Numerical Synthesis of an Optimal Low-Sidelobe Beam Pattern for a Microphone Array

This letter describes a numerical algorithm for synthesizing optimal low-sidelobe beampatterns. The pattern synthesis problem is formulated as a constrained optimization that minimizes the spatially weighted energy arriving at the array subject to unit gain in the look direction and a constant sidelobe level. The weighting takes on the form of a sensor correlation matrix, parameterized between uncorrelated sensor noise and correlated signal arrival terms according to a balancing factor. Setting the balancing factor to its extreme values of 0 and 1, produces, respectively, the optimal Riblet-Chebyshev and Delay-and-Sum type beamformers. In between, the method generates a low-sidelobe beamformer with varying beamwidths that provides a trade-off between White Noise Gain and Directivity Index. Simulation examples demonstrate optimal and intermediate designs for uniform and non-uniform sensor spacings.