Steerable frequency-invariant beamforming for arbitrary arrays

Frequency-invariant beamforming aims to parameterize array filter coefficients such that the spectral and spatial response profiles of the array can be adjusted independently. Solutions to this problem have been presented for specific sensor configurations often requiring a larger number of sensors. However, in practical applications, the number and location of sensors are often restricted. This paper proposes to find an optimal linear basis transformation that decouples the frequency response from the spatial response. A least-squares optimal basis transform can be computed numerically for arbitrary sensor configurations, for which typically no exact analytical solutions are available. This transform can be further combined with a spherical harmonics basis resulting in readily steerable broadband beams. This solution to broadband beamforming effectively decouples the array geometry from the steering geometry. Furthermore, for frequency-invariant beams, this approach results in a significant reduction in the number of beam-design parameters. Here, the method is demonstrated for an optimal design of far-field response for an irregular linear array with as few as three sensors.