On the Fundamental Limits of MIMO Massive Multiple Access Channels

In this paper, we study multiple-antenna wireless communication networks, where a large number of devices simultaneously communicate with an access point. The capacity region of multiple-input multiple-output massive multiple access channels (MIMO mMAC) is investigated. While joint typicality decoding is utilized to establish the achievability of capacity region for conventional MAC with fixed number of the users, the technique is not directly applicable for the MIMO mMAC. Instead, an information-theoretic approach based on Gallager's error exponent analysis is exploited to characterize the finite dimension region of the MIMO mMAC. Theoretical results reveal that the region is dominated by the sum rate constraint only, and the individual user rates are dominated by specific factors that correspond to the allocation of the sum rate. The rate in conventional MAC is not achievable when the number of users is comparable with codelength, which is due to the fact that successive interference cancellation cannot guarantee an arbitrary small error decoding probability for MIMO mMAC. The results further imply that, asymptotically, the individual user rate is independent of the number of transmit antennas, and channel hardening makes the individual user rate close to that when only statistic knowledge of channel is available at transmitter. The finite dimension region of MIMO mMAC is a generalization of the symmetric rate in Chen et al. (2017).