  This paper explores the idea of using redirective reconfigurable intelligent
surfaces (RedRIS) to overcome many of the challenges associated with the
conventional reflective 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.
