A polarimetric covariance matrix concept for random radar targets

A covariance matrix concept for reciprocal random targets is presented which describes the polarisation dependence of the mean radar observables, i.e. the signatures of powers and correlation of the backscattered wave components, by unitary similarity transformations. Thus, important polarimetric invariances are preserved and limiting conditions for the backscattered powers revealed. As an important result, the derivatives of all covariance matrix elements with respect to the transmitter polarisation can be determined, involving only the covariance matrix elements. These derivatives physically describe how rapidly the measurable radar observables vary if the transmitter polarisation is changed. Analytical and numerical methods are presented, finally, to determine the optimal polarisations of the co- and crosspolar power signatures