Interference cancellation for wideband and narrowband communications systems is provided without apriori knowledge of statistical information about an interfering signal. In one embodiment a demodulator circuit can operate in an environment where a “no lock” situation would normally occur to remove the interference and acquire signals in low signal-to-noise ratio conditions and high signal-to-interference ration conditions. In other embodiments, performance is improved by introducing statistics of the interfering signal, and these statistics regarding the communications channel and interference properties (i.e., characteristics of the interfering signal) can be adaptive or “learned” in other embodiments.