Distributed estimation in wireless sensor networks with imperfect channel estimation

In this paper, we study distributed estimation with wireless sensor networks (WSN) when channel estimation is imperfect. A robust distributed maximum likelihood (ML) estimator of the unknown parameter is proposed, which improves the performance of the traditional ML estimator with imperfect channel estimation. By maximizing the effective signal to noise ratio (SNR) at the fusion center (FC), we find that the optimal length of the training sequence is the square root of the length of the quantized observation at each node. Simulations are provided to evaluate the performance of the robust method and to validate the theoretical optimal length.