Multiobjective beampattern optimization in collaborative beamforming via NSGA-II with selective distance

Collaborative beamforming is usually characterized by high, asymmetrical sidelobe levels due to the randomness of node locations. Previous works have shown that the optimization methods aiming to reduce the peak sidelobe level (PSL) alone do not guarantee the overall sidelobe reduction of the beampattern, especially when the nodes are random and cannot be manipulated. Hence, this paper proposes a multiobjective amplitude and phase optimization technique with two objective functions: PSL minimization and directivity maximization, in order to improve the beampattern. A novel selective Euclidean distance approach in the nondominated sorting genetic algorithm II (NSGA-II) is proposed to steer the candidate solutions toward a better solution. Results obtained by the proposed NSGA with selective distance (NSGA-SD) are compared with the single-objective PSL optimization performed using both GA and particle swarm optimization. The proposed multiobjective NSGA provides up to 40% improvement in PSL reduction and 50% improvement in directivity maximization and up to 10% increased performance compared to the legacy NSGA-II. The analysis of the optimization method when considering mutual coupling between the nodes shows that this improvement is valid when the inter-node Euclidean separations are large.