Investigation of nonunique solutions in the synthesis problems of radiating systems with a flat aperture according to the prescribed amplitude directivity pattern

There is continued study of a problem of non- unique solutions in synthesis problems of the radiating systems with a plane aperture depending on values of two parameters characterizing the size of aperture and solid angle where the required amplitude directivity pattern (DP) is given. The existence and properties of real (initial) solutions of the four types are elucidated. The ramification of initial solutions of the second type is investigated. In the first approximation there are found analytical expressions of complex solutions that branching from real solution, and was found out their main properties. Numerical experiments on the study of the efficiency of real and branched complex solutions are carried out.