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

arXiv: https://arxiv.org/abs/2205.00429 · HTML: https://mlsanity.com/paper/2205.00429/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2022.

## Built on by (most cited first, 4 of 4)

- [Transformer-Based Power Optimization for Max-Min Fairness in Cell-Free Massive MIMO](https://mlsanity.com/paper/2503.03561/) (2025)
- [Linear Attention for Joint Power Optimization and User-Centric Clustering in Cell-Free Networks](https://mlsanity.com/paper/2512.17466/) (2025)
- [A Learning-Based Approach to Approximate Coded Computation](https://mlsanity.com/paper/2205.09818/) (2022)
- [Tree Meets Transformer: A Hybrid Architecture for Scalable Power Allocation in Cell-Free Networks](https://mlsanity.com/paper/2512.22639/) (2025)

## Abstract (arXiv)

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.