1. Compressed Sensing Based UWB System Peng Zhang Wireless Networking System Lab WiNSys

2. Outline Quick Review on CS Filter Based CS CS Based Channel Estimation CS Based UWB System Simulation Results Issues and Conclusions

3. RIP Quick Review of CS Sparse signal can be reconstructed from random measurements However… –Matrices are non-causal –Causal system is more common in communications

4. Filter Based CS (LTI System) Filter based structure is more appropriate to model communication system –Causality –Quasi-toeplitz matrix p is quasi-toeplitz If… –p satisfied RIP –a is sparse Then… –CS will work! =X apy

5. CS Based UWB System Proposed system –Channel estimation –Signal reconstruction

6. CS Based Channel Estimation Goal : –Estimate the 5 GHz bandwidth channel impulse response at 500 Msps rate –Use the result in reconstruction matrix

7. CS Based Channel Estimation Architecture

8. CS Based Channel Estimation Condition –Channel is sparse in time domain Yes! –PN matrix satisfied RIP Yes! –Sufficient measurements –SNR

9. CS Based Channel Estimation Sufficient measurements –Not all samples have contribution –To get sufficient measurements Long signal duration at RX Higher sampling rate at RX –Sampling rate can be low if Signal has longer duration –Longer PN sequence or –Longer channel delay spread

10. Channel Estimation Simulation Get the original indoor channel under estimation: –3 GHz~ 8 GHz VNA data –Use matching pursuit with SINC function as basis to get TDL model –Time domain resolution = 50 ps (20 Gsps)

11. Channel Estimation Simulation Estimation –PN length = 1024 ns, PN rate = 20 Gsps –Receiver sampling rate = 500 Msps –Use BPDN, SNR / Sample at RX= 10 dB

12. Channel Estimation Simulation How to evaluate the result? –Mean square errors? –Supports? Though the result is not accurate, we found that it performs good in CS-based UWB system

13. CS Based UWB System Goal: –Reconstruct transmitted sequence with sub-GHz sampling rate

14. System Configuration Symbol based bit sequence –256 bins per symbol –Bin width = 1ns –1 position is occupied in each symbol Pulse generator –3~8 GHz Gaussian pulse –Shapes the spectrum ……

15. System Configuration Incoherent filter –FIR filter using PN sequence –PN sequence length = 128 ns –Bandwidth of the transfer function: 3~8 GHz Channel –Real TDL channel model –Same as previous one No down-conversion at RX

16. System Configuration Reconstruction –Sampling rate: 500 Msps, << 16 Gsps, Nyquist rate Measurement duration = 512 ns –no ISI between measurements –Basis pursuit de-noise (BPDN) We use the estimated channel to form

17. Simulation Results Simulation configuration –System sampling rate: 20 Gsps –Block error rate VS SNR / sample at receiver –Perfect synchronization –2000 simulations for each plot –Perfect/Imperfect channel estimation –Various sub-Gsps sampling rate 125 Msps, 250 Msps, 500 Msps –Use Sparselab to perform BPDN

18. Simulation Results

19. 500 Msps performs good –Error free for 2000 simulations at -5 dB Estimated channel has similar performance Higher sampling rate has better performance –More sufficient measurements

20. Other Issues Does PN + Channel fits RIP? Efficient BPDN algorithm for hardware? –Now each run for BPDN is about 0.1 s on Intel Core 2 –Matrix size is 256*5120 Synchronization –Get the right matrix for reconstruction Data rate –Now only use 1 position in 256 bins –Data rate = 16 Mb/s Tractable performance –BPDN performance varies sharply with different parameters

21. Conclusion CS computation complexity trades for hardware complexity –No down-conversion, no Nyquist rate sampling Only 1/20 of Nyquist rate Even slower for high SNR –Huge size matrix, computation complexity and synchronization would be big problems for processing

22. References [1]Emmanuel Candès, “Compressive Sampling”, in Int. Congress of Mathematics, 3, pp. 1433-1452, Madrid, Spain, 2006. [2]Joel Tropp, Michael Wakin, Marco Duarte, Dror Baron, and Richard Baraniuk, “Random Filters for Compressive Sampling and Reconstruction”, in IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Toulouse, France, May 2006. [3]Richard Baraniuk and Philippe Steeghs, “Compressive radar imaging”, in IEEE Radar Conference, Waltham, Massachusetts, April 2007. [4]Scott Shaobing Chen,David L. Donoho,Michael A. Saunders, “Atomic Decomposition by Basis Pursuit”, SIAM Journal on Scientific Computing, pp. 33-61, 1998.

23. Discussion

24. Thank you!