Spherical harmonics based optimal minimum sidelobe beamforming for spherical sensor arrays

We propose an optimal minimum sidelobe modal beamforming approach based on the spherical harmonics decomposition for spherical sensor arrays, which provide the ability of three-dimensional broad-band beampattern synthesis. The spherical harmonics domain array processing problem is expressed with a matrix formulation. The weight vector design problem is written as a multiply constrained problem, so that the resulting beamformer can provide a suitable trade-off among mutually conflicting beamforming objectives, such as the lowest sidelobe level, beamwidth, multi-null steering, robustness and so on. The multiply constrained problem is formulated as a convex form of second-order cone programming which is computationally tractable. The main advantage of this method over classical element-space array processing approaches is that the frequency dependent components can be pre-decoupled and removed from angular dependent spherical harmonics, so the same beampattern could be used over a frequency range with a single set of array weights, and the complexity of broad-band beamforming optimization algorithms can be reduced.