Game Theoretic Dynamic Channel Allocation for Frequency-Selective Interference Channels

We consider the problem of distributed channel allocation in large networks under the frequency-selective interference channel. Our goal is to design a utility function for a non-cooperative game such that all of its pure Nash equilibria have close to optimal global performance. Performance is measured by the weighted sum of achievable rates. Such a game formulation is very attractive as a basis for a fully distributed channel allocation since it requires no communication between users. We propose a novel technique to analyze the Nash equilibria of a random interference game, determined by the random channel gains. Our analysis is asymptotic in the number of players. First we present a natural non-cooperative game where the utility of each player is his achievable rate. It is shown that, asymptotically in the number of players and for strong enough interference, this game exhibits many bad equilibria. Then we propose a novel non-cooperative M Frequency-Selective Interference Channel Game (M-FSIG), as a slight modification of the former, where the utility of each player is artificially limited. We prove that even its worst equilibrium has asymptotically optimal weighted sum-rate for any interference regime and even for correlated channels. This is based on an order statistics analysis of the fading channels that is valid for a broad class of fading distributions (including Rayleigh, Rician, m-Nakagami and more). In order to exploit these results algorithmically we propose a modified Fictitious Play algorithm that can be implemented distributedly. We carry out simulations that show its fast convergence to the proven pure Nash equilibria. Index Terms frequency-selective fading channels, ad hoc networks, channel allocation, random games, utility design.