Error Exponents for Bias Detection of a Correlated Process over a MAC Fading Channel

Abstract

In this paper, we analyze a binary hypothesis testing problem using a wireless sensor network (WSN). Using Large Deviation Theory (LDT), we compute the exponents of the error probabilities for the detection of a constant under a correlated process. Each sensor transmits its local measurement trough a multiple-access (MAC) fading channel with a line-of-sight (LOS) component to the fusion center (FC) using an uncoded analog scheme. The FC decides if the constant is present or not. We examine the behavior of the error exponents as function of the correlation process and the fading LOS component. We also show that this scheme is asymptotically optimal, i.e., it achieves the centralized error exponents when the number of sensors approaches to infinity even when the fading LOS paths betweenthe sensors and the FC are not so strong and the underlaying process is correlated. In this way, neither feedback between the FC and the sensors nor cooperation between sensors is necessary to provide a sufficient statistic to the FC.