The Variable Step-Size Gauss-Seidel Pseudo Affine Projection Algorithm

N echo cancellation systems, an adaptive filter algorithm is used to reduce the echo. The echo path is usually modeled by a linear filter. The well known normalized least-mean- square (NLMS) algorithm has been widely used, but converges very slowly. The affine projection algorithm (APA) can be considered as a generalization of the NLMS algorithm that provides a much improved convergence speed compared to LMS-type algorithms, although it is sensitive to high level of noise (1). It has a performance that rivals with the more complex recursive least-squares (RLS) algorithms in many situations. However, the fast affine projection (FAP) algorithm proposed in (2,3) suffers from numerical instability when implemented with an embedded fast RLS algorithm. A key element in other proposed FAP algorithms is the approach to solve the encountered linear system. The choice of the approach (i.e., direct or iterative) determines the stability and robustness of the FAP algorithm. Several proposed FAP algorithms use an approximation that leads to simpler algorithms if the step size is 1 P (non-relaxed case) or close