Error exponents for bias detection of a correlated process over a MAC fading channel

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 through a multiple-access (MAC) Rician 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 a function of the correlation process and the fading LOS component. We also show that this scheme achieves the centralized error exponents when the number of sensors approaches infinity even when the fading LOS paths between the 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 the sensors is necessary to provide a sufficient statistic to the FC.