A Low-Complexity 2-D FIR Parallelogram Filter for Broadband Beamforming with Sparse Linear Arrays

Broadband beamformers designed as two-dimensional (2-D) spatially-interpolated finite-extent impulse responses (FIR) filters, using a cascade structure, cannot employ sparse linear arrays despite significantly reducing the computational complexity. This happens due to the fact that the 2-D masking filter requires spatial samples equal to the spatial order at the input. Therefore, the output of the 2-D spatially-interpolated prototype filter should be computed for more than one spatial index. In order to address this limitation, we propose a 2-D spatially-interpolated FIR filter using a parallel structure. With the proposed structure, both 2-D spatially-interpolated prototype filter and the 2-D masking filter need to compute the output only for one spatial index, therefore allowing to employ sparse linear arrays. In order to support broadband beamforming, we design the 2-D FIR filter to have a parallelogram passband. Furthermore, we design the 2-D FIR filter to have linear phase response and to be optimal in the minimax sense. The simulation results confirm that the proposed 2-D FIR filter provides a considerable reduction in the number of antennas, compared to previously proposed 2-D FIR filters, with a slight degradation in the fidelity of enhanced broadband signals, which are distorted by strong radio frequency interference and noise signals.