Apparatus, and an associated method, for the receive part of a receiving station, such as a mobile station or other transceiver of a cellular communication system. Selection is made of filter characteristics to be exhibited by an adaptive, input noise whitening filter. A noise estimator estimates a noise component of a noise sequence. An autocorrelation estimator estimates the noise-component autocorrelation. A determination is made as to whether the autocorrelation exceeds a threshold. If so, filter characteristics are selected to cause the input noise whitening filter to operate to inject whitening noise into the received sequence.