Optimizing Radiation Patterns of Thinned Arrays with Deep Nulls Fixed through Their Representation in the Schelkunoff Unit Circle and a Simulated Annealing Algorithm

Abstract

The present work develops an innovative methodology for fixing deep nulls in radiation patterns of symmetrical thinned arrays while maintaining a low side lobe level (SLL) and a high directivity, implementing an optimization strategy based on the simulated annealing algorithm (SA). This procedure optimizes a cost function that has a term for each characteristic of the desired radiation pattern and can distinguish between the deep nulls and the filled ones depending on whether they are on the Schelkunoff unit circle or not. Then, a direct extension of the methodology for planar arrays based on the separable distribution procedure is addressed. Consequently, some examples with half-wavelength spacing are presented, where the fixing of one, two, or three deep nulls in arrays of 40, 60, and 80 elements are illustrated as well as an extension to a 40 × 40-element planar array with rectangular grid and rectangular boundary, with two deep nulls fixed on each one of its main axes. Additionally, a comparison of the obtained results with a genetic algorithm (GA) alternative is performed. The main advantage of the proposed method is its ability to fix deep nulls in the radiation patterns, while maintaining an easy feeding network implementation.