Time, Angle and Range Averaging of Radar Echoes from Distributed Targets

Abstract

In radar meteorology, the average of the weather echo power is used in the computation of reflectivity, liquid water content, rainfall rate, etc. The uncertainty in measuring or estimating average weather echo power is then important in establishing confidence in the above computed values. To help establish a confidence level, we note that there exists a unique relationship between the weather radar echo correlation function and the receiver detected output correlation function. This unique relationship is used here to calculate the variance of the average (mean) weather echo estimates. Another measure of uncertainty related to the variance is the number (or equivalent number) of independent samples. In this work, we show the equivalent number of independent samples for average weather echoes at the output of three common radar receivers: linear, logarithmic and square law. This is shown for correlated samples of receiver output at different times, angles and ranges, Gaussian-shaped Doppler spectra and antenna patterns, a rectangular transmitted pulse, and an infinite bandwidth receiver.