A. V. Ashihmin, V. V. Negrobov, Yu. G. Pasternak, Yu. A. Rembovsky

In a number of publications of present article-s authors the opportunity of a field-s approximation near to three-dimensional scatterer, by measured results of its values with the help the antenna array in finite number of points of the closed contour has been shown. Thus use of the aprioristic information on geometry and material properties of the antenna array-s carrier chassis, underlying surface and another nearby scatterers is not required. As a result of the carried out researches it has been found out, that for approximation of a field close to the scatterer, a various approaches and methods, can be used, in particular: a methods of the theory of analytical functions of complex variable (Cauchy integral; Laurent series, etc.); the classical electrodynamics tool (Kirchhoff integral; a method of auxiliary sources of a field; a method of a "brilliant" points - allocation, etc.). It has been shown, that Use of the approximated field-s spatial readouts forming "virtual" antenna array, can be useful to essential increase of radio engineering systems - resolution of an angular coordinates, accuracy of an angular coordinates - estimation of radio emission-s sources, increase of capacity. Also the opportunity of efficiency increase of spatial distribution of antenna array elements near to the carrier chassis, estimated on criterion of mi-nimization of frequency- and azimuthal-averaged coordinate of an error of the field's phase distribution measurement deformed as a result of dispersion of waves on the antenna system carrier chassis has been shown. In the present work an attempt of classification of various ways of "virtual" antenna array-s formation and their substantiation from positions of an electrodynamic principle of fields - sources equivalence is undertaken. It is shown, that the theory of "virtual" antenna arrays can be constructed on the basis of use of the tool of Kirchhoff integral, Lorentz lemma and a method of point sources. Expressions and numerical ratios for errors of the field-s description on contours by physically existing and "virtual" antenna array, and also on a contour of an auxiliary field sources - location are received. Equivalence of methods of the field's description on a contour by the "virtual" antenna array, based on use of the tool of Kirchhoff integral and representation of a field as superposition of fields several points (or linear) sources is shown. The developed method the "virtual" antenna array, can be used not only in various radio engineering appendices: radiocommunication, radiolocation, radionavigation, electronic warfare, etc., but also in various technical appendices of optics and acoustics, also can be used for the description electromagnetic (or acoustic) fields close to scatterers with the any form, the sizes and material properties, without use of the aprioristic information on characteristics and parameters of scattering object (the antenna array-s carrier chassis, a support mast, and also other objects). In particular, the "virtual" antenna array method can be used for improvement of the basic characteristics of radio engineering, optical and acoustic systems: increases of accuracy of radio and acoustic radiation sources - coordinates - measurement, an increase of equipment-s resolution on angular and linear coordinates, an elimination of sources - direction finding ambiguity, an increase of radio engineering, optical and acoustic equipment-s capacity, an increase of a priori unknown geometrical and material properties - research accuracy, etc., due to formation the "virtual" antenna array with an any location and number of elements. Let-s especially note that the suggested "virtual" antenna array-s method can be rather effective in various complexes in which the technologies of processing of signals SIMO (Single Input, Multiple Output) and MIMO (Multiple Input, Multiple Output) is realized, used for essential increase of capacity in conditions of signals - multipath propagation. The suggested method allows to restore an electromagnetic (or acoustic) fields - structure near to any scatterer with a priori unknown parameters, thus technical result - improvement of the basic characteristics of radio engineering, optical and acoustic systems is achieved due to restoration of a field-s structure in the spatial areas corresponding to the minimal distortions degree of received (or radiated) waves by scatterer. It is necessary to note also, that the "virtual" antenna array-s formation with an any configuration and number of elements allows to optimize structure and parameters of the real antenna system by criterion of minimization of distortions of its directional diagram by the carrier chassis (a support mast with tension wires, blocks of the equipment and by others nearby scatterers), thus doesn-t require carrying out of the big number of computing operations and any natural experimental researches. Restoration of an electromagnetic (or acoustic) fields - structure can be made with the help of the most various algorithms, for example: based on use the properties of harmonious functions (scalar and vector fields), the theory of functions complex variable (in particular - theories and appendices of analytical functions), approximations of a field in "internal" and "external" areas in relation to the antenna array of stationary, mobile or onboard basing with the help of any system of functions having property of completeness in considered area of space ( , ).