Eigenvalue Signal Processing for Weather Radar Polarimetry: Removing the Bias Induced by Antenna Coherent Cross-Channel Coupling

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 the bias due to antenna coherent cross-channel coupling and is applicable in the LDR mode, the ATSR mode and the STSR orthogonal mode of weather radar measurements. In this paper, we focus on the LDR mode and consider copolar reflectivity at horizontal transmit (Z_HH), cross-polar reflectivity at horizontal transmit (Z_VH), linear depolarization ratio at horizontal transmit (LDRH) and degree of polarization at horizontal transmit (DOP_H). The ESP (ESP) method is substantiated by an experiment carried out in November 2012 using C-band weather radar with a parabolic reflector located at the Selex ES-Gematronik facilities in Neuss, Germany. The experiment involved 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 eigenvaluederived variables are invariant with respect to antenna coherent cross-channel coupling. This property had to be expected, since the eigenvalues of the Coherency matrix are SU(2) invariant.