Time-Domain Computation of Mean and Variance of Doppler Spectra

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  • a Laboratory for Atmospheric Probing, University of Chicago, Chicago, IL 60637
  • | b Illinois State Water Survey, Urbana, IL 61801
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Abstract

The mean VT, variance σT2 and signal-to-noise ratio SNRT of Doppler spectra from precipitation in a thunderstorm and from radar signal reflecting chaff have been estimated by an objective thresholding scheme. Using pulse-pair algorithms the mean VP and the variance of the spectra were estimated with and without correction for noise (σ22 and σ12, respectively). A new technique is proposed for estimation of the Doppler variance σ32 using R(τ) and R(2τ), and a similar technique for the signal-to-noise ratio, SNR3, using R(0), R(τ) and R(2τ), where R(X) is the signal autocorrelation at lag X and τ the inter-pulse period of the radar. In the derivation of these functions, a Gaussian-Doppler spectrum was assumed. It has been found that VP agrees closely with VT, and σ22 and σ32 agree closely with σT2 for SNRT≳5 dB. The estimators σ22 and σ32 are superior to σ12 for the estimation of Doppler variance. In contrast to σ22, σ32 does not require explicit knowledge of the signal-to-noise ratio. The estimator σ12 is seen to routinely give a poor estimate of Doppler spectral variance for all SNRT values. The estimators SNRT and SNR3 agree closely with each other for SNRT≳5 dB.

Abstract

The mean VT, variance σT2 and signal-to-noise ratio SNRT of Doppler spectra from precipitation in a thunderstorm and from radar signal reflecting chaff have been estimated by an objective thresholding scheme. Using pulse-pair algorithms the mean VP and the variance of the spectra were estimated with and without correction for noise (σ22 and σ12, respectively). A new technique is proposed for estimation of the Doppler variance σ32 using R(τ) and R(2τ), and a similar technique for the signal-to-noise ratio, SNR3, using R(0), R(τ) and R(2τ), where R(X) is the signal autocorrelation at lag X and τ the inter-pulse period of the radar. In the derivation of these functions, a Gaussian-Doppler spectrum was assumed. It has been found that VP agrees closely with VT, and σ22 and σ32 agree closely with σT2 for SNRT≳5 dB. The estimators σ22 and σ32 are superior to σ12 for the estimation of Doppler variance. In contrast to σ22, σ32 does not require explicit knowledge of the signal-to-noise ratio. The estimator σ12 is seen to routinely give a poor estimate of Doppler spectral variance for all SNRT values. The estimators SNRT and SNR3 agree closely with each other for SNRT≳5 dB.

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