Decentralized detection in wireless sensor networks with channel fading statistics

Existing channel aware signal processing design for decentralized detection in wireless sensor networks typically assumes the clairvoyant case, i.e., global information regarding the transmission channels is known at the design stage. In this paper, we consider the distributed detection problem where only the channel fading statistics, instead of the instant channel state information (CSI), is available to the designer. We investigate the design of local decision rules for the following two cases: 1. Fusion center has the instant CSI; 2. Fusion center does not have the instant CSI. We show that, for both cases, the optimal local decision rules that minimize the error probability at the fusion center amount to a likelihood-ratio test (LRT), as in the previous work with known CSI. The proposed approach enables distributed design for a decentralized detection problem.