Distributed Coalition Formation and Bandwidth Allocation in Ad Hoc Cognitive Radio Networks

In this paper we analyze the problem of distributed coalition formation (CF) and bandwidth allocation in ad hoc cognitive radio networks. We develop a CF algorithm to self organize distributed secondary links into disjoint coalitions and apply the concept of frequency reuse over different coalitions, such that the members of each coalition will transmit over orthogonal sub-bands with the available spectrum being optimally allocated among them. We formulate the problem as a CF game in partition form with non-transferable utility and propose a distributed algorithm through which players may join/leave a coalition based on their individual preferences. We study the convergence properties of the proposed CF rule and present means to guarantee Nash-stability. In addition, we also describe graceful exit procedures if a CF process leads to oscillations. We show that a grand/singleton structure will emerge in the network at very low/high SNR and analytically derive the lower bound on the probability that a general network partition, other than grand/singleton structure, is stable. Performance analysis shows the effectiveness of the proposed coalition formation algorithm with optimal bandwidth allocation over a wide SNR range and indicates a substantial gain in terms of average payoff per link over existing coalition formation techniques.