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

• Published in: IEEE signal processing letters Vol. 21; no. 8; pp. 914 - 917
• Main Authors: Yoomi Hur, Young-Cheol Park, Abel, Jonathan S., Dae Hee Youn
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Array signal processing; Arrays; Balancing; Beam pattern synthesis; Chebyshev approximation; Correlation; Gain; Mathematical models; microphone array signal processing; Microphones; optimal beamforming; Optimization; Sensors; Signal processing algorithms; Synthesis; White noise
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2014.2320916

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.