Synthesis of amplitude-phase distribution and shape of a planar antenna aperture for a given power pattern

The problem of synthesis of an optimum shape of a planar aperture and optimum amplitude-phase distribution over this aperture corresponding to a given power pattern is considered. The functional, which ensures minimization of the mean-square deflection of the magnitudes of the given pattern and of the synthesized one in the area of the main lobe and minimization of the sidelobes, is used as the optimization criterion. The problem of determination of the optimum functions of the shape or a planar aperture and of the excitation over this aperture is reduced to the determination of solution of the system of two nonlinear integral equations. The numerical algorithms of solution of these equations are based on utilization of the method of successive approximations and the Newton-Kantorovich method. The numerical results of synthesis of partial power patterns with rectangular and triangular outlines are presented