Constant Directivity Loudspeaker Beamforming

Loudspeaker array beamforming is a common signal processing technique for acoustic directivity control and robust audio reproduction. Unlike their microphone counterpart, loudspeaker constraints are often heterogeneous due to arrayed transducers with varying operating ranges in frequency, acoustic-electrical sensitivity, efficiency, and directivity. This work proposes a frequency-regularization method for generalized Rayleigh quotient directivity specifications and two novel beamformer designs that optimize for maximum efficiency constant directivity (MECD) and maximum sensitivity constant directivity (MSCD). We derive fast converging and analytic solutions from their quadratic equality constrained quadratic program formulations. Experiments optimize generalized directivity index constrained beamformer designs for a full-band heterogeneous array.