A <i>k</i> -space approach to modeling multi-channel parametric array loudspeaker systems

Multi-channel parametric array loudspeaker (MCPAL) systems offer enhanced flexibility and promise for generating highly directional audio beams in real-world applications. However, efficient and accurate prediction of their generated sound fields remains a major challenge due to the complex nonlinear behavior and multi-channel signal processing involved. To overcome this obstacle, we propose a k-space approach for modeling arbitrary MCPAL systems arranged on a baffled planar surface. In our method, the linear ultrasound field is first solved using the angular spectrum approach, and the quasilinear audio sound field is subsequently computed efficiently in k-space. By leveraging three-dimensional fast Fourier transforms, our approach not only achieves high computational efficiency but also maintains accuracy without relying on the paraxial approximation. For typical configurations studied, the proposed method demonstrates a speed-up of more than 4 orders of magnitude, compared to the direct integration method. Our proposed approach paved the way for simulating and designing advanced MCPAL systems.