Proportionate-type normalized least mean square algorithm with gain allocation motivated by minimization of mean-square-weight deviation for colored input

In previous work, a water-filling algorithm was proposed which sought to minimize the mean square error (MSE) at any given time by optimally choosing the gains (i.e. step-sizes) each time instance. This work relied on the assumption that the input signal was white. In this paper, an algorithm is derived which operates when the input signal is colored. The proposed algorithm minimizes the mean square weight deviation which is important in many applications such as system identification. Additionally, it is shown that by minimizing the mean square weight deviation, an upper bound on the MSE is also minimized. The proposed algorithm offers improved misalignment and learning curve convergence rates relative to other standard algorithms.