A steerable non-paraxial Gaussian beam expansion for a steerable parametric array loudspeaker

A steerable parametric array loudspeaker (PAL) aims to steer a highly directional audio beam without the need to mechanically rotate the source. The Gaussian beam expansion (GBE) method is often used to model PALs because it is a computationally efficient approach, however the method relies on a paraxial approximation that can result in significant inaccuracies at large steering angles. To address this limitation, a steerable non-paraxial GBE is proposed in this article, where the mainlobe of the steered ultrasonic beam is included in the calculation by rotating the coordinate system. A non-paraxial approximation is then used to improve the accuracy of the method when integrating the virtual audio sources. The numerical results obtained using the proposed method are compared against those using the conventional GBE, as well as an exact solution. For a typical configuration, it is shown that for a conventional GBE the prediction error can be more than 30 dB at large angles, whereas the proposed method reduces this to less than 1 dB. The advantage of the proposed method is more significant at large steering angles, low audio frequencies, and those locations outside of the paraxial region. This improvement in performance is achieved with a computational cost that remains the same as the conventional GBE.