On the convergence behavior of recursive adaptive noise cancellation structure in the presence of crosstalk

In this paper, we address the problem of determining the equilibrium point of a feedback structure for two-channel adaptive noise cancellation in the presence of crosstalk. We focus on an important characteristic of adaptive filters, namely the steady-state mean-square error that remains after the algorithm has converged but independently of the considered algorithm. Our approach relies on analysis of the relationships between the desired signals and their artifacts (distortion, residual noise) at the system outputs. We show that the equilibrium state is obtained when the energy of the distortion on the output signals is the same on each channel. Using this equilibrium state, we provide answers to questions for which no satisfactory answers are currently available for this structure. Examples are given to illustrate that even qualitatively, these answers can be good approximations. Results of simulations sustain our claims.