Hybrid Beamforming for RIS-Aided Communications: Fitness Landscape Analysis and Niching Genetic Algorithm

TL;DR

This paper analyzes the complex optimization landscape of RIS-aided beamforming and introduces a niching genetic algorithm to effectively find multiple local optima, significantly improving communication capacity in large-scale systems.

Contribution

It provides the first fitness landscape analysis for RIS beamforming and proposes a novel niching genetic algorithm to better handle multi-modal optimization problems.

Findings

Landscape is rugged and multi-modal with many local peaks.

The proposed algorithm outperforms existing methods in capacity gains.

Effective in large-scale RIS scenarios.

Abstract

Reconfigurable Intelligent Surface (RIS) is a revolutionizing approach to provide cost-effective yet energy-efficient communications. The transmit beamforming of the base station (BS) and discrete phase shifts of the RIS are jointly optimized to provide high quality of service. However, existing works ignore the high dependence between the large number of phase shifts and estimate them separately, consequently, easily getting trapped into local optima. To investigate the number and distribution of local optima, we conduct a fitness landscape analysis on the sum rate maximization problems. Two landscape features, the fitness distribution correlation and autocorrelation, are employed to investigate the ruggedness of landscape. The investigation results indicate that the landscape exhibits a rugged, multi-modal structure, i.e., has many local peaks, particularly in the cases with large-scale RISs. To handle the multi-modal landscape structure, we propose a novel niching genetic algorithm to solve the sum rate maximization problem. Particularly, a niching technique, nearest-better clustering, is incorporated to partition the population into several neighborhood species, thereby locating multiple local optima and enhance the global search ability. We also present a minimum species size to further improve the convergence speed. Simulation results demonstrate that our method achieves significant capacity gains compared to existing algorithms, particularly in the cases with large-scale RISs.