Performance of proportionate-type NLMS algorithm with gain allocation proportional to the mean square weight deviation

The complex colored water-filling algorithm for gain allocation has been shown to provide improved mean square error convergence performance, relative to standard complex proportionate-type normalized least mean square algorithms. This algorithm requires sorting operations and matrix multiplication on the order of the size of the impulse response at each iteration. In this paper, the mean square weight deviation and two suboptimal gain allocation algorithms are presented. They are motivated by similar algorithms introduced before for real-valued signals and systems. The presented algorithms no longer require sorting. It is shown that they provide significant computational complexity savings while maintaining comparable mean square error convergence performance. The algorithms are also investigated in the case of unknown input correlation matrix and speech input signals.