A Compressed Sensing Based UWB Communication System

1. A Compressed Sensing Based UWB Communication System Final presentation Anatklempner Spring 2012 SupervisED BY: MaliSAmarijan Yoninaeldar

2. Contents • Background • UWB – Ultra Wideband • Project Motivation • Compressed Sensing • Project overview • Project Goals • Project Tasks • Channel Estimation • Theoretical Analysis • Implementation & Results • Signal Detection • Summary

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

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

7. 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.

8. 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.

9. Compressed Sensing • The main idea: • A signal is called M-sparse if it can be written as the sum of M known basis functions:

10. 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).

11. 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.

12. Simulation Environment Block-Diagram of the system: Channel Estimation Signal Generator Multipath Channel Detection Correlator Based Detector/ Rake Receiver To be implemented according to IEEE 802.15.4a standard

13. 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.

14. 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).

15. Currently: Phase I – Channel Estimation Block-Diagram of the process: Signal Generator Multipath Channel Analog pre-processing A/D Conversion Reconstruction Algorithm Randomized Hadamard Scheme/ Random Filter Variants of the MP algorithm To be implemented according to IEEE 802.15.4a standard

16. 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).

17. 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 .

18. Channel Estimation - Theory Channel output: The received pilot waveform: where is the channel noise. The pilot waveform in each frame:

19. 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:

20. 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.

21. 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.

22. 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.

23. Channel Estimation - Implementation The channel estimation system was implemented in MATLAB according to the theoretical description.

24. 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.

25. 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

26. 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

27. Channel Estimation - Results An exaple for channel estimation with SNR=25[dB]

28. 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.

29. Signal Detection - Theory Rake receiver structure:

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

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

32. 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.

33. Thank You!

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36. References [17] E. Lagunas Targarona, "Sparse channel estimation based on compressed sensing theory for UWB systems," Master Thesis, Department of Signal Theory and Communications, UniversitatPolitencnica 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.