Synthesis of a shaped beam pattern for a non-uniformly spaced, phase constrained linear array

The amplitudes, phases, and positions of the radiating elements of a non-uniformly spaced array which produce a csc/sup 2/ shaped beam pattern are found by a search over constrained space. The radiating elements´ magnitudes, phases, and positions must be constrained in order to realize physically producible patterns. Implicitly constraining the radiating elements´ magnitudes, phases, and positions allows the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to be used rather than an algorithm with explicit constraints. This technique optimizes both the pattern ripple in the shaped region and the sidelobe level in the sidelobe region while simultaneously restricting the radiating elements´ magnitude, phase, and position to physically achievable values. In order to assess the utility of the proposed technique a comparison is made with results from the Orchard-Elliott (1985) technique for uniformly spaced arrays. In addition, the implementation of the results of the implicitly constrained synthesis and the Orchard-Elliott synthesis in an end fed overlay coupled stripline array is discussed. Compared to the Orchard-Elliott results, the pattern ripple in the shaped region, the element-to-element magnitude and phase variation, and the power delivered to the load are substantially less for the implicitly constrained synthesis results.