Modeling of plane waveguide array using the variational approach and aperture orthogonal polynomials method

The synthesis problem of the waveguide array according to the prescribed amplitude radiation pattern is considered. The mutual coupling of the separate elements of array is taken into account in the process of solution of a direct problem (analysis problem). Variational statement of the synthesis problem and application of the aperture orthogonal polynomials (AOP) method, are considered as alternative approaches to solve the synthesis problem. The functional representing a mean-square deviation of the prescribed and received radiation patterns is minimized, as well as the expansion of sought amplitude-phase distribution of current, in the series by some kind of AOP that implies the finding the expansion coefficients, are used for finding the optimal amplitude distributions of current in array. The corresponding nonlinear equations are reduced; and the modeling results are shown.