Standard deviation of the copolar correlation coefficient for simultaneous transmission and reception of vertical and horizontal polarized weather radar signals

The perturbation method is used to derive the variance of the zero-lag copolar correlation coefficient, |rho(HV)|, for a radar simultaneously transmitting and receiving both horizontal and vertical polarization. The variance of |rho(HV)| is a function of its expected value, the number of samples, the normalized Doppler velocity spectrum width, sigma(vn), and the signal-to-noise ratio in the receivers. Assuming the covariances and cross covariance of the radar signals are represented by zero-mean complex Gaussian processes, the precision of the estimate of |rho(HV)| for alternate and simultaneous transmission and reception of horizontal and vertical polarization is discussed. Calculations show that variations in the expected value of |rho(HV)| from 0.7 to 0.98 lead to a decrease in the precision of the estimate of |rho(HV)| of more than one order of magnitude: for narrow spectra (sigma(vn) < 0.04) the estimates do not depend on the sampling scheme used but on the number of samples taken, and at larger spectrum widths (σ(vn) > 0.1) the simultaneous scheme can be more than one order of magnitude more precise than the alternate scheme. Furthermore, for good precision the signal-to-noise ratio should exceed 10 dB.