R-Meter Correction for Boxcar-ing and Receiver Noise in Incoherent Weather Radars

Abstract

Conventional R-meter theory (which ignores boxcar-ing and receiver noise) is briefly reviewed. The R-meter reading of a noisless, boxcar-ed radar is derived and compared to that predicted by the conventional theory. It is shown that the level-crossing rate of boxcar-ed video does not depend solely on the Doppler spectral variance but also on other aspects of the Doppler spectral shape. For a given level-crossing rate the variance can, however, be bracketed within fairly tight bounds. The effect of receiver noise on the level crossing rate of boxcar-ed video is analyzed and a family of curves is derived which, to within an accuracy of ±5%, yield the (corrected) standard deviation of the Doppler spectrum from a knowledge of the R-meter reading and the signal-to-noise ratio. Although these curves were calculated for a linear receiver, they are also shown to be usable with a logarithmic i.f. amplifier if a small additional correction is applied.