Time-Domain Computation of Mean and Variance of Doppler Spectra

Abstract

The mean V_T, variance σ_T² 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 V_P 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 V_P agrees closely with V_T, and σ₂² and σ₃² agree closely with σ_T² 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.