Efficient gridless wideband sparse array synthesis with tapped delay-lines

In this paper, we propose a new wideband sparse array synthesis method based on gridless compressed sensing to solve the basis mismatch problem for discrete grids. Considering the tapped delay-lines (TDL) structure for space-time domain processing, and using successive frequency-varying atoms for sparse representation of wideband signals, an arbitrary sampling-atomic norm minimization is introduced to model the group sparsity-constrained wideband arrays in which the positions and the excitation values of array element are obtained with a high freedom. The above nonconvex problem is then transformed into a convex relaxation, which is solved using the Prolate Spheroidal Wave Functions (PSWFs). The experimental results show that the proposed sparse array design has higher matching accuracy and sparsity, compared with the discretized wideband sparse array design, which verifies the effectiveness and efficiency of this method.