Multi-user MIMO communications: towards multi-antenna spectrum sharing and coexistence

Wireless spectrum is a scarce commodity. 5G and beyond cellular systems are venturing more and more into unlicensed spectrum, leading to increased coexistence of a multitude of wireless systems. To tackle this coexistence, efficient spectrum utilization techniques, such as spectrum sharing (SS) and full-duplex (FD) transmission have been considered, allowing also simultaneous transmission and sensing, opening up avenues for new random-access schemes. On the other hand, much research has been done on multi-user (MU) MIMO communications. Nevertheless, almost all current spectrum sharing schemes in standardized wireless systems are based on taking turns in spectrum occupation, whereas multiple antennas can enable simultaneous co-existence. The objective of this tutorial is to provide an overview of the following ingredients: 1) key SS approaches (from cognitive radio to enhanced Licensed Shared Access (eLSA), WiFi-5G coexistence, Automated Frequency Coordination (AFC) in WiFi7 etc.); 2) reminder of what we can do with multiple antennas (SU MIMO, MU MIMO, Interference Alignment), multi-antenna cognitive radio paradigms, including Channel State Information at the Transmitter (CSIT) acquisition and channel reciprocity calibration issues, dynamic TDD, reciprocity-based beamforming; 3) state-of-the-art MU-MIMO transmitter/receiver designs for various utility optimization problems, rate balancing, weighted sum rate, uplink/downlink duality; perfect CSIT designs: from weighted sum rate to weighted sum MSE, minorization maximization, Signal to Leakage plus Noise, Interference Aware Water Filling, Deterministic Annealing for global optimization or local optimum identification, interference covariance shaping and constrained optimization duality, power method for reduced complexity generalized eigenvectors; imperfect CSIT designs: imperfect CSIT channel models, location based CSIT, pathwise and non-Kronecker models, CSIT acquisition, distributed designs, utility optimization with imperfect CSIT, naïve UL/DL duality. In summary, in this tutorial we review the state of the art on transmitter/receiver design in MIMO systems, including some recent developments. But we also point out a variety of open problems that persist. In particular we provide various takes on distributed solutions and complexity reduction (e.g. beam space), leading to a tradeoff between performance/overhead/complexity, allowing some suboptimality (e.g. reduced-order zero-forcing) for significant complexity reductions (e.g. non-iterative designs), overhead reduction (eg naïve UL/DL duality); various takes on CSIT acquisition, including covariance CSIT, prediction for TDD etc. Various takes on utility functions: can we do everything with weighted sum rate?