On Convergence of Proportionate-Type Normalized Least Mean Square Algorithms

In this paper, a new convergence analysis is presented for a well-known sparse adaptive filter family, namely, the proportionate-type normalized least mean square (PtNLMS) algorithms, where, unlike all the existing approaches, no assumption of whiteness is made on the input. The analysis relies on a “transform” domain based model of the PtNLMS algorithms and brings out certain new convergence features not reported earlier. In particular, it establishes the universality of the steady-state excess mean square error formula derived earlier under white input assumption. In addition, it brings out a new relation between the mean square deviation of each tap weight and the corresponding gain factor used in the PtNLMS algorithm.