An Optimized Monte Carlo Procedure and Its Application in Electromagnetic Scattering From Rough Surfaces

In this paper, we propose an optimized Monte Carlo procedure with the variance reduction technique incorporated. The proposed method makes use of some auxiliary variables which embed the correlation information intrinsic in the iteration process; hence, the procedure can be systemized. The use of intrinsic information and the capability to systemize the procedure draw the essential difference of the proposed method with the control variable method in the Monte Carlo literature. The expression for the variance is derived, and an appropriate optimization problem is solved. The analysis of electromagnetic scattering from rough surfaces presents an ideal testbed for the proposed method. For 1-D surfaces considered in this paper, the simulation results have demonstrated that the proposed method can be three to five times faster than the conventional Monte Carlo procedure for the horizontal polarization and approximately two to four times faster for the vertical polarization. Moreover, it shows smoother angular patterns. Since the proposed method is quite general because of the following: 1) no specification is made about how the iterations should be carried out; hence, advanced techniques can be combined to offer the maximum efficiency, and 2) the quantity of interest needs not to be the scattering coefficient, problems such as those encountered in random medium may be treated using the proposed method.