The Algorithm for Retrieving the Surface Waves Parameters Using Doppler Spectrum Measurements at Small Incident Angles

In this paper, we present an algorithm for retrieving all the second statistical moments of the sea surface that affect the scattering of waves at small angles of incidence. A feature of this algorithm is the analysis of the spectral characteristics of the reflected waves only, without taking into account the backscattering cross section. The analysis of the width and the shift of the Doppler spectrum (DS) allows us to use the obtained algorithm without the preliminary instrumental calibration, which is necessary for the backscattering cross section. We give final expressions for calculating the width and the shift of the DS in the monostatic problem statement for small angles of incidence. We obtain the expressions within the framework of the Kirchhoff approximation, which makes them reliable only in the quasi-specular reflection region. Features of these formulas are the description of the surface by five statistical moments of the second order and taking into account the anisotropic antenna pattern (AP). To solve the inverse problem of retrieving sea surface parameters, we propose a measurement scheme including three motionless transceiver antennas with different APs. For this measurement scheme, we give analytical expressions for all five unknown parameters of surface waves. Also, we give a theoretical analysis of the accuracy of the algorithm obtained for different wind speeds and wind directions. All the results are valid for the scattering of both acoustic and electromagnetic waves.