To quickly and robustly detect the presence of an incumbent user and rapidly relinquish the spectrum to the incumbent user when necessary, carrier recovery is performed in a receiver of the secondary user's cognitive or software radio prior to performing correlation detection with an upsampled reference signal to correct for large frequency offsets and improve the performance of the correlation detector. To detect a received signal, a pilot value is added to a reference signal. The reference signal is upsampled to a sampling frequency of the received signal. The upsampled reference signal is correlated with a demodulated baseband signal to produce a correlation value. It is then determined whether the received signal is present if the correlation value is greater than a predetermined detection threshold value.