Optimal Decentralized Linear Precoding for Wideband Non-Cooperative Interference Systems based on Game Theory

Abstract

In this paper we formulate the problem of finding the optimal pre- coding/multiplexing strategy in an infrastructureless multiuser scenario as a noncooperative game. We first consider the theoretical problem of maximizing mutual information on each link, given constraints on the spectral mask and transmit power. Then, to accommodate practical implementation aspects, we focus on the competitive maximization of the transmission rate on each link, using finite order constellations, under the same constraints as above plus a constraint on the average error probability. We prove that in both cases a NE always exists and the optimal precoding/multiplexing strategy leads to a (pure strategy) diagonal transmission for all the users. Thanks to this result, we can reduce both original complicated matrix-valued games to a simpler unified vector power control game. Thus, we derive sufficient conditions for the uniqueness of the NE of such a game, that are proved to have a broader validity than conditions known in the literature for special cases of our game. Finally, we show that the Nash equilibria of the vector game can be reached using the so-called asynchronous iterative waterfilling algorithm.