A new perspective on the convergence and stability of NLMS Hammerstein filters

This paper is devoted to the analysis of the convergence and stability of adaptive Hammerstein filters using the normalized least-mean-square (NLMS) algorithm. Such an analysis provides a new perspective on the update process of Hammerstein filters by focusing on the simultaneous update of the two cascaded structures (nonlinearity and linear filter) composing these filters. In this context, it is shown that the impact of the simultaneous update, which is often overlooked in the open literature, is of fundamental importance for choosing the adaptive algorithm parameters and, thus, to ensure the algorithm stability and obtain faster convergence. Simulation results confirm the effectiveness of the design guidelines obtained using the proposed analysis approach.