A Compressed Sensing Based
UWB Communication System
1
F I N A L P R ESEN TA TI O N
ANAT KLEMPNER
SPRING 2012
SUPERVISED BY: MALISA MARIJAN
YONINA ELDAR
Contents
2
 Background



UWB – Ultra Wideband
Project Motivation
Compressed Sensing
 Project overview


Project Goals
Project Tasks
 Channel Estimation


Theoretical Analysis
Implementation & Results
 Signal Detection
 Summary
UWB
3
 A technology for transmitting information in bands
occupying over 500 MHz bandwidth.
 Used for short-range communication
 Very low Power Spectral Density
UWB - Advantages
4
 Useful for communication systems that require:
High bandwidth
 Low power consumption
 Shared spectrum resources

UWB - Applications
5
 In communications:
High speed, multi-user wireless networks.
 Wireless Personal Area Networks / Local Area
Networks
 Indoor communication

UWB - Applications
6
 Radar
Through-wall imaging and motion sensing radar
 Underground imaging

 Long distance , Low data rate applications
 Sensor networks
 High precision location systems
Project Motivation
7
 The problem:

The UWB signal has very high bandwidth, and
therefore the UWB receiver requires high-speed
analog-to-digital converters.

High sampling rates are required for accurate UWB
channel estimation.
Project Motivation
8
 The proposed approach relies on the following UWB
signal properties:

The received UWB signal is rich in multipath diversity.

The UWB signal received by transmitting an ultrashort pulse through a multipath UWB channel has a
sparse representation.
Compressed Sensing
9
 The main idea:

A signal is called M-sparse if it can be written as the
sum of M known basis functions:
M
x 

i
i 1
i
 
Compressed Sensing
10

An M-sparse signal can be reconstructed using a few
number of random projections of the signal into a
random basis which is incoherent with the basis in
which the signal is sparse, thus enabling reduced
sampling rate.
y  x
Where Φ is the random projection matrix
(measurement matrix).
Project Goals
11
 We wish to build a simulation environment for an
UWB communication system with compressed
sensing based channel estimation.
 The system will be based on the IEEE 802.15.4a
standard for UWB communication.
 The simulation environment will be used to compare
different compressed sensing strategies.
Simulation Environment
12
 Block-Diagram of the system:
Channel
Estimation
Signal
Generator
Multipath
Channel
To be implemented
according to IEEE
802.15.4a standard
Detection
Correlator Based
Detector/ Rake
Receiver
Project Tasks
13
 Phase 1 - Simulate the system and perform the
channel estimation.
Performance parameter: MSE of the estimation error
as a function of the number of measurements.
 Phase 2 - Simulate signal detection methods: the
RAKE receiver .
Performance parameter: BER vs. input SNR for
different sampling rates and number of pilot
symbols.
Further Research Possibilities
14
 Phase 3- Compare the MSE and BER performance
for the different sampling schemes: the randomized
Hadamard scheme, Xampling method, and the
random filter.
 Phase 4 -Compare the MSE and BER performance
for the different sampling schemes and the
reconstruction algorithms (e.g. , OMP, eOMP, and
CoSaMP).
Currently: Phase I – Channel Estimation
15
 Block-Diagram of the process:
Signal
Generator
Multipath
Channel
To be implemented
according to IEEE
802.15.4a standard
Analog
preprocessing
Randomized
Hadamard
Scheme/
Random Filter
A/D
Conversion
Reconstruction
Algorithm
Variants of
the MP
algorithm
Channel Estimation - Theory
16
 The signal:
Each block of data contains pilot symbols, which
are used to estimate the channel parameters,
and can be described as:
s t  
N p 1
 p  t  iT 
f
i0
where 𝑝 𝑡 is the transmission pulse. (Shape
defined in the standard).
Channel Estimation - Theory
17
 Multipath Channel:
A fading channel can be described as:
h t  
L 1
   t   
l
l
l0
where 𝐿 is the number of multipaths, 𝛼𝑙 is the
l-th propagation path, and 𝜏𝑙 is the delay of the
l-th propagation path.
The goal of channel estimation is to estimate
channel parameters 𝛼𝑙 , 𝜏𝑙 𝐿−1
.
𝑙=0
Channel Estimation - Theory
18
 Channel output:
The received pilot waveform:
s
r
t   s t   h t   w t 
where 𝑤 𝑡 is the channel noise.
The pilot waveform in each frame:
x t   p t   h t  
L 1
  p t   
l
l0
l
Channel Estimation - Theory
19
 Signal Model:
An arbitrary signal can be described as a vector
of its samples.
The received signal in our case, can be written as
a vector 𝑥 in the form:
x  
where the non-zero coefficients of 𝜃 represent
the channel gains, and Ψ is a Toeplitz Matrix
with the elements:  k , j  p   k  j  T s 
Channel Estimation - Theory
20
 Analog Pre-Processing:
 Our goal is to achieve random projections of the signal.

There are several ways to achieve random projections, the first
method that will bet tested is the Randomized Hadamard
Scheme.
Channel Estimation - Theory
21
 Analog Pre-Processing – Randomized Hadamard
Scheme:

The sampling matrix: 𝜙 = 𝑅𝐻𝑆 is used to create the sampled
signal:
𝑦 =𝜙 𝑥+𝑤

R is a sub-sampling matrix – contains only one (Randomly
chosen) non-zero value in each row.
H is the Hadamard matrix.
S is a diagonal matrix with a random binary modulation
sequence on its digonal.


Channel Estimation - Theory
22
 Reconstruction Problem:
 The problem of finding unknown channel parameters can be
described as:
m in 


1
s .t . y    
This problem can be solved using variants of the Matching
Pursuit (MP) Algorithm.
We will first try to use the OMP Algorithm – Orthogonal
Matching pursuit.
Channel Estimation - Implementation
23
 The channel estimation system was implemented in
MATLAB according to the theoretical description.
Channel Estimation - Implementation
24
 Channel Model Implementation:
 The UWB channel was at first implemented according to the
IEEE 802.15.4a standard, using the code for channel
generation which is given in the standard.

The generated channel did not have the desired sparsity
property, despite results shown in previous papers.

It was decided to implement a simple version of the UWB
channel.
Channel Estimation - Implementation
25
 Channel Model Implementation:
 The suggested simplified model:
Ray arrival rate is Poisson distributed.
 Channel energy is exponentially decaying.

Example of generated channel
Channel Estimation - Results
26
 The criterion used to evaluate the results is the MSE
between the estimated and the original channel.
 Results were achieved using a single pilot symbol.
MSE Vs. SNR for Channel Estimation
Channel Estimation - Results
27
An exaple for channel estimation with SNR=25[dB]
Signal Detection - Theory
28
 The signal at the input of the detector can be
represented as:
r t   x t   h t   w t  
L 1
  x t     w t 
l
l
l0
 𝑤(𝑡) is the sum of noise and MUI, and it is assumed
to be a white Gaussian process.
Signal Detection - Theory
29
 Rake receiver structure:
Signal Detection - Theory
30
 Rake receiver structure:
 Where v i  t  
waveform.
si  t   si  t  TBPM
, and s i  t  is the signal
Signal Detection - Theory
31
 The decision statistics is calculated using:
 i  1  T dsym
L 1
zi 
 ˆ

l
l0
r  t  v i  t  iT dsym  ˆl  dt
iT dsym
 The estimated bit:
0
bi  
1
zi  0
else
Summary
32
 In this project I learned the basics of the theory of
compressed sensing and its application to UWB
communications.
 In the first stage, channel estimation was performed.
 The signal detection phase was not successfully
implemented in this project.
Thank You!
33
References
34
[1]
J. L. Paredes, et al., "Ultra-wideband compressed sensing: Channel
estimation," Selected Topics in Signal Processing, IEEE Journal of, vol. 1, pp.
383-395, 2007.
[2]
A. Barbieri, et al., "Compressed channel estimation and data detection
algorithms for IR-UWB," 2011, pp. 360-364.
[3]
F. M. Naini, et al., "Compressive sampling of pulse trains: Spread the
spectrum!," 2009, pp. 2877-2880.
[4]
G. Z. Karabulut and A. Yongacoglu, "Sparse channel estimation using
orthogonal matching pursuit algorithm," 2004, pp. 3880-3884 Vol. 6.
[5]
J. A. Tropp and A. C. Gilbert, "Signal recovery from random
measurements via orthogonal matching pursuit," Information Theory, IEEE
Transactions on, vol. 53, pp. 4655-4666, 2007.
[6]
IEEE Std 802.15.4a™-2007
[7]
J. Zhang, et al., "UWB systems for wireless sensor networks,"
Proceedings of the IEEE, vol. 97, pp. 313-331, 2009.
[8]
A. F. Molisch, et al., "A comprehensive standardized model for
ultrawideband propagation channels," Antennas and Propagation, IEEE
Transactions on, vol. 54, pp. 3151-3166, 2006.
References
35
[9]
A. F. Molisch, et al., "IEEE 802.15. 4a channel model-final report," IEEE
P, vol. 15, 2004.
[10]
A. Saleh, R. A. Valenzuela, “A statistical model for indoor multipath
propagation,” IEEE J. Selected Areas Comm., vol. 5, pp. 138–137, Feb. 1987.
[11]
M. Basaran, et al., "The effect of channel models on compressed sensing
based UWB channel estimation," 2011, pp. 375-379.
[12]
B. Mielczarek, et al., "Performance of coherent UWB Rake receivers with
channel estimators," 2003, pp. 1880-1884 Vol. 3.
[13]
T. Heikkilä, "Rake receiver," S-72.333 Postgraduate Course in Radio
Communications, 2004.
[14]
V. Lottici, et al., "Channel estimation for ultra-wideband
communications," Selected Areas in Communications, IEEE Journal on, vol. 20,
pp. 1638-1645, 2002.
[15]
J. D. Choi and W. E. Stark, "Performance of ultra-wideband
communications with suboptimal receivers in multipath channels," Selected Areas
in Communications, IEEE Journal on, vol. 20, pp. 1754-1766, 2002.
[16]
E. Lagunas and M. Najar, "Sparse channel estimation based on
compressed sensing for ultra wideband systems," 2011, pp. 365-369.
References
36
[17]
E. Lagunas Targarona, "Sparse channel estimation based on compressed
sensing theory for UWB systems," Master Thesis, Department of Signal Theory
and Communications, Universitat Politencnica de Catalunya, Barcelona, 2010.
[18]
D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from
incomplete and inaccurate samples," Applied and Computational Harmonic
Analysis, vol. 26, pp. 301-321, 2009.
[19]
G. Gui, et al., "Sparse multipath channel estimation using compressive
sampling matching pursuit algorithm," Arxiv preprint arXiv:1005.2270, 2010.
[20]
J. A. Tropp, et al., "Random filters for compressive sampling and
reconstruction," 2006, pp. III-III.
[21]
H. Yu and S. Guo, "Pre-filtering ultra-wideband channel estimation based
on compressed sensing," 2010, pp. 110-114.
[22]
P. Zhang, et al., "A compressed sensing based ultra-wideband
communication system," 2009, pp. 1-5.
[23]
L. Shi, et al., "Ultra-wideband channel estimation based on Bayesian
compressive sensing," 2010, pp. 779-782.