Circuits, Systems, and Signal Processing

, Volume 38, Issue 1, pp 455–469 | Cite as

A Variable Step-Size Shrinkage Set-Membership Affine Projection Algorithm for Noisy Input

  • Kaili Yin
  • Haiquan ZhaoEmail author
Short Paper


To solve the conflicting requirement of fast convergence and low steady-state misalignment, a variable step-size shrinkage set-membership affine projection algorithm is proposed, which is efficient for the correlated input signal and noisy input environments. The new variable step size is derived by minimizing the square of noise-free a posteriori error, and the shrinkage method is employed to estimate the second-order statistics of the noise-free a priori error vector. Moreover, the stability analysis of the algorithm is conducted. Simulations demonstrate the effectiveness of the proposed algorithm for various noisy input environments.


Noisy input Affine projection algorithm Variable step size Shrinkage Echo cancelations 



The authors would like to thank Dr. Lu Lu (Southwest Jiaotong University) for polishing the language. This work was partially supported by National Science Foundation of People’s Republic of China (Grants 61571374, 61271340, 61433011).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Electrical EngineeringSouthwest Jiaotong UniversityChengduChina
  2. 2.Key Laboratory of Magnetic Suspension Technology and Maglev VehicleMinistry of EducationChengduChina

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