Antenna arrays synthesis by the given amplitude directivity pattern with due regard for the mutual coupling of radiators

This paper described a numerical method of solving the synthesis problems of the antenna arrays by the given amplitude directivity pattern (DP), which takes into account the mutual coupling of radiators. For solving the analysis problem we used the sharp electrodynamics and appropriate mathematical models of antenna array, that gives an opportunity to regard the vector character of the electromagnetic field and the mutual coupling of radiators. Smoothing functionals are used for the variational statements of the amplitude-phase and phase synthesis problems. The existence theorems are proved, the numerical algorithms for solutions finding are constructed and justified. It is shown that nonlinear synthesis problems have nonunique solutions, their number and the qualitative characteristics depend on properties of the given amplitude DP symmetry and electrical sizes of the array.