Perturbation-Theory-Based Method for Initial Arrangement of Large-Spacing Aperiodic Scanning Arrays

The large-spacing array saves radiation elements under a fixed aperture to reduce energy consumption and cost. However, the issue it faces is the grating lobe, which limits its application. As a typical and reliable method, the global optimization algorithm obtains the large-spacing aperiodic scanning arrays (LSASAs) with global iterative search. Nevertheless, as the array scale expands and the aperiodicity complicates further, the time cost is unacceptable, and even the algorithm cannot converge. A time-saving solution is to give a reasonable initial arrangement to reduce the time cost of subsequent optimization. Even it can be used directly due to its excellent performance. Therefore, a quasi-analytical method for generating the initial arrangement of LSASA is proposed by adapting the idea of the perturbation theory. Then, the initial arrangements of different scales and spacings obtained within a brief timeframe are used to verify the effectiveness. Moreover, a
$4\times8$
array with a relative impedance bandwidth of 21% and an average spacing of one wavelength is fabricated. The results show that the array realizes the beam steering of ±30° and ±60° with the sidelobe level (SLL) less than −9.0 and −8.3 dB in the E- and H-planes. Notedly, these LSASAs are obtained in mere seconds.