The fast subsampled-updating fast affine projection (FSU FAP) algorithm

The Fast affine Projection (FAP) Algorithm is the fast version of the AP algorithm which is a generalization of the well-known Normalized Least-Mean-Square (NLMS) algorithm. The AP algorithm shows performances that are near to those of the Recursive Least-Squares al- gorithms while its computational complexity is nearly the same as the LMS algorithm one. Moreover, recent research has enlightened the strong tracking ability of the AP algorithm, rendering it very interesting for adaptive systems that evolve within highly non-stationary en- vironments. In order to reduce the O(2N) (N is the filter length) computational complexity of the FAP algorithm, we apply the Subsampled-Updating approach in which the filter estimate is provided at a subsampled rate, say every M samples. Using the FFT technique when com- puting the products of vectors with Toeplitz matrices leads to the Fast Subsampled-Updating FAP (FSU FAP) algorithm which is mathematically equivalent to the AP algorithm. The FSU FAP algorithm shows a low computational complexity for relatively large filters while presenting good convergence and tracking performances. This makes the FSU FAP algorithm a challenging candidate for applications such as acoustic echo cancellation.