Adaptive filtering using the least-mean mixed-norms algorithm and its application to echo cancellation.

Abstract

Echo is a debiliting problem for full-duplex data transmission over the telephone network and hence must be cancelled. This echo tends to divide into two distinct components which exhibit quite different characteristics. The recently proposed least-mean mixed-norms algorithm utilizes this difference to achieve a higher degree of cancellation as compared to the single-norm algorithm that is usually used. In this thesis, the least-mean mixed-norms algorithm is studied for a general pair of error nonlinerities. In particualar, the convergence of the algorithm is studied and its performance is evaluated for both correlated and independent identically-distributed inputs. The calculus of variations is then used to determine the optimum pair of nonlinearities for each input. These optimum nonlinearities are expressed in terms of the additive-noise probability density function (pdf). Approximating the pdf using the Gram-Charlier expansion provides a practical way for implementing the optimal nonlinearities. All of the above theoretical developments encompass and extend many existing results. Simulation was finally used to demonstrate the advantages of the least-mean mixed-norms algorithm over the single-norm algorithm for half-duplex data transmission.