Frequency invariant beamforming for arbitrary planar arrays

In this paper, we present the adaptation to the least-square solution for frequency invariant beamforming to arbitrary planar arrays. This formulation is easily steerable thanks to the decoupling of spatial and spectral constraints. This is achieved with a basis of spherical harmonics polynomials, which parametrize the array response in a term dependent on frequency and a term dependent on the array geometry. Furthermore, the parametrization of the array response Bessel functions decouples the frequency term, which becomes independent of the geometry of the planar array, and allows steering in azimuth and elevation independently. The planar array response is approximated using virtual sensor modeling, which transform any two dimensional planar array in a virtual linear sensors, where azimuth and elevation are separable and can be steered independently.