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Decentralized detection of stochastic signals in power-constrained sensor networks

Decentralized detection of a stochastic signal in a total average power constrained wireless sensor network is considered. Assuming amplify-and-relay local processing, the fusion performance is derived in closed-form under both Bayesian and Neyman-Pearson optimality, in the case of conditionally independent signal samples. An important observation is that the average fusion probability of error does not improve monotonically with the number of sensors unlike in the case of deterministic signal detection reported in Chamberland, J et al., (2004). In particular, there is an optimal number of sensors that minimizes the probability of error, which depends on both observation signal-to-noise ratio (SNR) as well channel SNR.