A study of two adaptive filters in tandem

The tandem of adaptive filters is common in practice. An example is the tandem of echo cancellers in telecommunication networks. This paper analyzes the convergence characteristics and tracking behavior of two adaptive filters in tandem, together with a comparison of its performance with a single adaptive filter. The adaptive algorithm considered is the LMS and the analysis is on mean-square. The coefficient errors correspond to noise, lag bias and lag variance are examined separately. The theoretical results are corroborated with simulations. The study shows that the tandem of two adaptive filters decreases the convergence speed compared to a single adaptive filter. In addition, in steady state and when the step-size is small, tandeming increases the coefficient variance due to noise by a factor of 2.5, the coefficient variance due to tracking lag by a factor of 1.5, but decreases the mean-square coefficient bias due to lag by a factor of 2.