Lens-Type Redirective Intelligent Surfaces for Multi-User MIMO Communication

This paper explores the idea of using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">redirective</i> reconfigurable intelligent surfaces (RedRIS) to overcome many of the challenges associated with the conventional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reflective</i> RIS. We develop a framework for jointly optimizing the switching matrix of the lens-type RedRIS ports along with the active precoding matrix at the base station (BS) and the receive scaling factor. A joint non-convex optimization problem is formulated under the minimum mean-square error (MMSE) criterion with the aim to maximize the spectral efficiency of each user. In the single-cell scenario, the optimum active precoding matrix at the multi-antenna BS and the receive scaling factor are found in closed-form by applying Lagrange optimization, while the optimal switching matrix of the lens-type RedRIS is obtained by means of a newly developed alternating optimization algorithm. We then extend the framework to the multi-cell scenario with single-antenna base stations that are aided by the same lens-type RedRIS. We further present two methods for reducing the number of effective connections of the RedRIS ports that result in appreciable overhead savings while enhancing the robustness of the system. The proposed RedRIS-based schemes are gauged against conventional reflective RIS-aided systems under both perfect and imperfect channel state information (CSI). The simulation results show the superiority of the proposed schemes in terms of overall throughput while incurring much less control overhead.