Sparsity-optimised farrow structure variable fractional delay filter for wideband array

In this paper, a new sparsity-optimised Farrow structure variable fractional delay (SFS-VFD) filter is proposed to address the aperture effect in wideband array. Our method is based on coefficient (anti-)symmetry and optimises the number and orders of its sub-filters, greatly reducing the non-zero coefficients. The established cost function is formulated as a parametric minimisation problem with multiple regularisation constraints, and solved by the modified three-block alternating direction multiplier method (MTB-ADMM), which is improved by introducing core variable correction items to ensure stable and fast convergence. Experimental results show that the SFS-VFD filter reduces the complexity of the system by decreasing the use of multipliers and adders while ensuring high delay accuracy. In wideband array, the SFS-VFD filter effectively corrects the aperture effect and achieves precise beam pointing.