Multi-Objective Optimization of UAV Relay Deployment for Air-to-Ground Communications via Distributed Collaborative Beamforming

Uncrewed aerial vehicle (UAV) relay systems based on distributed collaborative beamforming (DCB) present significant opportunities for enhancing uplink transmission in emerging 6G wireless networks. However, the distributed nature of UAV positioning often results in beamforming degradation, leading to reduced communication quality. To address this issue, this paper proposes a flexible UAV relay deployment strategy under varying network constraints. The strategy operates in two stages: it first determines the minimum number of UAVs required to guarantee received signal strength (RSS) above a predefined threshold, and then jointly optimizes the UAV positions and excitation current weights by formulating a multi-objective optimization problem (MOP). The MOP aims to minimize the maximum sidelobe level (SLL) and propulsion energy consumption while maximizing the transmission rate. We propose an enhanced multi-objective evolutionary algorithm, BSINSGA-II, which integrates beetle swarm optimization (BSO) into the non-dominated sorting genetic algorithm II (NSGA-II). This integration enhances the global search capability and mitigates the risk of convergence to local optima. Furthermore, the good point set combined with K-means clustering is employed to generate a uniformly distributed initial population, thereby improving convergence performance and solution quality. Simulation results demonstrate that the proposed strategy not only determines the minimum number of UAVs for reliable relay communication, but also significantly reduces energy consumption, suppresses the maximum SLL and improves transmission rate compared to benchmark approaches.