Normalized LMS 1.1 2003/07/11 13:42:09 GMT-5 2004/05/11 11:46:50.185 GMT-5 Douglas L. Jones dl-jones@uiuc.edu Kyle Clarkson kclarks@rice.edu Douglas L. Jones dl-jones@uiuc.edu In "normalized" LMS, the gradient step factor μ is normalized by the energy of the data vector: μ NLMS α X k H X k σ where α is usually 1 2 and σ is a very small number introduced to prevent division by zero if X k H X k is very small. W k + 1 W k 1 X H X e k X k The normalization has several interpretations corresponds to the 2nd-order convergence bound makes the algorithm independent of signal scalings adjusts W k + 1 to give zero error with current input: W k + 1 X k d k minimizes mean effort at time k 1 NLMS usually converges much more quickly than LMS at very little extra cost; NLMS is very commonly used. In some applications, normalization is so universal that "we use the LMS algorithm" implies normalization as well.