Title :
Stability of variable and random stepsize LMS
Author :
Gelfand, Saul B. ; Wei, Yongbin ; Krogmeier, James V.
Author_Institution :
Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA
Abstract :
The stability of variable stepsize LMS (VSLMS) algorithms with uncorrelated stationary Gaussian data is studied. It is found that when the stepsize is determined by the past data, the boundedness of the step size by the usual stability condition of fixed stepsize LMS is sufficient for the stability of VSLMS. When the stepsize is also related to the current data, the above constraint is no longer sufficient. Instead, both the upper bound and the lower bound of the stepsize must be within a smaller region. An exact expression of the stability region is developed for a single tap filter. The results are verified by computer simulations
Keywords :
Gaussian processes; adaptive filters; adaptive signal processing; filtering theory; least mean squares methods; numerical stability; adaptive filter; algorithms; computer simulations; current data; exact expression; fixed stepsize LMS; lower bound; past data; random stepsize LMS; single tap filter; stability condition; stability region; uncorrelated stationary Gaussian data; upper bound; variable stepsize LMS; Algorithm design and analysis; Convergence; Data engineering; Data models; Eigenvalues and eigenfunctions; Least squares approximation; Resonance light scattering; Stability analysis; Steady-state; Sufficient conditions;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on
Conference_Location :
Munich
Print_ISBN :
0-8186-7919-0
DOI :
10.1109/ICASSP.1997.598927
