Efficient approximate implementations of the fast affine projection algorithm using orthogonal transforms

The recently-introduced fast affine projection (FAP) adaptive filter has performance rivalling that of the RLS adaptive filter in many situations. However, the sliding-window RLS algorithm embedded within the FAP adaptive filter can be too complex to implement in some cases. We describe an alternate implementation of the FAP adaptive filter that uses orthogonal transforms to approximately calculate the affine projection. Simulations show that the performance of this simplified algorithm is nearly as good as the original algorithm when the transform is chosen properly. In addition, we provide a gradient step size (GSS) method for enhancing the performance of the FAP adaptive filter in nonstationary signal environments.