Non Stationary Noise Removal from Speech Signals using Variable Step Size Strategy

The aim of this paper is to implement various adaptive noise cancellers (ANC) for speech enhancement based on gradient descent approach, namely the least-mean square (LMS) algorithm and then enhanced to variable step size strategy. In practical application of the LMS algorithm, a key parameter is the step size. As is well known, if the step size is large, the convergence rate of the LMS algorithm will be rapid, but the steady-state mean square error (MSE) will increase. On the other hand, if the step size is small, the steady state MSE will be small, but the convergence rate will be slow. Thus, the step size provides a trade-off between the convergence rate and the steady-state MSE of the LMS algorithm. An intuitive way to improve the performance of the LMS algorithm is to make the step size variable rather than fixed, that is, choose large step size values during the initial convergence of the LMS algorithm, and use small step size values when the system is close to its steady state, which results in Variable Step Size LMS (VSSLMS) algorithms. By utilizing such an approach, both a fast convergence rate and a small steady-state MSE can be obtained. By using this approach various forms of VSSLMS algorithms are implemented. These are robust variable step-size LMS (RVSSLMS) algorithm providing fast convergence at early stages of adaptation and modified robust variable step-size LMS (MRVSSLMS) algorithm. The performance of these algorithms is compared with conventional LMS and Kowngs VSSLMS algorithm. Finally we applied these algorithms on speech enhancement application. Simulation results confirms that the implemented RVSSLMS and MRVSSLMS are superior than conventional algorithms in terms of convergence rate and signal to noise ratio improvement (SNRI). Keywords— Adaptive filtering, LMS algorithm, Noise Cancellation, Speech Processing, Variable Step Size.