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.