Power scheduling between channel and parameter estimation for homogeneous sensor networks

This paper investigates the effect of channel estimation error (CEE) on the performance of distributed estimation of an unknown parameter in wireless sensor networks (WSNs). Firstly, considering the maximum likelihood estimator (MLE) of the unknown parameter has a high complexity preventing its practical implementation, a suboptimal ML estimator is derived as a low complexity alternative. Considering training pilots are used to estimate the unknown channel, the power scheduling between the training pilots and sensor observation in the homogeneous sensing environment is derived. Since the final average mean square error (MSE) depends on the unknown parameter, a lower bound of the MSE is minimized to compensate the CEE. A closed-form power scheduling policy is presented, which shows that more than 50% power should be allocated to sensor observation transmission. Simulation results demonstrate that the presented power scheduling policy has better performance than the equal power scheduling policy, and even performs close to the optimal power scheduling, which is derived based on the knowledge of the unknown parameter.