Improved LMS-type adaptive filtering algorithms using a new maximum eigenvalue bound estimation scheme

This paper proposes a new recursive scheme for estimating the maximum eigenvalue bound for autocorrelation matrices and its application to the stepsize selection in least mean squares (LMS)-type adaptive filters. This scheme is developed from the Gershgorin circle theorem and the recursive nature of estimating the correlation matrix. The bound of the maximum eigenvalue of a L × L correlation matrix can be recursively estimated in O(L) arithmetic complexity. Applying this new recursive estimate to the stepsize selection of LMS-type algorithms, the problem of over-estimating the maximum eigenvalue bound and hence the under-estimation of the stepsize in the conventional trace estimator is ameliorated. This significantly improves the transient convergence and tracking speed of LMS-type algorithms. To lower the extra steady state error caused by the use of bigger stepsizes, an effective switching mechanism is designed and incorporated into the proposed algorithms so that a smaller stepsize can be invoked near the steady state. The superior performance of the proposed algorithms is verified by numerical and computer simulations.