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The statistical distribution that describes the received signal is important in the study of signal propagation for wireless communication and remote sensing. We study the effects of random rough surfaces with both 2- and 3-dimensional numerical simulations of Maxwell equations. Two methods are used in the Monte Carlo simulations. In the frequency domain method, the sparse matrix canonical grid (SMCG) method is used to solve the method of moments (MoM) matrix equation. Then the time domain signal is calculated by Fourier transform. In the time domain method, the time domain integral equation (TDIE) is used to calculate the time domain result directly. In the simulations, signal sources such as a narrow band CW signal and an ultra-wide band (UWB) signal are considered. The statistics of the scattered fields are analyzed. Results show that UWB has less fading compared with the narrow band pulse.