We present a novel digital signal processing procedure, named Eigenvalue Signal Processing (henceforth ESP), patented by the first author with Brookhaven Science Associates in 2013. The method enables the removal of antenna coherent cross-channel coupling in weather radar measurements at LDR mode and ATSR mode. In this work we focus on the LDR mode and consider reflectivity at horizontal transmit (ZH), linear depolarization ratio at horizontal transmit (LDRH) and degree of polarization at horizontal transmit (DOPH). The eigenvalue signal processing method is substantiated by an experiment carried out in November 2012 with a parabolic reflector C-band weather radar located at the Selex Systems Integration (SI) facilities in Neuss, Germany. The experiment consists of the comparison of weather radar measurements taken 1.5 minutes apart in two hardware configurations, namely with cross-coupling on (cc_on) and cross-coupling off (cc_off). It is experimentally demonstrated that eigenvalue-derived variables are invariant with respect to antenna cross-channel coupling. This property had to be expected, since the eigenvalues of the Coherency matrix are SU (2) invariant.