A unified framework for adaptive filter algorithms with variable step-size

Employing a recently introduced framework within which a large number of classical and modern adaptive filter algorithms can be viewed as special cases, we extend this framework to cover block normalized LMS (BNLMS) and normalized data reusing LMS (NDRLMS) adaptive filter algorithms. Accordingly, we develop a generic variable step-size adaptive filter. Variable step-size normalized LMS (VSSNLMS) and VSS affine projection algorithms (VSSAPA) are particular examples of adaptive algorithms covered by this generic variable step-size adaptive filter. In this paper we introduce two new VSS adaptive filter algorithms named the variable step-size BNLMS (VSSBNLMS) and the variable step-size NDRLMS (VSSNDRLMS) based on the generic VSS adaptive filter. The proposed algorithms show the higher convergence rate and lower steady-state mean square error compared to the ordinary BNLMS and NDRLMS algorithms.