Phased array speakers are often designed with uniform element spacing, which limits beam steering capability and sidelobe control under practical aperture and hardware constraints. This study presents an optimization-driven modelling framework for parametric array loudspeakers (PALs) that systematically links array layout synthesis with high-fidelity directivity prediction, by combining a frequency-domain convolution model with a finite element method (FEM) pipeline. We formulate array layout synthesis as a constrained optimization problem and employ particle swarm optimization (PSO) to determine non-uniform element positions that suppress sidelobes while preserving mainlobe integrity across steering angles. By integrating linear acoustic field simulation with far-field directivity prediction, the framework serves as a computationally efficient surrogate model suitable for iterative design under non-ideal spacing conditions. Simulation results and laboratory measurements demonstrate that the optimized non-uniform arrays achieve consistently lower sidelobe levels and more concentrated mainlobes than conventional uniform configurations. These results validate the proposed framework as a practical and reproducible solution for steering-capable PAL design when the conventional λ/2 spacing constraint cannot be satisfied and establish a foundation for subsequent robustness and sensitivity analyses.
Mei et al. (Thu,) studied this question.