Time-Domain Computation of Mean and Variance of Doppler Spectra

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.