Distributed estimation in sensor networks over binary symmetric channels

We consider distributed parameter estimation using quantized observations in wireless sensor networks (WSN) over binary symmetric channels. Due to stringent bandwidth and power constraints, each sensor quantizes its local observation into one bit of information. Previously, adaptive quantization (AQ) schemes were developed under the assumption of perfect communication links in the WSN. In this paper we propose an adaptive quantization scheme for a WSN with channel links modeled as binary symmetric channels. A Hidden Markov Model (HMM) framework is introduced to model the adaptive quantization scheme. We propose an expectation maximization based estimator at the fusion center to form an estimate from the quantized bits. Approximate closed form solutions for the Cramer-Rao lower bounds are developed for the proposed estimation problem. We analyze the performance of the proposed quantization scheme and estimator under different criteria. Numerical simulation results are shown for the proposed adaptive quantization and estimation scheme under different scenarios. The simulation results indicate that the proposed quantization scheme and estimator are robust and can provide superior performance for crossover rates up to 10%.