Network-welfare maximization for Cognitive Radio Networks via optimal matching

In this paper, we consider the network-welfare optimization for a Cognitive Radio Network (CRN) consisting of multiple Primary-Users (PUs) and multiple Secondary-Users (SUs). For each pair of PU and SU, the interaction between them is modeled as a Stackelberg game where the PU shares its licensed channel with the SU by charging the interference, and the SU is allowed to access the PU channel by paying the interference fee. The objective of the CRN thus is to maximize the network-welfare of all PUs and SUs by forming optimal pairs among them, which can be considered as a Maximum Weight Matching (MWM) problem on a bipartite graph. We first propose an efficient algorithm to quantify the optimal social welfare associated with each pair of PU and SU. Then, by exploiting the special structure of the MWM problem, we propose two algorithms, namely, a modified Belief Propagation (BP) algorithm and a heuristic algorithm based on Simulated Annealing (SA) to determine the optimal matching.