Various methods and systems are provided for related to adaptive systems using correntropy. In one embodiment, a signal processing device includes a processing unit and a memory storing an adaptive system executable in the at least one processing unit. The adaptive system includes modules that, when executed by the processing unit, cause the signal processing device to adaptively filter a desired signal using a correntropy cost function. In another embodiment, a method includes adjusting a coefficient of an adaptive filter based at least in part on a correntropy cost function signal, providing an adaptive filter output signal based at least in part on the adjusted coefficient and a reference signal, and determining an error signal based at least in part on a received signal and the adaptive filter output signal.