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A Compressed Sensing Based UWB Communication System. Mid-Semester presentation Anat klempner Spring 2012 SupervisED BY: MaliSA marijan Yonina eldar. Contents. Background UWB – Ultra Wideband Project Motivation Compressed Sensing Project overview Project Goals Project Tasks - PowerPoint PPT Presentation
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1
MID-SEMESTER PRESENTATION
ANAT KLEMPNERSPRING 2012
SUPERVISED BY: MALISA MARIJAN YONINA ELDAR
A Compressed Sensing Based UWB
Communication System
2
Contents
Background UWB – Ultra Wideband Project Motivation Compressed Sensing
Project overview Project Goals Project Tasks
Channel Estimation Theoretical Analysis
What’s Next?
3
UWB
A technology for transmitting information in bands occupying over 500 MHz bandwidth.
Used for short-range communicationVery low Power Spectral Density
4
UWB - Advantages
Useful for communication systems that require: High bandwidth Low power consumption Shared spectrum resources
5
UWB - Applications
In communications: High speed, multi-user wireless networks. Wireless Personal Area Networks / Local Area
Networks Indoor communication
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UWB - Applications
Radar Through-wall imaging and motion sensing radar Underground imaging
Long distance , Low data rate applications Sensor networks High precision location systems
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Project Motivation
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.
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Project Motivation
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 ultra-short pulse through a multipath UWB channel has a sparse representation.
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Compressed Sensing
The main idea: A signal is called M-sparse if it can be written
as the sum of M known basis functions:
1
M
i ii
x
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Compressed Sensing
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.
Where Φ is the random projection matrix (measurement matrix).
y x
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Project Goals
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.
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Simulation Environment
Block-Diagram of the system:
Signal Generat
or
Multipath
ChannelDetection
Channel Estimation
To be implemented according to
IEEE 802.15.4a standard
Correlator Based Detector/ Rake
Receiver
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Project Tasks
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: correlator-based detector and the RAKE receiver .Performance parameter: BER vs. input SNR for different sampling rates and number of pilot symbols.
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Project Tasks
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).
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Currently: Phase I – Channel Estimation
Block-Diagram of the process:
Signal Generat
or
Multipath
Channel
Analog pre-
processing
A/D Conversio
n
Reconstruction Algorithm
To be implemented according to
IEEE 802.15.4a standard
Randomized Hadamard Scheme/ Random
Filter
Variants of the MP
algorithm
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Channel Estimation - Theory
The signal:Each block of data contains pilot symbols,
which are used to estimate the channel parameters, and can be described as:
where is the transmission pulse. (Shape defined in the standard).
1
0
pN
fi
s t p t iT
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Channel Estimation - Theory
Multipath Channel:A fading channel can be described as:
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
L
l ll
h t t
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Channel Estimation - Theory
Channel output:The received pilot waveform:
where is the channel noise.
The pilot waveform in each frame:
rs t s t h t w t
1
0
L
l ll
x t p t h t p t
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Channel Estimation - Theory
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:
where the non-zero coefficients of represent the channel gains, and is a Toeplitz Matrix with the elements:
x
,k j sp k j T
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Channel Estimation - Theory
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.
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Channel Estimation - Theory
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.
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Channel Estimation - Theory
Reconstruction Problem: The problem of finding unknown channel parameters
can be described as:
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.
1min . .s t y
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What’s Next?
Simulate system according to IEEE 802.15.4a standard.
Perform channel estimation and evaluate performance.
Simulate signal detection methods.
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Thank You!