Yu. I. Choni, A. E. Tsoupikov

Under conditions that a desired amplitude pattern and electromagnetic compatibility are required, antenna array synthesis can be formulated as a minimization of the following goal function G(U1,...UN) = ||Ao(θ,φ) exp(jψ(θ,φ) ? F(θ,φ)||2 +  ||E||2, where Ao(θ,φ) is a desired amplitude pattern, ψ(θ,φ) is an uncertain phase pattern which gives an additional way for improving the solution, F(θ,φ) is an antenna pattern corresponding to а current distribution {U1,..UN}, E is a near-field in a controlled region S. As usual, the minimization of function G(U1,...UN) can be reduced to a system of N linear equations. It is not difficult to show that the goal function value is being decreased steadily as a result of following iteration algorithm of phase pattern optimization. At the first iteration they use an arbitrary function as a phase pattern ψ(θ,φ), solve the relevant equations system and determine а new phase pattern ψ1(θ,φ) which corresponds to the obtained solution. At the next iteration the new phase pattern is used as a phase pattern ψ(θ,φ) and so on. They stop the iteration process if the phase patterns become practically unchangeable. It seems to be a sound idea to determine a geometric configuration of a designed antenna array by enlarging one-by-one the number of elements. At what the new element has to be selected according to a criterion controlling the element ability to improve antenna amplitude pattern and reduce field energy. Such a criterion can be calculated as the cosine of the angle between two abstract vectors being assembled from patterns and fields corresponding to the antenna array and a new source. A number of computations illustrates the optimization algorithms particularities. It is revealed that phase pattern optimization is а very effective way to improve antenna array characteristics as reducing of field energy in a region S follows improving amplitude pattern. For instance, due to the spatial phase pattern being obtained with the proposed algorithm it is possible to initiate such a near field structure that demonstrate an amazing effect as if electromagnetic field flows around the region S and forms а pattern which is intrinsic one to the aperture being not obstructed. Such an effect is impossible in wide spread situations when a spherical phase pattern with center in the middle of aperture is demanded.