Coverage Area Optimized Static Reflecting Surfaces

We consider a Static Reflecting Surface (SRS) assisted communication system, with an SRS deployed to assist communication in an area of a cell with poor connection to a massive multiple-input multiple-output Base Station (BS). The SRS has a high number of reflecting elements, with a static phase shift matrix, optimized offline at installation for serving a user population in the coverage area. To find the phase shift matrix at the SRS and the BS beamformer, we formulate a joint optimization problem aiming to maximize the average spectrum efficiency in the area, assuming line-of-sight communication between SRS and BS, as well as between SRS and the area. To tackle the problem, we decouple the BS beamforming and SRS phase shifter design problems. We assume that the BS beamforming is optimized in the operation phase based on the instantaneous end-to-end channel. Based on this we formulate the phase shifter design problem considering an upper bound of the spectrum efficiency, and a collection of sample locations in the area. Projected gradient ascent and convex relaxation approaches are used to obtain the phase shifters. In addition we consider wide-beam designs for the SRS to steer energy evenly at the target area. For this, we numerically find an approximate ideal wide beam, as well as constant moudulus prolate spheroidal sequences. We evaluate the spectrum efficiency performance of the designed phase shifters both in a single- and multi-user scenario, considering a single and multiple SRSs, where each SRS is optimized to serve the area. In the simulated scenario, an SRS loses between 37% and 60% in average spectrum efficiency, as compared to a fully dynamic Reconfigurable Intelligent Surface (RIS) of the same size with real-time electronic control of the phase shifter. The performance gap between a dynamically optimized RIS and an SRS shrinks with an increasing number of simultaneous users.