A new forced LMS-based adaptive algorithm utilizing the principle of potential energy

In this paper, we propose a new gradient-based adaptive algorithm, in which the conventional LMS update recursion is modified by introducing a damping factor, which emulates the force acting on a free-moving object in a gravitational field. The contribution of the damping factor being introduced is controlled by an exponential function, which eliminates its effect whenever the squared error signal is less than a given threshold. Furthermore, we show via stability analysis that the control parameter can assume both positive and negative values. Implementing a negative control parameter transforms our algorithm to a time-varying Leaky-type LMS algorithm, which exhibits bias-free performance, unlike that for the conventional Leaky-LMS algorithm. With positive contribution, the algorithm exhibits improved convergence speeds with a smoothing property in stationary, nonstationary power and correlated noisy environments. Several simulation examples are persented to verify the validity of the new algorithm compared with the LMS, including echo cancellation in telephone networks and noise cancellation in transient and PCG signals.