LYAPUNOV TUNING OF THE LEAKY LMS ALGORITHM FOR SINGLE-SOURCE, SINGLE-POINT NOISE CANCELLATION

Least-mean square (LMS) algorithms, which are commonly used for adaptive feedforward noise cancellation, have performance issues related to insufficient excitation, non-stationary reference inputs, finite-precision arithmetic, quantisation noise and measurement noise. Such factors cause weight drift and potential instability in the conventional LMS algorithm. Here, we analyse the stability and performance of the leaky LMS algorithm, which is widely used to correct weight drift. A Lyapunov tuning method is developed to find an adaptive leakage parameter and adaptive step size that provide optimum performance and retain stability in the presence of measurement noise on the reference input of known variance. The method accounts for non-persistent excitation conditions and non-stationary reference inputs and requires no a priori knowledge of the reference input signal characteristics other than a lower bound on its magnitude or a minimum signal-to-noise ratio. The Lyapunov tuning method is demonstrated for three candidate adaptive leakage and step size parameter combinations, each of which is a function of the instantaneous measured reference input, measurement noise variance, and/or filter length. These candidates illustrate stability vs performance tradeoffs in the leaky LMS algorithm elicited through the Lyapunov tuning method. The performance of each candidate Lyapunov tuned algorithm is evaluated experimentally in a single source, single-point acoustic noise cancellation system.