A new iterative method in numerical pattern synthesis

Abstract

AbstractIn general, in the problem of directivity synthesis, the objective function for optimizing the gain and conditions for constraining the fields of the sidelobe levels must be taken into account together. These kinds of problems had been solved by the so‐called quadratic programming method among other mathematical programming methods, but when the element number becomes large, so must the sidelobe constraint condition number. Thus this method becomes rather difficult in practice.In this paper such a directivity synthesis problem will be formulated as an optimization problem in which Lagrange multipliers will be employed for the objective function which is in quadratic form. Thus, the problem will be solved approximately by introducing Lemez' best‐approximation concept; the solutions will be obtained by use of an extremely simple and rapidly converging iteration‐numerical approach.Although this approach may occasionally yield solutions which are not optimized, its results will be sufficiently close to the optimized solution that it is a practical one. Since, especially, the iteration calculations can be attained by merely considering simultaneous equations, as a computer‐oriented method, this approach can yield solutions more rapidly than the quadratic programming method for a large number of elements.