# Max-Min Fair Transmit Precoding for Multi-group Multicasting in Massive MIMO

## TL;DR

This paper investigates max-min fairness precoding in massive MIMO multicasting, deriving closed-form solutions across various scenarios to optimize spectral efficiency considering practical system constraints.

## Contribution

It provides a comprehensive analysis and closed-form solutions for the max-min fairness problem in multi-group multicasting in massive MIMO, covering multiple transmission and pilot strategies.

## Key findings

- Closed-form spectral efficiency expressions for all scenarios.
- Guidelines for selecting multicasting schemes based on system parameters.
- Optimal pilot and data transmission policies for max-min fairness.

## Abstract

This paper considers the downlink precoding for physical layer multicasting in massive multiple-input-multiple-output (MIMO) systems. We study the max-min fairness (MMF) problem, where channel state information (CSI) at the transmitter is used to design precoding vectors that maximize the minimum spectral efficiency (SE) of the system, given fixed power budgets for uplink training and downlink transmission. Our system model accounts for channel estimation, pilot contamination, arbitrary pathlosses, and multi-group multicasting. We consider six scenarios with different transmission technologies (unicast and multicast), different pilot assignment strategies (dedicated or shared pilot assignments), and different precoding schemes (maximum ratio transmission and zero forcing), and derive achievable spectral efficiencies for all possible combinations. Then we solve the MMF problem for each of these scenarios and for any given pilot length we find the SE maximizing uplink pilot and downlink data transmission policies, all in closed-forms. We use these results to draw a general guideline for massive MIMO multicasting design, where for a given number of base station antennas, number of users, and coherence interval length, we determine the multicasting scheme that shall be used.