A Non-Cooperative Power Control Game in Delay-Constrained Multiple-Access Networks

TL;DR

This paper introduces a game-theoretic model for power control in delay-constrained multiple-access networks, deriving Nash equilibria and analyzing how delay constraints impact network capacity and user utilities.

Contribution

It develops a non-cooperative power control game considering delay constraints, proves the existence and uniqueness of Nash equilibrium, and provides explicit utility expressions for various detectors.

Findings

Delay constraints reduce network capacity.

Explicit utility expressions for different detectors.

Delay constraints significantly impact user utilities.

Abstract

A game-theoretic approach for studying power control in multiple-access networks with transmission delay constraints is proposed. A non-cooperative power control game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying the user's delay requirements. The utility function measures the number of reliable bits transmitted per joule of energy and the user's delay constraint is modeled as an upper bound on the delay outage probability. The Nash equilibrium for the proposed game is derived, and its existence and uniqueness are proved. Using a large-system analysis, explicit expressions for the utilities achieved at equilibrium are obtained for the matched filter, decorrelating and minimum mean square error multiuser detectors. The effects of delay constraints on the users' utilities (in bits/Joule) and network capacity (i.e., the maximum number of users that can be supported) are quantified.