Performance of game theoretic power control algorithms in interference limited wireless fading channels

We consider a game-theoretic power control algorithm in interference limited fading channels, where we propose a distributed (non-cooperative) algorithm to optimize the induced fading outage probability by maximizing the certainty equivalent margin (CEM). We prove that the problem of maximizing CEM is the same (up to an upper bound) as minimizing the induced outage fading probability, and provide a distributed game theoretic power control algorithm. I. I NTRODUCTION The mathematical theory of games was introduced by John Von Neumann and Oskar Morgenstern in 1944 [9]. In the late 1970’s game theory became an important tool in the analyst’s hand whenever he or she faces a situation in which a player’s decision depends on what the other players did or will do. A core idea of game theory is the way strategic interactions between rational agents (players), generates outcomes according to the players’ preferences [5],[10]. A player in a non-cooperative game responds to the actions of other players by choosing a strategy (from his strategy space) in an attempt to optimize a target function that quantifies the quality level, i.e. its level of satisfaction. In a cellular communications system, users desire to have a high SIR (signal-to-interference ratio) at the BS (base station) coupled with the lowest possible transmit power. It is very important in such systems to have a high SIR, because this will be reflected in a low error rate, a more reliable system, and high channel capacity, which mean that users can send at higher bit rates [6],[7]. It is also important to decrease the transmit power because low power levels lead to longer battery life and helps alleviate the ever present near-far problem in CDMA systems [8]. In power control algorithms exploiting game theory, the tendency of each user is to increase his/her transmit power in response to other users’ actions, leading to a sequence of power vectors that converges to a point where no user has incentive to increase his/her individual power. This operating point is called a Nash equilibrium. In many cases, and due to the lack of cooperation between the users (players), this point is not efficient, in the sense that it is not the most desirable social point [4]. The most desirable social point is called a Pareto optimal point, and may be viewed as the equilibrium point where no user can improve his level of satisfaction without harming at least one other user in the network. The power control problem for wireless data CDMA systems was first addressed in the game theoretic framework in [3], then in a more detailed manner in [2] and [4]. In [1] the authors introduced a tight bound that relate the induced channel fading outage probability to the signal-to-interference margin where the signal power and the interference noise power were replaced by their mean. This enabled them to use Perron-Frobenius eigenvalue theory to allocate the power in order to obtain the optimal outage probability. For a general case, when there are bounds on the transmitted powers and other constraints, they showed that this problem can be posed as a geometric program. Using the geometric program framework enabled them to solve the optimization problem of outage probability efficiently and globally. The global solution for the optimization problem of the outage probability was based on the presence of a centralized controller or collector to collect data about path gains between the transmitters and the receivers in the cellular communications system. In this paper the work in [1] to optimize the outage probability and the certainty-equivalent margin in a centralized fashion, which dealt with Rayleigh wireless fading channels, is considered by providing a non-centralized solution.