N M kb 1 1% 1 kb N M N M N + M ez43-rf2 N M M N/( N) 2 3 WSN Donoho Candès [6], [7] N x x N s x N N Ψ (1) x = Ψs (1) s x s K x
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1 Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 1 1,2 1 N M N + M ez43-rf2 N M M N/( N) 1. (WSN) Sink WSN WSN WSN 1 Graduate School of Information Science and Technology, The University of Tokyo 2 School of Electrical and Computer Engineering, Georgia Institute of Technology WSN Estrin CPU 1 [1]Handy 1, bit 1 m CPU 3,, [2] [3], [4] [] c 212 Information Processing Society of Japan 1
2 N M kb 1 1% 1 kb N M N M N + M ez43-rf2 N M M N/( N) 2 3 WSN Donoho Candès [6], [7] N x x N s x N N Ψ (1) x = Ψs (1) s x s K x Ψ K N M M N Φ M d (2) M << N 2.2 d = Φx = ΦΨs (2) (2) (2) Φ Ψ d s x (2) x (3) (2) s l s ŝ x s l n s n l s minimize ŝ subject to d = ΦΨŝ (3) l NP [8] (4) l l 1 s [], [8] Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 minimize ŝ 1 subject to d = ΦΨŝ (4) c 212 Information Processing Society of Japan 2
3 Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 1 MCU 1 l 1 x M () [] M c µ 2 (Φ, Ψ) K log N () c µ(φ, Ψ) Ψ j ψ j Φ i ϕ i (6) [] (6) ϕ i, ψ j ϕ i ψ j µ(φ, Ψ) = N max ϕ i, ψ j [1, N] (6) 1 i,j N l l z 1 M = 2 N = 3 K = l 1 l 1 1 l 1 l 1 ( 1 x,y,z ) 2.3 (6) µ(φ, Ψ) = 1 Φ,Ψ Candès ±1 [] (4) (3) (Restricted Isometry Property RIP) K v (7) δ K (, 1) 1 δ K ΦΨv 2 2 v δ K (7) Candès δ 2K < 2 1 K (4) [9] ±1 3 [1], [11] 2.4 N M N = 128 M = 8, 32, 64 1kB 4kB 8kB 1 Micro Controller Unit(MCU) 1 1 1kB N M 3. WSN WSN c 212 Information Processing Society of Japan 3
4 Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 (x 1 ) x1 x 2 x1 x2. xn Time Proceeds Time Proceeds x 1 x 2 x N φ 11x 1 φ 21x 1. φ M1x 1 φ 11x 1 + φ 21x 2 φ 21x 1 + φ 22x 2. φ M1x 1 + φ M2x 2 N i=1 φ1ixi N i=1 φ2ixi. N i=1 φmixi Data sensed x 1 x 2 x N Node AP 3 WSN 2 WSN 3.1 WSN WSN Bajwa Compressive Wireless Sensing [12] Fusion Center FC D P Mahmudimanesh ID ID [13] 3.2 WSN WSN Chong Compressive Data Gathering [14] 2 Sink Sink N O(N 2 ) Chong 2 x j M M [14] M << N Nguyen NETCOMPRESS [1] 3.3 WSN 3 AP N M WSN N M N + M 4.1 Φ (8) ϕ i (j) ϕ i j 1 k N 1 i N ϕ i (mod(n, k + i 1)) = ϕ 1 (k) mod(a, b) a b 1 c 212 Information Processing Society of Japan 4
![N (7) RIP Bajwa [16] ϕ 1,1 ϕ 1,2 ϕ 1,3 ϕ 1,N ϕ 1,2 ϕ 1,3 ϕ 1,4 ϕ 1,1 Φ =.](/docs-images/88/116097995/images/5-0.jpg "... (8) Algorithm 1 Compression x[n] : Signal to sense d[m] : Sensing data Φ[N] : Measurement matrix")
![idx[m] : Random number from to N 1 i =,j = : Iteration indices if ith data x[i] sensed then while j <](/docs-images/88/116097995/images/5-1.jpg "M do d[j] x[i] Φ[mod((i+idx[j]),N)] j j + 1 end while i i + 1 end if Vol.212-HCI-1 No.2 Vol.")
![212-UBI-36 No.2 212/11/2 ϕ 1,M ϕ 1,M+1 ϕ 1,M+2 ϕ 1,M 1 4.2 N [17] 1 N M Φ M N + M 4.](/docs-images/88/116097995/images/5-2.jpg "3 1 d k d k x Φ k ϕ k = (ϕ k,1 ϕ k,2... ϕ k,n ) d k = N i= x kϕ k,i 1 i x i Φ i ϕ i = (ϕ 1,i ϕ 2,i.")
![.. ϕ N,i ) T x i ϕ i d N. 4 3V Multimeter Agilent 3441A/11A 4 ez43- RF2 ez43-rf2[18].](/docs-images/88/116097995/images/5-3.jpg "1 Texas Instruments ez43-rf2 1 1 144 N = 144 ez43-rf2 4.")
5 N (7) RIP Bajwa [16] ϕ 1,1 ϕ 1,2 ϕ 1,3 ϕ 1,N ϕ 1,2 ϕ 1,3 ϕ 1,4 ϕ 1,1 Φ =.... (8) Algorithm 1 Compression x[n] : Signal to sense d[m] : Sensing data Φ[N] : Measurement matrix idx[m] : Random number from to N 1 i =,j = : Iteration indices if ith data x[i] sensed then while j < M do d[j] x[i] Φ[mod((i+idx[j]),N)] j j + 1 end while i i + 1 end if Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 ϕ 1,M ϕ 1,M+1 ϕ 1,M+2 ϕ 1,M N [17] 1 N M Φ M N + M d k d k x Φ k ϕ k = (ϕ k,1 ϕ k,2... ϕ k,n ) d k = N i= x kϕ k,i 1 i x i Φ i ϕ i = (ϕ 1,i ϕ 2,i... ϕ N,i ) T x i ϕ i d N. 4 3V Multimeter Agilent 3441A/11A 4 ez43- RF2 ez43-rf2[18].1 Texas Instruments ez43-rf N = 144 ez43-rf2 4.2 Φ ±1 Φ = {+1, 1} Agilent 3441A/11A 4 ez43-rf2 3V M =3 3 2 ms 2 2 ms 3 ma c 212 Information Processing Society of Japan
6 情報処理学会研究報告 Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/ Compression TX M = Energy consumption [mj] 1 7 TX Compress Size of message Current consumption [ma] Time [ms] M = 1 16 ma.3 1 ms.2 M = ms 6 3 V M = 1 4. µj M M 4. M µj O(NM) N 4. N 144 µj N M.281 M N µj.3 M M M = mj 7 4. M µj mj 1 8 M 16 M < 16 1 M N 24.6% N M M N M mj M N M.98 N c 212 Information Processing Society of Japan 6
7 Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 Data logger for! soil moisture sensor 16 8 Soil moisture sensor (Decagon EC-) /23 9/24 9/2 9/26 9/27 9/28 9/29 M N 9 N M M M N/( N) M 9 9 N M 1 M N.4 1 DECAGON EC- 1 Emb [19] /9/23 : 212/9/29 11:9 9/26 9/27 1: 9/29 12: 9/ N =144 Soil moisture ADC data : 12: : 12: : 12: : 12: : 12: : 12: : 12: : 11 M (Normarized Mean Square Error, NMSE) 1 12 NMSE=1 9/23 9/28 9/29 l 1 2 NMSE=1 M 9 M N = 144 M = 12 c 212 Information Processing Society of Japan 7
8 情報処理学会研究報告 Vol.212-HCI-1 No.2 Vol.212-UBI-36 No.2 212/11/2 Soil moisture ADC data / /24 9/2 9/26 9/27 9/28 9/29 NMSE=1 " 2 NMSE=1 M Date M Calc. energy TX energy" Total energy" Saved energy" [mj] [mj] [mj] [%] Sept Sept Sept Sept Sept Sept Sept N = M 2 3% M M M = 83 19% 6. N M N + M ez43-rf2 N M M N/( N) NEDO 24 [1] Estrin, D., Sayeed, A. and Srivastava, M.: Wireless Sensor Networks, ACM Mobicom, Tutorial, Atlanta, USA (22). [2] Handy, M. J., Hasse, M. and Timmermann, D.: Low Energy Adaptive Clustering Hierarchy with Deterministic Cluster-Head Selection, 4th International Workshop on Mobile and Wireless Communications Network, pp. 9/ (22). [3] Cristescu, R., Beferull-Lozano, B., Vetterli, M. and Wattenhofer, R.: Network correlated data gathering with explicit communication: NP-completeness and algorithms, Networking, IEEE/ACM Trans. on, Vol. 14, pp (26). [4] Ciancio, A., Pattem, S., Ortega, A. and Krishnamachari, B.: Energy-efficient data representation and routing for wireless sensor networks based on a distributed wavelet compression algorithm, Proc. of the th international conf. on IPSN, Tennessee, USA, pp (26). [] Candès, E. and Wakin, M.: An introduction to compressive sampling, IEEE Signal Processing Magazine, Vol. 2, No. 2, pp (28). [6] Donoho, D.: Compressed sensing, Information Theory, IEEE Transactions on, Vol. 2, No. 4, pp (26). [7] Candès, E.: Compressive Sampling, Proceedings of the International Congress of Mathematicians, Vol. 3, pp (26). [8] Baraniuk, R.: Compressive sensing, IEEE Signal Processing Magazine, Vol. 24, No. 4, p. 118 (27). [9] Candès, E.: The restricted isometry property and its implications for compressed sensing, Comptes Rendus Mathematique, Vol. 346, No. 9-1, pp (28). [1] Baraniuk, R., Davenport, M., DeVore, R. and Wakin, M.: A Simple Proof of the Restricted Isometry Property for Random Matrices, Constructive Approximation, Vol. 28, No. 3, pp (28). [11] Rudelson, M. and Vershynin, R.: Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements, Information Sciences and Systems, 26 4th Annual Conference on, pp (26). [12] Bajwa, W., Haupt, J., Sayeed, A. and Nowak, R.: Compressive Wireless Sensing, Proc. of the th international conf. on IPSN, Tennessee, USA, pp (26). [13] Mahmudimanesh, M., Khelil, A. and Suri, N.: Reordering for Better Compressibility: Efficient Spatial Sampling in Wireless Sensor Networks, 21 IEEE International Conf. on Sensor Networks, Ubiquitous, and Trustworthy Computing, California, USA, pp. 7 (21). [14] Luo, C., Wu, F., Sun, J. and Chen, C. W.: Compressive Data Gathering for Large-Scale Wireless Sensor Networks, Proc. of the 1th Annual Int. Conf. on Mobi- Com, pp (29). [1] Nguyen, N., Jones, D. and Krishnamurthy, S.: Netcompress: Coupling network coding and compressed sensing for efficient data communication in wireless sensor networks, IEEE Workshop on Signal Processing Systems(SIPS), San Francisco, USA, pp (21). [16] Bajwa, W. U., Haupt, J. D., Raz, G. M., Wright, S. J. and Nowak, R. D.: Toeplitz-Structured Compressed Sensing Matrices, Statistical Signal Processing, IEEE/SP 14th Workshop on, pp (27). [17] Yin, W., Morgan, S., Yang, J. and Zhang, Y.: Practical Compressive Sensing with Toeplitz and Circulant Matrices (21). [18] TEXAS INSTRUMENTS: ez43- RF2 Development Tool User s Guide, [19] DECAGON: DECAGON DEVICES, c 212 Information Processing Society of Japan 8
25 11M15133 0.40 0.44 n O(n 2 ) O(n) 0.33 0.52 O(n) 0.36 0.52 O(n) 2 0.48 0.52
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