Fitness landscape analysis and niching genetic approach for hybrid beamforming in RIS-aided communications

Reconfigurable intelligent surface (RIS) is a revolutionizing technology to achieve cost-effective communications. The active beamforming at the base station (BS) and the discrete phase shifts at RIS should be jointly designed to customize the propagation environment. However, current phase-shift setting methods ignore the non-separable property of phase shifts, degrading the performance, especially in cases with a large-sized RIS. To understand the problem characteristics related to the phase shifts and further tailor an eligible method with such characteristics, this paper, for the first time, analyzes the fitness landscape of the sum-rate maximization problem (maximizing the sum rate of users in a downlink multi-user multiple-input single-output system assisted by a RIS). Results show that the problem has a severe unstructured and rugged landscape, especially in cases with a large-sized RIS. This observation answers why current methods are ineligible and provides insightful guidance for designing a more intelligent method. With the landscape findings in mind, this paper introduces a niching genetic algorithm to solve the problem. In particular, the niching idea is employed to locate multiple local optima. These local optima act as stepping stones to facilitate approaching the global optima. Simulation results demonstrate that the proposed niching genetic algorithm obtains significant capacity gains over current methods in cases with large-sized RIS.