P. N. Bashly, Y. A. Kuznetsov

In the vast majority of works devoted to the synthesis of optimum amplitude-phase distribution of antenna array, solved the problem of determining the complex amplitudes of the currents in all elements of the lattice. Such an approach is not always justified, since the order of optimization problem to be solved corresponds to the number of antenna array elements and becomes significant for the antenna array with a large number of elements. However, studies have shown that a number of applications of synthesis of antenna arrays is sufficient to manage complex amplitudes of the currents in the elements. Such arrays are quasioptimal. The purpose of this study is to develop a method of choice for non-regulated elements in the antenna array, allowing up to solving an optimization problem to determine the best version of the distribution of non-regulated items. The synthesis problem of antenna array with a functional as a ratio of Hermitian forms adequately studied in many papers. Synthesis problem of optimal and quasi-arrays associated with the definition of eigenvectors of the matrices corresponding to their maximal eigenvalues. And the transformations leading to a decrease in the order of Hermitian forms, clearly link these matrices. Therefore, there arises the problem of finding the optimal solution of the problem of synthesis with the functional as a ratio of Hermitian forms the basis of analysis of matrices of Hermitian forms and shapes of the beam formed by this attitude. We have made a spectral analysis of the beam for the problem of hermitian forms quasioptimal control-array antenna. The analysis estimates the lower boundary of the maximal eigenvalue of the pencil of Hermitian forms. Using this interface, in particular when the matrix in the numerator of the functional of the first rank, and there is an inverse dependence of the maximum eigenvalue of the beam shapes and minimal eigenvalue in the denominator to determine the best option unregulated distribution of elements in the antenna array, and thus achieve a minimum reduction energy characteristics of the antenna arrays at significantly reducing computing costs.