Compressive Data Gathering for Large-Scale Wireless Sensor Networks

Chong Luo Feng WuShanghai Jiao Tong University Microsoft Research Asia

Jun Sun Chang Wen ChenShanghai Jiao Tong University SUNY at Buffalo, NY 14260-

2000, USA

MobiCom 2009, Sep. 20-25

Outline

• Compression techniques on sensor networks– Compression with explicit communication– Distributed source coding– Compressive Sensing(sampling)

• Proposed Compressive Data Gathering– Data gathering diagram– Compressive sensing

• Simulation• Conclusions

Compression Techniques on Sensor Networks

• Compression with explicit communication• Cristescu et al. (2006) proposed a joint entropy coding

approach

1 2X1

H(X2|X1)

X1, H(X2|X1)

EZLMS Link: http://www.powercam.cc/slide/3023

Distributed Wavelet Transform

• Assumptions: piecewise smooth data – Ciancio et al. (2006) and A’cimovi’c et al. (2005)

(1) Even nodes first broadcast their readings. (2) Upon receiving the readings from both sides, odd nodes compute the high pass coefficients

h(·)(3) Then, odd nodes transmit h(·) back and even nodes compute the low pass coefficients l(·)(4) After the transform, nodes transmit significant coefficients to the sink

Distributed Source Coding-- Slepian-Wolf coding

D. Slepian and J. K. Wolf (1973)

EZLMS Link: http://www.powercam.cc/slide/3189

Compressive Sensing

y XMeasurement matrix

Compressive Sensing

y transform basis

scoefficient

X

Compressive Sensing

y

transform basis

scoefficient

G. Quer et al. (2009)

x11 x12 x13 x14

x21 x22 x23 x24

… … .. ..… .. … …

X

Example of the considered multi-hop topology.

Irregular network setting [4](1) Graph wavelet(2) Diffusion wavelet

Network Scenario Setting

Measurement matrix Built on routing path

Routing path mm xy 111

random }1,1{1

mmm xyy 2212

mmm xyy 3323

mmm xyy 4434

…………………………………………

……………… ……………………

mlm

y ,........ ml321

nx

xxx

.3

2

1

Proposed Compressive Data Gathering-- Measurement Matrix

Proposed Compressive Data Gathering-- Measurement Matrix

Goal:(1) Reduce global

communication cost.

(2) Load balance

Proposed Compressive Data Gathering-- Measurement Matrix

44, di 55, di

66, di

6

3,

jjji d

Proposed Compressive Data Gathering-- Data Recovery

• Conditions:(1)

(2) Incoherence: correlation between and

kk MnkCM4 ~ 3 :Suggestion

log),(2

matrixt measuremen Random :Suggestion

|,|max),(,1 jiNji

N

Reconstruction: optimization

syss

osubject t ||||min 1

Linear programmingOrthogonal matching pursuit (OMP)

Recover Data with Abnormal Readings

Proposed SolutionNormal reading

Deviated values of abnormal readings

New basis

NS-2 Simulation

• Topology:– Chain vs. Grid

• Data sparsity is assumed to be 5%.– For example, when N = 1000, K = 50, and M = 200

Capacity-- Chain topology

• N=1000• The distance between

adjacent nodes are 10 meters

Capacity-- Grid topology

• N=1089• 33 rows x 33 cols• The distance between adjacent

nodes is 14 meters

Packet Loss Rate-- Grid topology

Experiments on Real Data Sets-- CTD Data from Ocean

K=40M=100

Experiments on Real Data Sets-- CTD Data from Ocean

Experiments on Real Data Sets-- Temperature in Data Center

Experiments on Real Data Sets-- Temperature in Data Center

Low spatial correlation : not sparse

Experiments on Real Data Sets-- Temperature in Data Center

• Sort di in ascending order according to their sensing values at a particular moment t0

– The resulting readings are piece-wise smooth.

– server temperatures do not change violently,• sensor readings collected

within a relatively short time period can also be regard as piece-wise smooth if organized in the same order.

• N=498

Experiments on Real Data Sets-- Temperature in Data Center

Conclusions

• This paper proposed a novel scheme for energy efficient data gathering in large scale wireless sensor networks based on compressive sampling theory.– Convert compress-then-transmit process into

compress-with-transmission process• We have shown that CDG can achieve a

capacity gain of N/M over baseline transmission.