Application of Simplified Line Searches in the Design of Adaptive Envelope-Constrained Filters

Envelope-constrained (EC) filtering is to design a finite impulse response filter such that the output of the filter is guaranteed to lie within a prescribed output pulse mask with respect to a given input pulse. The standard unconstrained least mean squares (LMS) or recursive least squares (RLS) algorithms are not applicable to this kind of adaptive filtering problem coupled with inequality constraints. A new type of recursive algorithms were proposed recently for designing an adaptive EC filter, and the corresponding convergence properties were established. In this paper, it is shown that faster convergence can be achieved hy incorporating a simplified line search into the developed recursive algorithms. The modified recursive algorithms are very efficient, and very simple to implement.