Performance of multiple LMS adaptive filters in tandem

The tandem of adaptive filters can occur in practice such as in echo cancel lation application for voice communications. This paper analyzes the perfor mance of a number of adaptive filters in tandem. The adaptation algorithm i s assumed to be least mean square (LMS). The analysis includes learning tra jectory, steady-state excess error due to noise, tracking lag bias, and tra ck mg lag variance. Recursive formulae for their computation are derived. T he analysis is exact under Gaussian input and independency assumption. It d oes not restrict the step size of the filters in tandem to be identical. Th e validity of the theoretical development is corroborated by simulations. T he results indicate that in the special case of equal and small step size, both the steady-state excess error due to noise and the tracking lag varian ce increase approximately linearly with the number of filters in tandem, wh ereas the tracking lag bias decreases approximately exponentially with the number of filters in tandem. Consequently, the tandem of adaptive filters c an improve the tracking capability of an adaptive system in the situation w here the step size is small or the dynamics of an unknown system to be mode led is high.