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In this paper, we investigate distributed inference schemes, overbinary-valued Markov random fields, which are realized by the beliefpropagation (BP) algorithm. We first show that a decision variable obtained bythe BP algorithm in a network of distributed agents can be approximated by alinear fusion of all the local log-likelihood ratios. The proposed approachclarifies how the BP algorithm works, simplifies the statistical analysis ofits behavior, and enables us to develop a performance optimization frameworkfor the BP-based distributed inference systems. Next, we propose a blindlearning-adaptation scheme to optimize the system performance when there is noinformation available a priori describing the statistical behavior of thewireless environment concerned. In addition, we propose a blind thresholdadaptation method to guarantee a certain performance level in a BP-baseddistributed detection system. To clarify the points discussed, we design anovel linear-BP-based distributed spectrum sensing scheme for cognitive radionetworks and illustrate the performance improvement obtained, over an existingBP-based detection method, via computer simulations.

Optimization of the Belief-Propagation Algorithm for Distributed Detection by Linear Data-Fusion Techniques