Hybrid Nonlinear Transceiver Optimization for the RIS-Aided MIMO Downlink

The hybrid nonlinear transceiver optimization problem of reconfigurable intelligent surface (RIS)-aided multi-user multiple-input multiple-output (MU-MIMO) downlink is investigated. Specifically, the Tomlinson-Harashima precoder (THP) and transmit (TPC) base station are jointly optimized with linear digital receivers mobile users. triangular feedback matrix THP optimal solution derived in closed form based on a inequality. Moreover, order to tackle nonconvexity constant-modulus constraints imposed analog TPC, Majorization-Minimization (MM) framework proposed, which strikes trade-off between implementation complexity system performance manner. Explicitly, our MM-based capable optimizing TPC dynamically manner an element-by-element, column-by-column, row-by-row or block-by-block basis. algorithm proposed for phase shifting at RIS, also suffers from constraints. In algorithm, RIS can be partitioned into series subarrays striking different vs. tradeoffs. Finally, numerical results demonstrate advantages techniques.