Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 60, Issue 7, Pages 3896-3901Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2012.2191777
Keywords
Distributed estimation; dithering; minimax CRLB; probabilistic quantization
Categories
Funding
- National Science Foundation [0925854]
- Air Force Office of Scientific Research [FA-9550-10-C-0179]
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [0925854] Funding Source: National Science Foundation
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We consider the design of identical one-bit probabilistic quantizers for distributed estimation in sensor networks. We assume the parameter-range to be finite and known and use the maximum Cramer-Rao lower bound (CRB) over the parameter-range as our performance metric. We restrict our theoretical analysis to the class of antisymmetric quantizers and determine a set of conditions for which the probabilistic quantizer function is greatly simplified. We identify a broad class of noise distributions, which includes Gaussian noise in the low-SNR regime, for which the often used threshold-quantizer is found to be minimax-optimal. Aided with theoretical results, we formulate an optimization problem to obtain the optimum minimax-CRB quantizer. For a wide range of noise distributions, we demonstrate the superior performance of the new quantizer-particularly in the moderate to high-SNR regime.
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