Optimal Identical Binary Quantizer Design for Distributed Estimation
Abstract
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 Cram\'er-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.
Cite
@article{arxiv.1205.6907,
title = {Optimal Identical Binary Quantizer Design for Distributed Estimation},
author = {Swarnendu Kar and Hao Chen and Pramod K. Varshney},
journal= {arXiv preprint arXiv:1205.6907},
year = {2012}
}
Comments
6 pages, 3 figures, This paper has been accepted for publication in IEEE Transactions in Signal Processing