Synthesis of two-dimensional antenna arrays by the method of generalized separation of variables

The method of generalized separation of variables is used to solve the problem of synthesis of antenna array with given form according to a given amplitude radiation pattern.  An approximate solution obtained as a sum of terms with separated indexes.  Such terms are calculated successively one by one at each step of the method from the condition of minimum of the corresponding functional.  The minimization problem is reduced to the problem of solving the system of non-linear algebraic equations.  General approaches of the method are specified for the cases of flat rectangular, flat hexagonal and cylindrical arrays.  Proper attention has been paid to building effective computing procedures.  The numerical results of solving several model problems are given.  It is shown that the method allows us to get a satisfactory solution from a practical point of view in two to three steps.

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Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 386–397 (2019)