Abstract
A fast pencil beam synthesis method for large-scale non-uniformly spaced four-dimensional (4D) arrays is presented in this study. It separates a non-uniformly spaced 4D array into several excitations dependent ‘conventional arrays’ with an identical array structure. Far-field radiation patterns of the two ‘conventional arrays’ correspond to the patterns at the centre frequency and the sidebands, respectively. An interpolation in a least square sense is then used to interpolate the non-uniform array structure with a uniform virtual array structure. Therefore, the iterative fast Fourier transform (IFT) method can be used to synthesise the two dependent ‘conventional arrays’ with a uniform virtual array structure. Owing to the efficiency of the fast Fourier transform, the proposed method is measurably faster than existing methods, especially for ultra-large-scale 4D arrays. Numerical examples including non-uniformly spaced 4D linear array (1024 elements) and non-uniformly spaced 4D planar array (32 × 32 = 1024 elements) are presented to validate the efficiency of the proposed method.
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