Massive MIMO Has Unlimited Capacity

The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.

I. Introduction

The Shannon capacity of a channel manifests the spectral efficiency (SE) that it supports. Massive MIMO (multiple-input multiple-output) improves the sum SE of cellular networks by spatial multiplexing of a large number of user equipments (UEs) per cell [1]. It is therefore considered a key time-division duplex (TDD) technology for the next generation of cellular networks [2]–[4]. The main difference between Massive MIMO and classical multiuser MIMO is the large number of antennas, , at each base station (BS) whose signals are processed by individual radio-frequency chains. By exploiting channel estimates for coherent receive combining, the uplink signal power of a desired UE is reinforced by a factor , while the power of the noise and independent interference does not increase. The same principle holds for the transmit precoding in the downlink. Since the channel estimates are obtained by uplink pilot signaling and the pilot resources are limited by the channel coherence time, the same pilots must be reused in multiple cells. This leads to pilot contamination which has two main consequences: the channel estimation quality is reduced due to pilot interference and the channel estimate of a desired UE is correlated with the channels to the interfering UEs that use the same pilot. Marzetta showed in his seminal paper [1] that the interference from these UEs during data transmission is also reinforced by a factor , under the assumptions of maximum ratio (MR) combining/precoding and independent and identically distributed (i.i.d.) Rayleigh fading channels. This means that pilot contamination creates a finite SE limit as .