The optimum error nonlinearity in LMS adaptation with an independent and identically distributed input

Tareq Al-Naffouri, Azzedine Zerguine, Maamar Bettayeb

Research output: Contribution to journalConference articlepeer-review


The class of LMS algorithms employing a general error nonlinearity is considered. The calculus of variations is employed to obtain the optimum error nonlinearity for an independent and identically distributed input. The nonlinearity represents a unifying view of error nonlinearities in LMS adaptation. In particular, it subsumes two recently developed optimum nonlinearities for arbitrary and Gaussian inputs. Moreover, several more familiar algorithms such as the LMS algorithm, the least-mean fourth (LMF) algorithm and its family, and the mixed norm algorithm employ (non)linearities that are actually approximations of the optimum nonlinearity.

Original languageEnglish (US)
Article number7075229
JournalEuropean Signal Processing Conference
Issue numberMarch
StatePublished - Mar 31 2000
Event2000 10th European Signal Processing Conference, EUSIPCO 2000 - Tampere, Finland
Duration: Sep 4 2000Sep 8 2000

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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