Detection and Estimation in Wireless SensorNetworks

Israfil Bahçeci

Department of Electrical EngineeringTOBB ETÜ

June 28, 2012

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Outline

Introduction

Problem Setup

Estimation

Detection

Conclusions

References

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Outline

Introduction

Problem Setup

Estimation

Detection

Conclusions

References

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Wireless Sensor Networks

I Many nodes, preferablycheap

I Power/energy/bandwidth limitedI Wireless medium

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Functionality and Utility

I DetectionI False alarm and

detection probabilityI Estimation

I Estimation error

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Typical Problems

I Deployment optimizationI Node densityI Node location

I Wireless networking and communicationsI Achievable rate/distortion regionsI Source/channel coding problemsI Quantization/coding/analog transmissionI Power control and interference management, energy efficiencyI Centralized vs. distributedI Multiple access vs. Orthogonal accessI Single vs. multiple fusion centerI Path selection and shortest path algorithms

I Self-organizationI Node failure & self-healing

I Information securityI Access to informationI Node intrusion, e.g. Byzantine attack

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Typical Network Configurations

Parallel network

Serial network

Hierarchical network

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Outline

Introduction

Problem Setup

Estimation

Detection

Conclusions

References

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System Model

I Let n0, n1, . . . , nN−1 denote the sensor nodesI Let ui is the observed samples at node ni

I Let hi,j is the channel gain from nj to niI hi,j include the effect of antenna gains and long term channel losses

I For transmission from nm to nk, received signal:

rk[t] = hk,msm[t] +N−1∑

i=0,i 6=m

Ii[t]hk,isi[t] + wk[t]

I Transmitted signal at nm: sm[t] = g(um, rm)

I Bandwidth and energy constraints

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Metrics

I DetectionI Detection probability (correct decision)I False alarm/miss probability (erroneous decision)

I EstimationI Mean-square error, E(|θ − θ|2)

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Observation Statistics

I Independent observationsI Correlated observations

I Dense deployment

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Outline

Introduction

Problem Setup

Estimation

Detection

Conclusions

References

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Estimation Under Bandwidth Constraints I

I Universal estimation [1]I Each sensor has 1 sample from a noisy observation and can send

1 bit (0 or 1 per local estimateI ui = θ + ni, θ ∼ [−V,V] and ni ∼ fU(u), V = UI if fU(u) ≥ µ is known, N ≥ 1

4ε2µ2

I if fU(u) is unknown, N ≥ U2

4ε2 , e.g., binary messaging requires only atmost 4 times more sensor nodes

I Sample mean estimation [2, 3]I ui = θ + ni, ni ∼ N(0, σ2)I Maximum likelihood estimator available for both identical

thresholds, non-identical thresholdsI Fixed step size difference, τk+1 − τk > σ equal to noise variance is

close to optimalityI Parameter with a small dynamic range: 1 bit quantization is

sufficientI Relaxing 1 bit constraint, a step size equal to noise variance is

good for practical cases

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Estimation Under Bandwidth Constraints II

I Inhomogeneous environment [4]I Local information compressed to a number of bits proportional to

logarithm of its local observation SNRI Fusion center only needs the received quantized messages and

use the length of the message in final estimationI No need for noise pdf at the FC, each sensor needs its local SNRI The MSE of this estimator achieves 25/8 times the MSE of BLUE

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Compression and Estimation

I The above bandwidth constrained schemes compress the signalsto a few bits

I An overview of several cases of distributed estimation [5]I Same order of MSE performance achieved by a centralized

estimation is doable under various bandwidth constrainedschemes under different knowledge levels for the observationnoise statistics

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Power Control for Distributed Estimation

I Estimation with digital modulation [6]I Joint design of universal estimator and uncoded QAM modulationI Optimal quantization and transmit power levels to minimize MSEI Bah channel or bad observation⇒ lower quantization level, or

inactiveI Estimation with analog modulation [7]

I Correlated data observation, e.g., a random fieldI Non-linear measurement issues also consideredI Linear MMSE + numerical power control optimization

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Source-Channel Coding for Distributed Estimation

I Wyner-Ziv source coding based strategies for a general treenetwork [8]

I Achievable region for a generic one-step communication withside-information

I Application of one-step solution to a tree network: A sensor usesits own observations, all messages it received + statisticalinformation for the observation made by decoder and messagesreceived by the decoder

I Rate-distortion bounds for the Quadratic Gaussian case isdetermined

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CEO problem and distributed estimation

I CEO problem: Estimation with a parallel configurationI Admissible sum-rate distortion regions [9]I Local observations separately encoded and transmitted to a CEOI Closed form solution to rate allocation for the Quadratic Gaussian

CEO problemI Rate-constrained estimation for CEO problem [10]

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Distributed Quantization and Estimation

I Adaptive quantization [11]I Bandwidth constraint, so only one bit quantizationI Dynamic adjustment of quantization threshold based on feedback

from other sensor nodesI Distributed Delta modulation

I Quantizer precision for large networks [12]I xi = θ + ni for all nodesI Identical, noncooperative uniform scalar quantization at each node

achieves same asymptotics as optimal schemeI If observation SNR is high, few nodes with fine quantization is betterI There exists an optimal number of sensors for this quantization, not

all sensors needed

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Cooperative Communications

I Cooperative diversity for distributed estimation [13]I Several cooperative relaying schemes exists that achieve spatial

diversityI Multiple access channel, r[n] =

∑Ni=1 xi[n] + w[n]

I Amplify-forward or decode-forward based distributed estimationachieve same asymptotic performance

I Collection of correlated data: spatial sampling (one sensor out of agroup of correlated sensor nodes)

I Selective transmission is good for loose distortion, but needsimproved cooperation for strict distortion constraint

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Linear Distributed Estimation

I Parallel configuration with all linear processing for a coherentGaussian network with MAC [14]

I Linear observation modelI Linear encoding at the transmitter: MAC allows for a closed-form

expression for encodingI Linear MMSE at the fusion centerI Optimal power allocation allows distributed implementation

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Estimation Diversity and Energy Efficiency

I Analog transmission of xi = θi + ni, to a fusion center [15, 16]I Fixed data vs. correlated dataI BLUE vs. MMSEI Estimation outage and estimation diversity (slope of outage

probability)I Full diversity can be achieved on the number of sensor nodesI Power control for fixed data vs. correlated data

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Distributed Kalman Filtering

I Distributed estimation of a dynamically varying signal with a linearobservation model [17]

I Need to exchange messages between neighbor nodesI 2-step estimation

I Step 1: Kalman-like estimation based only on local observationsI Step 2: Information fusion via a consensus matrix after receiving

messages from neighborsI Design problems: Optimal Kalman gain, and consensus matrix,

based on the amount of message exchange

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Distributed Data Gathering with a Dense SensorNetwork

I Estimation of a observable random field at a collector node [18]I Transport capacity of many-to-one channel ∼ O(logN) can be

achieved by an amplify-forward scheme, even under subject tototal power constraint

I Unbounded transport capacity for many-to-one channel with onlyfinite total average power

I Gaussian spatially bandlimited processes are observable (e.g., itcan be estimated at a collector node with a finite MSE for a certainbandwidth and total average power level)

I This is true even for lossy source encoder composed of asingle-dimensional quantization followed by a Slepian-Wolf encoder

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Outline

Introduction

Problem Setup

Estimation

Detection

Conclusions

References

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Distributed Detection with Multiple Sensors

I An overview on various distributed detection strategies [19]I Error-free transmission of local decisions to a fusion centerI Independent local observationsI Likelihood ratio tests, for both Neyman-Pearson and Bayes’

formulation, are optimal at both local sensor nodes and fusioncenters

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Bandwidth/Power Constrained Distributed Detection I

I Binary detection over a parallel network with MAC [20]I Specifying the power, bandwidth, error tolerance fixed the

information rates of sensors for this MACI Minimization of Chernoff exponent for the decision at the FCI Asymptotically, for Gaussian and exponential observation, having R

identical binary sensors, e.g., 1 bit/sensor for a rate-R MACchannel, is optimal

I Not true for some other statistical distributionsI Having more sensors is better than having detailed information

from each nodeI Asymptotic detection for power constrained network [21]

I Joint power constraint + AWGN at sensor-to-fusion center channelI Having identical sensor nodes, e.g., each node using the same

scheme, is asymptotically optimalI Optimal transmission power levels for binary nodes observing

Gaussian source

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Energy Efficient Distributed Detection

I Energy and bandwidth constraints taken into account [22]I Detection performance subject to system cost due to transmission

power and measurement errorsI Randomization over the choice of measurements and when to

send/no sendI Joint optimization over sensor nodes allows the optimization per

node

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Parallel and Serial Detection over Fading Channel

I The communications are all Rayleigh fading [23, 24]I Binary detection and binary antipodal modulation for decision

transmissionI Channel state information need to be obtained at the receiver

nodeI Suitable likelihood ratios at all nodes are optimal with known CSI

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Optimal Distributed Detection over Noisy Channel

I Non-ideal channels to fusion center [25, 26]I Detection at fusion center needs to consider the CSI in case of

fadingI LRTs are shown to be optimal in the sense that they minimize

error probability at the fusion center

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Type-Based Distributed Detection

I Each local sensor generates a histogram, or type of itsobservation over time and forwards the type to fusion center[27, 28]

I MAC where fusion center receives a superposition of transmittedlocal signals attain a better detection performance relative toorthogonal MAC

I Histogram fusion at the fusion center is asymptotically optimal andobservation statistics need to be known only at the fusion cener

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Outline

Introduction

Problem Setup

Estimation

Detection

Conclusions

References

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Remarks

I Diverse applications and many research topicsI Many open problems

I Joint design of local/global processing and network operation,routing

I Cooperative sensing/routingI Network life time maximization via data aggregation, joint

source/channel coding, and power controlI New paradigms for detection estimation under constraints of WSNsI Detection/estimation at multiple fusion center, distributed

congestion control

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Outline

Introduction

Problem Setup

Estimation

Detection

Conclusions

References

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References I

[1] Zhi-Quan Luo,“Universal decentralized estimation in a bandwidth constrained sensor network,”Information Theory, IEEE Transactions on, vol. 51, no. 6, pp. 2210 –2219, june 2005.

[2] A. Ribeiro and G.B. Giannakis,“Bandwidth-constrained distributed estimation for wireless sensor networks-part i: Gaussian case,”Signal Processing, IEEE Transactions on, vol. 54, no. 3, pp. 1131 – 1143, march 2006.

[3] A. Ribeiro and G.B. Giannakis,“Bandwidth-constrained distributed estimation for wireless sensor networks-part ii: unknown probability density function,”Signal Processing, IEEE Transactions on, vol. 54, no. 7, pp. 2784 –2796, july 2006.

[4] J.-J. Xiao and Z.-Q. Luo,“Decentralized estimation in an inhomogeneous sensing environment,”Information Theory, IEEE Transactions on, vol. 51, no. 10, pp. 3564 –3575, oct. 2005.

[5] Jin-Jun Xiao, A. Ribeiro, Zhi-Quan Luo, and G.B. Giannakis,“Distributed compression-estimation using wireless sensor networks,”Signal Processing Magazine, IEEE, vol. 23, no. 4, pp. 27 – 41, july 2006.

[6] Jin-Jun Xiao, Shuguang Cui, Zhi-Quan Luo, and A.J. Goldsmith,“Power scheduling of universal decentralized estimation in sensor networks,”Signal Processing, IEEE Transactions on, vol. 54, no. 2, pp. 413 – 422, feb. 2006.

[7] Jun Fang and Hongbin Li,“Power constrained distributed estimation with correlated sensor data,”Signal Processing, IEEE Transactions on, vol. 57, no. 8, pp. 3292 –3297, aug. 2009.

[8] S.C. Draper and G.W. Wornell,“Side information aware coding strategies for sensor networks,”Selected Areas in Communications, IEEE Journal on, vol. 22, no. 6, pp. 966 – 976, aug. 2004.

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References II

[9] Jun Chen, Xin Zhang, T. Berger, and S.B. Wicker,“An upper bound on the sum-rate distortion function and its corresponding rate allocation schemes for the ceo problem,”Selected Areas in Communications, IEEE Journal on, vol. 22, no. 6, pp. 977 – 987, aug. 2004.

[10] P. Ishwar, R. Puri, K. Ramchandran, and S.S. Pradhan,“On rate-constrained distributed estimation in unreliable sensor networks,”Selected Areas in Communications, IEEE Journal on, vol. 23, no. 4, pp. 765 – 775, april 2005.

[11] Hongbin Li and Jun Fang,“Distributed adaptive quantization and estimation for wireless sensor networks,”Signal Processing Letters, IEEE, vol. 14, no. 10, pp. 669 –672, oct. 2007.

[12] S. Marano, V. Matta, and P. Willett,“Quantizer precision for distributed estimation in a large sensor network,”Signal Processing, IEEE Transactions on, vol. 54, no. 10, pp. 4073 –4078, oct. 2006.

[13] Y-W. Hong, W.-J. Huang, F-H. Chiu, and C.-C.J. Kuo,“Cooperative communications in resource-constrained wireless networks,”Signal Processing Magazine, IEEE, vol. 24, no. 3, pp. 47 –57, may 2007.

[14] Jin-Jun Xiao, Shuguang Cui, Zhi-Quan Luo, and A.J. Goldsmith,“Linear coherent decentralized estimation,”Signal Processing, IEEE Transactions on, vol. 56, no. 2, pp. 757 –770, feb. 2008.

[15] Shuguang Cui, Jin-Jun Xiao, A.J. Goldsmith, Zhi-Quan Luo, and H.V. Poor,“Estimation diversity and energy efficiency in distributed sensing,”Signal Processing, IEEE Transactions on, vol. 55, no. 9, pp. 4683 –4695, sept. 2007.

[16] I. Bahceci and A. Khandani,“Linear estimation of correlated data in wireless sensor networks with optimum power allocation and analog modulation,”Communications, IEEE Transactions on, vol. 56, no. 7, pp. 1146 –1156, july 2008.

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References III

[17] R. Carli, A. Chiuso, L. Schenato, and S. Zampieri,“Distributed kalman filtering based on consensus strategies,”Selected Areas in Communications, IEEE Journal on, vol. 26, no. 4, pp. 622 –633, may 2008.

[18] H. El Gamal,“On the scaling laws of dense wireless sensor networks: the data gathering channel,”Information Theory, IEEE Transactions on, vol. 51, no. 3, pp. 1229 –1234, march 2005.

[19] R. Viswanathan and P.K. Varshney,“Distributed detection with multiple sensors i. fundamentals,”Proceedings of the IEEE, vol. 85, no. 1, pp. 54 –63, jan 1997.

[20] J.-F. Chamberland and V.V. Veeravalli,“Decentralized detection in sensor networks,”Signal Processing, IEEE Transactions on, vol. 51, no. 2, pp. 407 – 416, feb 2003.

[21] J.-F. Chamberland and V.V. Veeravalli,“Asymptotic results for decentralized detection in power constrained wireless sensor networks,”Selected Areas in Communications, IEEE Journal on, vol. 22, no. 6, pp. 1007 – 1015, aug. 2004.

[22] S. Appadwedula, V.V. Veeravalli, and D.L. Jones,“Energy-efficient detection in sensor networks,”Selected Areas in Communications, IEEE Journal on, vol. 23, no. 4, pp. 693 – 702, april 2005.

[23] I. Bahceci, G. Al-Regib, and Y. Altunbasak,“Parallel distributed detection for wireless sensor networks: performance analysis and design,”in Global Telecommunications Conference, 2005. GLOBECOM ’05. IEEE, dec. 2005, vol. 4, pp. 5 pp. –2424.

[24] I. Bahceci, G. Al-Regib, and Y. Altunbasak,“Serial distributed detection for wireless sensor networks,”in Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on, sept. 2005, pp. 830 –834.

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References IV

[25] B. Chen and P.K. Willett,“On the optimality of the likelihood-ratio test for local sensor decision rules in the presence of nonideal channels,”Information Theory, IEEE Transactions on, vol. 51, no. 2, pp. 693 –699, feb. 2005.

[26] Biao Chen, Lang Tong, and P.K. Varshney,“Channel-aware distributed detection in wireless sensor networks,”Signal Processing Magazine, IEEE, vol. 23, no. 4, pp. 16 – 26, july 2006.

[27] Ke Liu and A.M. Sayeed,“Type-based decentralized detection in wireless sensor networks,”Signal Processing, IEEE Transactions on, vol. 55, no. 5, pp. 1899 –1910, may 2007.

[28] Gokhan Mergen, Vidyut Naware, and Lang Tong,“Asymptotic detection performance of type-based multiple access over multiaccess fading channels,”Signal Processing, IEEE Transactions on, vol. 55, no. 3, pp. 1081 –1092, march 2007.

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