Beamwidth and useable bandwidth of delay-steered microphone arrays

Automatic delay steering of microphone arrays improves sound pickup in large rooms. But steering to wave-arrival directions away from broadside degrades the acuity of the beam and diminishes the useable bandwidth of the array. This paper derives quantitative relations for the variation in beamwidth and bandwidth for one-dimensional, uniform, unweighted arrays composed of (2N + 1) receivers spaced by distance d. The results show how the upper and lower useful frequencies and the beam acuity are conditioned not only by receiver spacing and frequency, but also by wave-arrival direction and steering direction. The relations developed permit detailed design of steerable arrays for specified frequency range and spatial coverage.