Applications of the implicitly constrained synthesis technique

An implicitly constrained synthesis technique is used to examine the effects of the number of radiating elements on csc/sup 2/ shaped beam pattern synthesis for both uniformly and non-uniformly spaced linear arrays. Compared to the base line Orchard-Elliott (1985) results for both the uniformly and non-uniformly spaced linear arrays a substantial reduction in the number of radiating elements results in minimal distortion to the shaped beam pattern. In addition the non-uniformly spaced arrays have significantly greater directivity and significantly less shaped beam pattern ripple than the uniformly spaced linear arrays. This technique is also applied to nonseparable planar distributions for both pencil and shaped beams. Pattern ripple, sidelobe level, and element magnitude and phase variation can be controlled.