Steady state analysis of 2-D LMS adaptive filters using the independence assumption

In this paper, we consider the steady state mean square error (MSE) analysi s for 2-D LMS adaptive filtering algorithm in which the filter's weights ar e updated along both vertical and horizontal directions as a doubly-indexed dynamical system. The MSE analysis is conducted using the well-known indep endence assumption. First we show that computation of the weight-error cova riance matrix for doubly-indexed 2-D LMS algorithm requires an approximatio n for the weight-error correlation coefficients at large spatial lags.:Then we propose a method to solve this problem. Further discussion is carried o ut for the special case when the input signal is white Gaussian. It is show n 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 mea n. Simulation experiments are presented to support the obtained analytical results.