FINAL PRESENTATION ANAT KLEMPNER SPRING 2012 SUPERVISED BY: MALISA MARIJAN YONINA ELDAR A Compressed Sensing Based UWB Communication System 1

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 A technology for transmitting information in bands occupying over 500 MHz bandwidth. Used for short-range communication Very low Power Spectral Density 3

UWB - Advantages Useful for communication systems that require:  High bandwidth  Low power consumption  Shared spectrum resources 4

UWB - Applications In communications:  High speed, multi-user wireless networks.  Wireless Personal Area Networks / Local Area Networks  Indoor communication 5

UWB - Applications Radar  Through-wall imaging and motion sensing radar  Underground imaging Long distance, Low data rate applications  Sensor networks  High precision location systems 6

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. 7

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. 8

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:

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. Where Φ is the random projection matrix (measurement matrix).

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 a standard for UWB communication. The simulation environment will be used to compare different compressed sensing strategies. 11

Simulation Environment 12 Block-Diagram of the system: Signal Generator Multipath Channel Detection Channel Estimation To be implemented according to IEEE a standard Correlator Based Detector/ Rake Receiver

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. 13

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). 14

Currently: Phase I – Channel Estimation 15 Block-Diagram of the process: Signal Generator Multipath Channel Analog pre- processing A/D Conversion Reconstruction Algorithm To be implemented according to IEEE a standard Randomized Hadamard Scheme/ Random Filter Variants of the MP algorithm

Channel Estimation - Theory 16

Channel Estimation - Theory 17

Channel Estimation - Theory 18

Channel Estimation - Theory 19

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

Channel Estimation - Theory 22 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.

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 a 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

Signal Detection - Theory 29 Rake receiver structure:

Signal Detection - Theory 30 Rake receiver structure: Where, and is the signal waveform.

Signal Detection - Theory 31 The decision statistics is calculated using: The estimated bit:

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.

33 Thank You!

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 , [2]A. Barbieri, et al., "Compressed channel estimation and data detection algorithms for IR-UWB," 2011, pp [3]F. M. Naini, et al., "Compressive sampling of pulse trains: Spread the spectrum!," 2009, pp [4]G. Z. Karabulut and A. Yongacoglu, "Sparse channel estimation using orthogonal matching pursuit algorithm," 2004, pp 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 , [6]IEEE Std a™-2007 [7]J. Zhang, et al., "UWB systems for wireless sensor networks," Proceedings of the IEEE, vol. 97, pp , [8]A. F. Molisch, et al., "A comprehensive standardized model for ultrawideband propagation channels," Antennas and Propagation, IEEE Transactions on, vol. 54, pp , 2006.

References 35 [9]A. F. Molisch, et al., "IEEE a channel model-final report," IEEE P, vol. 15, [10]A. Saleh, R. A. Valenzuela, “A statistical model for indoor multipath propagation,” IEEE J. Selected Areas Comm., vol. 5, pp. 138–137, Feb [11]M. Basaran, et al., "The effect of channel models on compressed sensing based UWB channel estimation," 2011, pp [12]B. Mielczarek, et al., "Performance of coherent UWB Rake receivers with channel estimators," 2003, pp Vol. 3. [13]T. Heikkilä, "Rake receiver," S Postgraduate Course in Radio Communications, [14]V. Lottici, et al., "Channel estimation for ultra-wideband communications," Selected Areas in Communications, IEEE Journal on, vol. 20, pp , [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 , [16]E. Lagunas and M. Najar, "Sparse channel estimation based on compressed sensing for ultra wideband systems," 2011, pp

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, [18]D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, vol. 26, pp , [19]G. Gui, et al., "Sparse multipath channel estimation using compressive sampling matching pursuit algorithm," Arxiv preprint arXiv: , [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 [22]P. Zhang, et al., "A compressed sensing based ultra-wideband communication system," 2009, pp [23]L. Shi, et al., "Ultra-wideband channel estimation based on Bayesian compressive sensing," 2010, pp