Fast computation of wideband beam pattern of large three-dimensional arbitrary arrays

In order to solve the problem that computation of wideband Beam Patterns(BPs) of large three-dimensional(3-D) arrays is too slow to meet the requirements of designing large array using the conventional frequency-domain Direct Method(DM),a fast method is proposed for computation of wideband BPs of large 3-Darbitrary arrays.Based on the previous frequency-domain methods of computing wideband BPs of 2-D arrays using 2-D Nonuniform Fast Fourier Transform(NUFFT),the proposed method applies 3-D NUFFT as well as nonlinear interpolation to realize fast computation of wideband BPs of 3-D arrays,in which the third space frequency variable is brought in by conversion of the phase term related to the vertical coordinate of 3-D arrays.The minimum number of divisions of spatial frequency is theoretically deduced to meet the accuracy requirements of BP interpolation.Theoretical analyses show that computational cost of the proposed method is reduced by about one order of magnitude compared with the conventional DM,while keeping the computational error around 1%.Simulations are conducted to verify the theoretical conclusions.The proposed method makes it possible to design large 3-D wideband arrays by using optimizing algorithms which need massive iterations.