Optimal Power Control for Multiuser CDMA Channels

TL;DR

This paper investigates the power allocation problem in multiuser CDMA systems, demonstrating convexity of the power region, and proposing a game-theoretic approach to optimize power control.

Contribution

It introduces a convex and monotone framework for power control, including minimal elements and a Nash bargaining perspective, advancing multiuser CDMA power management.

Findings

Power region is convex in linear and log scale

Existence of a componentwise minimal power element

Nash bargaining solution for power optimization

Abstract

In this paper, we define the power region as the set of power allocations for K users such that everybody meets a minimum signal-to-interference ratio (SIR). The SIR is modeled in a multiuser CDMA system with fixed linear receiver and signature sequences. We show that the power region is convex in linear and logarithmic scale. It furthermore has a componentwise minimal element. Power constraints are included by the intersection with the set of all viable power adjustments. In this framework, we aim at minimizing the total expended power by minimizing a componentwise monotone functional. If the feasible power region is nonempty, the minimum is attained. Otherwise, as a solution to balance conflicting interests, we suggest the projection of the minimum point in the power region onto the set of viable power settings. Finally, with an appropriate utility function, the problem of minimizing the total expended power can be seen as finding the Nash bargaining solution, which sheds light on power assignment from a game theoretic point of view. Convexity and componentwise monotonicity are essential prerequisites for this result.