Performance improvement and statistical behavior analysis of adaptive filters

Abstract

Performance improvement and statistical behavior analysis of stochastic gradient-based algorithms for adaptive filters are studied in this thesis, where we are mainly concerned with the least mean square (LMS) algorithm and three computationally simplified versions of the LMS algorithm: the signed-error algorithm, the signed-regressor algorithm and the sign-sign algorithm which are obtained by clipping the estimation error signal, the reference input data and both of them, respectively. In the first half of this thesis, analyzing the statistical behaviors of the signed-regressor and the sign-sign algorithms for adaptive transversal filters with correlated Gaussian data, we get propagation equations for the first and second moments of the filter coefficients and stability conditions of the propagation equations derived. And also we derived relationships between the step size and the mean square error in the steady state for each algorithm. Comparing the new results derived for the signed-regressor and the sign-sign algorithms with the previous ones for the signed-error and the LMS algorithms, we observe some impressive properties: analogies between the signed-error algorithm and the signed-regressor algorithm; similarities among the expressions for the statistical behaviors of the four algorithms; relative performance among the four algorithms in the convergence rate and the steady-state misadjustment. In the last half, we suggest two methodologies to improve the performance of adaptive filters, and we derive new algorithms with the fast convergence in the transient phase and the low misadjustment in the steady state based on the suggested methods. We evaluate the expressions for the statistical behaviors of the new algorithms, and also we find relationships between the steady-state error and the step size or corresponding parameters. Applying the method of modification of the error-performance surface, the first methodology suggested, we get a new steepest desc...