INVITED
PAPER
Coexistence Between UWB and
Narrow-Band Wireless
Communication Systems
Analysis of ultra-wide-band (UWB) systems reveals that the design of these very
promising systems requires understanding of the effects of interference to and from
narrow-band systems.
By Marco Chiani, Senior Member IEEE , and Andrea Giorgetti, Member IEEE
ABSTRACT
|
Ultra-wide-band (UWB) signals are suitable for
underlay communications, over a frequency band where,
possibly, other systems are active. Such coexistence of UWB
and other systems is possible if the mutual interference has a
small impact on their respective performance. This paper aims
to present recent results on the interference and coexistence
among UWB systems and other conventional narrow-band (NB)
systems. Specifically, we consider a point-to-point UWB (NB)
link under the interference generated by a finite number of NB
(UWB) radio transmitters. We consider channels including
additive white Gaussian noise and multipath fading both for
the victim and the interfering links, and different receiver
architectures. While our main focus is on UWB systems based
on impulse radio, wide-band systems employing carrier-based
direct-sequence spread-spectrum and orthogonal frequencydivision multiplexing are also considered.
KEYWORDS
|
Code-division multiple access; coexistence;
multicarrier modulation; narrow-band interference; spreadspectrum systems; ultra-wide-band systems
I. INTRODUCTION
The definition of ultra-wide-band signals is related to the
occupied frequency bandwidth: for example, in the United
States, a signal is classified by the Federal Communications
Commission (FCC) in [1] as UWB if its bandwidth is larger
Manuscript received July 17, 2008; revised September 1, 2008. Current version
published March 18, 2009. This work was supported by the European Commission
under the FP7 ICT integrated project CoExisting Short Range Radio by Advanced UltraWideBand Radio Technology (EUWB).
The authors are with DEIS, WiLAB, University of Bologna, 47023 Cesena, Italy
(e-mail: marco.chiani@unibo.it; andrea.giorgetti@unibo.it).
Digital Object Identifier: 10.1109/JPROC.2008.2008778
0018-9219/$25.00 Ó 2009 IEEE
than 500 MHz or its fractional bandwidth is at least 20%; in
Europe [2] a bandwidth of at least 50 MHz is indicated.
Often it is also true (although not implied by the definition)
that the UWB wireless system adopts a spread spectrum (SS)
technique.1 The most important properties that make UWB
systems attractive are:
1) accurate position location and ranging due to fine
delay resolution;
2) possible easier material penetration when used
over low-frequency bands;
3) multiple-access capability through SS techniques;
4) underlay and covert communications due to low
power spectral density (PSD)2;
5) reduced fading due to finer multipath resolution
[4]–[14].
Due to its large transmission bandwidth, any UWB system
must be able to cope with severe frequency-selective channels
caused by wireless multipath propagation. In impulse radio
(IR), a low duty-cycle train of extremely short positionmodulated or amplitude-modulated pulses is used to build a
SS signal, where multipath can be exploited for instance with
Rake or transmitted-reference (TR) receivers. The
corresponding system can be indicated as UWB-IR with
pulse position modulation (PPM) or pulse amplitude
modulation (PAM). Furthermore, multiple users can be
accommodated with time-hopping (TH) or direct-sequence
(DS) techniques [4]–[7]. Due to their suitability to counteract
frequency-selective channels, multicarrier modulations such
as orthogonal frequency-division multiplexing (OFDM) may
1
Loosely speaking, a SS system is one using a bandwidth substantially
greater than its Shannon bandwidth [3].
2
Note that only the usage of codes with low code rate (such as for
instance spreading codes) can produce reliable communications with
signals having a PSD substantially below the noise level.
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
Table 1 List of Acronyms
be also used to realize UWB systems, eventually combined
with SS techniques. In particular, the WiMedia Alliance
solution for high data rates is based on multiband (MB)
OFDM, where frequency-hopping (FH) over a small number
232
of carriers is used for interference mitigation.3 Although
currently the most investigated solutions are based on IR or
OFDM, UWB systems can in principle be built with conventional single-carrier based modulation techniques, as, for
example, M-ary phase-shift keying (M-PSK), with any of the
conventional techniques known for SS communication.
Whatever the choice, the deployment of UWB systems,
which may overlap with several frequency bands allocated
to radio-communication services, requires that they
coexist and contend with a variety of interfering signals
and must also ensure that they do not interfere with
narrow-band radio as well as navigation systems operating
in these dedicated bands. For example, unlicensed commercial systems are currently envisioned to operate with
low PSD levels over already populated frequency bands in
the United States, in Europe, and for the Asia-Pacific
telecommunity, including Japan, China, Korea, Singapore,
and Australia.
Operating with low transmission power in an extremely large transmission bandwidth, UWB SS radios have
also been under consideration for military networks because they inherently provide a covertness property, with
low probability of detection and interception (LPD/LPI)
capabilities [10]–[12], [15]. Moreover, intentional jamming
has to be considered in many military scenarios.
For these reasons, the efficient design and successful
operation of UWB systems must consider, besides the
interference due to other UWB users [multiuser interference (MUI)], both the interference coming from NB users
where the UWB system is the victim and the interferers are
the NB users, and the interference caused to NB users
where the NB system is the victim and the interferers are
the UWB users.
In those cases where, despite the SS nature of the UWB
signals, the performance would be too deteriorated, suitable
techniques for interference mitigation can be implemented,
such as those based on detect and avoid (DAA) or on
multiple antenna systems.4 Due to their characteristics,
UWB systems are considered among the key technologies in
the context of cognitive radio [16]–[19].
We also want to point out that the coexistence represents
an important issue for ranging and localization algorithms
based on UWB technology. To this aim, in [20] and [21], the
authors investigate the performance of time-of-arrival (ToA)
ranging algorithms in the presence of NB interference and
propose an interference mitigation technique.
This paper presents recent advances on the study of
interference and coexistence among UWB systems and other
conventional NB systems. We consider a realistic situation
where the wireless channels include additive white Gaussian
noise (AWGN) and multipath fading for both the victim’s
3
www.wimedia.org.
In DAA, the UWB system detects the interfered bands and avoids
receiving (and possibly transmitting) energy in those bands.
4
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
Fig. 1. Power spectral density of UWB and NB signals.
link and the interfering links. The paper’s main focus is on
UWB systems based on impulse radio, while other wideband systems employing sinusoidal carrier-based directsequence spread-spectrum (DS-SS) and OFDM will be
treated more briefly. In both cases, it is assumed that the
bandwidth of the UWB signal WUWB is large compared to
that of the NB signal WNB , as illustrated in Fig. 1.
We start with a scenario consisting of a point-to-point
UWB (NB) link under the interference generated by a
single NB (UWB) radio transmitter, then extending the
analysis to a finite number of interfering nodes.
This paper is organized as follows. Section II presents
the scenarios, channel models, and modulation systems. In
Section III, the performance of a UWB node with NB
interferers is studied. In this section, we consider impulse
radio and carrier-based DS UWB systems. In Section IV,
we consider a UWB system built with OFDM techniques in
the presence of NB interference. The effect of UWB
interfering signals on NB systems is discussed in Section V.
Examples and case studies are studied in Section VI.
Concluding remarks are given in Section VII.
Fig. 2. The coexistence scenario between a NB and a UWB
communication.
UWB transmitter to a NB receiver, as well as the opposite
case of a NB transmitter interfering with a UWB receiver.
A second scenario consists of an interfering network
composed of a victim link in the presence of multiple
interferers (see Fig. 3). The number of interferers may be
deterministic or random. Moreover, the positions of the
interferers can be deterministically known, or random
variables with some given spatial statistical distribution. For
example, when the number of interferers and their positions
are not known a priori, we may treat them as random
variables characterized by a spatial Poisson point process. In
this case, the position of the interferers is modeled according
to a homogeneous Poisson point process in the twodimensional plane [22]–[23]. This scenario, which is the
subject of [24] in this Special Issue, has been investigated in
[22], [23], and [25]–[28].
II . COEXISTENCE SCENARIOS
AND SYSTEMS
Classification of coexistence scenarios, where victim and
interfering links can be either NB or UWB, involves mainly
three aspects: the spatial configuration of the system, the
characteristics of the radio channels, and the type of NB
and UWB systems involved.
A. Spatial Configuration of the System
The first scenario, which is also the basis for the others,
consists of one victim point-to-point link subject to
interference due to a single interfering node. This situation
is depicted in Fig. 2, where we have interference from a
Fig. 3. The coexisting scenario with a network of interferers.
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
B. Channel Model
Realistic channel models for wireless systems are
characterized by path loss (or its reciprocal, path gain),
shadowing, and flat or frequency-selective multipath fading.
Several path loss laws for NB systems have been
developed to model specific propagation scenarios. The
simplest model assumes the average signal strength to
decay as R with the distance R between the transmitter
and the receiver. The parameter is environmentdependent and can approximately range from 0.5 (e.g.,
hallways inside buildings) to 2 (e.g., urban environments).5
With this model, the link is characterized by a signal
amplitude path gain
L¼
K
R
(1)
with a given constant K. More complex models can be found
in the literature to represent specific propagation environments [29], [30]. The path gain model (1) as well as many
other models assume implicitly that the signal is NB so that
the channel is described considering the behavior at a specific
frequency. This is no longer valid for UWB signals, for which
specific path gain models have been developed. These models
still include a dependence with the distance with law R ,
and a dependence on the frequency with a law f k for some
constant k that depends on the antennas and on the scenario
[31]–[35].
To capture the shadowing effect, the received signal
strength S is modeled as a log-normal random variable
(RV) with probability distribution function given by
1
1
2 s
fS ðsÞ ¼ pffiffiffiffiffiffi exp 2 ln
;
2
s 2
s0
(2)
where is the median of S. A useful fact is that a lognormal RV S with parameters and can be expressed as
S ¼ eG , where G N ð0; 1Þ.6 A log-normal shadowing
model is commonly adopted for both NB [30] and UWB
systems [31]–[33].
Multipath fading is another important aspect that affects
the performance of UWB systems. To account for frequencyselective behavior of the propagation, we consider linear
time-invariant channels with both dense multipaths [36],
[37] and clustered multipaths [31]. In both cases, the realvalued channel impulse response (CIR) can be written as
hU ðtÞ ¼
L
X
hk ðt tk Þ
heU ðtÞ ¼ LU eU GU hU ðtÞ
(4)
where the median value of the shadowing is implicitly
¼ LU .
On the other hand, the NB channels exhibit frequencynonselective behavior, with median value of the shadowing
LN , fading amplitude N , and phase shift N . In the
following, we consider different possible statistics for N ,
while the phase shift N is assumed as a RV uniformly
distributed in [0,2).
For OFDM systems with N subcarriers spaced f apart,
operating over frequency-selective channels, we consider for
simplicity a block fading channel (BFC) model in the
frequency domain (see Fig. 4). The frequency response jHðf Þj
is constant in blocks of Nsb consecutive subcarriers for each
channel realization, and taking random, independent values
from block to block [38]–[40]. In particular, when Nsb ¼ 1,
the fading is independent from subcarrier to subcarrier, while
Nsb ¼ N corresponds to a frequency-flat channel.
In physical terms, Nsb f is related to the coherence
bandwidth of the channel [40], [41]. For example, let us
assume a channel with equivalent low-pass impulse
(3)
k¼1
5
We refer to as the Bamplitude loss exponent,[ which corresponds
to a decay in signal amplitude, not in signal power.
6
We denote with N ða; bÞ the Gaussian distribution with mean a and
variance b.
234
where ðÞ is the Dirac-delta function, L is the number of
multipath components, and hk and tk denote the gain and
delay of the kth path, respectively. In general, the gain hk
can be written as hk ¼ jhk je|k , with jhk j and k denoting the
magnitude and phase, respectively. In particular, the
parameter jhk j represents the fading magnitude, while
k 2 f0; g with equal probability accounts for the random
phase inversion that can occur due to reflections. In
addition, without loss of generality, we can consider a
normalized
P power dispersion profile (PDP) of the channel
so that Lk¼1 k ¼ 1, where k ¼ IEfjhk j2 g. Based on this
model, and assuming the path gain to be constant within the
signal band, the overall CIR of the UWB link becomes
Fig. 4. Block fading channel in the frequency domain used for OFDM:
illustration of a realization. N is the number of subcarriers, fi is the
frequency of the i th subcarrier, Nsb is the number of subcarriers per
block (related to the channel coherence bandwidth), and Nb is the total
number of blocks over the whole band.
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
P
response hðtÞ ¼ Lk¼1 k ejk ðt tk Þ, where k ejk are
complex RVs describing the L path gains and tk are the
path delays. Consider a channel model with independent
Rayleigh distributed path amplitudes k , independent and
uniformly distributed phases k 2 ½0; 2Þ,P
and fixed time
L
2
delays
t
,
with
PDP
normalized
so
that
k
k¼1 IEfk g ¼
PL
k¼1 k ¼ 1. With
P these assumptions, the frequency
response Hðf Þ ¼ Lk¼1 k ejk ej2ftk of the channel is a
wide-sense stationary complex Gaussian random process in
the frequency domain. It has been verified by simulation
[41] that the channel gain jHðf Þj can be approximated by a
BFC with Nsb implicitly defined as the integer such that
rðNsb f Þ 0:2
where
P P rðzÞ ¼ covfjHðf Þj; jHðf þzÞjg=covfjHðf Þj; jHðf Þjg ’
k
l k l cos½2zðtk tl Þ is the normalized frequency
autocovariance of jHðf Þj.
C. UWB Systems
Different techniques can been considered for UWB
communications. A classification of some of the most
important systems is reported below.
1) Impulse Radio: Impulse radio is based on the
transmission of low duty-cycle signals composed of very
short pulses with subnanosecond duration and employing
multiple-access techniques such as TH, DS, or a combination
of both [4]–[7]. With IR, wide-band coherent communication is possible by adopting, for example, the Rake receiver
in order to exploit the inherent diversity of the channel and
capture the energy of all paths at the receiver [4]–[6]. As an
alternative to coherent UWB systems, a reference signal can
be transmitted along with the data, leading to a signaling
scheme referred to as TR [42]. Due to its simplicity, there is
renewed interest in TR signaling for UWB systems, which
can exploit multipath diversity inherent in the environment
without the need for channel estimation and stringent
acquisition [36]. The receiver can simply be an autocorrelation receiver (AcR), which can be modified to include
noise averaging or variable integration for better performance [36], [43]. Since TR signaling allocates a significant
part of the symbol energy to transmitting reference pulses,
differential encoding over consecutive symbols can also be
used to alleviate inefficient resource usage [36].
For both carrierless and carrier-based IR-UWB and
DS-SS systems, the transmitted UWB signal assuming
binary signaling can be written in general as
qffiffiffiffiffiffi X
sðtÞ ¼ EU
bðt iTb ; di Þ
b
di 2 f0; 1g
(5)
i
where bðt; di Þ is a unit-energy waveform used to transmit the
ith information bit, di , EU
b is the energy per transmitted bit,
and Tb is the bit duration. Specifically, bðt; 0Þ and bðt; 1Þ are
the wide bandwidth waveforms used to transmit bits 0 and 1,
respectively. We assume that data bits di are independent
and equiprobable. Note that in (5), the waveform bðt; di Þ is
general and could include TH, DS, or their combinations. In
this regard, it can also be used with reference to conventional carrier-based DS code-division multiple-access
(CDMA) systems, where bðt; di Þ is obtained by multiplying
the data with a pseudonoise (PN) or Gold spreading
sequence and with the sinusoidal carrier. Therefore, all
results we give for UWB-IR are equally valid for conventional (non low duty-cycle) carrier-based DS-CDMA.
2) Sinusoidal Carrier-Based Systems: UWB signals can
also be obtained with conventional sinusoidal carrierbased SS methods, with multiple access based on code
division such as DS-CDMA or FH-CDMA. These systems
have been widely adopted and studied, and their advantages, including narrow-band interference (NBI) rejection
capability, are well known (at least over frequencynonselective channels) [42], [44]–[55].
It is worthwhile to mention two important facts that are
particular to these techniques when used in UWB systems.
First, implementing UWB systems employing a single-carrier
DS-CDMA system is not easy due to the very high chip rate,
which results in a large sampling rate for the analog-todigital converter (ADC) at the receiver. Furthermore, in the
presence of NBI, the envelope of the received composite
signal can exhibit large variations, and a large dynamic range
of the ADC is thus required.7 Another important challenge is
related to the coarse acquisition stage, which is difficult due
to the bandwidth of UWB signals and can become even more
difficult in the presence of NBI [58]–[61].
Moreover, for FH signals, we must define the time
window over which the spectrum is measured; this issue is
of particular importance when evaluating the effects of
FH-UWB systems on narrow-band receivers.8
3) OFDM and MB-OFDM: In OFDM, which is a MC
modulation technique, the data stream is divided into
multiple substreams, each transmitted over different
orthogonal subchannels centered at different subcarrier
frequencies. The technique used to modulate a subcarrier is
usually M-PSK or M-ary quadrature amplitude modulation
(M-QAM) and not necessarily the same for all subchannels.
The fading associated with each subchannel of the OFDM
signal can be considered frequency-flat provided that subchannels are sufficiently narrow compared to the coherence
7
Actually, these issues are common to all implementations of UWB
systems, including OFDM and IR-based UWB systems, whenever the
reception requires ADC of large bandwidth signals. To cope with these
problems, splitting the band into smaller subbands is one of the
techniques used. For this reason, multicarrier (MC) techniques are
proposed jointly with CDMA, where data modulate different subcarriers,
and subcarrier spectra are kept orthogonal [56], [57].
8
A discussion about measurements on frequency hopping modulated
systems can be found in [62], with particular reference to MB-OFDM.
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
bandwidth of the channel. This allows for two important
operations: 1) easy subchannel equalization that may consist
simply of a scaling and phase shifting of the subchannel
output (for the low-pass equivalent, this amounts to a
multiplication by a complex number, i.e., one-tap equalization); and 2) forward error correction (FEC) coding, where
the symbols of each codeword are interleaved across the
subchannels to correct substreams in error9 due to deep fades
caused by frequency selectivity of the channel or due to the
presence of NBI. Additionally, as for single-carrier systems,
interleaving in time where the codeword symbols are
transmitted over several OFDM frames can be used to cope
with the time variations of the channel. Moreover, if channel
state information (CSI) is available at the transmitter side,
OFDM allows easy adaptation to channel variation by
changing constellation size or transmit power for each
subband (adaptive loading) [63]–[65]. Among these challenges, it is important to mention the need for accurate
carrier frequency estimation at the receiver, and the implementation issues for the ADC related to the large bandwidth
and large dynamic range [peak-to-average ratio (PAR)] of the
signal. We remark again that the presence of NBI can cause
serious problems since it increases the PAR of the overall
signal at the ADC input [66], [67].
In general, if a large portion of the frequency band of an
OFDM signal is subject to interference, a high number of
subchannels will be in error; so, FEC with interleaving across
subchannels could be ineffective due to an excessively large
number of errors per codeword. To cope with these situations, one possibility is to hop the entire OFDM signal over
different hopping carriers, with the option of interleaving
each codeword over multiple hops. The resulting scheme is
a hybrid FH-OFDM system. For example, WiMedia uses a
scheme designated MB-OFDM for high-data-rate UWB
systems operating over the frequency band 3.1–0.6 GHz,
supporting data rates of up to 480 Mb/s [68]. The standard
divides the spectrum into 14 bands, each with a bandwidth
of 528 MHz. The first 12 bands are then grouped into four
band groups consisting of three bands each, and the last two
bands are grouped into a fifth band group. An OFDM frame
consisting of 122 subcarriers (100 data carriers, ten guard
carriers, and 12 pilot carriers) is used to transmit information
within a band, and FH is allowed over the bands within each
group. FEC coding with time and frequency-domain interleaving is used, across the subcarriers within a band, across
the frequency hopping bands, or over consecutive OFDM
frames, and combinations of these.
D. NB Systems
Many of the current wireless systems, including
mobile cellular systems, wireless metropolitan-area net9
Here a substream in error means that after filtering, sampling, and
data recovery, the received output data symbol for that substream is
different from the transmitted one. The maximum number of substreams
that can be corrected depends on the capability of the specific FEC and
interleaving strategy.
236
work (WMAN), wireless local-area network (WLAN),
wireless personal-area network (WPAN), and positioning
systems, are operating in frequency bands where UWB
signaling is allowed. Therefore, coexistence between NB
wireless systems and UWB systems is essential for the
efficient design and successful deployment of UWB
systems.
In the following, we investigate coexistence between
NB (single-carrier or MC) and UWB systems (IR or
MB-OFDM). We consider receiver architectures that do
not have information about the interference. If this information were available, more sophisticated (and usually
complex) techniques could be employed to mitigate the
interference effect. For example, a UWB node with some
knowledge of the interfering NB signal could use minimum mean-square error (MMSE) [or optimum combining]
reception to jointly minimize the effects of thermal noise
and interference [42], [44], [69]–[74]. Another possibility
when using FEC is to include some clamping circuits at the
input to the decoder to limit the potentially large excursions at the input level caused by interference, preventing
the FEC decoder’s decision metric from being dominated
by these extreme level swings [42, p. 453].
The main metric we use to evaluate the coexistence is
the average error probability [bit error probability (BEP)
and codeword error probability] of the victim link in the
presence of the interference. Another useful metric that
can be adopted when slowly varying fading is present is
the outage probability, that is, the probability that the
victim link experiences a BEP greater than a given
threshold [75]–[77]. In particular, in the interfering
network scenario where the position of the interfering
nodes is not known, assuming they do not change their
positions significantly during the interval of interest (e.g.,
a symbol or packet duration), it would be insightful to
condition the interference analysis on a given realization
of the distances and shadowing of the interferers. This
leads to the study of the error outage probability of the
victim link [24], [27], [28].
I II . IMPULSE-BASED UWB IN THE
PRES E NCE OF NB I NTE RFERE NCE
Previous work on performance analysis of transmission
schemes in the presence of NB interferers has been
largely focused on DS-SS systems in AWGN channels. In
general, there are two main approaches to modeling of
the NB interfering signals: one consists in approximating
a NB signal with a tone; the other is to approximate a
NB signal as a Gaussian process, usually white, i.e., with
PSD constant over the band WNB in Fig. 1 and zero
elsewhere.
For the case of a single tone interferer, the BEP of
DS-SS systems is derived in [78] and [79] for AWGN
channels, and a comparison of several multiple-access
techniques is presented in [80] by neglecting the effects
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
of additive noise. For the case of multiple tone interferers,
an upper bound on the BEP was derived using the
Chernoff bound for AWGN channels in [46] and [47].
The performance of IR-UWB systems is analyzed, neglecting additive noise, assuming the presence of a single
Gaussian interferer in [14], and assuming multiple tone
interferers satisfying the Gaussian approximation in [81].
By assuming that multiple-access interference and a single
tone interfering signal are both Gaussian, IR-UWB is
investigated in [82] for AWGN channels and in [83] for
multipath fading channels. The effects of GSM and UMTS/
WCDMA systems on UWB-IR systems in AWGN channels
are investigated via simulation in [8] and [9]. Methods for
selecting parameters to improve the antijam capability of
UWB radios in AWGN are developed in [84] and [85]. The
use of notch filters to mitigate the effect of NB interference is investigated in [57] and [86] for CDMA overlay
and in [87] for UWB-IR systems.
The NBI can be a MC modulated (OFDM) signal.
Indeed, OFDM transmission schemes have been used in
recent years in many wireless systems such as digital
audio broadcasting (DAB), digital video broadcastingterrestrial (DVB-T), digital video broadcasting-handheld
(DVB-H), HiperLAN, IEEE 802.11a/g, and IEEE 802.16,
and are a candidate for 4G future mobile radio systems.
Hence, it is important to analyze also the possible
coexistence between UWB systems and OFDM-based
systems. A simulation approach for the performance
evaluation of TH and DS systems in the presence of an
OFDM IEEE 802.11a interfering signals can be found
in [88]. The analysis of possible coexistence between
TH-PPM systems and IEEE 802.11a devices is evaluated
in [89] under the assumption of frequency-flat fading on
the interference. In [90], a semianalytical approach to
evaluate the interference power at the output of the
matched filter (MF) is developed in an AWGN scenario,
and a closed-form BEP expression in the same scenario is
derived in [91]. It is also possible to adopt Rake reception
with MMSE techniques to mitigate the effect of
interference, provided that its statistical properties are
known [73], [92], [93]. In particular, in [73], the
performance of a Rake receiver in the presence of NB
interference is investigated and the improvements with
optimum combining are evaluated by means of a semianalytical approach.
In this section, we analyze the performance of a
generic binary SS system employing Rake reception in
frequency-selective channels with AWGN and NB interference [94]–[96]. We use an analytical framework based
on perturbation theory to analyze Rake reception in
realistic Nakagami-m channels like those arising in UWB
communications. The approach is general and can be used
for both IR and DS-CDMA. We also extend the analysis to
OFDM interferers [41] and to UWB systems employing
transmitted reference [36], [97]. Results are given in terms
of BEP, emphasizing the role of AWGN and multipath.
Fig. 5. The SS system with NB interference and additive noise.
A. Rake Reception in the Presence of NBI
We present here the general equations describing Rake
reception in the presence of a fixed number of NB interferers. This will be specialized in the next sections for
AWGN and multipath channels.
We start with the single interferer case. We consider a
binary communication system, with the transmitted signal
described by (5), employing MF reception. A block
diagram of the system is depicted in Fig. 5, where Hðf Þ
is the MF transfer function.
To study both carrier-based and carrierless systems, the
equivalent low-pass notation is not used. Therefore, the
signals are all real valued. The NB interfering signals are
approximated by sinusoidal tones, which leads to a
tractable problem. It is shown in [94] that such an
approximation is accurate if the bandwidth of the NB
interferer is smaller than the bit rate of the UWB signal.
We consider a generic time-invariant channel with
impulse response hU ðtÞ for the desired UWB signal. The
overall received signal rðtÞ due to the desired signal
described in (5) plus NI additional independent interferers
and noise is then given by
rðtÞ ¼
qffiffiffiffiffiffi X
rb ðt iTb ; di Þ þ rI ðtÞ þ zðtÞ
EU
b
(6)
i
where
rI ðtÞ ¼
NI
X
pffiffiffiffiffiffi
2In n cosð2fn ðt n Þ þ n Þ
(7)
n¼1
is the interference contribution, rb ðtÞ ¼ hU ðtÞ bðtÞ10 is
the received bit waveform, and In is the power of the nth
interferer having frequency fn , random phase n , and
random time shift n . The channel gain n for the nth
interfering NB signal is normalized to have unit power
gain, i.e., IEf2n g ¼ 1. The AWGN noise with two-sided
PSD N0 =2 is represented by zðtÞ.
10
The notation stands for convolution.
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237
Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
The received signal in (6) includes AWGN and
interference. If only AWGN is present, the optimum
receiver consists of a filter, matched to the difference
vðtÞ ¼ rb ðt; 0Þ rb ðt; 1Þ (or, equivalently, a correlator with
template vðtÞ) followed by a sampler. In the presence of
multipath, this adaptive MF is realized as the well-known
Rake receiver.
We now consider the detection of d0 , with pulses satisfying the Nyquist criterion, or introducing, in any case,
negligible intersymbol interference. Considering perfect
synchronization with the desired signal, the MF output uðtÞ
at the appropriate sampling instant t0 can be written as
uðt0 Þ ¼ s0 þ þ n0
(8)
pffiffiffiffiffi R t0
where s0 ¼ Eub 1
rb ðt; d0 ÞvðtÞdt is the desired signal
contribution
¼
NI
X
pffiffiffiffiffiffi
2In n jHðfn Þj cos n
(9)
n¼1
is the interference term, and n0 is the noise
R 1 sample with
zero mean and variance 2 ¼ ðN0 =2Þ 1 v2 ðtÞdt. Note
that the integration range is determined by the support of
the template function vðtÞ.
The performance of a MF Rreceiver is dependent on the
1
correlation coefficient ¼ 1 bðt; 0Þbðt; 1Þdt between
the two waveforms bðt; 0Þ and bðt; 1Þ, with 2 ½1; 1
and where ¼ 0 corresponds to orthogonal signaling. The
values 2 ð0; 1 and 2 ½1; 0Þ correspond, respectively,
to modulation schemes that are inferior and superior to
orthogonal modulation, and ¼ 1 corresponds to
antipodal modulation.
The MF is matched to the received waveform,11 so its
transfer function can be easily evaluated as12
9
>
=
Hðf Þ ¼ F rb ðt0 t; 0Þ rb ðt0 t; 1Þ :
>
;
:|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} >
8
>
<
(10)
¼vðt0 tÞ
In particular
jHðf Þj ¼ jH0 ðf Þj jF fhU ðtÞgj
(11)
where H0 ðf Þ ¼ F fbðt; 0Þ bðt; 1Þg. Note that (11) is
composed of two factors: the first ðjH0 ðf ÞjÞ depends on
11
As previously stated, we assume simple single-user receivers with no
estimation of the interference.
12
The notation F fg stands for the Fourier transform operator.
238
the waveforms used, while the second depends on the
channel impulse response of the desired signal. We remark
that H0 ðf Þ is the transfer function of the MF for AWGN
and frequency-flat fading scenarios.
One important consequence of (9) is that the effect of
tone interferers depends on the MF transfer function in
(11) evaluated at the frequencies of the interferers. In the
following, we will examine the performance of binary
wideband systems in different scenarios.
B. Performance With NBI and AWGN
By using the previously presented general description
of Rake reception in the presence of NBI, a first scenario of
interest is when the desired signal and interferers are not
subject to fading, i.e., hU ðtÞ ¼ ðtÞ and n ¼ 1,
n ¼ 1; . . . ; NI .
It has been shown that for this AWGN channel case,
the exact BEP can be written as a function of the signal-tonoise ratio (SNR) EU
b =N0 and the signal-to-interference
ratios (SIRs) S=In as [94]
0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
EU
b
ð1 ÞA
Pe ¼Q@
N0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!#
Z1"
NI
Y
1
In jH0 ðfn Þj2 2
1
J0 !
þ
S
Tb ð1Þ2
n¼1
0
sin !
!2 N0 1
exp U
d!
!
2 Eb 1 (12)
where S ¼ EU
b =Tb denotes the useful received power, QðÞ
is the Gaussian Q-function13 and J0 ðÞ is the 0th order
Bessel function of the first kind [99].
The right side of (12) is composed of two terms: the first
is the BEP for the binary system in AWGN only and the
second is the increase in BEP due to the presence of NI
interferers.
In [94], the analysis is extended to the average BEP
performance of binary UWB coherent systems in the
presence of flat-fading on both desired and interfering
signals. A further extension of this result to Rice fading for
the interferers can be found in [18] and [100].
C. Performance of Rake Receivers With Multipath,
NBI, and AWGN
We consider here a Rake receiver in the presence of a
single NB interferer and AWGN. For the UWB signal, we
consider a frequency-selective multipath fading channel
with impulse response (3), and for the NB signal we
assume a frequency-flat Rayleigh fading channel.
pffiffiffiffiffiffi R 1 2
Defined as QðxÞ ¼ ð1= 2Þ x ey =2 dy. Alternative representations, bounds, and exponential approximations can be found in [98].
13
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
Based on (3), the received waveform can be written as14
rb ðt; d0 Þ ¼
L
X
hk bðt tk ; d0 Þ:
dent Nakagami distributed paths with average power k
and Nakagami parameter mk , the average BEP with Rake
reception affected by a NB interferer becomes [94]
(13)
k¼1
Using (11), (13) implies that the Rake receiver can be
represented in the frequency domain as a filter with transfer function jHðf Þj ¼ jHU ðf ; h; tÞj jH0 ðf Þj, where
HU ðf ; h; tÞ ¼ F fhU ðtÞg ¼
L
X
hk ej2ftk
(14)
k¼1
with random vectors h ¼ ðh1 ; h2 ; . . . ; hL Þ and t ¼
ðt1 ; t2 ; . . . ; tL Þ denoting instantaneous path gains and
delays, respectively.
Thepffiffiffiffi
contribution (9) from one tone interferer is
¼ I 2IjHðfI Þj cos I , where I is the average received
interfering power, fI is the interferer carrier frequency, I
is the interferer phase uniformly distributed over ½0; 2Þ,
and I is the Rayleigh distributed fading.
Note again that the power of the interference at the
output of the Rake receiver is dependent on jHðfI Þj, which
is a function of the instantaneous CIR hU ðtÞ through h
and t.
The conditional BEP conditioned onpthe
instantaneous
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CIR can then be written as Pejh;t ¼ Qð 2~
ðh; tÞÞ, where
~ðh; tÞ ¼
2U ðhÞ
N0 2
1
EU
b
2
2
0 ðfI Þj jHU ðfI ;h;tÞj
þ SI 2TjHð1Þ
2
2 ðhÞ
b
(15)
U
is the instantaneous signal-to-(interference plus noise)
ratio (SINR) (i.e., conditioned
on the CIR) of the desired
P
UWB link and 2U ðhÞ ¼ Lk¼1 h2k . Through a Monte Carlo
approach, the conditional BEP Pejh;t can be averaged over
all possible CIR realizations to obtain the average bit error
probability Pe ¼ IEh;t fPejh;t g. With this approach, it is
possible to evaluate the average BEP, for example, considering IEEE 802.15.3a [33] and IEEE 802.15.4a [31], [32]
channel models, respectively.
When, as proposed in [34], the channel model can be
represented with a tapped delay line with independent
Nakagami distributed path amplitudes, it is possible to
derive the average BEP in closed form by means of perturbation theory [101], [102]. In particular, for indepen14
Note that other waveform distortions introduced, for example, by
UWB antennas can be taken into account by considering bðt; di Þ as the
received bit waveform. We assume only that these distortions are the same
for all waveforms received through the multiple paths.
1
Pe ’
Z=2 X
Ne
0
pi
i¼1
mk
L Y
ðqi Þ k
þ
1
d
sin2 mk
k¼1
(16)
where
ðxÞ ¼
N0 2
I jH0 ðfI Þj2 2x
þ
S Tb ð1 Þ2
EU
b 1
!1
(17)
is the mean SINR as a function of the average SNR,
EU
b =N0 , and the average SIR, S=I. The terms pi , qi ,
i ¼ 1; . . . ; Ne , are weights derived through the perturbation approach, and Ne is the number of terms in the
expansion. Considering the third-order expansion, we have
Ne ¼ 4 terms with weights
1
2 1
þ b; ; 2b; b
p¼
6
3 6
pffiffiffiffiffi
pffiffiffiffiffi
q ¼ ð0; 1; 1 þ 3a; 1 þ 2 3aÞ
(18)
where
a ¼ 1 2 ;
1 32 þ 23
b ¼ pffiffiffi
18 3ð1 2 Þ3=2
are functions of 2 and 3 that depend P
only on the
L
2
normalized
PDP
of
the
channel,
i.e.,
¼
2
k¼1 k and
PL
3
3 ¼ k¼1 k .
Using similar approaches, the above analysis can be
extended to FH interferers provided that the hopping
rate is small. In this case the BEP, conditioned on a
particular hopping frequency, is given by (12) and (16).
The BEP can then be obtained by further averaging (12)
and (16) over all hop frequencies accounting for
discontinuous interferers, i.e., interferers active only
for a fraction of time [100].
D. Examples of Victim Systems
Using the general approach developed in previous
sections, we can now evaluate the BEP for some important
IR spread-spectrum systems such as TH and DS with
binary pulse position modulation (BPPM) or binary pulse
amplitude modulation (BPAM), as well as carrier-based DS
binary phase-shift keying (BPSK).
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239
Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
Using the bit waveforms bðt; di Þ ¼ bðt di Þ for BPPM
and bðt; di Þ ¼ di bðtÞ for BPAM (or BPSK), the transmitted
signal can be written as
a unit-amplitude rectangular pulse gðtÞ with duration Tc ,
the transfer function of the MF receiver becomes
rffiffiffiffiffiffiffi
NX
s 1
2Tc
j2ðf f0 ÞkTc cDS
jH0 ðf Þj ¼
jsincððf f0 ÞTc Þj
(23)
k e
k¼0
Ns
qffiffiffiffiffiffi X
bðt iNs Tf di Þ ðBPPMÞ
sðtÞ ¼ EU
b
i
qffiffiffiffiffiffi X
di bðt iNs Tf Þ ðBPAM/BPSKÞ
sðtÞ ¼ EU
b
(19)
i
with the unit-energy waveform for each bit given by
bðtÞ ¼
N
s 1
X
TH
cDS
p
t
jT
c
T
f
c
j
j
(20)
j¼0
where Ns is the number of pulses used to transmit a single
information bit di , belonging to the set {0,1} for BPPM or
the set {1, 1} (through a simple mapping) for BPAM. The
parameter is the pulse position offset, pðtÞ is the signal
pulse with energy 1=Ns , and EU
b is the received bit energy.
The pulse repetition time (frame length) Tf and the bit
duration Tb are related by Tb ¼ Ns Tf . Finally, fcTH
j g is the
TH sequence, Tc is the TH chip width, and fcDS
j g is the DS
spreading sequence. The bit waveform (20) is valid for a
general transmitted scheme that combines TH and DS
and results in pure TH when cDS
¼ 1, 8j, and pure DS
j
when cTH
¼ 0, 8j.
j
The transfer function H0 ðf Þ in (11) is therefore
NX
s 1
T
DS j2f ðkTf þcTH
Þ
c
k
ck e
jH0 ðf Þj ¼ 2jPðf Þj
M
k¼0
(21)
where Pðf Þ is the Fourier transform of the pulse pðtÞ,
M ¼ 1 for BPAM and M ¼ j sinðf Þj for BPPM.
It is important to note that the approach presented
for baseband IR system is still valid for carrier-based
systems provided that the bit waveform bðtÞ includes the
carrier [94]. For example, considering the carrier-based
DS-BPSK adopted in conventional CDMA systems, the
transmitted signal can be written as (19), where the unitenergy bit waveform is
bðtÞ ¼
N
s 1
X
cDS
j gðt jTc Þ cosð2f0 t þ ’Þ
E. Extension to NBI Caused by OFDM Signals
Let us consider a general OFDM signal transmitted by
the interferer15
(22)
j¼0
where f0 is the carrier frequency, ’ is the phase of the carrier, and Tc is the DS chip duration. The pulse gðtÞ represents
the chip waveform, while fcDS
j g is the desired user’s
spreading sequence of length Ns with cDS
2 f1; 1g. For
j
240
where sincðxÞ ¼ sinðxÞ=x.
Therefore, the BEP for TH and DS systems with BPPM
and BPAM as well as DS-BPSK systems in the various
scenarios considered in previous sections is given by (12),
(16) and (17), together with (21) or (23). It is worthwhile
to remark that the effect of the interferers depends on
their carrier frequencies fn , and thus on the system
parameters through jH0 ðfn Þj in (21) or (23).
In particular, for DS-CDMA in AWGN, (12) and (23)
give an exact result, whereas prior results in [46] and [47]
provided upper bounds.
Note also that the BEP depends on the sequence (for TH
or DS) of the desired user through H0 ðf Þ. From the system
design point of view, this suggests the construction of
sequences that reduce the effect of NB interferers,
introducing, for example, notch frequencies where the
interferers operate [4], [17]–[19], [84], [85]. In a multipleaccess system, different users employing different spreading sequences have in general different BEP degradations
with respect to the same tone interferer. An average
performance can be calculated by averaging over the
sequences of all the users.
Furthermore, by looking at the transfer function of
the MF, we can compare the performance of TH and
DS schemes affected by NB interferers [81], [103]. For
example, for TH systems, there are frequencies at which the
Ns terms in the summation of (21) are all equal to one, so that
they add coherently and yield the largest receiving filter gain.
For these frequencies, (21) implies that, for a fixed Tb , the
power of the interferer at the output of the MF is
proportional to the length of the sequence Ns . Therefore,
in TH, the BEP performance with NBI degrades as Ns
increases. In contrast, the presence of the DS spreading in
(21) avoids this problem, so the effect of a NB interferer in
the worst case is independent of the length Ns for DS
systems.
( rffiffiffiffi
)
N
2I X X
i
j½2fn ðt
Þþ sOFDM ðtÞ ¼ Re
d gðt iTs Þe
N i n¼1 n
(24)
15
Refxg denotes the real part of the complex number x.
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
where I is the power of the OFDM interference, N is the
number of subcarriers, din are the complex symbols for the
nth subcarrier with IEfjdin j2 g ¼ 1, Ts is the symbol
duration, gðtÞ is the transmitted pulse waveform, and
fn ¼ fc þ f ðn 1 ðN 1Þ=2Þ are the subcarrier frequencies equally spaced by f and centered at fc . Since we
assume that the interferer is asynchronous with respect to
the desired signal, we model as a random time delay and
as an unknown carrier phase modeled as a RV uniformly
distributed in [0,2).
Now, whatever the type of modulation adopted for
each subcarrier (e.g., IEEE 802.11a/g adopts BPSK and
M-QAM), we model the OFDM interfering signal as a
sum of N different tones, obtained by removing all
amplitude variations on each subcarrier in (24).16 With
this model, the analysis for a single OFDM interferer
follows that of multiple NB signals.
We consider a generic time-invariant channel with
impulse response hU ðtÞ for the desired signal and hI ðtÞ for
the interferer. The overall received signal rðtÞ, due to the
desired signal (5) and the interferer, is given by (6) except
the interference contribution now given by
rffiffiffiffi N
2I X
rI ðtÞ ¼
jHI ðfn Þj cosð2fn ðt
Þþ þn þn Þ
N n¼1
function of the SNR, EU
b =N0 , and the SIR, S=I, becomes
pffiffiffi
Pe ¼ Qð Þ, with
¼
N
X
N0 1
I
1
þ
jH0 ðfn Þj2
2
U1
S NTb ð1 Þ n¼1
Eb
!1
: (27)
Note that this approach is simpler than the exact result (12).
The above analysis can be extended to evaluate the
performance of a single correlator receiver in a multipath
fading channel with Nakagami-m distributed paths amplitudes and AWGN. For the OFDM interference, we consider
a frequency-selective BFC HI ðf Þ with Rayleigh distributed
channel gains normalized to give IEfjHI ðf Þj2 g ¼ 1. In this
case, the average BEP expression as a function of the average
SNR, EU
b =N0 , and the average SIR, S=I, becomes [41]
1 m þ 21
Pe ¼ pffiffiffiffi
2 mðmÞ
Z1 NY
b 1
2
!2 N 0 1
exp
2 þ !2 =SIRi
2 EU
b 1
i¼0
0
1 3
!2
1 F1 m þ ; ; d!
2 2
4m
(28)
(25)
where the signal-to-interference ratio SIRi of the ith block is
where HI ðf Þ ¼ F fhI ðtÞg is the transfer function of the
channel experienced by the interfering signal, n are
independent identically distributed random phases due to
the data modulation symbols din , and n ¼ argfHI ðfn Þg.
First, we give the BEP expression for the MF receiver
in the presence of an OFDM interferer and AWGN. In this
case, hU ðtÞ ¼ ðtÞ and hI ðtÞ ¼ ðtÞ. Using (25), the interference contribution at the output of the MF receiver
becomes
rffiffiffiffi N
2I X
¼
jH0 ðfn Þj cosð2fn ðt0 Þþ þn þ’n Þ (26)
N n¼1
where ’n ¼ argfH0 ðfn Þg. At this point, we can follow two
different approaches. We first note the similarity of (26)
and (9); following the analysis of Section III-B with
NI ¼ N, we evaluate the exact BEP. For the purpose of
exposing an alternative method, we can adopt a Gaussian
approximation (GA), assuming a large number of carriers
(e.g., N greater than ten). In this case, the BEP as a
16
S Tb Nð1 Þ2
SIRi ¼ Pðiþ1ÞN
I n¼iN sb jH0 ðfn Þj2
sbþ1
and 1 F1 ð; ; Þ is the confluent hypergeometric function [99].
F. Extension to UWB Transmitted-Reference
Victim Systems
TR schemes represent a low-cost alternative to Rake
reception [36], [97], [104]. Performance of TR and
differential transmitted-reference signaling schemes is
derived through the sampling expansion approach for
AcR as well as a modified AcR in a broad class of dense
multipath channels [36]. This analysis is extended to
include NB interference in [97]. As in Section III-A, the
NB interference is modeled as a single-tone interferer with
Rayleigh distributed amplitude.
In time-domain TR signaling, the transmitted signal for a
single user can be decomposed into a reference signal block
and a data modulated signal block separated in time by Tr as
sðtÞ ¼
As will be apparent in the numerical results section, this model is in
excellent agreement with simulation results based on (24).
(29)
qffiffiffiffiffiffi X
bðt iTb Þ þ di bðt iTb Tr Þ
EU
b
|fflfflfflfflfflffl{zfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}
i
reference
data
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(30)
241
Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
where di 2 f1; 1g is the ith data bit, Ns =2 is the number of
transmitted signal pulses in each block, Tb ¼ Ns Tf , and
similarly to (20)
Ns
bðtÞ ¼
2 1
X
TH
cDS
j p t j2Tf cj Tc :
(31)
j¼0
Using the same notation as in Section III-A, the
received signal for TR signaling in the presence of AWGN
and a tone interferer can be written
gd0 ðjvÞ ¼
qffiffiffiffiffiffi X
rðtÞ ¼ EU
½rb ðt iTb Þ þ di rb ðt iTb Tr Þ
b
i
pffiffiffiffi
þ 2II cosð2fI t þ I Þ þ zðtÞ: (32)
The conventional AcR first passes the received signal
through a bandpass zonal filter (BPZF) with center
frequency fc and impulse response hZF ðtÞ to eliminate
out-of-band noise. If the bandwidth W of the BPZF is wide
enough, then the signal spectrum will pass through
undistorted. The received signal at the output of the
BPZF, denoted by erðtÞ ¼ rðtÞ hZF ðtÞ, is then correlated
with a delayed version of the reference signal, thus
collecting the received signal energy (in the absence of
interference and noise). The integration interval T of the
correlator determines the number of multipath components (or equivalently, the amount of energy) captured by
the receiver, as well as the amount of noise accumulated.
Assuming perfect synchronization at the receiver17 the
decision statistic for the data symbol d0 generated at the
output of the AcR for TR signaling is then given by
Ns
Z¼
2 1
X
j¼0
j2Tf þTr þcTH
j Tc þT
Z
erðtÞerðt Tr Þdt:
(33)
j2Tf þTr þcTH
j Tc
In [97] a Monte Carlo method as well as an approximate
analytical method to evaluate the BEP of TR signaling in
the presence of NB interference is presented. In particular,
a closed-form approximation for the BEP is
1 1
Pe ¼ þ
2 Z1
1
1 þ v2
q
1
Re
jv
jv
1 þ jv
0
Ref I ðgd0 ðjvÞÞgdv (34)
17
Actually, synchronization is not critical since the TR scheme is
particularly robust to synchronization errors. The sensitivity analysis of
synchronization errors, however, is beyond the scope of this paper.
242
where q ¼ Ns WT=2 and where P ðjvÞ is the characterLCAP
2
istic function of ¼ EU
with LCAP
k¼1 jhk j
b =N0
denoting the actual number of multipath components
captured by the AcR, while I ðjvÞ is the characteristic
function of 2I . For statistically independent resolvable
multipaths, the characteristic function ðjvÞ can be
expressed in closed form for a broad class of channel
fading statistics, while I ðjvÞ ¼ 1=ð1 jvÞ for Rayleigh
fading amplitude on the tone interferer [97]. The term
gd0 ðjvÞ is [97]
jv Ns IT
ð jv cosð2fI Tr ÞÞ:
1 þ v2 N0
(35)
Note that, contrary to the coherent systems analyzed in the
previous sections, the BEP for TR-AcR system depends
neither on the TH/DS code adopted nor on the spectrum of
the pulse adopted.
I V. OFDM-B AS E D UWB L INK I N T HE
PRES E NCE OF NB I NTE RFERE NCE
A. OFDM System Description
The effects of NBI on OFDM systems have been widely
analyzed (see, e.g., [66], [67], and [105]–[107] and
references therein), although often the complexity of the
system (frequency-selective channel models, FEC, etc.)
forces the use of simulation to assess the performance of a
particular scheme. It is found that the presence of NBI can
cause serious synchronization problems in pilot symbol
assisted OFDM and problems for the analog-to-digital
conversion, since NBI increases the PAR of the overall
signal at the ADC input. Several solutions have been
proposed, including the use of analog (before ADC) notch
filters [66], [67], [105], [106]. Here, our aim is to briefly
give the main elements that determine the performance of
an OFDM system in the presence of frequency-selective
fading and NBI, highlighting the essential role of errorcorrecting codes.
We consider a system where the transmitter has no CSI
(so, no bit-loading is possible), and quadrature phase-shift
keying (QPSK) is used on all subcarriers. The transmitter
is composed of a channel encoder, whose output bits are
interleaved among the subchannels, and an OFDM
modulator. The OFDM scheme allows the transmission
of complex data symbols di ði ¼ 1; 2; . . . NÞ, which belong
to a QPSK constellation set, over N parallel subchannels.
The symbol (or frame) duration is denoted by Ts . The
subchannel subdivision is obtained by means of an inverse
fast Fourier transform (IFFT) of order NFFT (N G NFFT to
accommodate virtual subcarriers). The subcarrier spacing
is f . At the IFFT output, the samples are converted from
parallel to serial and transmitted every Tc seconds (chip
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
time). A cyclic prefix (guard interval) is added to the
OFDM symbol (the IFFT output) in order to eliminate
the intersymbol interference among subchannels [108].
The duration of the cyclic prefix is Tg ¼ D Tc with
D integer. A reverse process is performed at the receiver
side. Due to the insertion of the cyclic prefix, a time
interval Tu ¼ NFFT Tc is dedicated to the transmission of
useful data, whereas the total OFDM symbol time is
Ts ¼ Tu þ Tg ¼ Tc ðNFFT þ DÞ. Thus, the efficiency factor due to the guard interval is
D ¼
Tu
NFFT
G 1:
¼
Ts NFFT þ D
(36)
If the maximum multipath delay Td is less than the guard
interval Tg , no intersymbol interference is present and the
complex received signal at the ith output of the FFT block
can be written as [109]
ri ¼ Hi di þ zi
(37)
where Hi ¼ Hðfi Þ is the channel transfer function gain at
the ith subcarrier fi and the random variable zi is zero-mean
complex Gaussian. We assume that a NBI is present with
power I over a fixed bandwidth WNB and model it as a
Gaussian process with PSD level EI ¼ I=WNB (see Fig. 6).
So, zi in (37) incorporates both the effects of thermal noise
and interference, when present, at the ith FFT output.
Assuming ideal phase offset compensation, perfect
carrier recovery, and time synchronization, the BEP
related to the ith subchannel is therefore [65], [109]
Pebi
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!
EU
b
¼Q
2Rc jHi j2 D
Ntoti
(38)
where Rc is the code rate, EU
b is the received energy per
information bit when jHi j ¼ 1, Ntoti ¼ N0 for the interference-free subchannels, and Ntoti ¼ N0 þ EI for the
interfered subchannels, with N0 denoting the one-sided
PSD of the thermal noise. As can be noted, the
performance at each subchannel depends on the channel
gain jHi j ¼ jHðfi Þj and on the NBI (if present). We
assume that the channel is slowly varying in time, such
that it can be considered constant during each OFDM
symbol; however, the channel is frequency-selective and
hence the gains jHi j are in general different across the
subchannels. Therefore, FEC is essential for OFDM,
since without it the performance would be highly
deteriorated by frequency-selective multipath propagation or NBI.
B. Coded OFDM in the Presence of NB Interference
To better understand the benefit of FEC on frequencyselective channels and NBI, let us consider a FEC code
with rate Rc , where a codeword of length n equal to the
number of subcarriers N is transmitted in parallel over the
N subchannels.18 To account for frequency-selectivity, we
assume a frequency domain BFC, where for each channel
realization the frequency response jHðfi Þj is constant for
blocks of Nsb consecutive subcarriers, taking, over the
ensemble of channel realizations, independent values from
block to block (see Fig. 4). In physical terms, Nsb is related
to the coherence bandwidth of the channel. The performance of FEC in BFC has been investigated for block codes
in [39] and for convolutional codes in [110]. For the sake of
simplicity here, we focus our attention on binary linear
block codes with hard decision decoding [39].19 Let us
define the vector
G ¼ ð1 ; 2 ; . . . ; Nb Þ
(39)
2
where i ¼ ðEU
b =N0 ÞRc jHi j D represents the instantaneous received SNR in the ith block (excluding NBI) and
Nb ¼ N=Nsb is the number of blocks per codeword (or per
OFDM symbol), all numbers being chosen as integers.
Let Xi be the number of errors in the ith block,
i ¼ 1; 2; . . . ; Nb . For the blocks where there is only
thermal noise, the probability mass function (PMF) of the
Fig. 6. Noise and SNR for an interfered block.
18
For QPSK modulation, a total of two codewords per OFDM symbol
can be transmitted.
19
Note that hard-decision decoding may be preferred in the presence
of NBI, since soft-decision decoding could erroneously consider
subcarriers with strong interference as highly reliable due to the large
received power.
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243
Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
discrete RV 0 Xi Nsb conditioned on the instantaneous SNR i is
pXi ji ðmÞ ¼ IPfm errors in the ith blockji g
(40)
Thus
pXi ðmÞ ¼
m Nsb N
I mþ N
I X
X
X
¼0
and the unconditional PMF is
pXi ðmÞ ¼ IPfm errors in the ith blockg:
(41)
ðNsb ; NI ; m; ; l; rÞ
r¼0
l¼0
IEi Pmþl
ði Þ Pþr
(45)
eb
eb ði Þ
in the presence of NBI. We assume that the decoder corrects
up to t symbol errors20; therefore, the codeword error
probability Pe is upper bounded by
It is easy to see that the two expressions can be evaluated as
Nsb m
pXi ji ðmÞ ¼
Peb ði Þ½1 Peb ði ÞNsb m ;
m
m ¼ 0; 1; . . . ; Nsb
Pe IPfX > tg
(42)
and
where
X¼
NX
Nsb sb m Nsb m
pXi ðmÞ ¼
ð1Þl
l
m
l¼0
lþm
IEi Peb
ði Þ ; m ¼ 0; 1; . . . ; Nsb
(43)
m X
Nsb NI m
Peb ði Þ
m
¼0
r¼0
Pþr
eb ði
Þ
Xi
(47)
is the total number of errors per codeword. Note that, due to
the nature of the BFC, the Xi s in (47) are statistically
independent, and thus
pX ðmÞ ¼ pX1 ðmÞ pX2 ðmÞ pX3 ðmÞ . . . pXNb ðmÞ (48)
where Nb 1 PMFs are given by (43) and one PMF is given
by (45). Once the PMF in (48) has been evaluated,21 the
codeword error probability can be bounded as
Pe N
X
pX ðmÞ:
(49)
m¼tþ1
½1 Peb ði ÞNsb NI mþ
NI P ði Þ½1 Peb ði ÞNI eb
m Nsb N
I mþ N
I X
X
X
¼
ðNsb ; NI ; m; ; l; rÞ
¼0
l¼0
mþl
Peb
ði Þ
Nb
X
i¼1
for the blocks where there is no NBI. When a single NB
interferer falls entirely with one block, there will be
NI WNB =f subchannels with interference, for which
we must consider both interference and noise (see Fig. 6),
and the remaining Nsb NI subchannels without interference, for which we only have the thermal noise.
In this case, we can write
pXi ji ðmÞ ¼
(46)
The previous evaluation requires only the knowledge of
the moments of Peb ðÞ over the distribution of .
Numerical examples obtained by using this analytical
approach will be presented in Section VI-C.
(44)
V. NB LINK IN THE PRESENCE OF
UWB-IR INTERFERENCE
where ¼ ð1þðEI =N0 ÞÞ1 ¼ ð1þðEU
b =N0 ÞRc 2ðI=SÞD ðN=
NI ÞÞ1 accounts for the noise level increase due to the
NBI, S is the power of the OFDM signal, S=I is the SIR, and
The effect of the interference that UWB transmitters can
cause to NB systems is one of the key issues for successful
deployment of UWB systems [87], [111]. As pointed out
Nsb NI
NI
ðNsb ; NI ; m; ; l; rÞ ¼
m
Nsb NI m þ NI ð1Þlþr :
l
r
20
In the presence of strong interference on NI subcarriers, an
erasures-and-errors correcting strategy could be used provided that the
receiver can detect those subcarriers and mark their outputs as erasures.
In this case, the error-correction capability for the remaining N NI
symbols becomes t NI =2.
21
The convolution can be evaluated efficiently using standard FFT
techniques.
244
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
in [1], this issue needs to be carefully investigated to
guarantee low levels of UWB interference to existing
wireless systems, and at the same time to avoid excessively
conservative restrictions to UWB systems that would
reduce the potential benefits of this technology and its
acceptance worldwide.
Coexistence among UWB systems and existing wireless
systems (such as GSM, UMTS, GPS, DCS1800, and FWA)
has been studied in [9] and [112] through simulations. The
effect of a single UWB interferer on an NB receiver in
AWGN channel is investigated in [113] through Monte
Carlo simulations and in [114] based on Gaussian
approximation. The extension of these results to spatially
distributed UWB interfering nodes that are outside a given
radius from the victim receiver is presented in [115].
The combined energy of multiple UWB signals at the
output of a square-law receiver was analyzed in [116] from
a shot noise perspective. The analysis of the performance
of NB receivers in the presence of OFDM-based UWB
interference is presented in [117].
Here we review some recent results on the performance
evaluation of NB systems affected by UWB interference for
different scenarios including AWGN and fading.
A. Coherent Reception in the Presence
of UWB Interference
We consider a NB transmitter that adopts a linear modulation scheme, such as M-PSK or M-QAM described as
qffiffiffiffiffiffiffiffi X
sN ðtÞ ¼ 2EN
ci gðt iTN Þ cosð2fc t þ i Þ
b
To account for the frequency-selective fading affecting
the UWB interference, we consider the impulse response
hU ðtÞ given in (3).22 On the other hand, the NB link
experiences a frequency-flat channel. Specifically, the
channel introduces a random amplitude factor 0 (normalized so that IEf20 g ¼ 1), as well as a phase 0 to the
received NB signal. We assume the NB receiver perfectly
estimates 0 , thus ensuring that coherent demodulation is
possible (for this reason, we can set 0 ¼ 0 without loss of
generality).
Under this system model, the received signal can be
written as
qffiffiffiffiffi X NX
s 1
a
rðtÞ ¼ 0 sN ðtÞþ EU
d
cDS
i
j wðt i;j Þ þ zðtÞ
b
i
(52)
j¼0
where wðtÞ ¼ pðtÞ hU ðtÞ is the received symbol waveform, i;j ¼ iTU þ dpi þ jTf þ cTH
j Tc þ U is the position
of the jth UWB pulse corresponding to the ith data symbol,
and zðtÞ is the AWGN with two-sided PSD N0 =2.
The NB receiver demodulates the received signal rðtÞ
using a MF. This can be accomplished
pffiffiffi by projecting
rðtÞ
onto
the
orthonormal
set
f
2gðtÞ cosð2fc tÞ;
pffiffiffi
2gðtÞ sinð2fc tÞg, obtaining the complex decision
statistic at the proper instant t0 , as
uðt0 Þ ¼ 0 c0 ej0 þ
(50)
qffiffiffiffiffiffi
EU
b þ n0
i
where EN
b is the energy per symbol, gðtÞ is the unit energy
pulse-shaping waveform satisfying the Nyquist criterion, TN
is the symbol period, ci and i are the amplitude and phase of
the ith data symbol, ci eji , respectively, and fc is the carrier
frequency of the NB signal. Symbols are normalized to give
IEfc2i g ¼ 1.
A single UWB interfering signal can be written as
sU ðtÞ ¼
qffiffiffiffiffiffi X
EU
dai bðt iTU dpi U Þ
b
(51)
i
where bðtÞ is the unit-energy symbol waveform given by
(20), which accounts for TH and/or DS multiple access
technique; TU ¼ Ns Tf is the UWB symbol period; fdai g and
fdpi g are independent and identically distributed PAM and
PPM data sequences; is the modulation index associated
with the PPM; and U is a random delay uniformly
distributed over the interval [0,TU ) modeling the asynchronism between the UWB interferer and the desired NB signal.
We consider an NB receiver based on a conventional
linear detector. Without loss of generality, we consider the
detection of symbol c0 ej0 .
where the contribution from the UWB interferer is given by
Z1
s 1
pffiffiffi X a NX
DS
¼ 2
di
cj
pðt i;j ÞgðtÞej2fc t dt (53)
i
j¼0
1
and n0 is a circularly symmetric complex Gaussian RV with
zero-mean and variance N0 =2 per dimension.
For a given channel realization, we define its Fourier
transform HU ðf Þ ¼ F fhU ðtÞg. Using Parseval’s theorem,
the interference contribution can be rewritten as
¼
s 1
X NX
pffiffiffi
j2fc i;j
2Pðfc ÞHU ðfc Þ
dai
cDS
j gð
i;j Þe
i
(54)
j¼0
where Pðf Þ ¼ F fpðtÞg and we have assumed that Pðf Þ and
HU ðf Þ are approximately constant over the frequency band
of the NB signal. Note that the amplitude of the
22
Note that here hU ðtÞ is the channel between the UWB transmitter
and the NB receiver.
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245
Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
the number of terms in the sum, representing the
interference contribution, is approximately the number of
UWB pulses per NB symbol. This approximation is more
accurate as the ratio TN =Tf becomes large. For example, in
[114], it is shown that the Gaussian approximation is quite
reasonable even for a moderate number of UWB pulses per
NB symbol, TN =Tf > 5.
For example, if the UWB interferer employs a
DS-BPAM, i.e., with dai 2 f1; 1g, dpi ¼ 0, cDS
j 2 f1; 1g
and cTH
¼
0,
the
interferer
term
is
zero-mean
with
j
power
s 1 X
2jPðfc Þj2 2jPðfc Þj2 NX
DS
þ
cDS
j ck
Tf
TU
j¼1 k¼0
j1
Fig. 7. Example of the interfering term at the output of an NB MF
caused by a UWB interferer. For illustration, only the real part of the
interfering term is depicted and a rectangular pulse gðtÞ is adopted.
interference contribution depends on the Fourier transform Pðfc Þ of the UWB pulse waveform [which also
influences the shape of the PSD of the signal (51)].
Useful insights may be obtained from (54) regarding
the mechanisms that dictate the effect of the UWB
interference on a NB receiver. It shows that the interference contribution is the sum of delayed versions of the
pulse gðtÞ with delays i;j . In fact, the conditions that Pðf Þ
and HU ðf Þ are flat around fc , adopted to derive (54), enable
us to approximate a train of UWB pulses having different
weights by a train of Dirac-delta functions with the same
weights in the time domain, driving the MF with impulse
response gðtÞ. This results in weighted replicas of
impulses gðtÞ at the output of the MF, where the weights
depend on Pðfc Þ; HU ðfc Þ; fdai g and fcDS
j g. This situation is
depicted in Fig. 7.
Based on this, we can distinguish two situations: the
first one corresponds to Tf > TN and leads to the presence
of one interfering pulse gðtÞ in some NB symbols and the
absence of interfering pulses in the remaining NB symbols;
the second one corresponds to the case where Tf TN ,
which means that one or more interfering pulses gðtÞ are
present in each of the NB symbols.
B. Performance With UWB Interference and AWGN
Let us consider an NB system affected by one UWB
interferer and in the presence of AWGN without fading, i.e.,
0 ¼ 1 and HU ðfc Þ ¼ 1. The performance of the NB system
depends on the statistical distribution of the interfering term
(54). If the exact statistical distribution is not known, it is
always possible to evaluate the performance, for instance, in
terms of error probability, through Monte Carlo simulations
[113].23 In many cases of practical interest, when Tf TN , it
is possible to resort to the Gaussian approximation of since
23
Note that the range of the summation of i in (54) can be truncated
depending on the duration of the shaping pulse gðtÞ relative to TU .
246
2 ¼
Rg ððjkÞTf Þ2 cosð2fc ðjkÞTf Þ (55)
R1
where Rg ð
Þ ¼ 1 gðtÞgðt Þdt is the autocorrelation
function of the pulse gðtÞ.24 If TU TN (i.e., the symbol
rate of the UWB interferer is greater than that of the NB
user), the expression can be further simplified to25
2
2 N
s 1
X
2
Pðf
Þ
j
j
c
j2fc kTf 2 ¼
cDS
:
k e
TU k¼0
(56)
Note that (56) is proportional to the PSD of the
transmitted UWB signal around fc and is therefore
dependent on the DS spreading code.26 This result
emphasizes the fact that a proper adoption of sequence
in the UWB link can reduce the effect of a UWB
interference on a NB link.27 Moreover, in such cases,
the Gaussian approximation accounts for the interference
as a raising of the noise floor corresponding to the received
PSD of the interferer. This leads to a simple evaluation of
the performance of the NB system when the PSD of the
UWB interference at the NB receiver is known.
The corresponding symbol error probability (SEP) can
be found by taking the well-known error probability
expressions for coherent detection of linear modulations in
the presence of AWGN, where the total noise variance is
qffiffiffiffiffiffi
2
EU
b þ N0 instead of N0 . Note that this substitution is
valid for any linear modulation, allowing all results to be
extended to include the effect of interference. For
24
The expression (55) is conditioned on the DS code fcDS
j g.
Note that (54) and (55) are valid when Pðf Þ, i.e., the Fourier
transform of the single pulse, is flat over the NB receiver bandwidth, while
(56) requires additionally that TU TN , which means that the PSD of the
UWB interferer needs be flat within the band of the NB signal. While the
first condition is generally valid, the second condition should be verified
since it depends on the choice of sequence.
26
If the DS is assumed to be random with equiprobable values
f1, 1g, (55) simplifies into 2 ¼ 2jPðfc Þj2 =Tf .
27
Similar considerations can be drawn also for TH signalling schemes.
25
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
instance, for the case where the NB transmitter
pffiffiffiffiffi employs
BPSK, the resulting BEP becomes Pe ¼ Qð 2Þ, where
¼
N0 I TU 2
þ S TN
EN
b
!1
(57)
is the SINR, which depends on the average signal-to-noise
ratio of the NB link, EN
b =N0 , and the average signal-toU
interference ratio S=I, where S ¼ EN
b =TN and I ¼ Eb =TU .
C. Performance With Fading, UWB Interference,
and AWGN
When the desired signal and the interference are both
subject to fading, in [118] it has been shown that the
Gaussian approximation for the interference is reasonable
from the perspective of evaluating the SEP even with a
single interferer, provided that the desired signal is subject
to Rayleigh fading. Thus a Gaussian approximation can be
used without verifying the conditions in Section V-B as
long as the desired signal is subject to Rayleigh fading.
For example, if the UWB interferer employs a
DS-BPAM, and assuming that the channel gain of the
interfering link is Rayleigh distributed with unitary power,
i.e., IEfjHU ðfc Þj2 g ¼ 1, the interferer term is zero-mean
with power given by (55). Accordingly, the SEP can be
found by taking the well-known error probability expressions for coherent detection of linear modulations in the
presence
of AWGN and fast fading [119], using
qffiffiffiffiffiffi
2
EU
b þ N0 instead of N0 for the total noise variance.
For the case where the NB transmitter employs BPSK, the
resulting BEP becomes
1 1
Pe ¼ 2 2
rffiffiffiffiffiffiffiffiffiffiffi
1þ
(58)
where is given by (57).
D. Extensions to OFDM Signals
1) OFDM Link in the Presence of UWB Interference: The
previous analysis can be also used for NB systems employing
OFDM signaling. In particular, the Gaussian approximation
for UWB-IR signals impairing a NB OFDM link can be used,
provided that the NB link experiences fading [118], or if the
duration of the OFDM symbols is large compared to the
pulse repetition time of the UWB signal. A detailed analysis
for this case can be found in [120].
2) NB Link in the Presence of OFDM-Based UWB
Interference: Similarly, if the UWB signals are obtained
with a MC technique as in MB-OFDM, the same reasoning
used for the IR applies. More precisely, the effects of MB-
OFDM on NB systems can be evaluated by using the GA
for the MB-OFDM provided that the NB channel
experiences fading [118]. The GA for the effects of a
MB-OFDM on an NB link is accurate even in the absence
of fading on the useful link, provided that there is a
sufficiently large number of interfering OFDM symbols for
each NB symbol, i.e., if the duration of the NB symbols is
large compared to the duration of the MB-OFDM symbols.
These observations have been also confirmed in [117].
VI . NUMERICAL EXAMPLES
A. UWB-IR Reception With NB Interference
In this section, we evaluate the performance of a UWBIR coherent DS-BPAM system in the presence of NB
interference using the analytical approach developed in
Section III. The received pulse pðtÞ is modelled as the
sixth derivative of a Gaussian pulse with energy 1=Ns as
[4], [5], [41]
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi"
2
4
640
t
t
1 12
pðtÞ ¼
þ162
231Ns p
p
p
#
64 3 t 6 2ðt=
p Þ2
e
15
p
(59)
where p ¼ 0:192 ns is the pulse duration parameter. We
set a frame length Tf ¼ 50 ns and Ns ¼ 16 pulses per bit,
so that the bit rate of the system is 1=TU ¼ 1:25 Mbit/s.
Since the modulation is antipodal, the correlation parameter is ¼ 1. The Fourier transform of pðtÞ is
83
2 2
Pðf Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi p13=2 f 6 e2f p :
3 1155Ns
(60)
We consider a NB interfering system with frequency
fc ¼ 5:010 GHz.
To better understand the effect of the pulse shape and
of the sequence of the desired user on the MF, Fig. 8 shows
pffiffiffiffiffi
the normalized transfer function H0 ðf Þ ¼ H0 ðf Þ= Tb
around fI using (21), for two different DS sequences. For
the DS-BPAM system considered, the transfer function
(21) is the product of two factors: the first is related to the
spectrum of the pulse (60) (which
large bandwidth)
PNs 1hasDSa j2fkT
f
and the second is related to j k¼0
ck e
j, which has
an oscillatory behavior for Ns > 1, resulting in frequency
selectivity, as depicted in Fig. 8.
It can be seen that H0 ðf Þ, and consequently the
BEP performance, depends on the carrier frequency of
the interference, pulse shape, and choice of the
spreading sequence. In the following, we will use
j Ns1
fcDS
j g ¼ fð1Þ gj¼0 .
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247
Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
Regarding the PDP, we consider an exponential PDP
[34], [94] given by
k ¼
Fig. 8. The normalized transfer function of the MF around
Ns 1
fI ¼ 5:010 GHz for two different DS codes: code 1) fcjDS g ¼ fð1Þj gj¼0
Ns 1
and code 2) fcjDS g ¼ fð1Þdj=2e gj¼0 .
The BEP for UWB reception in the presence of a
single NB interferer and AWGN as a function of the SNR
is plotted in Fig. 9 using (12) for different values of the
SIR S=I.
We next investigate the performance of UWB Rake
receivers on frequency-selective multipath fading channels
in the presence of NB interference. In particular, we
consider independent Nakagami distributed paths with
different Nakagami parameters for each path [94] according to
mk ¼ m1 eðk1Þ=
k ¼ 1; 2; . . . ; L
(61)
where m1 ¼ 3 and ¼ 4 controls the decay of the
m-parameters.
Fig. 9. BEP for the DS-BPAM system considered with a
single tone interferer and AWGN.
248
e1= 1 k=
e
1 eL=
k ¼ 1; 2; . . . ; L
(62)
where ¼ 3 is a decay constant that controls the multipath
dispersion. For such channels, the BEP performance with
UWB Rake receiver in the presence of a single NB
interferer and AWGN is plotted in Fig. 10. In [94], the tone
approximation is validated in several scenarios by means of
signal level simulations.
Figs. 9 and 10 show that the UWB system can tolerate
quite a large level of NB interference in the three different
scenarios considered. However, due to the low transmitted
power currently allowed for UWB systems (typically on the
order of 1 mW), it is not unlikely to have a scenario with
strong NB interferers (for example, the transmitted power
in IEEE 802.11a is in the range 0.1–1 W) producing a SIR
well below 20 dB. So, this apparent robustness to
interference may not be sufficient in some situations, and
proper countermeasures must be employed. For example,
note that with the spreading sequence 2) of Fig. 8, a much
larger interference level can be tolerated for the considered value of the interferer carrier frequency.
B. UWB-IR Reception With OFDM Interference
Here we show the performance of a UWB-IR employing TH-BPPM in the presence of a NB OFDM signal and
AWGN using the analytical approach developed in
Section III-E. We consider Ns ¼ 4 and the pulse shape
given in (59) with Tf ¼ 100 ns and ¼ 0:068 ns. The
resulting correlation parameter is ¼ 0:824. Furthermore, we consider a user with a TH sequence
fcTH
j g ¼ f0; 10; 5; 20g and with Tc ¼ 0:5 ns.
Fig. 10. BEP for the DS-BPAM system considered with Rake
reception and L ¼ 8 paths with a tone interferer.
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
Fig. 11. The normalized transfer function of the matched filter
around f0 ¼ 5745 MHz and the N ¼ 52 subcarriers of the
IEEE 802.11a interferer.
The interferer is of the type IEEE 802.11a and is
operating in the U-NII upper band with center frequency
fc ¼ 5:745 GHz. This standard adopts an OFDM scheme
utilizing N ¼ 52 subcarriers spaced by f ¼ 0:3125 MHz
with different modulations: BPSK, QPSK, 16-QAM, and
64-QAM. Four of the N subcarriers are used to transmit
BPSK modulated pilot symbols. To better understand the
behavior of the MF as a function of Ns and the TH
sequence of the desired user, Fig.p11ffiffiffiffiffishows the normalized
transfer function H0 ðf Þ ¼ H0 ðf Þ= Tb around fc using (21).
The subcarriers of the interferer are also depicted to show
their contribution to the total interference. As can be seen,
the frequency selectivity of the MF plays a key role in
determining the effective (filtered) power of the interference at its output.
Fig. 12. BEP for the TH-BPPM system considered affected by an
IEEE 802.11a interferer. Comparison between analytical models
and simulation is given.
Fig. 13. The error probability per codeword of OFDM over a
BFC in the frequency domain with Nsb subcarriers per block,
QPSK over all useful 126 subcarriers, and a BCH code
with n ¼ 126, Rc ¼ 1=2, and t ¼ 10. The narrow-band
interference is over NI subcarriers, signal-to-interference
ratio SIR ¼ 0 dB.
Using the above parameters, the BEP of the UWB link
in the presence of NB OFDM interference and AWGN is
plotted in Fig. 12, as a function of the SNR.
In the figure, signal level simulation for different
modulations (i.e., data rate) according to the IEEE 802.11a
standard is compared with the exact N tone expression
(BN tones[ curve) derived in Section III-B and the
Gaussian approximation (27). As can be noted, both approximations are in good agreement with the simulation.
Even in this scenario, the performance of the UWB
system is significantly degraded only for quite low SIR
(below 20 dB), which, however, is not unlikely
depending on the spatial configuration of the nodes.
C. OFDM-Based UWB With NB Interference
In this section, we analyze a situation where an OFDMbased system is affected by an NB interferer, using the
analytical approach developed in Section IV. For example,
we report in Fig. 13 the codeword error probability for an
OFDM-based UWB system in the presence of NB interference. We assume a BFC in the frequency domain with
Nsb ¼ 1 and Nsb ¼ 6 symbols per block with exponentially
distributed SNR in each block (Rayleigh fading) and a single
NBI causing interference to NI ¼ 1; 2; and 6 subcarriers. If,
for example, the subcarrier spacing is f ¼ 4 MHz,
Nsb ¼ 6 corresponds to a band per block of 24 MHz and
NI ¼ 2 corresponds to an interferer with bandwidth
8 MHz. The average SIR is 0 dB, and the code is a shortened
BCH code [121] with code-rate Rc ¼ 1=2, n ¼ 126 with
correction capability of t ¼ 10 errors. Some observations are
in order here. First, the smaller the coherence bandwidth of
the channel (i.e., Nsb ), the better. This is due to the fact that
large coherence bandwidth can produce a large number of
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249
Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
errors per codeword, reducing the error correction
capability of the FEC code. Indeed, FEC codes are typically
designed to cope with independent symbol errors, while the
coherence in frequency would require a design that
accounts for correlation among errors [39], [110]. For the
same reason, it is better to have few subcarriers affected by
a strong interference rather than the same interfering
power spread over more subchannels. This is evident in
Fig. 13, where, with reference to the case Nsb ¼ 6, the
degradation in performance is limited when the NBI is on
one subchannel only ðNI ¼ 1Þ, while it is more pronounced
for NI ¼ 6, where the same interfering power is over six
subchannels. In fact, due to the choice of FEC coding with
hard decision decoding, the SIR does not play a significant
role when below 0 dB because, in that case, the interfered
subchannels experience a BEP close to 1/2. In this situation,
the effectiveness of the FEC is mainly affected by the
bandwidth WNB of the NB interferer.
D. NB Link in the Presence of UWB-IR Interference
In this section, we analyze the performance of a NB
victim link in the presence of UWB interference by using
the analytical approach presented in Section V.
We consider a NB link with BPSK modulation operating
at a bit rate 1=TN ¼ 100 Kbit/s and carrier frequency
fc ¼ 5:010 GHz. The UWB interferer employs DS-BPAM
with the same system parameters as in Section VI-A, i.e.,
with bit rate 1=TU ¼ 1:25 Mbit/s; frame duration Tf ¼
50 ns; Ns ¼ 16 pulses per bit with a DS code fcDS
j g¼
Ns 1
fð1Þj gj¼0 ; and sixth derivative received pulse pðtÞ with
parameter p ¼ 0:192 ns.
In Fig. 14, the BEP performance of the NB link in the
presence of a single UWB interferer and AWGN is plotted
using (56) and (57). Different SIRs are considered. The
case where the NB link experiences Rayleigh fading and
the UWB interferer is subject to frequency-selective fading
Fig. 15. BEP for the NB link in the presence of a UWB interferer.
The NB link experiences Rayleigh fading, whereas the UWB interferer
is subject to frequency-selective fading.
is shown in Fig. 15 using (56)–(58). Here the presence of
fading greatly deteriorates the performance. In both
Figs. 14 and 15, we can observe that the effect of a single
UWB interferer is almost negligible, and the performance is approximately unchanged, unless the SIR is below
20 dB. Since the UWB transmitted power is typically
much lower than that of the NB transmitter, to have such a
low SIR, the NB receiver has to be much closer to the UWB
transmitter than to the NB transmitter.
The numerical examples reported in this section have
shown that coexistence between UWB and NB systems
represents an important issue that requires proper
countermeasures to reduce the mutual interference. To
this aim, the cognitive radio (CR) paradigm, which
consists in analyzing the radio scene and then adapting
the transmitted waveforms for low spectral emissions in
occupied bands, represents a natural approach to mitigate
the mutual interference, thus improving coexistence and
spectrum utilization [16]–[19].
VII. CONCLUS ION
Fig. 14. BEP for the NB link in the presence of a UWB interferer
and on AWGN channel.
250
We reviewed the main results regarding coexistence
between ultra-wide-band and narrow-band systems.
We analyzed both impulse-based and OFDM-based
UWB systems, showing the impact of NB interference on
the performance. We considered AWGN and multipath
fading channels, both for the desired and interfering links,
and different receiver architectures. In particular, we have
illustrated the role of spreading sequences for IR-UWB
systems, and of coding for OFDM-based UWB systems.
For the dual scenario of a NB link in the presence of
UWB interference, we have shown the conditions under
which UWB interfering signals can be considered as
Gaussian noise. For this case, the Gaussian approximation
for the UWB interference is reasonable provided that the
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
NB link experiences Rayleigh fading, or that several UWB
pulses are received within each NB symbol duration.
The analysis presented has been used to reveal some
important issues regarding possible coexistence between
UWB and NB systems. Here we briefly summarize these
results.
Concerning UWB systems affected by NB interference,
we showed that the impact of the NB interference strongly
depends, for a UWB-IR coherent receiver, on the carrier
frequency of the interferer, the UWB pulse shape, and the
spreading code adopted. For example, we have shown that,
in a realistic setting, there is no significant performance
degradation in the UWB link for SIR on the order of 20 dB
or greater, the precise value depending on system
parameters and target error probability. However, due to
the low transmitted power level currently allowed for UWB
systems, which is typically much lower than for NB
transmitters, a scenario with strong NB interferers
producing very small SIR at the UWB receiver is not
unlikely. So, the inherent robustness of UWB systems to
NB interference may be not sufficient in some situations,
and proper countermeasures must be employed.
Similarly, for the dual case of NB systems affected by
UWB interference, we have shown that the effects of a
single UWB interferer are almost negligible, and the
performance of the NB links are practically unchanged for
sufficiently large SIR values (with our setting, greater than
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Proceedings of the IEEE | Vol. 97, No. 2, February 2009
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Chiani and Giorgetti: Coexistence Between UWB and Narrow-Band Wireless Communication Systems
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ABOUT THE AUTHORS
Marco Chiani (Senior Member, IEEE) was born in
Rimini, Italy, in April 1964. He received the
Dr. Ing. degree (magna cum laude) in electronic
engineering and the Ph.D. degree in electronic
engineering and computer science from the University of Bologna, Italy, in 1989 and 1993, respectively.
He is a full Professor with the II Engineering
Faculty, University of Bologna, where he is the Chair
in Telecommunication. During summer 2001, he
was a Visiting Scientist with AT&T Research Laboratories, Middletown, NJ. He is a frequent visitor at the Massachusetts
Institute of Technology (MIT), where he presently is a Research Affiliate. His
research interests include wireless communication systems, MIMO systems,
wireless multimedia, low-density parity check codes, and UWB. He is
leading the research unit of CNIT/University of Bologna on Joint Source and
Channel Coding for wireless video and is a Consultant to the European
Space Agency for the design and evaluation of error-correcting codes based
on LDPCC for space CCSDS applications.
Dr. Chiani has chaired, organized sessions, and served on the Technical
Program Committees of several IEEE international conferences. He was
Cochair of the Wireless Communications Symposium, ICC 2004. In January
2006, he received the ICNEWS award for fundamental contributions to the
theory and practice of wireless communications. He received the 2008 IEEE
ComSoc Radio Communications Committee Outstanding Service Award. He
is the past Chair (2002–2004) of the Radio Communications Committee,
IEEE Communication Society, and past Editor for Wireless Communication
(2000–2007) for the IEEE TRANSACTIONS ON COMMUNICATIONS.
254
Andrea Giorgetti (Member, IEEE) received the
Dr. Ing. degree (magna cum laude) in electronic
engineering and the Ph.D. degree in electronic
engineering and computer science from the University of Bologna, Italy, in 1999 and 2003,
respectively.
Since 2003, he has been with the Istituto di
Elettronica e di Ingegneria dell’Informazione e
delle Telecomunicazioni (IEIIT-BO) research unit,
National Research Council (CNR), Bologna. In 2005,
he was a Researcher with the National Research Council. Since 2006 he
has been an Assistant Professor with the II Engineering Faculty, University
of Bologna, where he joined the Department of Electronics, Computer
Sciences and Systems. During the spring of 2006, he was a Research
Affiliate with the Laboratory for Information and Decision Systems,
Massachusetts Institute of Technology, Cambridge, working on coexistence issues between ultra-wide-band and narrow-band wireless systems. His research interests include ultrawide bandwidth communication
systems, wireless sensor networks, and multiple-antenna systems.
He was Cochair of the Wireless Networking Symposium at the IEEE
International Conference on Communications (ICC 2008), Beijing, China,
May 2008, and is Cochair of the MAC track of the IEEE Wireless
Communications and Networking Conference (WCNC 2009), Budapest,
Hungary, April 2009.
Proceedings of the IEEE | Vol. 97, No. 2, February 2009
Authorized licensed use limited to: Oulu University. Downloaded on March 30, 2009 at 06:40 from IEEE Xplore. Restrictions apply.