Fast converging nonlinear echo cancellation based on optimum step size

Adaptive Volterra filter is generally known to track nonlinear echo path at slow convergence rate. An optimum time-and tap-variant step-size for second-order Volterra filter is proposed to speed up its convergence rate. The step-size is derived based on the MMSE criterion. As the optimum step-size needs to know the real echo path coefficient, an exponential echo-path model is proposed for practical implementations. Computer simulations are provided to validate the proposed algorithms.