The performance of the hybrid LMS adaptive algorithm

The hybrid least mean square (HLMS) adaptive filter is a filter with an adaptation algorithm that is a combination of the conventional LMS algorithm and the normalized LMS (NLMS) algorithm. In this paper, the performance of the HLMS adaptive filtering algorithm is investigated. To do so, an analytical expression, in terms of the transient mean square error (MSE), is derived with application to the adaptive line enhancer (ALE). Based on this expression, we are able to examine the convergence properties of the HLMS. Simulation data using the ALE as an application verifies the accuracy of the analytical results. The performance of the HLMS algorithm is also compared with the conventional LMS algorithm as well as the NLMS algorithm. From the simulation results, we observed that, in general, the HLMS algorithm performs more robustly than the conventional LMS and the NLMS algorithms. Since the HLMS algorithm is a combination of the LMS algorithm and the NLMS algorithm, the selection of the optimum switching point of the HLMS algorithm is also addressed using a numerical approach. Many interesting characteristics of the switching point are obtained which show the relationship with the relevant parameters of the HLMS adaptive filter. The sensitivity of the selection of switching point is also examined.