### Abstract

In this paper, we consider the steady state mean square error (MSE) analysis for 2-D LMS adaptive filtering algorithm in which the filter's weights are updated along both vertical and horizontal directions as a doubly-indexed dynamical system. The MSE analysis is conducted using the well-known independence assumption. First we show that computation of the weight-error covariance matrix for doubly-indexed 2-D LMS algorithm requires an approximation for the weight-error correlation coefficients 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 the convergence in the MSE sense occurs for step size range that is significantly smaller than the one necessary for the convergence of the mean. Simulation experiments are presented to support the obtained analytical results.

Original language | English |
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Pages (from-to) | 457-463 |

Number of pages | 7 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E82-A |

Issue number | 3 |

Publication status | Published - 1999 Jan 1 |

### Keywords

- 2-D LMS
- Doubly-indexed system
- Steady state analysis

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

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## Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E82-A*(3), 457-463.