Sum-Capacity of the MIMO Many-Access Gaussian Noise Channel

Providing massive connectivity is one of the key challenges for the next generation of wireless communication networks, and hence the capacity limits of massive connectivity need to be thoroughly studied. The uplink in the regime of massive connectivity is captured by the many-access channel (MnAC) model, assuming the number of users to be extremely large and comparable to the blocklength. This work investigates a generalized MnAC, in which the transmitters and/or the receiver can be equipped with multiple antennas, and the channel gain of each user is allowed to be different. This model is referred to as the multiple-input and multiple-output (MIMO) MnAC model. In the MnAC paradigm, the message length (i.e., the number of bits communicated) is not necessarily linear in the blocklength. Therefore, instead of the conventional code rate, the message length is studied and defined as a function of the blocklength. This work characterizes the sum-message-length capacity (SMC) of the MIMO Gaussian MnAC in the regime where the number of users increases sub-linearly in the blocklength (i.e., $K_{n} = o(n)$ ). The SMC is numerically compared to lower bounds on achievable rate at finite blocklengths and is shown to be a good approximation for system performance. The impact of the number of antennas per user on SMC is also investigated. While in the single antenna MnAC model the conventional code rate is always zero, it is shown that in the MIMO MnAC it is possible to achieve positive rate by increasing the number of antennas per user. Furthermore, the antenna-user index is defined and the SMC is characterized for different antenna-user joint regimes. This provides useful insights for future MIMO MnAC system design.