A. O. Manichev, A. S. Kondratiev, V. A. Balagurovskii

Phase-only synthesis is a complex mathematical problem, which generally allows only an approximate numerical solution. Most of the known synthesis procedures imply that the amplitude-phase distribution (APD) over the array elements is exactly known. At the same time, in practice the APD is realized with certain random errors (distortions), which result in filling the nulls of the array pattern averaged over the ensemble of random realizations of APD distortions. In the case of stationary independent distortions, the minimum level of the average array pattern is determined by the number of the array elements and their amplitudes, as well as the parameters of the APD distortions. This level is further referred to as the background level. Recently, a method for the phase-only formation of deep nulls in the pattern of a phased array with APD distortions was proposed. This method uses measured complex values of the array pattern. However, this method does not control the width of the formed nulls. This means that, generally, the angular width of these nulls can be unacceptably small, while, in practice, formation of wide nulls is often required (for example, in order to suppress interferences with extended frequency spectrum or interferences moving in space). If the array APD is exactly known, wide nulls can be formed via the phase-only synthesis of a group of closely spaced nulls in prescribed directions. Unfortunately, the presence of random distortions usually leads to substantial difference between perfect and real array APDs, and, hence, to filling of the pattern nulls. In order to form both deep and wide nulls in the pattern of an array with random APD distortions, the following two methods are proposed. Method 1: (i) The initial radiation pattern with wide nulls in prescribed directions is synthesized. (ii) The complex values of the voltage array pattern in the directions of interferences (basic directions) are measured. (iii) The initial complex values of the array pattern determined at step (ii) are used to form nulls in the prescribed directions by the univariate search technique. Method 2: (i) The complex values of the voltage array pattern in the directions of interferences (basic directions) are measured. (ii) In order to widen the formed nulls, several additional directions in the neighborhood of the respective basic directions are chosen. (iii) Nulls are formed by the univariate search technique in both basic and additional directions, the initial complex values of the array pattern being determined as follows: (a) in the basic directions, the measured values are used; (b) in each of the additional direction, the following linear approximation is used where is the approximated value and and are the complex constants whose values are determined so that synthesized average power pattern in the given direction of the additional null is no greater than the background level. The efficiency of the proposed methods was tested experimentally via formation of one null in the radiation pattern of an unequally spaced phased array with 384 uniformly excited elements.