Non-atomic Games for Multi-User Systems

TL;DR

This paper analyzes multi-user frequency selective fading channels using game theory to derive simple, large-system approximations of Nash equilibria for decentralized power control in uplink CDMA systems.

Contribution

It introduces a novel combination of asymptotic random matrix theory and non-atomic game theory to approximate Nash equilibria in large multi-user systems with frequency selective channels.

Findings

Explicit large-system expressions for Nash equilibria.

Effective decentralized power control schemes.

Insights into the impact of other mobiles on individual performance.

Abstract

In this contribution, the performance of a multi-user system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). We consider the realistic case of frequency selective channels for uplink CDMA. This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the Matched filter, the MMSE filter and the optimum filter. The goal of this paper is to derive simple expressions for the non-cooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of non-atomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows.