Necessary and Sufficient Conditions for Stability of LMS
1996 (English)Report (Other academic)
In a recent work (7), some general results on exponential stability of random linear equations are established which can be applied directly to the performance analysis of a wide class of adaptive algorithms including the basic LMS ones without requiring stationarity independency and boundedness assumptions of the system signals The current paper attempts to give a complete characterization of the exponential stability of the LMS algorithms by providing a necessary and sucient condition for such a stability in the case of possibly unbounded nonstationary and non mixing signals The results of this paper can be applied to a very large class of signals including those generated fromeg a Gaussian process via a timevarying linear lter As an application several novel and extended results on convergence and tracking performance of LMS are derived under various assumptions Neither stationarity nor Markov chain assumptions are necessarily required in the paper
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1996. , 25 p.
LiTH-ISY-R, ISSN 1400-3902 ; 1893
Least mean squares methods, LMS
IdentifiersURN: urn:nbn:se:liu:diva-55361ISRN: LiTH-ISY-R-1893OAI: oai:DiVA.org:liu-55361DiVA: diva2:316022