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

TL;DR

This paper enhances belief propagation for distributed detection by approximating it with linear data fusion, enabling performance optimization and adaptive thresholding in wireless networks, demonstrated through spectrum sensing in cognitive radio.

Contribution

It introduces a linear fusion approximation of BP decision variables, facilitating analysis and optimization of distributed inference systems.

Findings

Linear fusion approximates BP decision variables effectively.

Performance optimization schemes improve detection accuracy.

Adaptive thresholding guarantees specified detection performance.

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.