Affine projection and recursive least squares adaptive filters employing partial updates

We present order K affine projection and recursive least squares adaptive filters employing partial update schemes. The starting point of the work is the MMax tap-selection criterion in which, given a filter length L, only M coefficients are updated that correspond to the M largest magnitude elements of the regression vector. We extend this approach from its existing form of MMax-NLMS to new affine projection and recursive least squares schemes with supporting analysis and simulation results. We discuss the computational complexity of these approaches for two alternative sort procedures. Finally, we extend the MMax criterion to a multichannel case by introducing an exclusivity constraint and show the effectiveness of the resulting XM tap-selection criterion for application to stereophonic acoustic echo cancellation.