Compressed Sensing Based UWB System

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
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!

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
• 38 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 38 GHz
• Channel
• Real TDL channel model
• Same as previous one
• No down-conversion at RX

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System Configuration

• Reconstruction
• Sampling rate
• 500 Msps, ltlt 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
Simulation Results

• 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 2565120
• 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.

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Discussion
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Thank you!