Capacity Scaling of Massive MIMO in Strong Spatial Correlation Regimes

Abstract

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 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. Index TermsLarge-scale MIMO, asymptotic capacity scaling, multiplexing gain, correlated fading channels. arXiv:1812.08898v1 [cs.IT] 21 Dec 2018 K M = 0, i.e., K is finite or at most grows slower than M . For instance, if KL > M , the linear independence of the subspaces of covariance matrices in [12], [13] is never attainable. Likewise, if lim inf M →∞ K M > 0, then the asymptotic linear independence of covariance matrices in [16] does not hold any longer. Therefore, the results based on the linear independence of the signal subspaces or of the covariance matrices cannot capture the capacity scaling with respect to the ratio K M > 0, as both M and K grow large. This poses a fundamental methodological question since in reality we are in the presence of a finite system with given M and K. Which of the following large system analyses will produce the more meaningful prediction of its behavior: considering finite K and letting M → ∞ [1], [2], [16] or considering both K and M → ∞ with fixed ratio equal to the actual ratio K M of the practical finite system [4]? We claim that the latter methodology yields a more relevant asymptotics.

Impact of Strong Spatial Correlation on the Capacity Scaling of Massive MIMO

“…Since the noise power per antenna is normalized, P ul can be regarded as the transmit SNR per user, and SNR denotes the normalized transmit SNR per cell. Although we only describe the uplink MIMO, main results in this work are extended to the downlink [11].…”

“…where the definitions of T T T k and T T T k can be found in [11]. A proof of the second term caused by pilot contamination in the denominator of (9) is particularly given in Appendix.…”

“…A proof of the second term caused by pilot contamination in the denominator of (9) is particularly given in Appendix. For this, we extended the standard technique of deterministic equivalents in a few aspects in [11]: 1) the unbounded spectral norm of channel covariance matrices with respect to M and 2) the partial random Fourier correlation model for which the trace lemma in [8,Lem. 2.7] (see also [9, Thm.…”

“…and we haveγ MF ul, k P ul trΛ k , where we used a direct combination of [11,Cor. 1 and 2] and then [11,Lem. 8].…”

Channel Correlation Diversity in MU-MIMO Systems – Analysis and Measurements

“…In stark contrast, a different set of investigations has shown that correlation can enhance MU-MIMO performance [11][12][13][14][15][16][17][18][19][20]. Collectively, a critical observation from these studies is that the departing spread of electromagnetic energy from the BS can arrive at the terminals with substantially different power angular spectra, leading to variations in the channel statistics.…”