Performance comparison of two implementations of the leaky LMS adaptive filter

The leaky LMS adaptive filter can be implemented either directly or by adding random white noise to the input signal of the LMS adaptive filter. In this correspondence, we analyze and compare the mean-square performances of these two adaptive filter implementations for system identification 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 differences are negligible.