A control system and method for controlling a spread spectrum receiver such as a generalized Rake (G-Rake) receiver or chip equalizer based on a frequency shift (fD) of a received signal. A hybrid channel estimator outputs a low-rate channel estimate such as a slot average channel estimate if fD is less than or equal to a threshold value. If fD is greater than the threshold, a plurality of high-rate channel estimates such as interpolated channel estimates is produced. An impairment covariance matrix estimates correlations between impairment on different fingers of the G-Rake receiver. The update rate of the matrix is controlled dependent on the value of fD. A combining weights calculator then calculates sets of combining weights based on the channel estimates and the impairment correlation estimates.