Computationally Efficient Phase Configuration Design for Reconfigurable Intelligent Surface–Assisted Space Shift Keying With Passive Beamforming

This letter presents a new phase configuration design algorithm for systems employing reconfigurable intelligent surface (RIS)–assisted space shift keying (SSK) signaling with passive beamforming (PB), known as the RIS-SSK-PB scheme. In contrast to other RIS-SSK schemes which requires the phase configuration of RIS being adjusted at the symbol rate, the RIS-SSK-PB scheme allows the phase configuration to be adjusted at a rate inversely proportional to channel coherent time and hence significantly reduces the system overhead. Motivated by the fact that existing phase configuration design algorithms for RIS-SSK-PB are either not applicable due to the overwhelming complexity or admit substantial performance degradation in scenarios where the RIS consists of a large number of elements, a more balanced algorithm design is proposed in this letter. The main idea of the proposed algorithm is to first approximate the original non-smooth, nonconvex objective function in the formulated optimization problem with a smooth and convex one and then suitably exploit the structure of the constraint set to achieve high computational efficiency. Therefore, compared with existing RIS-SSK-PB algorithms, the proposed algorithm can achieve a lower bit error rate with a considerably lower complexity, as verified through extensive simulations.