A Characterization of Max-Min SIR-Balanced Power Allocation with Applications

TL;DR

This paper characterizes the max-min SIR-balanced power allocation in interference-limited wireless networks with general convex power constraints, proposing algorithms for centralized and distributed solutions to optimize network performance.

Contribution

It provides a novel characterization of max-min SIR balancing under general constraints and introduces algorithms for distributed implementation using saddle point and Perron root methods.

Findings

Characterization of max-min SIR-balanced power allocation

Algorithms for distributed power control and beamforming

Insights into weight vector computation in wireless networks

Abstract

We consider a power-controlled wireless network with an established network topology in which the communication links (transmitter-receiver pairs) are corrupted by the co-channel interference and background noise. We have fairly general power constraints since the vector of transmit powers is confined to belong to an arbitrary convex polytope. The interference is completely determined by a so-called gain matrix. Assuming irreducibility of this gain matrix, we provide an elegant characterization of the max-min SIR-balanced power allocation under such general power constraints. This characterization gives rise to two types of algorithms for computing the max-min SIR-balanced power allocation. One of the algorithms is a utility-based power control algorithm to maximize a weighted sum of the utilities of the link SIRs. Our results show how to choose the weight vector and utility function so that the utility-based solution is equal to the solution of the max-min SIR-balancing problem. The algorithm is not amenable to distributed implementation as the weights are global variables. In order to mitigate the problem of computing the weight vector in distributed wireless networks, we point out a saddle point characterization of the Perron root of some extended gain matrices and discuss how this characterization can be used in the design of algorithms in which each link iteratively updates its weight vector in parallel to the power control recursion. Finally, the paper provides a basis for the development of distributed power control and beamforming algorithms to find a global solution of the max-min SIR-balancing problem.