Closed-form max-min power control for some cellular and cell-free massive MIMO networks

TL;DR

This paper derives a closed-form solution for max-min power control in cellular and cell-free massive MIMO networks, simplifying previous iterative methods and providing insights into network regimes.

Contribution

It introduces a closed-form solution based on spectral radius analysis for max-min power control problems, contrasting with prior iterative approaches.

Findings

Closed-form solution depends on spectral radius of matrices.

Provides an asymptotically tight bound for optimal utility.

Offers a simple rule to distinguish noise-limited and interference-limited regimes.

Abstract

Many common instances of power control problems for cellular and cell-free massive MIMO networks can be interpreted as max-min utility optimization problems involving affine interference mappings and polyhedral constraints. We show that these problems admit a closed-form solution which depends on the spectral radius of known matrices. In contrast, previous solutions in the literature have been indirectly obtained using iterative algorithms based on the bisection method, or on fixed-point iterations. Furthermore, we also show an asymptotically tight bound for the optimal utility, which in turn provides a simple rule of thumb for evaluating whether the network is operating in the noise or interference limited regime. We finally illustrate our results by focusing on classical max-min fair power control for cell-free massive MIMO networks.