Research Article
Variable Is Better Than Invariable: Sparse
VSS-NLMS Algorithms with Application to Adaptive MIMO
Channel Estimation
Guan Gui,
1
Zhang-xin Chen,
2
Li Xu,
1
Qun Wan,
2
Jiyan Huang,
2
and Fumiyuki Adachi
3
1
Department of Electronics and Information Systems, Akita Prefectural University, Akita 015-0055, Japan
2
Department of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
3
Department of Communications Engineering, Tohoku University, Sendai 980-8579, Japan
Correspondence should be addressed to Guan Gui; guiguan@akita-pu.ac.jp
Received February ; Accepted May ; Published June
Academic Editor: Serkan Ery
´
ılmaz
Copyright © Guan Gui et al. is 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, dierent sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, dierence between sparse ISS-
NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the eectiveness
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.
1. Introduction
High-rate data broadband transmission over multiple-input
multiple-output (MIMO) channel has become one of the
mainstream techniques for the next generation communi-
cation systems []. e major motivation is due to the fact
that MIMO technology, as shown in Figure ,isawayof
using multiple antennas to simultaneously transmit multiple
streams of data in wireless communications [] and hence
it can bring considerable improvements such as data rate,
reliability, and energy eciency. In fact, coherent receivers
require accurate channel state information (CSI) since the
received signals are distorted by multipath fading transmis-
sion. e accurate estimation of channel impulse response
(CIR) is a crucial aspect and challenging issue in coherent
modulation and its accuracy has a signicant impact on the
overall performance of the communication system.
During last decades, there exist many channel estimation
methods which were proposed for MIMO systems [–].
All these methods are categorized into two groups. e
rst group contains the linear channel estimation methods,
for example, least squares (LS) algorithm, based on the
assumption of dense CIRs. By applying these approaches,
the performance of linear methods depends only on the size
of MIMO channel. Note that narrowband MIMO channel
may be modeled as dense channel model because of its
very short time delay spread. Accurately, broadband MIMO
channel is oen modeled as sparse channel model [–].
A typical example of sparse channel is shown in Figure .
It is well known that linear channel estimation methods are
Hindawi Publishing Corporation
e Scientific World Journal
Volume 2014, Article ID 274897, 10 pages
http://dx.doi.org/10.1155/2014/274897