Final Presentation - High Speed Digital Systems Lab

Report
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   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  is the number of multipaths,  is the
l-th propagation path, and  is the delay of the
l-th propagation path.
The goal of channel estimation is to estimate
channel parameters  ,  −1
.
=0
Channel Estimation - Theory
18
 Channel output:
The received pilot waveform:
s
r
t   s t   h t   w t 
where   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  in the form:
x  
where the non-zero coefficients of  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:  =  is used to create the sampled
signal:
 = +

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
 () 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
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[2]
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[3]
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[4]
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[5]
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References
35
[9]
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[10]
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[14]
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References
36
[17]
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[20]
J. A. Tropp, et al., "Random filters for compressive sampling and
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