S. E. Mishchenko - Dr.Sci. (Eng.), Professor, Head of Dedicated Laboratory, Science and Research Institute of physics, Southern Federal University (Rostov-on-Don). E-mail: mihome@yandex.ru
N. V. Shatsky - C.Sci. (Eng.), Associate Professor, Senior Research Scientist, Science and Research Institute of physics, Southern Federal University (Rostov-on-Don). E-mail: shatskiy@sfedu.ru

At the decision of problems of synthesis, statistical theory of antennas allows to determine the statistical characteristics of the directivity of the antennas taking into account the fluctuations amplitude-phase distribution. The use of this approach allows to simulate the directional characteristics of the actual antenna systems with regard to their design features or rejections of elements. In the digital antenna lattice or in the active antenna lattice failures amplifiers in channels can be modeled by reducing the complex amplitudes of weight coefficients compared with the given values. The aim of the research is to develop a method of amplitude-phase synthesis of digital array antenna taking into account the amplitude distribution fluctuations and rejections of individual antenna elements. The mathematical model of the array antenna with the formation of amplitude-phase distribution with random errors of amplitudes and phases of complex weighting coefficients is proposed. Vector amplitude-phase distribution is represented as the sum of the regular part and a random error. The fluctuations of amplitudes and phases reflect the range of parameters of summation scheme. The summation scheme consists of low noise amplifier, frequency converter and multi-digit analog-to-digital converter in each channel. Solution of the problem of amplitude-phase synthesis of taking into account the developed mathematical model of the antenna array is obtained with classical gradient descent method. The efficiency of the proposed approach is confirmed by the results of the numerical simulation. The 64-element linear equidistant antenna array was considered. In the course of the studies examined the impact of rejects of elements on the solution of the synthesis problem. It is shown that the obtained solution of the problem of synthesis allows to reduce the distortion of the shape of the main beam in case of element rejection. Thus, if we have the statistics of antenna array elements rejection, the formulated amplitude-phase synthesis problem is in minimization of the standard deviation of the given directional diagram and average directional diagram according to the power with regard to fluctuations of amplitude-phase distribution and statistical dates about frequencies element rejects.