Minimum mean squared error impulse noise estimation and cancellation

Impulses are infrequent bursts of high amplitude noise. A wide-band communications or data acquisition receiver has a fast sampling rate, so it can capture many samples of each impulse waveform. The arrival of an impulse can be identified by its distinct waveform and amplitude. The paper models impulse waveforms as a vector subspace of low dimension. Formulas are derived for the minimum mean squared error (MMSE) estimation of the arrival time and amplitudes of impulses, given that a set of vectors that spans the subspace is known. Formulas are also derived for the adaptive MMSE estimation of a set of vectors that spans the subspace. The values of the mean squared error (MSE) of the amplitude estimates are determined. It is shown how the theory can be used to cancel impulse noise. Correlated impulse noise arriving at a reference input can be used to estimate and cancel the primary input impulse noise. The MMSE coefficients for impulse noise cancellation are derived and presented. Simulations are presented that use the equations and methods derived in the paper for modeling and canceling impulse noise measured on copper telephone loops for asymmetric digital subscriber lines (ADSL)