# Max-Min Fairness Design for MIMO Interference Channels: a Minorization-Maximization Approach

## TL;DR

This paper introduces an efficient minorization-maximization algorithm for designing linear precoders in MIMO interference channels to achieve max-min fairness, handling non-convex optimization with convergence guarantees.

## Contribution

It proposes a novel MM-based method that solves SOCPs iteratively for max-min fairness in MIMO-IC, including robustness to uncertainties in noise and CSI.

## Key findings

- Algorithm converges to stationary points.
- Effective in scenarios with noise and CSI uncertainties.
- Outperforms existing methods in simulations.

## Abstract

We address the problem of linear precoder (beamformer) design in a multiple-input multiple-output interference channel (MIMO-IC). The aim is to design the transmit covariance matrices in order to achieve max-min utility fairness for all users. The corresponding optimization problem is non-convex and NP-hard in general. We devise an efficient algorithm based on the minorization-maximization (MM) technique to obtain quality solutions to this problem. The proposed method solves a second-order cone convex program (SOCP) at each iteration. We prove that the devised method converges to stationary points of the problem. We also extend our algorithm to the case where there are uncertainties in the noise covariance matrices or channel state information (CSI). Simulation results show the effectiveness of the proposed method compared with its main competitor.