Design of Superdirective Planar Arrays With Sparse Aperiodic Layouts for Processing Broadband Signals via 3-D Beamforming

Planar arrays are used jointly with filter-and-sum beamforming to achieve 3-D spatial discrimination in processing broadband signals. In these systems, the beams are steered in various directions to investigate a given portion of space. The band can be so wide as to require both superdirective performance (to increase directivity at low frequencies) and sparse aperiodic layouts (to avoid grating lobes at high frequencies). We propose an original method to simultaneously optimize the transducer positions and the coefficients of the Finite Impulse Response FIR filters, providing a solution that maintains its validity for whatever steering direction inside a predefined region of interest. A hybrid strategy, analytical for the coefficients and stochastic for the positions, is devised to minimize the beam pattern (BP) energy while maintaining an unaltered signal from the steering direction and controlling the side lobes. The robustness of the superdirectivity is achieved by taking into account the probability density functions for the characteristics of realistic transducers. A distinctive feature of our method is its ability to maintain the computational tractability of the addressed optimization problem by drastically reducing the burden of evaluating the cost function. The obtained results, addressing tens of transducers and several octaves of band, demonstrate the effectiveness of the proposed method in terms of directivity, contrast, and robustness.