Asymptotic Optimality of Massive MIMO Systems Using Densely Spaced Transmit Antennas

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. Index Terms Massive multiple-input multiple-output (MIMO) systems, uniform linear antenna arrays, antenna spacing, faster-than-Nyquist signaling, large-system analysis.