V.A. Voloshin, A.Yu. Larin, S.E. Mishchenko, A.S. Trekin
To solve the problems of phase synthesis of antenna arrays are widely used method is the projected gradient. In the known literature, it is shown that the resulting synthesis solution strongly depends on the choice of the goal function.
We found analytical expressions for the components of the gradient of the two goal functions. These two goal functions describe the value of the mean-square deviation of the synthesized radiation pattern from a given pattern. Here, the first goal functions allows you to estimate the magnitude of the deviations in the space of complex radiation patterns, and the second – in the space of the amplitude patterns. It is shown that the gradients of goal functions for the two analytical expressions can be reduced to a single representation. This means that under certain initial conditions, iterative procedures for solving phase synthesis can still be matched. In solving the problem of synthesis in the space of complex patterns all the integral coefficients can be found in advance of the iterative procedure. In the space of the amplitude radiation patterns part of the integral coefficients to be specified at each step of the iterative process, which could have a significant impact on the performance of the method of synthesis.
In the numerical studies have provided estimates of the projected gradient method, the speed depending on the choice of the goal function. It is shown that the quality of the solution phase synthesis in the space of complex radiation patterns influence the choice of the phase diagram given orientation. On the example of the cosecant synthesis problem in the space of amplitude patterns is established that the phase pattern can be approximated by a linear function. This allowed a reasonable choice of a complex given pattern and get the solution phase synthesis of antenna array in the space of complex patterns, which coincide with the solution phase synthesis in the space of the amplitude radiation patterns.