Scattering from random rough surface has been of interest for decades. Several

methods were proposed to solve this problem, and Kirchho approximation (KA)

and small perturbation method (SMP) are among the most popular. Both methods

provide accurate results on rst order scattering, and the range of validity is limited

and cross-polarization scattering coecient is zero for these two methods unless these

two methods are carried out for higher orders. Furthermore, it is complicated for

higher order formulation and multiple scattering and shadowing are neglected in these

classic methods.

Extension of these two methods has been made in order to x these problems.

However, it is usually complicated and problem specic. While small slope approximation

is one of the most widely used methods to bridge KA and SMP, it is not easy

to implement in a general form. Two scale model can be employed to solve scattering

problems for a tilted perturbation plane, the range of validity is limited.

A new model is proposed in this thesis to deal with cross-polarization scattering

phenomenon on perfect electric conducting random surfaces. Integral equation

is adopted in this model. While integral equation method is often combined with

numerical method to solve the scattering coecient, the proposed model solves the

integral equation iteratively by analytic approximation. We utilize some approximations

on the randomness of the surface, and obtain an explicit expression. It is shown

that this expression achieves agreement with SMP method in second order.