Variable step size NLMS algorithm based in correlation criterion

A new variable step size Least Mean Square (LMS) FIR adaptive filter algorithm (VS-BC) is proposed. In the VS-BC algorithm the step size adjustment (α) is controlled by using the correlation between the output error (e(n)) and the adaptive filter output (y(n)). At small times, e(n) and y(n) are correlated which will cause a large α providing faster tracking. When the algorithm converges, the correlation will result in a small size α to yield smaller misadjustments. Computer simulations show that the proposed VS-BC algorithm achieves a better Echo Return Loss Enhancement (ERLE) than a conventional NLMS Algorithm. The VS-BC algorithm was also compared with another variable step algorithm, achieving the VS-BC a better ERLE when the additive noise is incremented.