A Distance Based Comparison of Optimal Power Allocation to Distributed Sensors in a Wireless Sensor Network

This paper addresses the optimal power allocation issue in a distributed sensor network assuming imperfect communication between the fusion center and the sensors. Noisy orthogonal channels are considered and optimal power allocation is achieved by maximizing statistical distance measures between the probability densities of the received signal under each of two hypotheses. While J-divergence measure has been considered in [1], its lack of closed form expression and complexity in calculation motivates the need to investigate other measures for mixture densities. We evaluate two statistical distance measures with closed form expressions and compare their performance with that of J-divergence for the system model introduced in [1]. Specifically, we consider elemental J-divergence and elemental L2 distance as candidate performance metrics. We illustrate that power allocation using the proposed measures is less complex relative to power allocation considering J-divergence as given in [1].