Abstract—This paper presents a family variable step-size (VSS) affine projection (AP) adaptive filtering algorithms with good convergence speed and low steady state mean square error features. In the following, the family of VSS selective partial updates (SPU) affine projection algorithms are established which reduce the computational complexity. The stability bounds of the family of APA and SPU-APA algorithms are analyzed based on the energy conservation arguments. This analysis does not need to assume a Gaussian or white distribution for the regressors. We demonstrate the good performance of the proposed algorithms through simulations in system identification and acoustic echo cancellation scenarios.

Index Terms—Adaptive filter, affine projection, selective partial update, variable step-size, stability analysis.

Mohammad Shams Esfand Abadi (M. S. E. Abadi) is with the Shahid Rajaee University, Department of Electrical Engineering, Tehran, Iran, Email: mshams@srttu.edu. Azizollah Gholipour and Vahid Mehrdad are MSc students in Shahid Rajaee University, Email: vmehrdad@srttu.edu. Majid Noroozi is the BSc student in Shahid Rajaee University, Email:. mnroozi@srttu.edu.

Cite: Mohammad Shams Esfand Abadi, Vahid Mehrdad, Azizollah Gholipour and Majid Noroozi, "A Family of Variable Step-Size Affine Projection Adaptive Filtering Algorithms,"  International  Journal  of  Computer  and
Electrical Engineering vol. 2, no. 3, pp. 447-459, 2010.