Synthesis of Large Nonuniform Spaced $4\mathsf{D}$ Linear Arrays Using an Iterative FFT Method

A fast pattern synthesis method for large nonuniform spaced four dimensional (4D) linear arrays is shown in this paper. It firstly separates a nonuniform spaced 4D array into two dependent `conventional arrays', whose far-field patterns correspond to the patterns at the center frequency and the sidebands, respectively. An interpolation is then introduced to interpolate the nonuniform array structure with uniform virtual array structure. The iterative fast Fourier transform (FFT) method can be thus used to synthesize the two dependent `conventional arrays'. Thanks to the high efficiency of the FFT, the proposed method is greatly suitable for the synthesis of ultra-large 4D arrays. Numerical example is presented to show the effectiveness of the proposed method.