# Large-System Analysis of Massive MIMO with Optimal M-MMSE Processing

## TL;DR

This paper analyzes the spectral efficiency of Massive MIMO uplink networks with optimal M-MMSE processing when both the number of antennas and users grow large, providing accurate approximations validated by simulations.

## Contribution

It extends previous asymptotic analysis to the regime where both antennas and users grow large with a fixed ratio, using random matrix theory for practical system insights.

## Key findings

- Spectral efficiency grows unboundedly with large M and K.
- Derived low-complexity, accurate approximations for system performance.
- Validated approximations through simulations for realistic system sizes.

## Abstract

We consider the uplink of a Massive MIMO network with $L$ cells, each comprising a BS with $M$ antennas and $K$ single-antenna user equipments. Recently, [1] studied the asymptotic spectral efficiency of such networks with optimal multicell minimum mean-squared error (M-MMSE) processing when $M\to \infty$ and $K$ is kept fixed. Remarkably, [1] proved that, for practical channels with spatial correlation, the spectral efficiency grows unboundedly, even with pilot contamination. In this paper, we extend the analysis from [1] to the alternative regime in which $M,K\to \infty$ with a given ratio. Tools from random matrix theory are used to compute low-complexity approximations which are proved to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations.