Cross-Correlation of Radar Signals Separated in Frequency Bistatically Reflected by a Water Surface

Reliable and up-to-date information on the parameters of sea waves is in demand in solving a wide range of fundamental and applied problems, in particular, those related to meteorology and oceanology. Expanding the possibilities of remote sensing can be achieved using dual-frequency radars. During the study, an analytical formula was obtained for the cross-correlation function of two radar signals reflected in the quasi-specular region, which are close in frequency. The problem is considered in a general form for the bistatic sensing using the Kirchhoff approximation. The solution considers the radiation patterns of the emitting and receiving antennas, which can be set as asymmetric. The reflecting water surface is described by 4 statistical parameters: height variance, slope variance in two perpendicular planes, and correlation coefficient of slopes in two perpendicular planes. Also, an expression is given for the case of emission and reception of signals strictly along the normal to the undisturbed water surface, which is like the measurement scheme of a satellite radar altimeter. In the experiment, it is proposed to measure the modulus of the correlation coefficient, the expression for which, in a particular case, was obtained in the work. The resulting expressions can be used to create new remote sensing schemes for retrieving the variances of wave heights and slopes, as well as the correlation coefficient of slopes in two perpendicular planes.