP), IEEE International
Conference on, 2011, pp. 3884–3887.
[45] Y. C. Liang, Y. Zeng, E. C. Y. Peh, and A. T. Hoang,
“Sensing-throughput tradeoff for cognitive radio networks,”
Wireless Communications, IEEE Transactions on, vol. 7,
no. 4, pp. 1326–1337, 2008.
[46] P. Lu and H.-C. Yang, “Sum-rate analysis of multiuser mimo
system with zero-forcing transmit beamforming,” Communications, IEEE Transactions on, vol. 57, no. 9, pp. 2585–2589,
2009.
[47] T.-X. Luan, L. Dong, K. Xiao, and X.-D. Zhang, “Blind
multiband joint detection in cognitive radio networks based
on model selection,” in Wireless Communications Networking and Mobile Computing (WiCOM), 2010 6th International
Conference on, Sept 2010, pp. 1–4.
University of Genova – DITEN
152
BIBLIOGRAPHY
[48] J. Ma, G. Li, and B.-H. Juang, “Signal processing in cognitive
radio,” Proceedings of the IEEE, vol. 97, no. 5, pp. 805–823,
May 2009.
[49] M. Maddah-Ali, A. Motahari, and A. Khandani, “Communication over mimo x channels: Interference alignment, decomposition, and performance analysis,” Information Theory, IEEE Transactions on, vol. 54, no. 8, pp. 3457–3470,
2008.
[50] D. Makovoz, “Noise variance estimation in signal processing,”
in Signal Processing and Information Technology, 2006 IEEE
International Symposium on, Aug 2006, pp. 364–369.
[51] A. Mertins,
Signal Analysis:
Wavelets,
Filter Banks, Time-Frequency Transforms and Applications.
John Wiley and Sons., Chichester, 1999.
[Online]. Available: http://www.amazon.com/gp/search?
index=books&linkCode=qs&keywords=0471986267
[52] C. D. Meyer, Matrix analysis and applied linear algebra.
SIAM, 2000. [Online]. Available: http://www.ec-securehost.
com/SIAM/ot71.html
[53] M. Mishali and Y. C. Eldar, “Blind multiband signal reconstruction: Compressed sensing for analog signals,” Signal
Processing, IEEE Transactions on, vol. 57, no. 3, pp. 993–
1009, 2009.
[54] R. Mochaourab and E. Jorswieck, “Optimal beamforming
in interference networks with perfect local channel information,” Signal Processing, IEEE Transactions on, vol. 59,
no. 3, pp. 1128–1141, 2011.
University of Genova – DITEN
BIBLIOGRAPHY
153
[55] P. Morerio, K. Dabcevic, L. Marcenaro, and C. Regazzoni,
“Distributed cognitive radio architecture with automatic frequency switching,” in Complexity in Engineering (COMPENG), 2012, 2012, pp. 1–4.
[56] D. Needell and J. A. Tropp, “Cosamp: iterative signal
recovery from incomplete and inaccurate samples,” Commun.
ACM, vol. 53, no. 12, pp. 93–100, Dec. 2010. [Online].
Available: http://doi.acm.org/10.1145/1859204.1859229
[57] A. Pandharipande and J. P. M. G. Linnartz, “Performance
analysis of primary user detection in a multiple antenna cognitive radio,” in Communications, 2007. ICC ’07. IEEE International Conference on, June 2007, pp. 6482–6486.
[58] K. Phan, S. Vorobyov, N. Sidiropoulos, and C. Tellambura,
“Spectrum sharing in wireless networks via qos-aware secondary multicast beamforming,” Signal Processing, IEEE
Transactions on, vol. 57, no. 6, pp. 2323–2335, 2009.
[59] W. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proceedings of the IEEE, vol. 57, no. 1,
pp. 58–68, 1969.
[60] Z. Quan, S. Cui, A. H. Sayed, and H. Poor, “Wideband
spectrum sensing in cognitive radio networks,” in Communications, 2008. ICC ’08. IEEE International Conference on,
2008, pp. 901–906.
[61] Z. Quan, S. Cui, A. Sayed, and H. Poor, “Optimal multiband joint detection for spectrum sensing in cognitive radio
networks,” Signal Processing, IEEE Transactions on, vol. 57,
no. 3, pp. 1128–1140, 2009.
University of Genova – DITEN
154
BIBLIOGRAPHY
[62] V. Rodoplu and T. Meng, “Minimum energy mobile wireless
networks,” in Communications, 1998. ICC 98. Conference
Record. 1998 IEEE International Conference on, vol. 3, 1998,
pp. 1633–1639 vol.3.
[63] S. Stotas and A. Nallanathan, “Optimal sensing time and
power allocation in multiband cognitive radio networks,”
Communications, IEEE Transactions on, vol. 59, no. 1, pp.
226–235, 2011.
[64] H. Sun, C. Wei-Yu, J. Jing, A. Nallanathan, and H. Poor,
“Wideband spectrum sensing with sub-nyquist sampling in
cognitive radios,” Signal Processing, IEEE Transactions on,
vol. 60, no. 11, pp. 6068–6073, 2012.
[65] H. Sun, A. Nallanathan, C.-X. Wang, and Y. Chen, “Wideband spectrum sensing for cognitive radio networks: a survey,” Wireless Communications, IEEE, vol. 20, no. 2, pp.
74–81, 2013.
[66] A. Taherpour, S. Gazor, and M. Nasiri-Kenari, “Wideband
spectrum sensing in unknown white gaussian noise,” Communications, IET, vol. 2, no. 6, pp. 763–771, July 2008.
[67] L. T. Tan and H.-Y. Kong, “A novel and efficient mixedsignal compressed sensing for wide-band cognitive radio,” in
Strategic Technology (IFOST), 2010 International Forum on,
2010, pp. 27–32.
[68] W. Tang, M. Shakir, M. Imran, R. Tafazolli, and M.-S.
Alouini, “Throughput analysis for cognitive radio networks
with multiple primary users and imperfect spectrum sensing,” Communications, IET, vol. 6, no. 17, pp. 2787–2795,
2012.
University of Genova – DITEN
BIBLIOGRAPHY
155
[69] Z. Tian and G. B. Giannakis, “A wavelet approach to wideband spectrum sensing for cognitive radios,” in Cognitive Radio Oriented Wireless Networks and Communications, 2006.
1st International Conference on, 2006, pp. 1–5.
[70] L. N. Trefethen and D. B. III., Numerical Linear Algebra.
SIAM, 1997. [Online]. Available: http://www.ec-securehost.
com/SIAM/ot50.html
[71] J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” Information Theory, IEEE Transactions on, vol. 53, no. 12, pp.
4655–4666, 2007.
[72] J. Tropp, J. Laska, M. Duarte, J. Romberg, and R. Baraniuk,
“Beyond nyquist: Efficient sampling of sparse bandlimited
signals,” Information Theory, IEEE Transactions on, vol. 56,
no. 1, pp. 520–544, 2010.
[73] R. Umar and U. H. S. Asrar, “A comparative study of
spectrum awareness techniques for cognitive radio oriented
wireless networks,” Physical Communication, no. 0, pp. –,
2012. [Online]. Available: http://www.sciencedirect.com/
science/article/pii/S1874490712000687
[74] J. Unnikrishnan and V. Veeravalli, “Cooperative spectrum
sensing and detection for cognitive radio,” in Global Telecommunications Conference, 2007. GLOBECOM ’07. IEEE, Nov
2007, pp. 2972–2976.
[75] P. K. Varshney, “Distributed detection and data fusion,”
Springer-Verlag,1st ed.,” Book chapter, 1996.
[76] Y. Wang, A. Pandharipande, Y. Polo, and G. Leus, “Distributed compressive wide-band spectrum sensing,” in InforUniversity of Genova – DITEN
156
BIBLIOGRAPHY
mation Theory and Applications Workshop, 2009, 2009, pp.
178–183.
[77] ——, “Distributed compressive wide-band spectrum sensing,” in Information Theory and Applications Workshop,
2009, 2009, pp. 178–183.
[78] T. Wimalajeewa and P. K. Varshney, “Cooperative
sparsity pattern recovery in distributed networks via
distributed-omp,” in Proc. IEEE International Conference
on Acoustics, Speech, and Signal Processing (ICASSP’13),,
no. 0, pp. –, Vancouver, Canada, May 2013. [Online].
Available:
http://www.sciencedirect.com/science/article/
pii/S1874490712000687
[79] P. Xiao and M. Sellathurai, “Improved linear transmit processing for single-user and multi-user mimo communications
systems,” Signal Processing, IEEE Transactions on, vol. 58,
no. 3, pp. 1768–1779, 2010.
[80] Z. Ye, G. Memik, and J. Grosspietsch, “Energy detection using estimated noise variance for spectrum sensing in cognitive
radio networks,” in Wireless Communications and Networking Conference, 2008. WCNC 2008. IEEE, March 2008, pp.
711–716.
[81] T. Yoo and A. Goldsmith, “On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming,” Selected Areas in Communications, IEEE Journal on,
vol. 24, no. 3, pp. 528–541, 2006.
[82] T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for cognitive radio applications,” Communications
Surveys Tutorials, IEEE, vol. 11, no. 1, pp. 116–130, 2009.
University of Genova – DITEN
BIBLIOGRAPHY
157
[83] C. Zhang, W. Xu, and M. Chen, “Hybrid zero-forcing
beamforming/orthogonal beamforming with user selection for
mimo broadcast channels,” Communications Letters, IEEE,
vol. 13, no. 1, pp. 10–12, 2009.
[84] R. Zhang, F. Gao, and Y.-C. Liang, “Cognitive beamforming
made practical: Effective interference channel and learningthroughput tradeoff,” in Signal Processing Advances in Wireless Communications, 2009. SPAWC ’09. IEEE 10th Workshop on, 2009, pp. 588–592.
[85] R. Zhang and Y.-C. Liang, “Exploiting multi-antennas for
opportunistic spectrum sharing in cognitive radio networks,”
Selected Topics in Signal Processing, IEEE Journal of, vol. 2,
no. 1, pp. 88–102, 2008.
[86] Q. Zhao and A. Swami, “A survey of dynamic spectrum
access: Signal processing and networking perspectives,” in
Acoustics, Speech and Signal Processing, 2007. ICASSP
2007. IEEE International Conference on, vol. 4, 2007, pp.
IV–1349–IV–1352.
University of Genova – DITEN
158
BIBLIOGRAPHY
University of Genova – DITEN
Acknowledgements
Over three years working towards my Ph.D. degree, I was very
lucky to receive the help of many people. Without their kind support and advice, I would not have been able to complete this
thesis. It is a huge opportunity for me to thank all of them.
This research project would not have been possible without the
support of many people. I would like to express my sincere thanks
to my supervisor, Prof. Carlo Regazzoni, who has introduced me
into research, for his guidance, support, and patience. Without
his expert guidance and knowledge, it would have not been possible to come to an end with this dissertation. I feel very lucky and
absolutely happy to work with him. I would also like to thank my
cooperative colleague Prof. Mirco Rafetto and Dr. Lucio Marcenaro for their advice on grasping and dealing with a problem.
To my colleagues: Pietro, Simone, Stefano, Teddy, Muhit,
Francesca, Giuseppe, Luca, Matteo, because they have been more
than work colleagues but real friends.
Finally, I want to express my hearty gratitude to my family
members, particularly to my parents, my wife Afroza Akter, and
other family members for their unmeasurable love and support
which helped me to overcome the difficulties of living far away
159
160
BIBLIOGRAPHY
from my country. Thank you so much!
University of Genova – DITEN