A Framework for Multi-Functional Optimization in RIS-Aided Hybrid Analog-Digital MIMO Systems

Both the reconfigurable intelligent surface (RIS) and the hybrid analog-digital antenna array have been envisioned as two cost-effective and promising technologies for achieving various types of functionality enhancement of future wireless systems. In this paper, we develop a framework for the multi-functional optimization in the RIS-aided hybrid analog-digital multiple-input multiple-output (MIMO) system, where a board of performance metrics related to diverse system functionalities are considered, such as capacity and mean square error (MSE) for information transmission (IT), Cramer-Rao bound (CRB) for radar sensing, harvested energy for energy harvesting (EH) and so on. Under this framework, we focus on two types of multi-functional optimization problems, namely, the multi-objective multi-functional optimization and the single-objective optimization subject to multi-functional constraints, and propose a unified low-complexity algorithm by separately optimizing analog and digital matrix variables. Specifically, for the multi-objective optimization, we firstly propose the numerical quadratic optimization based (QuaOpt-based) algorithm and the low-complexity channel alignment based algorithm to separately optimize analog matrices, including the RIS reflecting matrix, the analog precoder and the analog equalizer. Then, for the optimization of digital precoder, the numerical semidefinite programming (SDP)-based algorithm and the QuaOpt-based algorithm are proposed to iteratively solve the digital precoder optimization problem, while the matrix-monotonic optimization based algorithm derives the optimal closed-form solution in low computational complexity. Whereas for the single-objective optimization, the above proposed algorithms are still applicable by applying the Lagrangian duality theory to tackle the multi-functional constraints. Numerical simulation results reveal that the proposed low-complexity algorithm can achieve comparable performance to numerical algorithms.