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The Scientific World Journal
Volume 2014 (2014), Article ID 937252, 15 pages
Research Article

Smooth Approximation -Norm Constrained Affine Projection Algorithm and Its Applications in Sparse Channel Estimation

Graduate School of Engineering, Kochi University of Technology, Kami-shi 782-8502, Japan

Received 10 December 2013; Accepted 30 January 2014; Published 26 March 2014

Academic Editors: G. Jovanovic Dolecek, C. Saravanan, and D. Tay

Copyright © 2014 Yingsong Li and Masanori Hamamura. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a smooth approximation -norm constrained affine projection algorithm (SL0-APA) to improve the convergence speed and the steady-state error of affine projection algorithm (APA) for sparse channel estimation. The proposed algorithm ensures improved performance in terms of the convergence speed and the steady-state error via the combination of a smooth approximation -norm (SL0) penalty on the coefficients into the standard APA cost function, which gives rise to a zero attractor that promotes the sparsity of the channel taps in the channel estimation and hence accelerates the convergence speed and reduces the steady-state error when the channel is sparse. The simulation results demonstrate that our proposed SL0-APA is superior to the standard APA and its sparsity-aware algorithms in terms of both the convergence speed and the steady-state behavior in a designated sparse channel. Furthermore, SL0-APA is shown to have smaller steady-state error than the previously proposed sparsity-aware algorithms when the number of nonzero taps in the sparse channel increases.