New closed solutions of the linear antenna synthesis problem according to amplitude radiation pattern

In the linear antenna case, the synthesis problem according to prescribed amplitude pattern is solved analytically with a limited numbers of complex parameters to be calculated. These parameters are defined from the set of transcendental equations. As they are nonunique, the optimal solution is chosen from the all obtained solutions. A measure of the synthesis effectivity is offered. The case, when the given amplitude pattern is constant inside the limited angle, is considered in detail and numerical results are presented