About one method of solution of the synthesis problems of radiating systems after the given power directivity pattern

A numerical solution method of the synthesis problems of radiating systems after the given power directivity pattern (DP) is presented. On the operational level the variational statement of the problems that takes into account a mean-square discrepancy between the given and synthesized DPs, and also weighed restriction on norm the extrinsic sources of excitation is considered. The existence theorems of quasi-solutions are proved. It is shown that the problem has a nonunique solution. Numerical algorithms of their determination are built and discussed.