On the Stationarity of Signal Scattering by Two-Dimensional Slightly Rough Random Surfaces

We present statistical properties of signal scattering by two-dimensional slightly rough random surface. The work concerns the intermediate-field zone. Calculations are carried out within the framework of the first-order small perturbation method. The surface is assumed to be ergodic and stationary and the height distribution to be Gaussian. Under an oblique incidence, we demonstrate that the first-order scattered field is not wide-sense stationary. For a given altitude, under the normal incidence, the scattered field is a strictly stationary random process. By using the stationary phase method, we show that the scattered field becomes asymptotically a strictly stationary random process when increasing the altitude of the observation point. We also define the condition that must be satisfied by an antenna transfer function so that the measured scattered field becomes stationary and ergodic.