Convergence analysis of two-dimensional LMS FIR filters

Maha Shadaydeh, Masayuki Kawamata

Research output: Contribution to journalConference articlepeer-review


In this paper, we consider the steady state Mean Square Error (MSE) analysis for 2-D LMS algorithm in which the filter's weights are updated in both vertical and horizontal directions using Fornasini and Marchesini (F-M) state space model. The MSE analysis is conducted using the well-known independence assumption. First we show that computation of the Weight-Error Correlation Matrix (WECM) for F-M model-based 2-D LMS algorithm requires an approximation for the WECMs at large spatial lags. Then we propose a method to solve this problem. Further discussion is carried out for the special case when the input signal is white Gaussian. It is shown that a more strict condition on the upper bounds of the used step size values is required to ensure the convergence of the 2-D LMS in the MSE sense. Simulation experiments are presented to support the obtained analytical results.

Original languageEnglish
Pages (from-to)348-353
Number of pages6
JournalConference Record of the Asilomar Conference on Signals, Systems and Computers
Publication statusPublished - 1998 Jan 1
EventProceedings of the 1997 31st Asilomar Conference on Signals, Systems & Computers. Part 1 (of 2) - Pacific Grove, CA, USA
Duration: 1997 Nov 21997 Nov 5

ASJC Scopus subject areas

  • Hardware and Architecture
  • Signal Processing
  • Electrical and Electronic Engineering


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