Affine projection algorithms: Evolution to smart and fast algorithms and applications

Affine projection algorithm encompasses a family of configurable algorithms designed to improve the performance of other adaptive algorithms, mainly LMS based ones, especially when input data is highly correlated. The computational cost of the affine projection algorithm depends largely on the projection order, which in turn conditions the speed of convergence, thus high speed of convergence implies usually high computational cost. Some real-time applications (especially multichannel) using the affine projection algorithm can not be implemented in the existing general-purpose hardware, because of this several improvements of the affine projection algorithm have been proposed to make it more computationally efficient and more versatile in terms of performance. This paper outlines the evolution of the affine projection algorithm and its variants, in order to get an efficient and self-reconfigurable algorithm. Furthermore new improvements over the existing low cost and variable step size and projection order versions are proposed to give examples of the new generation of affine projection algorithms.