Using Prony´s Method To Synthesize Discrete Arrays for Prescribed Source Distributions and Exponentiated Patterns

Antenna pattern synthesis remains an important topic in electromagnetics. One goal of continuing interest has been that of developing an array of discrete sources that replicate the radiation pattern of continuous sources such as an aperture radiator or some current distribution. Another is to determine a discrete array that produces a prescribed radiation pattern. This paper outlines a procedure based on Prony´s method for finding discrete-source arrays to accomplish these goals. A variety of problems are presented to demonstrate the performance of Prony pattern synthesis. In addition, discussed is the use of singular-value analysis to establish the rank of a given pattern, the synthesis of arrays that produce exponentiated patterns, and the effect of noisy source strengths on the realized patterns.