Affine projection algorithm with adaptive error constraint

A new affine projection algorithm (APA) which incorporates an adaptive constraint on the cost function is proposed, which is developed by constraining the cost function to statistics of the channel noise and replacing it as an adaptive constraint parameter. The motivation behind this work is that the use of partial knowledge of a channel in adaptation would be beneficial for improving convergence performance. Developing a constrained optimisation problem with adaptive error constraint and solving it using a stochastic root finding scheme, an adaptive error constrained APA (AEC-APA) is developed. Through the experiments, the proposed AEC-APA has proven to be promising in that it accomplishes both fast and accurate convergence compared to the classical APAs.