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FINAL PRESENTATION

ANAT KLEMPNERSPRING 2012

SUPERVISED BY: MALISA MARIJAN YONINA ELDAR

A Compressed Sensing Based UWB

Communication System

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Contents

Background UWB – Ultra Wideband Project Motivation Compressed Sensing

Project overview Project Goals Project Tasks

Channel Estimation Theoretical Analysis Implementation & Results

Signal DetectionSummary

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UWB

A technology for transmitting information in bands occupying over 500 MHz bandwidth.

Used for short-range communicationVery low Power Spectral Density

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UWB - Advantages

Useful for communication systems that require: High bandwidth Low power consumption Shared spectrum resources

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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: the RAKE receiver .Performance parameter: BER vs. input SNR for different sampling rates and number of pilot symbols.

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Further Research Possibilities

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

nReconstruction 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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Channel Estimation - Implementation

The channel estimation system was implemented in MATLAB according to the theoretical description.

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Channel Estimation - Implementation

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.

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Channel Estimation - Implementation

Channel Model Implementation: The suggested simplified model:

Ray arrival rate is Poisson distributed. Channel energy is exponentially decaying.

Example of generated channel

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Channel Estimation - Results

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

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Channel Estimation - Results

An exaple for channel estimation with SNR=25[dB]

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Signal Detection - Theory

The signal at the input of the detector can be represented as:

is the sum of noise and MUI, and it is assumed to be a white Gaussian process.

1

0

L

l ll

r t x t h t w t x t w t

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Signal Detection - Theory

Rake receiver structure:

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Signal Detection - Theory

Rake receiver structure:

Where , and is the signal waveform.

i i i BPMv t s t s t T is t

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Signal Detection - Theory

The decision statistics is calculated using:

The estimated bit:

11

0

ˆ ˆdsym

dsym

i TL

i l i dsym ll iT

z r t v t iT dt

0 01

ii

zb

else

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Summary

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.

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Thank You!

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References

[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.

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References

[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.

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References

[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.