Statistical mechanics approach for the detection of multiple wireless sources via a sensor network

In this paper, we apply statistical mechanics methods to the problem of detection of multiple primary wireless sources by a wireless sensor network. We assume that the location of the primary sources is known, but that the channel connecting them to the sensors is random. The sensor network tries to detect which sources are emitting by employing a belief propagation algorithm. We use the Replica approach to estimate the probability of error and we provide analytical expressions and numerical results for the case of random connectivity between sources and sensor nodes, for the fading channel model. This method can provide a simple way to calculate performance metrics for the detection problem.