Robust Broadband Differential Beamforming for Fully Steerable Linear Superarrays with Prescribed Nulls

Linear superarrays (LSAs) are linear microphone arrays composed of omnidirectional and first-order directional microphones, and their mixed-sensor manifold supports fully steerable differential beamforming. Building on established null-based target-beampattern theory and WNG-constrained beampattern-error design, this paper develops their joint realization for an LSA. Given a look direction and N prescribed null offsets, the corresponding Nth-order differential reference is obtained through the established null-constrained polynomial relation under the stated nonsingularity condition. The LSA weights are then obtained by minimizing the mean-squared beampattern error (MSBE) over the full array plane, subject to exact distortionless and null constraints and a prescribed white noise gain (WNG) lower bound. For the adopted omnidirectional/first-order-directional LSA model, the angular-integral matrices in the MSBE objective are evaluated analytically, while the final weights are obtained from the resulting convex program. Numerical simulations for the evaluated configurations show lower broadband MSBE than the maximum-WNG NC baseline, stable steering, and more consistent broadband patterns than the tested finite-order Jacobi-Anger designs. Anechoic-chamber measurements with an 11-element prototype further confirm that the main lobe, null structure, and steering behavior are retained in measured free-field responses.