Asymptotic Optimality of Massive MIMO Systems Using Densely Spaced Transmit Antennas

TL;DR

This paper investigates the effects of densely spacing antennas in massive MIMO systems, showing that beyond a certain point, denser spacing does not improve capacity, but certain modulation schemes can approach optimal rates.

Contribution

It demonstrates that denser antenna spacing does not increase normalized capacity and links MIMO transmission to faster-than-Nyquist signaling, providing new insights into antenna design.

Findings

Densely spacing antennas does not improve normalized capacity.

Normalized achievable rate of QPSK converges to the Gaussian capacity.

Results are based on large-system limit analysis.

Abstract

This paper considers a deterministic physical model of massive multiple-input multiple-output (MIMO) systems with uniform linear antenna arrays. It is known that the maximum spatial degrees of freedom is achieved by spacing antenna elements at half the carrier wavelength. The purpose of this paper is to investigate the impacts of spacing antennas more densely than the critical separation. The achievable rates of MIMO systems are evaluated in the large-system limit, where the lengths of transmit and receive antenna arrays tend to infinity with the antenna separations kept constant. The main results are twofold: One is that, under a mild assumption of channel instances, spacing antennas densely cannot improve the capacity of MIMO systems normalized by the spatial degrees of freedom. The other is that the normalized achievable rate of quadrature phase-shift keying converges to the normalized capacity achieved by optimal Gaussian signaling, as the transmit antenna separation tends to zero after taking the large-system limit. The latter result is based on mathematical similarity between MIMO transmission and faster-than-Nyquist signaling in signal space representations.