1041-1135 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See
http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/LPT.2015.2435009, IEEE Photonics Technology Letters
SUBMITTED TO IEEE PHOTONICS TECHNOLOGY LETTERS 1
Space-Collaborative Constellation Designs for
MIMO Indoor Visible Light Communications
Yi-Jun Zhu, Member, IEEE, Wang-Feng Liang, Jian-Kang Zhang, Senior Member, IEEE and Yan-Yu Zhang
Abstract—In conventional multi-input multi-output (MIMO)
visible light communication (VLC) techniques such as repetition
coding (RC), spatial multiplexing (SMP) and spatial modulation
(SM), the transmitted symbols through different light-emitting
diodes (LEDs) located different space are usually generated from
unipolar pulse amplitude modulation (PAM) constellations inde-
pendently. In this letter, we propose a novel constellation design
for MIMO indoor VLC systems, in which the two symbols from
two spaces collaborate so closely that the average optical power
is minimized under the constraint that the minimum Euclidean
distance is fixed. Therefore, this new constellation is called space-
collaborative constellation (CC). Computer simulations show that
CC always has better error performance than SM and SMP, and
also has better error performance than RC for most of good
channels as well as for some really bad channels.
Index Terms—Light-emitting diode (LED), visible light com-
munication (VLC), multi-input multi-output (MIMO), collabora-
tive constellation (CC), spatial modulation (SM).
I. INTRODUCTION
A
S a complementary technology with a great promise to
alleviate shortage of wireless spectrum resources, VLC
has drawn tremendous attention around the world [1], [2].
Since intensity modulation with direct detection (IM/DD) has
its own important features such as low-complexity and low-
cost implementation, it is commonly used in indoor short-
range VLC systems. In contrast to radio frequency (RF) in
which information is embedded in the carrier, IM/DD systems
carry information on the intensity of the optical power [2]–[4].
Basically, VLC system mainly utilizes commercial LED
lamps as the transmitters. The indoor illumination levels and
the line of sight (LOS) characteristic of VLC can provide
at least 60dB SNR at the receiver [5], [6]. Moreover, there
are large numbers of lighting lamps in a room and each
lamp is made up of multiple LEDs as well. Hence, VLC
naturally constitutes a MIMO system. In addition, the MIMO
VLC channel is normally under static LOS conditions, whose
correlation is related to the parameters of the LEDs array
and the photo diodes (PDs) array. Sometimes, the channel
matrix has strong correlation, which affects the transmission
performance seriously [5], [7]. In practical experiment system-
s, many efforts have been made to construct a channel matrix
This work was supported in part by Grant No. 61271253 from China Na-
tional Science Foundation Council and in part by Grant No. 2013AA013603
from China National ”863” Program.
Yi-Jun Zhu, Wang-Feng Liang and Yan-Yu Zhang are with the De-
partment of Communication Engineering, Zhengzhou Information Science
and Technology Institute, Henan Province (450000), China. Emails: yijun-
zhu1976@outlook.com, 787666734@qq.com, zhangyanyu521@hotmail.com.
Jian-Kang Zhang is with the Department of Electrical and Computer Engi-
neering, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton,
Ontario, Canada. Email: jkangzhang@mail.ece.mcmaster.ca.
with low correlation, such as inducing power imbalance [6],
increasing the LEDs spacing distance [7] and using fisheye
lens [8].
It is known that RC is the simplest MIMO transmission
technique, which simultaneously emits the same signal from
all transmitters, to achieve good performance in free-space
optical communications [6], [9]. In [9], it was shown that RC
outperforms orthogonal space-time block codes (OSTBCs). In
SM, the conventional signal constellation diagram is extended
to the spatial dimension, in which only one transmitter is
activated at any symbol duration. SM has a lower decoding
complexity compared with other MIMO schemes [10], [11].
Since independent data streams are simultaneously emitted
from all transmitters in SMP, it has the highest spectrum
efficiency when channel correlation are sufficiently low [6]. In
RC, SM and SMP, symbols among the transmitting LEDs are
generated from constellations independently, it is not optimal
when considering about energy utilization.
In this letter, a new collaborative constellation design for
VLC MIMO is presented. By designing unipolar r-levels pulse
amplitude modulation (r-PAM) symbols of the transmitters
jointly, we achieve better power-efficiency for a given mini-
mum Euclidean distance. The simulation results show that the
performance of CC is always better than SM and SMP for
different channels, and is better than RC in general, except
for conditions with high correlation channel at low spectral
efficiency.
II. SYSTEM MODEL
Let us consider an indoor visible light communication
system with M transmitting antennas (LEDs) and N receiving
antennas (photo-detectors). Its discrete-time baseband MIMO
channel model can be represented as
y = Hs + n, (1)
where n is the sum of ambient shot light noise and thermal
noise with zero mean and a variance σ
2
[5]. It is assumed
that M data symbols s
1
, s
2
, · · · , s
M
are chosen randomly,
equally-likely and independently to form an input data vector
s = [s
1
, s
2
, · · · , s
M
]
T
∈ A
M
, where A is a given modu-
lation constellation. The received signal vector is denoted by
y = [y
1
, y
2
, · · · , y
N
]
T
. Notation H denotes an N ×M channel
matrix, in which h
nm
is the non-negative and real coefficient
between the mth transmitter antenna and the nth receiver
antenna. In this letter, we assume an indoor environment with
LOS characteristic, where the channel gain of a VLC link is