Amplitude and Phase Statistics for Bistatic Scattering from Rough Surfaces

In this paper we study the statistical characteristics of scattering from rough surfaces. By assuming normal-distributed and correlated real and imaginary scattering components, we derive analytical probability density functions (pdfs) for the amplitude and phase. The amplitude pdf is in the form of an infinite sum of modified Bessel functions while the phase pdf is expressed in terms of the error function. The analytical amplitude and phase distributions are verified by comparing with both the empirical distributions of simulated data and experimental measurements. Simulated data sets are derived from Monte Carlo simulations of bistatic scattering from ocean-like rough surfaces. Experimental data were collected from monostatic measurements conducted at a wind-roughened reservoir with an S-band polarimetric radar. These simulated and experimental results show that the amplitude and phase pdfs vary with wind speed, observation angle, and polarization. The TM wave is observed to have a wider amplitude distribution than a TE wave. The phase of the scattered field is not uniformly distributed, especially under the low wind condition. The analytical amplitude and phase distributions are in good agreement with the empirical distributions of both simulated and experimental data sets.