# Sum Rate and Fairness Analysis for the MU-MIMO Downlink under PSK Signalling: Interference Suppression vs Exploitation

## TL;DR

This paper compares sum rate performance of MU-MIMO downlink systems with PSK signaling under different precoding schemes, deriving analytical expressions and proposing a power allocation for fairness, showing CI's superiority.

## Contribution

It provides new analytical formulas for sum rate in MU-MIMO with PSK and introduces a power allocation scheme to enhance fairness among users.

## Key findings

- Constructive interference (CI) outperforms zero forcing (ZF) and no precoding schemes.
- CI offers higher fairness among users.
- The proposed power allocation scheme maximizes fairness index.

## Abstract

In this paper, we analyze the sum rate performance of multi-user multiple-input multiple-output (MU-MIMO) systems, with a finite constellation phase-shift keying (PSK) input alphabet. We analytically calculate and compare the achievable sum rate in three downlink transmission scenarios: 1) without precoding, 2) with zero forcing (ZF) precoding 3) with closed form constructive interference (CI) precoding technique. In light of this, new analytical expressions for the average sum rate are derived in the three cases, and Monte Carlo simulations are provided throughout to validate the analysis. Furthermore, based on the derived expressions, a power allocation scheme that can ensure fairness among the users is also proposed. The results in this work demonstrate that, the CI strictly outperforms the other two schemes, and the performance gap between the considered schemes increases with increase in the MIMO size. In addition, the CI provides higher fairness and the power allocation algorithm proposed in this paper can achieve maximum fairness index.