Capacity Scaling of Massive MIMO in Strong Spatial Correlation Regimes

• Published in: IEEE transactions on information theory Vol. 66; no. 5; pp. 3040 - 3064
• Main Authors: Nam, Junyoung, Caire, Giuseppe, Debbah, Merouane, Poor, H. Vincent
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Antenna arrays; Antennas; asymptotic capacity scaling; Asymptotic properties; correlated fading channels; Correlation; Covariance matrix; Decontamination; Eigenvalues; Eigenvectors; Engineering Sciences; Fading; Large-scale MIMO; Lower bounds; Massive MIMO; Mathematical analysis; Matrix algebra; Matrix methods; MIMO (control systems); Multiplexing; multiplexing gain; random matrix theory; Scaling laws; Signal to noise ratio; Subspaces; Large-scale MIMO; multiplexing gain; correlated fading channels; asymptotic capacity scaling
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2019.2961323

This paper investigates the capacity scaling of multicell massive MIMO systems in the presence of spatially correlated fading. In particular, we focus on the strong spatial correlation regimes where the covariance matrix of each user channel vector has a rank that scales sublinearly with the number of base station antennas, as the latter grows to infinity. We also consider the case where the covariance eigenvectors corresponding to the non-zero eigenvalues span randomly selected subspaces. For this channel model, referred to as the "random sparse angular support" model, we characterize the asymptotic capacity scaling law in the limit of large number of antennas. To achieve the asymptotic capacity results, statistical spatial despreading based on the second-order channel statistics plays a pivotal role in terms of pilot decontamination and interference suppression. A remarkable result is that even when the number of users scales linearly with base station antennas, a linear growth of the capacity with respect to the number of antennas is achievable under the sparse angular support model. We also note that the achievable rate lower bound based on massive MIMO "channel hardening", widely used in the massive MIMO literature, yields rather loose results in the strong spatial correlation regimes and may significantly underestimate the achievable rate of massive MIMO. This work therefore considers an alternative bounding technique which is better suited to the strong correlation regimes. In fading channels with sparse angular support, it is further shown that spatial despreading (spreading) in uplink (downlink) has a more prominent impact on the performance of massive MIMO than channel hardening.