4338 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 9, SEPTEMBER 2015
Coded MIMO With Asymmetric Constellation Sizes
Chen Qian, Zhaocheng Wang, Senior Member, IEEE, Zhaohua Lu,
Linglong Dai, Member, IEEE, and Sheng Chen, Fellow, IEEE
Abstract—An asymmetric constellation scheme for coded multiple-
input–multiple-output (MIMO) transmission is proposed, which applies
different constellation mappings to different transmit streams and care-
fully selects the coding rates for different transmit streams. An improved
power allocation is derived to naturally incorporate with the coding rate
selection and to further enhance the achievable performance. The pro-
posed scheme provides more flexible choices of data rate selection, and by
employing fixed-complexity sphere decoding (FSD) detection, it achieves
better performance with reduced detection complexity in comparison with
the conventional MIMO using the FSD-based detection with the same
constellation set for all streams.
Index Terms—Coding rate selection, constellation set, extrinsic infor-
mation transfer (EXIT) chart, multiple-input–multiple-output (MIMO),
power allocation.
I. INTRODUCTION
Multiple-input–multiple-output (MIMO) has been considered as a
promising technology for wireless communications due to its potential
to improve the spectral efficiency and the reliability over fading
channels. For example, the 3rd Generation Partnership Project (3GPP)
Long-Term Evolution Advanced (LTE-A) [1] supports up to 8 ×
8 MIMO transmission. Recently, the next-generation mobile broad-
casting system, known as digital video broadcasting next-generation
handheld (DVB-NGH), has also considered to exploit the spatial mul-
tiplexing to improve the spectral efficiency by using 2 × 2MIMO[2].
Most existing studies on MIMO technology in the literature focus
on the assumption that all transmit streams use the same constellation
set, and the investigation on the different constellation sets applied to
different streams is seldom carried out. However, by transmitting dif-
ferent constellation-mapped data streams through different antennas,
more options of data rate selection will be provided and the flexibility
of the multiple service support can be improved. Although the analysis
in this area is limited, this kind of systems has been adopted by some
commercial standards, such as LTE-A and DVB-NGH.
Many existing MIMO schemes are not suitable for transmitting dif-
ferent constellation-mapped data over different antennas. Some exist-
ing unequal error protection (UEP) schemes use different constellation
sets to provide different protections for the information sequences with
Manuscript received February 7, 2014; revised May 20, 2014 and July 23,
2014; accepted October 2, 2014. Date of publication October 7, 2014; date
of current version September 15, 2015. This work was supported in part by the
National High Technology Research and Development Program of China under
Grant 2012AA011704, by the National Natural Science Foundation of China
under Grant 61271266, by Beijing Natural Science Foundation under Grant
4142027, by ZTE under Fund Project CON1307250001, and by the Founda-
tion of Shenzhen Government. The review of this paper was coordinated by
Prof. Y. Fang.
C. Qian, Z. Wang, and L. Dai are with Tsinghua National Laboratory
for Information Science and Technology (TNList), Department of Electronic
Engineering, Tsinghua University, Beijing 100084, China (e-mail: qc8802@
gmail.com; cwang@mail.tsinghua.edu.cn; daill@tsinghua.edu.cn).
Z. Lu is with ZTE Corporation, Shenzhen 518000, China (e-mail: lu.
zhaohua@zte.com.cn).
S. Chen is with the School of Electronics and Computer Science, University
of Southampton, Southampton SO17 1BJ, U.K., and also with King Abdulaziz
University, Jeddah 22254, Saudi Arabia (e-mail: sqc@ecs.soton.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2014.2361646
different importance or priorities [3], [4]. However, it is difficult to
apply these schemes when the different data streams all have the same
importance. Moreover, the data rates or system throughputs provided
by UEP schemes vary according to the detection conditions, and they
cannot provide a fixed data rate to meet a required system through-
put all the time. The vertical Bell Laboratories layered space–time
(V-BLAST) architecture [5] can transmit independent data streams
over different transmit antennas to exploit spatial multiplexing. It is
well known that owing to MIMO interchannel interference, the optimal
maximum-likelihood detection suffers from exponentially growing
complexity. Low-complexity suboptimal detection schemes such as
serial interference cancelation are typically applied. When different
constellation sets are used for different streams, however, if the same
code and equal power allocation are applied to all streams, then the
error propagation of the transmit stream with the worst performance
will be serious and this will degrade the overall performance severely.
Thus, the coding rate and the power allocation have to be investigated
carefully.
Power allocation is important to realize spatial multiplexing under
MIMO channels and has been studied in detail [6]–[9]. However, most
power-allocation algorithms, including the famous “water-filling” al-
gorithm, “mercury–water-filling” algorithm [8], and the optimum pre-
coder, aim at maximizing the mutual information on the complex
MIMO vector channel [9], and they only consider the uncoded sys-
tems without turbo detection while imposing the assumption that the
transmitter has perfect knowledge of channel conditions, which may
be unrealistic.
In this paper, we have proposed a coded MIMO transmission
scheme with different constellation sets for different transmit streams,
and we carefully select the coding rates and allocate power val-
ues for different constellation-mapped data streams to ensure good
performance. The basic idea is to “match” different streams with
different constellation sets by properly selecting coding rates and
power allocation so that all the streams have approximately the same
performance. For illustration purposes and concise analysis, we will
mainly consider the case of two different constellation sizes, but the
concept and approach can be applied generically. Unlike the con-
ventional power-allocation-based approach, the proposed method is
designed to utilize the turbo detection at the receiver and does not rely
on the feedback of channel state information (CSI) to the transmitter.
In contrast to the method based on experimental results given in [10], a
simple closed-form approach to power allocation is presented and the
fixed-complexity sphere decoding (FSD) detection algorithm for the
proposed scheme is also discussed. The proposed scheme offers more
options of data rate selection, and furthermore, it is simple and
efficient. The convergence analysis with the aid of extrinsic informa-
tion transfer (EXIT) chart also demonstrates the effectiveness of our
asymmetric constellation scheme. Simulation results show that, given
the same data rate, our scheme achieves better performance in com-
parison with the conventional MIMO counterpart using the FSD-based
detection algorithm while imposing lower implementation complexity.
II. S
YSTEM MODEL
Consider the MIMO system with N transmit antennas and M
receive antennas, which is shown in Fig. 1. N independent bit streams
{b
n
}
N
n=1
are encoded by N channel encoders to obtain the encoded bit
streams {c
n
}
N
n=1
. After interleaving, every B
n
bit from the nth stream
is mapped to a symbol selected from the constellation set S
n
with
Q
n
= 2
B
n
as its cardinality. The constellation set used by each stream
can be different. The symbol streams {s
n
}
N
n=1
arethenpassedtothe
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