A receiving apparatus Doppler spread estimator includes a receiver receiving signals over a transmission channel that varies over time due to fading and converting the signals to digital samples for processing. A stationarizer operatively associated with the receiver stationarizes the digital samples. An estimator is operatively associated with the stationarizer for estimating spectral density of the stationarized digital samples. The correlator is operatively coupled to the estimator for correlating the spectral density estimates with functions corresponding to hypotheses of plural Doppler spread values to select one of the Doppler spread values as an estimate of actual Doppler spread.