Algorithm of the Radar Imaging by Using the Wideband Signals with the Distorted Signal Phases

Abstract

The problem of restoring an image by its Fourier transform is considered when the Fourier transform contains phase distortions. The nature of these distortions and their values are arbitrary. The criterion for the quality of the phase distortion estimates is suggested. It can be used to select the image which is mostly like the true one. The nature of the true image is also arbitrary. The only condition for the true image is that it is real and positive for all the points of the restored area. The other condition for the task is that the recovered image is calculated as the absolute value of the inverse Fourier transform. The algorithm for the search of the compensating phases satisfying the criterion is not considered for the general case; however, the task of the radar imaging based on the wideband signal and the time synthesis of the aperture is treated in detail. The physical basis for the task is a wideband pulse radar signal reflected by a moving object. As a result, a two-dimensional aperture is synthesized along the range, due to the super resolution, and along the velocity, according to the motion of the object. The radar signals are received by a single receiver. The image is reconstructed on the basis of these signals by using the maximum likelihood technique. The method uses the coherent processing of the signals. In practice, the coherence can be destroyed (due to some atmospheric turbulence or equipment instability, due to some inaccuracy in defining the motion). We assume that the objects to be observed are located at the far zone. For this task and on the basis of the suggested criterion, we develop an approximate algorithm for searching the best compensating phases in the radar signal. The quality of the images is tested with the help of simulation.