MPPCAD: Minimum Power Pattern Constrained Adaptive Differential Beamforming

This paper investigates the design of adaptive differential beamforming using small-spacing linear microphone arrays. We express the differential beamformer as a linear function of the target beampattern coefficients through orthogonal polynomial expansions. Consequently, the design of the beamformer reduces to optimizing these coefficients. To ensure that the maximum array response consistently aligns with the look direction, we derive constraints on the target beampattern coefficients, resulting in two convex sets for the first two orders of beampatterns. This approach uncovers numerous effective beampatterns beyond traditional options such as dipole, cardioid, supercardioid, and hypercardioid. By minimizing the power of the array output while adhering to the beampattern constraints, we develop the MPPCAD beamformer. Simulation results demonstrate that the proposed beamformer significantly enhances speech quality compared to classical differential beamformers.