Constrained Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework

Conventional multi-user multiple-input multiple-output (MU-MIMO) mainly focused on Gaussian signaling, independent and identically distributed (IID) channels, and a limited number of users. It will be laborious to cope with the heterogeneous requirements in next-generation wireless communications, such as various transmission data, complicated communication scenarios, and unprecedented massive user access. Therefore, this paper studies a generalized MU-MIMO (GMU-MIMO) system with more generalized and practical constraints, i.e., practical channel coding, non-Gaussian signaling, right-unitarily-invariant channels (covering Rayleigh fading channel matrices, certain ill-conditioned and correlated channel matrices, etc.), and massive users and antennas. These generalized assumptions bring new challenges in theory and practice. For example, there is no accurate constrained capacity region analysis for GMU-MIMO. In addition, it is unclear how to achieve constrained-capacity-optimal performance with practical complexity. To address these challenges, a unified framework is proposed to derive the constrained capacity region of GMU-MIMO and design a constrained-capacity-optimal transceiver, which jointly considers encoding, modulation, detection, and decoding. Group asymmetry is developed to group users according to their rates, which makes a tradeoff between user rate allocation and implementation complexity. Specifically, the constrained capacity region of group-asymmetric GMU-MIMO is characterized by using the minimum mean-square error (MMSE) optimality of orthogonal/vector approximate message passing (OAMP/VAMP) and the relationship between mutual information and MMSE. Furthermore, a theoretically optimal multi-user OAMP/VAMP receiver and practical multi-user low-density parity-check (MU-LDPC) codes are proposed to achieve the constrained capacity region of group-asymmetric GMU-MIMO. Numerical results demonstrate that the proposed MU-LDPC coded GMU-MIMO systems achieve asymptotic performance within 0.2 dB from the theoretical sum capacity. Moreover, their finite-length performances are about 1 similar to 2 dB away from the associated sum capacity of GMU-MIMO.