Under a fixed laboratory frame, the electromagnetic theory of the scattering of a plane wave of arbitrary polarizations incidence from arbitrary angles by a uniaxial anisotropic medium was obtained for the first time, and could be solved analytically from an eigensystem determined by a uniaxial anisotropic medium. By applying the boundary conditions at respective interfaces of the coated spherical structure, the unknown expansion coefficients can be obtained from the incident field and the electromagnetic fields in the anisotropic medium, and from the scattered field. Not only did the numerical results demonstrate the validity of our proposed theory but this paper shall also provide discussions in relation to some general cases (under arbitrary incident angles) of bistatic radar cross section
