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

Compressed Sensing Based UWB System

Peng Zhang

Wireless Networking System Lab

WiNSys

Outline

• Quick Review on CS

• Filter Based CS

• CS Based Channel Estimation

• CS Based UWB System

• Simulation Results

• Issues and Conclusions

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

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

y n a n p n

CS Based UWB System

• Proposed system

– Channel estimation– Signal reconstruction

CS Based Channel Estimation

• Goal:– Estimate the 5 GHz bandwidth channel impulse

response at 500 Msps rate

– Use the result in reconstruction matrix

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SNR = 10 dB, Channel bandwidth = 5 GHzPN duration = 1024 ns, Sampling rate = 500 Msps

Time, ns

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plit

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Time, ns

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Estimated Channel

Real ChannelEstimated Channel

Real Channel

CS Based Channel Estimation

• Architecture

CS Based Channel Estimation

• Condition– Channel is sparse in time domain

• Yes!

– PN matrix satisfied RIP• Yes!

– Sufficient measurements– SNR

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

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Time, ns

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Illustration of efficient samples

Continuous signal

Down sampled signal

InefficientEfficient

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)

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Time, ns

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Indoor channel, 5 GHz bandwidth, from rectangular windowed VNA data

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0.450-path channel impulse response after deconvolution

Time, ns

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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

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SNR = 10 dB, Channel bandwidth = 5 GHzPN duration = 1024 ns, Sampling rate = 500 Msps

Time, ns

Am

plit

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Time, ns

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Estimated Channel

Real Channel

Estimated Channel

Real Channel

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

CS Based UWB System

• Goal:– Reconstruct transmitted sequence with sub-GHz

sampling rate

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

……

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

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

y n '

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

Simulation Results

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SNR per Sample, dB

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Symbol Error Rate VS SNR, RX sampling rate = 500 Msps, 250 Msps and 125 Msps

500 Msps, Perfect Channel Estimation500 Msps, Imperfect Channel Estimation

250 Msps, Perfect Channel Estimation

250 Msps, Imperfect Channel Estimation

125 Msps, Perfect Channel Estimation125 Msps, Imperfect Channel Estimation

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

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

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

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.

Discussion

Thank you!