Synthesis of shaped beam antenna patterns using implicitly constrained current elements

The amplitude and phase values of the current elements of a linear array which produce a shaped-beam antenna pattern are found by a search over constrained space rather than through placement of pattern zeroes. The current elements must be constrained to realize physically producible patterns. Implicitly constraining the current elements enables Powell's direction set algorithm (DSA) to be used rather than a more elaborate explicitly constrained algorithm. In contrast with conventional methods, the zeroes of the pattern function in the sidelobe region are not constrained to lie on the Schelkunoff unit circle. To assess the utility of the proposed technique, a comparison is made with previously published results. Compared to conventional approaches, the resulting current element-to-element variation is significantly less, which minimizes mutual coupling difficulties. Both traveling-wave and center-fed designs are possible with the technique outlined in this paper.