Notes on invariant characters of radar cross sections

It has been proved in a former paper (see Ke, Y.A., Proc. Int. Conf. of Radar, 2000) that three average radar cross sections (RCSs) have a simple relationship, S_mav:S_pav:S_vav = 3:2:1, where S_mav is RCS for polarization matched radar, S_pav is RCS for common antenna radar and S_vav is RCS for cross polarization radar. The relations are valid for an arbitrary target, at arbitrary aspect-angle and at arbitrary polarization base. So, we may call it the "3-2-1" theorem in radar theory. Here, the average is the probability mean and it is assumed that the radar transmitting polarization runs on the Poincare polarization sphere with uniformly distributed probability density function. Some further notes on the "3-2-1" theorem are presented, including a more general proof, showing its validity for random radar scattering matrices