Optimization of Linearized Belief Propagation for Distributed Detection

Abstract

In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a network of distributed agents can be approximated by a linear fusion of all the local log-likelihood ratios. The proposed approach clarifies how the BP algorithm works, simplifies the statistical analysis of its behavior, and enables us to develop a performance optimization framework for the BP-based distributed inference systems. Next, we propose a blind learning-adaptation scheme to optimize the system performance when there is no information available a priori describing the statistical behavior of the wireless environment concerned. In addition, we propose a blind threshold adaptation method to guarantee a certain performance level in a BP-based distributed detection system. To clarify the points discussed, we design a novel linear-BP-based distributed spectrum sensing scheme for cognitive radio networks and illustrate the performance improvement obtained, over an existing BP-based detection method, via computer simulations.

Modeling and Mitigating Errors in Belief Propagation for Distributed Detection

“…The proposed blind adaptation modifies the parameters of the BP and the decision threshold at each node, in accordance with the error statistics and channel conditions, to mitigate the impact of errors and to enhance the detection performance. To summarize, we extend the works in [5] and [6] by the following contributions:…”

“…J kj 's are calculated as in Eq. ( 16) in [5] by processing a window of T sensing outcomes. Note that θ k in ( 14) is merged into γ k without having any impact on the rest of the analysis.…”

“…In [5], we have developed a systematic framework for analyzing the behavior of BP and optimizing its performance in a distributed detection scenario. In particular, we have shown that the decision variables built by the BP algorithm are, approximately, linear combinations of the local likelihoods in the network.…”

“…In particular, we have shown that the decision variables built by the BP algorithm are, approximately, linear combinations of the local likelihoods in the network. Consequently, we have derived in [5] closed-form relationships for the system performance metrics and formulated a distributed optimization scheme to achieve a near-optimal detection performance. Moreover, we have discussed the relationship between the BP and the max-product algorithms in [6] where we extend the proposed framework in [5] to optimize the performance of the max-product algorithm in a distributed detection scenario.…”

“…Consequently, we have derived in [5] closed-form relationships for the system performance metrics and formulated a distributed optimization scheme to achieve a near-optimal detection performance. Moreover, we have discussed the relationship between the BP and the max-product algorithms in [6] where we extend the proposed framework in [5] to optimize the performance of the max-product algorithm in a distributed detection scenario. In this paper, we further extend that framework to gain insight into the impact of computation and communication errors, in a BP iteration, on the resulting decision variables and to effectively mitigate that impact.…”