On Convergence of Proportionate-Type Normalized Least Mean Square Algorithms


During this paper, a new convergence analysis is presented for a widely known sparse adaptive filter family, particularly, the proportionate-kind normalized least mean square (PtNLMS) algorithms, where, in contrast to all the present approaches, no assumption of whiteness is made on the input. The analysis depends on a “rework” domain based model of the PtNLMS algorithms and brings out certain new convergence options not reported earlier. In particular, it establishes the universality of the steady-state excess mean sq. error formula derived earlier beneath white input assumption. In addition, it brings out a replacement relation between the mean square deviation of every faucet weight and the corresponding gain factor employed in the PtNLMS algorithm.

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