Residual noise reduction in sign algorithm

The residual noise of the sign algorithm can be reduced by adding a uniformly distributed noise (dithering) to the sign algorithm input signal. In this paper, a simple equation for the residual noise reduction factor (RNRF) is derived for the case in which the noise in the sign algorithm input signal has a two-level discrete amplitude distribution. It is demonstrated that the RNRF is proportional to the ratio between the amplitude of the input noise and the adaptation step.