Bias in Copolar Correlation Coefficient Caused by Antenna Radiation Patterns

We present a theoretical study of the bias in the copolar correlation coefficient caused by cross-polar radiation patterns and by unmatched horizontal and vertical copolar radiation patterns. The analysis of the bias induced by cross-polarization radiation is carried out for both modes of operation of polarimetric radars, designated as the simultaneous transmission and reception of horizontally and vertically polarized waves and the alternate transmission of horizontally and vertically polarized waves, respectively. The bias caused by unmatched horizontal and vertical copolar radiation patterns as a function of slight differences in pointing angles and beamwidths is also analyzed. In well-designed weather radars, for the purpose of hydrometeor classification, the overall acceptable bias in the copolar correlation coefficient should be less than about 0.01. The levels of cross-to-copolar gain ratios for acceptable performance are indicated. Ultimately, pointing angle and beamwidth tolerances are indicated for horizontal and vertical copolar antenna patterns.