Convex combination of affine projection algorithms

It is well known that performance of adaptive filters is mainly a compromise among computational complexity, speed of convergence and steady-state behavior. The affine projection (AP) algorithm offers a good convergence speed that increases with the projection order N and a computational complexity that can be reduced by applying different fast strategies. However, its steady-state mean square error (MSE) worsens when N grows. This work introduces the convex combination of two AP adaptive filters in order to improve the performance capabilities of the overall filter. The purpose of the convex AP approach is to improve the convergence performance of a single AP algorithm but not at the expense of an increase of the steady-state MSE. To achieve this we combine two AP filters with different projection orders, one of high N order that performs faster than other with a lower order but with a better MSE. Moreover, the computational cost of the AP combination scheme would be similar to that of the higher order AP filter working separately. Simulation results have validated the proposed approach.