Increasing the Angular Resolution and Range of Measuring Systems Using Ultra-Wideband Signals

The problem of obtaining three-dimensional radio images of objects with increased resolution based on the use of ultra-wide-band pulse signals and new methods of their digital processing is considered. The inverse problem of reconstructing the image of a signal source with a resolution exceeding the Rayleigh criterion has been solved numerically. Mathematically, the problem is reduced to solving the Fredholm integral equation of the first kind by numerical methods based on the representation of the solution in the form of decomposition into systems of orthogonal functions. The method of selecting the systems of functions used, which increases the stability of solutions, is substantiated. Variational problems of optimizing the shape and duration of ultra-wide-band pulses have been solved, ensuring the maximum possible signal-to-noise ratio during location studies of objects with fully or partially known signal reflection characteristics. The proposed procedures make it possible to increase the range of measuring systems, and also make it possible to increase the stability of solutions to inverse problems. It is shown that the use of the developed methods for achieving super-resolution to process ultra-wideband signals dramatically improves the quality of 3D images of objects in the radio range.