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Cognitive radio sensing through belief propagation and distributed consensus

This paper studies distributed algorithms for cooperative spectrum sensing. Formulating the problem as one of computing-on-graph, we evaluate two important classes of algorithms, belief propagation (BP) and distribute consensus (DC). We detail the exact operations of these algorithms for the spectrum sensing application, and provide rigorous algorithmic study on their properties and especially the convergence. Unlike the DC algorithm where convergence to the global optimum is guaranteed irrespective of the network topology, the BP algorithm does not usually converge. We provide a graphtransformation mechanism to evaluate the conditions for its convergence and the speed. Our analysis provides useful insight into how the two algorithms arising from drastically different theoretical grounds can serve a common purpose. Specifically, it is shown that belief propagation is an algorithm of “less is more” and hence favors sparse graphs, whereas distributed consensus is an algorithm of “the more the merrier” and hence favors dense graphs. Simulations confirm the analytical results.