Compressive Sampling for Energy Efficient Event Detection

Transcription

1 Compressive Sampling for Energy Efficient Event Detection Zainul Charbiwala, Younghun Kim, Sadaf Zahedi, Jonathan Friedman, and Mani B. Srivastava Physical Signal Sampling Processing Communication Detection

2 Event Detection in Wireless Sensor Networks i Rij j 2

3 Event Detection in Wireless Sensor Networks i Rij j When noise is non-gaussian: 2

4 Event Detection in Wireless Sensor Networks i Rij j When noise is non-gaussian: Need to detect some unique feature of the signal 2

5 Event Detection in Wireless Sensor Networks i Rij j When noise is non-gaussian: Need to detect some unique feature of the signal Computing features locally is expensive, so is transmitting raw data 2

6 Event Detection in Wireless Sensor Networks i Rij j When noise is non-gaussian: Need to detect some unique feature of the signal Computing features locally is expensive, so is transmitting raw data Feature computation = compression in the feature space 2

7 Compressive Sampling Physical Signal Sampling Compression Communication Detection 3

8 Compressive Sampling Physical Signal Sampling Compression Communication Detection Physical Signal Compressive Sampling Communication Decoding Detection Shifts computation to fusion center 3

9 Compressive Sampling Physical Signal x n Sampling z = I n x Time domain samples Physical Signal x n Compressive Sampling z = Φx k x n k < n Incoherent domain samples 4

10 Compressive Sampling Physical Signal Sampling Compression Compressed domain samples x n z = I n x y = Ψz n x n Physical Signal x n Compressive Sampling z = Φx k x n k < n Decoding y = argmin y y 1 s.t. z = ΦΨ 1 y Compressed domain samples 5

11 Compressive Sampling Physical Signal Sampling Compression Compressed domain samples x n z = I n x y = Ψz n x n How do we generate Φ and compute incoherent samples? Physical Signal x n Compressive Sampling z = Φx k x n k < n Decoding y = argmin y y 1 s.t. z = ΦΨ 1 y Compressed domain samples 5

12 Taking Incoherent Projections Gaussian: independent realizations of x N (0, 1 n ) z = Φ 6

13 Taking Incoherent Projections Gaussian: independent realizations of x N (0, 1 n ) z = Φ Needs a priori Nyquist sampling and storage for x and Φ Needs kn 2 FPU multiplications, k(n-1) additions and kn 2 memory accesses 6

14 Taking Incoherent Projections Realizations of equiprobable Bernoulli RV x +1 n, 1 n z = Φ 7

15 Taking Incoherent Projections Realizations of equiprobable Bernoulli RV x +1 n, 1 n z = Φ Needs a priori Nyquist sampling and storage for x and Φ Needs k(n-1) additions and kn 2 memory accesses but no multiplications 7

16 Taking Incoherent Projections Uniform Random Sampling x z = Φ 8

17 Taking Incoherent Projections Uniform Random Sampling x z = Φ Needs a priori Nyquist sampling & storage for x but Φ can be generated on-the-fly Needs k memory accesses but no multiplications or additions Need higher k because matrix is sparse 8

18 Taking Incoherent Projections Causal Uniform Random Sampling (sorted Φ from URS) z = Φ x 9

19 Taking Incoherent Projections Causal Uniform Random Sampling (sorted Φ from URS) z = Φ x Need to generate, sort and store Φ (but no a priori sampling or storage for x) Needs k memory accesses but no multiplications or additions May violate ADC hold time 9

20 Causal Uniform Random Sampling on-the-fly Use an additive random process t 0 = 0 t i+1 = t i + τ i τ i N (µ,r 2 µ 2 ) 10

21 Causal Uniform Random Sampling on-the-fly Use an additive random process t 0 = 0 t i+1 = t i + τ i τ i N (µ,r 2 µ 2 ) 10

22 Causal Uniform Random Sampling on-the-fly Use an additive random process t 0 = 0 t i+1 = t i + τ i τ i N (µ,r 2 µ 2 ) Need to truncate the negative tail of Gaussian PDF to ensure causality and feasibility 10

23 Causal Uniform Random Sampling on-the-fly Use an additive random process x z = Φ 11

24 Causal Uniform Random Sampling on-the-fly Use an additive random process x z = Φ Can generate Φ on-the-fly and do not need to sample or store x a priori Needs k memory accesses but no multiplications or additions 11

25 Modifying CS for Detection 12

26 Modifying CS for Detection CS is geared toward sparse signal reconstruction What if we wanted to detect a signal feature instead? 12

27 Modifying CS for Detection CS is geared toward sparse signal reconstruction What if we wanted to detect a signal feature instead? y = argmin y y 1 y = arg min y W y 1 s.t. z = ΦΨ 1 y s.t. z = ΦΨ 1 y Proposed solution: Weighted Basis Pursuit Intuitive idea: Reduce penalty on features of interest 12

28 Example: Detecting 450Hz Tone (a) FFT of original 450Hz tone at!10db SNR (b) BP recovery with 300Hz sampling FFT magnitude FFT magnitude (c) BP recovery with 30Hz sampling Frequency (Hz) (d) Weighted BP recovery with 30Hz sampling Frequency (Hz) 1.4: Frequency (FFT) coefficients for the CS reconstruction of a 450Hz tone at -10dB ifferent sampling rates and recovery strategies. terference prone environment, can be considerably lower if full CS recovery is not req 13

29 Evaluation Process Generate Tone+Noise Sensing Mote Base Station Collect Samples x + η z = Φx + η Simulate Random Projections Weighted Basis Pursuit ŷ Tone Detection H Acoustic Tone Detection 14

30 Per-Module Energy Consumption 23456(789: %! $! #! "! ;<= >?) 001 ;D<<A<E(1A85(78F:! "!!! C+! +!! #+!! "!&'( )* "!&'( )* #!&'( )* #!&'( )* $!&'( )* $!&'( )* #+!&' )* #+!&' )* "!#%&',-.* ;<= >?) 001 "!#%&',-.* "!#%&',*/001 "!#%&',*/001 FFT computation higher than transmission cost Highest consumer in CS is the random number generator 15

31 Detection Performance - Simulation !10dB SNR 0dB SNR 10dB SNR IRBP BP WBP P e Sampling Rate (Hz) Sampling Rate (Hz) Sampling Rate (Hz) Detection near perfect above 0dB with 30Hz sampling rate Improvement in performance due to weighting at high SNR 16

32 Detection Performance - Experiments !10dB SNR 0dB SNR 10dB SNR IRBP BP WBP P e Sampling Rate (Hz) Sampling Rate (Hz) Sampling Rate (Hz) Some deviation from simulation results due to ambient conditions 17

33 Detection Performance - Interference dB SINR 20dB SINR 10dB SINR BP WBP 0.3 P e Sampling Rate (Hz) Sampling Rate (Hz) Sampling Rate (Hz) Weighting does not help much against narrowband interference 18

34 Related Work Compressive Sensing [Donoho98], [Candes06], [Candes08], etc. Compressive Detection [Duarte06], [Khajehnejad09] Random Sampling [Bilinskis92], [Boyle07], [Dang08], etc 19

35 Summary Prudence at the sampling stage can deliver energy efficiency gains through the entire sensing chain Computing random projections on the fly is feasible by paying an extra cost in number of measurements Good pseudo-random number generation has nontrivial computation cost Detection performance with CS at par with Nyquist rate with a 30x rate reduction 20

36 Cost/Performance of RNGs Linear Feedback Shift Register Rnd ADC FFT Radio TX Multiplicative Linear Congruential Generator Power (mw) Mersenne-Twister Hz CS LFSR16 30Hz CS MLCG16 30Hz CS MT Hz CS MLCG Hz NyqS 1024Hz NS/FFT 21

37 Cost/Performance of RNGs Linear Feedback Shift Register Rnd ADC FFT Radio TX Multiplicative Linear Congruential Generator Power (mw) Mersenne-Twister Hz CS LFSR16 30Hz CS MLCG16 30Hz CS MT Hz CS MLCG Hz NyqS 1024Hz NS/FFT RIP constant indicates CS performance (lower is better) MLCG a little worse than MT Variation with LFSR very high 21

38 Thank You! Tech Report: Slides :

39 Geometric Interpretation of WBP (a) (b) (c) [E. Candes, M. Wakin, and S. Boyd, Enhancing sparsity by reweighted l1 minimization, Journal of Fourier Analysis and Applications, vol. 14, no. 5-6, pp , ] 23