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Standard Deviation of the Copolar Correlation Coefficient for Simultaneous Transmission and Reception of Vertical and Horizontal Polarized Weather Radar Signals

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  • 1 Centre Coopératif pour la Recherche en Mésométéorologie (CCRM), and Département des Sciences de la Terre et de l’Atmosphére, Université du Québec à Montréal, Montreal, Quebec, Canada
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Abstract

The perturbation method is used to derive the variance of the zero-lag copolar correlation coefficient,  | ρHV | , for a radar simultaneously transmitting and receiving both horizontal and vertical polarization. The variance of  | ρHV |  is a function of its expected value, the number of samples, the normalized Doppler velocity spectrum width, συn, 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  | ρHV |  for alternate and simultaneous transmission and reception of horizontal and vertical polarization is discussed. Calculations show that variations in the expected value of  | ρHV |  from 0.7 to 0.98 lead to a decrease in the precision of the estimate of  | ρHV |  of more than one order of magnitude: for narrow spectra (συn < 0.04) the estimates do not depend on the sampling scheme used but on the number of samples taken, and at larger spectrum widths (συn > 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.

Current affiliation: Ericsson Research Canada, Town of Mount Royal, Quebec, Canada

Corresponding author address: Enrico Torlaschi, Département des Sciences de la Terre et de l’Atmosphère, Université du Québec à Montréal, Case postale 8888, succursale Centre-Ville, Montreal, QC H3C 3P8, Canada. Email: torlaschi.enrico@uqam.ca

Abstract

The perturbation method is used to derive the variance of the zero-lag copolar correlation coefficient,  | ρHV | , for a radar simultaneously transmitting and receiving both horizontal and vertical polarization. The variance of  | ρHV |  is a function of its expected value, the number of samples, the normalized Doppler velocity spectrum width, συn, 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  | ρHV |  for alternate and simultaneous transmission and reception of horizontal and vertical polarization is discussed. Calculations show that variations in the expected value of  | ρHV |  from 0.7 to 0.98 lead to a decrease in the precision of the estimate of  | ρHV |  of more than one order of magnitude: for narrow spectra (συn < 0.04) the estimates do not depend on the sampling scheme used but on the number of samples taken, and at larger spectrum widths (συn > 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.

Current affiliation: Ericsson Research Canada, Town of Mount Royal, Quebec, Canada

Corresponding author address: Enrico Torlaschi, Département des Sciences de la Terre et de l’Atmosphère, Université du Québec à Montréal, Case postale 8888, succursale Centre-Ville, Montreal, QC H3C 3P8, Canada. Email: torlaschi.enrico@uqam.ca

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