Mathematical description of imaging processes in ultra-wideband active aperture synthesis systems using stochastic sounding signals

Abstract

Mathematical models of the fields of stochastic ultra-wideband signals that are necessary for solving problems of aperture synthesis of images using active radar methods are presented. The expediency of using V-transformations in these problems has been substantiated, the effectiveness of which has already been proven for the mathematical description of ultra-wideband spatio-temporal fields in the methods of passive and active radar, as well as remote sensing, that are used to solve problems of radio astronomy, medicine, navigation. Using modern methods of mathematical analysis and the theory of ultra-wideband systems, the physical essence of radio images obtained with the help of algorithms for coherent and incoherent signal processing is investigated. According to these algorithms, it is proposed to divide images into coherent and incoherent. Coherent images include those in which its amplitude and phase are recorded separately. In the case of an incoherent image, only its amplitude (power or related characteristic) is recorded. To describe of the obtained radio image structure, new concepts of the spectral density of the complex spatial coherence function (SDCSCF) and the spectral density of the spatial autocorrelation function of the amplitude-phase distribution (SDFSAF APD) are introduced. Application-use of functions is expedient and fundamentally necessary for solving problems of aperture synthesis using stochastic ultra-wideband signals. A mathematical description of the structures obtained by aperture synthesis of radio images is given. Here, studies are conducted for the general case of using a continuous (idealized) aperture, and for using an antenna system with spatially separated receiving elements. Simulation of the heuristic synthesized algorithm for constructing incoherent radio images is conducted. The possibility of using antenna arrays and synthesized aperture synthesis algorithms for solving problems of image formation in a survey located directly under the aircraft (at sounding angles close to vertical) are substantiated.