Deep null fixing on optimal compromise among sum and difference patterns of thinned arrays through the Schelkunoff unit circle representation.

Difference far-field patterns represent a way for pin-pointing a target in both azimuth and elevation, extremely useful in radar applications. At the present work, an innovative method for synthesizing good compromise solutions among sum and difference patterns providing low complexity of the antenna feeding network for uniform thinned arrays is addressed. This procedure uses a hybrid version of the Simulated Annealing algorithm (hybrid SA) to optimize a cost function of radiation characteristics for both sum and difference patterns as peak directivity and side lobe level (SLL) while fixing deep nulls. In this framework, examples of half-wavelength spaced linear arrays from 40 to 120 elements were analyzed, as well as an extension to planar arrays by means of separable distributions was developed. The performance of the method is analyzed with different examples and its potential outlined, showing the ability of fixing deep nulls in both sum and difference patterns which share the same uniform excitation relative amplitudes.

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

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.