Broadband Frequency-Invariant Broadside Beamforming with a Differential Loudspeaker Array

The directional loudspeaker array generating sound beam to the target listener is highly demanded in the application. The null-constraint-based differential beamforming has recently been applied to the loudspeaker line array to produce a broadside frequency-invariant radiation pattern. However, its effective frequency range is limited since it only pursues sound pressure matching in a few directions. In this paper, we develop the modal matching approach of the null-constrained method to control the beam pattern better. Specifically, we derive the modal domain target beam pattern of a broadside differential loudspeaker array from the information about the nulls. Then, we use the Jacobi-Anger expansion and modal matching to optimise the loudspeaker gains in the modal domain. In addition, a distortionless constraint in the broadside direction is included to achieve constant performance over the frequency band of interest. Simulation results show that the proposed method achieved more than double the effective frequency range with an invariant main lobe (broadside beam) up to 4 kHz, and better sound attenuation of the side lobes, compared to the existing methods.