It is known that nowadays antennas are widely used both as separate weakly directed radiators, particularly at superhigh-speed aircraft, and as elements of phasing antenna (PAA).

At first consider the problem of synthesis of a slot antennas. It is useful to present this problem as two separate problems, i. e. An internal and an external ones.

While the external problem consists in determination of the amplitude-phase distribution of a field in exposing an antenna in the prescribed radiation pattern, the internal problem consists in estimating the function of sources that realize the amplitude-phase distributions of a field that were found as a solution of the first problem. Thus, the external problem is the problem of synthesis of the radiation pattern, while the internal problem is that one of synthesis of the field amplitude-phase distribution.

A lot of papers of Russian and foreign authors are devoted to solution of the external problem. One can find an information at most of them, for example, in the well-known monograph [1], and we won't dwell on this problem.