Massive MIMO: How many antennas do we need?

TL;DR

This paper investigates the number of antennas required in massive MIMO systems to approach theoretical performance limits, analyzing finite N effects and comparing simple and advanced detection methods.

Contribution

It provides a finite-N analysis of massive MIMO, deriving antenna requirements for near-optimal performance and comparing matched filter and MMSE detection.

Findings

Number of antennas needed for ta performance is derived.

MMSE detection offers gains over matched filter.

Finite N effects are characterized with new random matrix theory results.

Abstract

We consider a multicell MIMO uplink channel where each base station (BS) is equipped with a large number of antennas N. The BSs are assumed to estimate their channels based on pilot sequences sent by the user terminals (UTs). Recent work has shown that, as N grows infinitely large, (i) the simplest form of user detection, i.e., the matched filter (MF), becomes optimal, (ii) the transmit power per UT can be made arbitrarily small, (iii) the system performance is limited by pilot contamination. The aim of this paper is to assess to which extent the above conclusions hold true for large, but finite N. In particular, we derive how many antennas per UT are needed to achieve \eta % of the ultimate performance. We then study how much can be gained through more sophisticated minimum-mean-square-error (MMSE) detection and how many more antennas are needed with the MF to achieve the same performance. Our analysis relies on novel results from random matrix theory which allow us to derive tight approximations of achievable rates with a class of linear receivers.