Proportionate affine projection sign algorithms for sparse system identification in impulsive interference

Two proportionate affine projection sign algorithms (APSAs) are proposed for system identification applications, such as network echo cancellation (NEC), where the impulse response is often real-valued with sparse coefficients and long filter length. The proposed proportionate-type algorithms can achieve fast convergence and low steady-state misalignment by adopting a proportionate regularization matrix to the APSA. Benefiting from the characteristic of Zi-norm algorithms, affine projection, and proportionate matrix, the new algorithms are robust to impulsive interferences and colored input, and achieve much faster convergence rate in sparse impulse responses than the original APSA, the normalized sign algorithm (NSA), and the proportionate least mean square (PNLMS) algorithm. The computational complexity of the new algorithms is lower than the affine projection algorithm (APA) family due to elimination of matrix inversion.