Method and apparatus for nonlinear-channel identification and estimation of nonlinear-distorted signals

The present disclosure provides methods and apparatuses for nonlinear channel identification and estimation of the distorted signals in digital data transmission systems that include signals traversing a dispersive nonlinear channel that produces noisy distorted signals. The identification and estimation are accomplished with an amplitude-based signal expansion and are adapted for changing nonlinear distortion effects using a Least-Means Square direct solution that includes a precomputed matrix.