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The Scientific World Journal
Volume 2014, Article ID 274897, 10 pages
Research Article

Variable Is Better Than Invariable: Sparse VSS-NLMS Algorithms with Application to Adaptive MIMO Channel Estimation

1Department of Electronics and Information Systems, Akita Prefectural University, Akita 015-0055, Japan
2Department of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
3Department of Communications Engineering, Tohoku University, Sendai 980-8579, Japan

Received 2 February 2014; Accepted 26 May 2014; Published 24 June 2014

Academic Editor: Serkan Eryílmaz

Copyright © 2014 Guan Gui et al. 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.


Channel estimation problem is one of the key technical issues in sparse frequency-selective fading multiple-input multiple-output (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) scheme. To estimate sparse MIMO channels, sparse invariable step-size normalized least mean square (ISS-NLMS) algorithms were applied to adaptive sparse channel estimation (ACSE). It is well known that step-size is a critical parameter which controls three aspects: algorithm stability, estimation performance, and computational cost. However, traditional methods are vulnerable to cause estimation performance loss because ISS cannot balance the three aspects simultaneously. In this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS) algorithms to improve the accuracy of MIMO channel estimators. First, ASCE is formulated in MIMO-OFDM systems. Second, different sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the effectiveness of the proposed algorithms for ASCE, several selected simulation results are shown to prove that the proposed sparse VSS-NLMS algorithms can achieve better estimation performance than the conventional methods via mean square error (MSE) and bit error rate (BER) metrics.