Performance Comparison of Two Implementations of the LeakyLMS Adaptive

{ The leaky LMS adaptive lter can be implemented either directly or by adding random white noise to the input signal of the LMS adaptive lter. In this paper, we analyze and compare the mean-square performances of these two adaptive lter implementations for system identiication tasks with zero mean i.i.d. input signals. Our results indicate that the performance of the direct implementation is superior to that of the random noise implementation in all respects. However, for small leakage factors, these performance diierences are negligible. Simulations verify the results of the analysis and the conclusions drawn.