TY - JOUR
T1 - Distributed adaptive quantization for wireless sensor networks
T2 - From delta modulation to maximum likelihood
AU - Fang, Jun
AU - Li, Hongbin
PY - 2008
Y1 - 2008
N2 - We consider distributed parameter estimation using quantized observations in wireless sensor networks (WSNs) where, due to bandwidth constraint, each sensor quantizes its local observation into one bit of information. A conventional fixed quantization (FQ) approach, which employs a fixed threshold for all sensors, incurs an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated. To address this difficulty, we propose a distributed adaptive quantization (AQ) approach, which, with sensors sequentially broadcasting their quantized data, allows each sensor to adaptively adjust its quantization threshold. Three AQ schemes are presented: 1) AQ-FS that involves distributed delta modulation (DM) with a fixed stepsize, 2) AQ-VS that employs DM with a variable stepsize, and 3) AQ-ML that adjusts the threshold through a maximum likelihood (ML) estimation process. The ML estimators associated with the three AQ schemes are developed and their corresponding Cramér-Rao bounds (CRBs) are analyzed. We show that our 1-bit AQ approach is asymptotically optimum, yielding an asymptotic CRB that is only π2 times that of the clairvoyant sample-mean estimator using unquantized observations.
AB - We consider distributed parameter estimation using quantized observations in wireless sensor networks (WSNs) where, due to bandwidth constraint, each sensor quantizes its local observation into one bit of information. A conventional fixed quantization (FQ) approach, which employs a fixed threshold for all sensors, incurs an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated. To address this difficulty, we propose a distributed adaptive quantization (AQ) approach, which, with sensors sequentially broadcasting their quantized data, allows each sensor to adaptively adjust its quantization threshold. Three AQ schemes are presented: 1) AQ-FS that involves distributed delta modulation (DM) with a fixed stepsize, 2) AQ-VS that employs DM with a variable stepsize, and 3) AQ-ML that adjusts the threshold through a maximum likelihood (ML) estimation process. The ML estimators associated with the three AQ schemes are developed and their corresponding Cramér-Rao bounds (CRBs) are analyzed. We show that our 1-bit AQ approach is asymptotically optimum, yielding an asymptotic CRB that is only π2 times that of the clairvoyant sample-mean estimator using unquantized observations.
KW - Adaptive quantization (AQ)
KW - Distributed estimation
KW - Wireless sensor networks (WSNs)
UR - http://www.scopus.com/inward/record.url?scp=54749151115&partnerID=8YFLogxK
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U2 - 10.1109/TSP.2008.928956
DO - 10.1109/TSP.2008.928956
M3 - Article
AN - SCOPUS:54749151115
SN - 1053-587X
VL - 56
SP - 5246
EP - 5257
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 10 II
ER -