A General Approach to the Design of the Fractional-Order Superdirective Beamformer

The superdirective beamformer (SD) with a linear array exhibits the maximum directivity factor (DF) in the isotropic noise field. Previously, a fractional-order SD (FO-SD) has been designed to achieve a compromise between the robustness and the DF. However, this method may suffer from two limitations. First, it only considers the Jacobi-Anger expansion-based beampattern synthesis. Second, it cannot control the DF in spherically isotropic noise field. To address these problems, we propose a general approach to the design of the FO-SD, which is a linear combination of two SDs with the integer order that can be designed with any beampattern synthesis method. Moreover, the proposed approach is able to control the WNG and the DF in both spherically and cylindrically isotropic noise field. Computer simulations substantiate the effectiveness of the proposed FO-SD over the existing SDs.