COHERENT RADAR IMAGING - SIGNAL-PROCESSING AND STATISTICAL PROPERTIES

The recently developed technique for imaging radar scattering irregula rities has opened a great scientific potential for ionospheric and atm ospheric coherent radars. These images are obtained by processing the diffraction pattern of the backscattered electromagnetic field at a fi nite number of sampling points on the ground. In this paper, we review the mathematical relationship between the statistical covariance of t hese samples, [(f) over cap (f) over cap(dagger)], and that of the rad iating object field to be imaged, [FFdagger], in a self-contained and comprehensive way. It is shown that these matrices are related in a Li near way by [(f) over cap (f) over cap(dagger)] = aM[FFdagger]M(dagger )a; where M is a discrete Fourier transform operator and a is a matri x operator representing the discrete and limited sampling of the field . The image, or brightness distribution, is the diagonal of [FFdagger] . The equation can be linearly inverted only in special cases. In most cases, inversion algorithms which make use of a priori information or maximum entropy constraints must be used. A naive (biased) ''image'' can be estimated in a manner analogous to an optical camera by simply applying an inverse DFT operator to the sampled field (f) over cap and evaluating the average power of the elements of the resulting vector (F) over cap. Such a transformation can be obtained either digitally o r in an analog way. For the latter we can use a Butler matrix consisti ng of properly interconnected transmission Lines. The case of radar ta rgets in the near field is included as a new contribution. This case i nvolves an additional matrix operator b, which is an analog of an opti cal lens used to compensate for the curvature of the phase fronts of t he backscattered field. This ''focusing'' can be done after the statis tics have been obtained. The formalism is derived for brightness distr ibutions representing total powers. However, the derived expressions h ave been extended to include ''color'' images for each of the frequenc y components of the sampled time series. The frequency filtering is ac hieved by estimating spectra and cross spectra of the sample time seri es, in lieu of the power and cross correlations used in the derivation .