Embodiments of the present invention include communication systems and methods using channel estimation based on cumulants. In one embodiment, the present invention includes a receiver comprising a sampler coupled to a communication channel for receiving an input signal and providing samples of the input signal at a first sample rate, a channel estimation circuit coupled to receive the sampled input signal, the channel estimation circuit estimating the amplitude response of the communication channel by autocorrelating the input signal, estimating the phase response of the communication channel using a fourth order cumulant of the input signal, and generating an estimated impulse response of the communication channel using the estimated amplitude response and the estimated phase response, and a channel initialization circuit coupled to the channel estimation circuit for configuring the receiver using the estimated impulse response.