Simplified Fast Affine Projection Algorithm in Echo Cancellation Tasks

This paper considers an adaptive echo canceller which can be used in tasks of acoustic or electrical echo cancellation. The solution of these tasks usually requires the usage of the adaptive filters with a large number of weights. This means that a lot of computational resources of hardware or software are required for the echo canceller implementation. The usage of the Fast (computationally efficient) Affine Projection (FAP) adaptive filtering algorithm ensures the adaptive filter functional efficiency and complexity tradeoff in the echo cancellation tasks. The algorithm consists of two groups of calculations: a fast calculation of the adaptive filter error and a fast calculation of the normalizing matrix and its inversion. The second group is based on the usage of some calculations adopted from the sliding window Fast Recursive Least Squares adaptive filtering algorithms. However these calculations are potentially unstable. The given paper presents a simplified stable version of the multichannel FAP algorithm. The simplification is achieved due to the diagonalization of the normalizing matrix that ensures a simple procedure of direct calculation of this matrix and its inversion. If the echo signal is noisy (and that what always happens in our real world) then the original and the simplified FAP algorithms demonstrate about the same performance. The simulation of the two-channel acoustic echo cancellers confirms this statement.