Coordinated Transmission for Visible Light Communication Systems by Hao Ma M.A.Sc., King Abdullah University of Science and Technology, 2012 B.Eng., Xi’an Jiaotong University, 2010 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate and Postdoctoral Studies (Electrical and Computer Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2017 c Hao Ma, 2017
165
Embed
Coordinated Transmission for Visible Light Communication Systems by Hao Ma MASc., King
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Coordinated Transmission for Visible Light Communication Systems
by
Hao Ma
M.A.Sc., King Abdullah University of Science and Technology, 2012
B.Eng., Xi’an Jiaotong University, 2010
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OF
Eye or Ear examination rooms 500Classroom for evening classes 500
Normal office work 500
Illuminance and Uniformity
The indoor illuminance level is determined by the DC current of LEDs. Various stan-
dardization bodies across different countries defined the required illuminance level for
the indoor environment [36, 37, 38]. In this thesis, we follow the requirement of the
European Norm (EN) 12464-1 standard [38] for the planning and design of lighting
installations. The area planning for indoor workplaces defines both task area and
immediate surrounding area. The task area is defined as the area in which the visual
work is carried out, while the immediate surrounding area is defined as a band sur-
rounding the task area within the field of vision with a minimum width of 0.5 m. The
task area can be used to perform different types of activities which require different
illumination levels. As specified in the European Norm (EN) 12464-1 standard, Table
1.1 provides the required illuminance level for a few different activities.
Aside from the illumination level, illuminance fluctuation across the indoor en-
vironment should also be restricted in order to guarantee a comfortable luminous
environment. Therefore, the term uniformity, defined as the ratio of the lowest to
the average illuminance value in a certain area, is introduced. According to the
European Norm (EN) 12464-1 standard, the minimum uniformity of task area and
immediate surrounding area is 0.60 and 0.40, respectively.
12
Chapter 1. Introduction
Amplitude Constraint
LEDs have a limited operating region which consists of both linear region and non-
linear region. The output optical power is linear with the forward current if LEDs
operate within the linear region. Otherwise, the current/optical conversion will dis-
play nonlinear characteristics similar to the nonlinearity of RF transmitters [39].
While pre-distortion can be used to (approximately) linearize the current/optical
conversion, the driving current of LEDs still needs to stay within a limited dynamic
range, beyond which the output intensity saturates. Therefore, the channel input of
VLC systems must satisfy a certain amplitude constraint in order to avoid clipping
distortion of the transmitted signal, which is different from the power constraint that
is usually considered in RF systems.
For single-carrier modulated signals, it is easier to put a constraint on its ampli-
tude to avoid overdriving LEDs, and thus signal clipping can be prevented. While for
multi-carrier modulation, like OFDM, signal clipping is unavoidable since the time-
domain signal follows a Gaussian distribution for large Inverse Fast Fourier Transform
(IFFT) sizes according to the Central Limit Theorem [40]. In this case, the current
signal should be pre-clipped before it is injected into the LEDs so that the driving
current lies within the dynamic range of the LEDs .
1.2.4 Modulation Techniques
VLC systems utilize the LED, which is an incoherent light source, as the transmitter.
VLC-enabled LEDs send information by varying the instantaneous intensity (i.e.
power) of the optical source in time. Data are not sent in the underlying phase or
amplitude of the optical carrier but rather only in its power. This modulation scheme
is called IM. As a result, only non-negative signals can be sent from the transmitter.
13
Chapter 1. Introduction
At the receiver, a photodiode performs the DD of the signal. It integrates the envelope
of the received field and outputs an electrical current in near proportion to the optical
power impinging on it. In the following, we will have a brief review of several VLC-
compatible modulation schemes.
Single-Carrier Modulation
IEEE 802.15.7 standardized three modulation schemes, namely on-off keying (OOK),
variable pulse-position modulation (V-PPM) and color shift keying (CSK) [9]. The
first two modulation schemes are compatible with single-chip LEDs (phosphor-based
LEDs) while CSK is targeted for multi-chip light sources (RGB LEDs) and detectors.
• On-Off Keying (OOK): Due to its simplicity, on-off keying is the most pop-
ular IM/DD modulation scheme. Each OOK symbol represents either an “ON”
state or an “OFF” state. Note that "ON" and "OFF" are just two logic levels
and do not necessarily require that the light source be turned off completely.
Different line code techniques can be applied to OOK. In the simplest form of
OOK, non-return-to-zero (NRZ) OOK, digital data is represented by the pres-
ence or absence of light. The IEEE 802.15.7 standard proposes the Manchester
coding instead of NRZ for VLC OOK. The Manchester line code encodes each
data bit in either low-to-high or high-to-low transition thus it is a DC balanced
code, which can avoid possible flicker [9].
• V-PPM:V-PPM combines both 2-PPM (pulse position modulation) and PWM
(pulse width modulation). In 2-PPM, the symbol duration is divided into two
slots of equal duration and the pulse corresponding to a certain bit is trans-
mitted in one of its two time slots within the symbol period, through which
the binary bit 1 and 0 are represented. V-PPM incorporates the characteristics
14
Chapter 1. Introduction
of PWM and extends 2-PPM by making the duty cycle percentage tunable in-
stead of fixing it at 50%. Pulse width of V-PPM can be adjusted based on the
dimming requirements. V-PPM has both the advantages of flicker avoidance
(2-PPM) and dimming control capability (PWM).
• Color Shift Keying (CSK): CSK applies to VLC systems that employ RGB
LEDs as the transmitter. In CSK, signals are transmitted imperceptibly via
varying the light output of each chip in the RGB triplet. The luminous flux and
the average perceived chromaticity of the light source remain constant, making
CSK free from flicker. Also, CSK generally enables higher data throughput
since it divides the visible light spectrum into three different communication
channels, in contrast to the two modulation schemes above which modulate the
same data over the entire visible light spectrum [41].
Multi-Carrier Modulation
Besides these standardized single-carrier modulation schemes, IM/DD compatible
multi-carrier modulation schemes are gaining popularity in both the research com-
munity [10, 11] and the industry [12]. OFDM has been widely used in RF com-
munications due to its robustness towards ISI caused by the dispersive channel and
the low complexity of frequency-domain receiving equalization. The VLC channel is
inherently dispersive due to the low-pass characteristics of LEDs and the reflections
of light waves. Therefore, optical OFDM can be applied to high-speed VLC systems
to combat ISI. However, due to the nature of IM/DD, the conventional OFDM used
in RF communications needs to be modified since the time-domain optical OFDM
signals for the IM/DD channel is required to be both real and non-negative in order
to modulate light intensity. In this subsection, we will have a brief overview of two
15
Chapter 1. Introduction
popular variations of optical OFDM [42]. The former has the same requirement as for
any baseband OFDM transmission, such as for digital subscriber lines (DSLs), where
it is also referred to as discrete multitone (DMT), or for power line communication
(PLC). In comparison, the latter is truly VLC specific.
• DC-Biased Optical OFDM: In DC-biased optical OFDM (DCO-OFDM),
the signal input to the inverse Fast Fourier Transform (FFT) module should
satisfy the Hermitian symmetry so that the output is real. A DC bias is added
to ensure the unipolarity of optical OFDM signal in DCO-OFDM. However, the
time-domain OFDM signal has a high peak-to-average power ratio (PAPR). In
order to bias all negative peaks, a large DC bias is required thus the power
efficiency decreases. Therefore, typically a moderate DC bias is used to bias
most of the negative components, while the rest of the negative components will
be clipped, and every information-carrying subcarrier will be contaminated by
the resulting clipping noise.
• Asymmetrically Clipped Optical OFDM: Similar to DCO-OFDM, asym-
metrically clipped optical OFDM (ACO-OFDM) also utilizes the Hermitian
symmetry to ensure a real output. The time-domain ACO-OFDM signal is
made positive by clipping all negative signal components. As the resulting
clipping noise will only affect the even subcarriers, ACO-OFDM only employs
odd subcarriers to carry data symbols and leave even subcarriers vacant [43].
Compared with DCO-OFDM, ACO-OFDM is less spectral efficient since half
of the subcarriers are unused. However, ACO-OFDM is more power efficient in
terms of average optical power for small constellation sizes [44].
16
Chapter 1. Introduction
1.3 Motivation and Contributions of the Thesis
At the time of starting the thesis work in 2012, most research on physical layer
transmission techniques in the VLC literature focused on point-to-point communica-
tion. However, despite the often dominating LoS propagation and the confinement of
light waves by opaque surfaces, the performance of a VLC attocell downlink can still
be severely degraded by interference from neighboring attocells, i.e., inter-attocell
interference (IAI). Typical lighting systems in indoor environments utilize multiple
wide-beam luminaires to provide user-friendly uniform illumination. From a com-
munications perspective, however, the use of wide-beam luminaries gives rise to in-
creased interference levels at areas in which the illumination footprints of luminaires
from different attocells overlap.
In order to alleviate the performance degradation for attocell-edge users, several
works in the literature have considered hybrid RF-VLC systems [45, 46, 47, 48]. In
such systems, the VLC attocells are deployed with non-overlapping footprints, and
the gaps are covered with RF femtocells. In other words, users who are beyond the
coverage of the VLC attocells are served by RF base stations. Despite its benefits,
a hybrid RF-VLC system would suffer from added complexity along with increased
handover overhead for users moving across different femtocells/attocells.
A different approach towards interference management for VLC attocells is to
use the so-called coordinated multipoint (CoMP) paradigm, wherein transmitters of
different attocells are connected through backbone networks like wired Ethernet or
powerline, and design their signals in a collaborative way. In Chapter 2, we propose
the joint transmission (JT) of multiple VLC attocells (i.e., VLC-enabled LED lu-
minaries) to turn the problem of overlap and thus interference into an advantage,
with PLC used as the network backbone. In JT, all the transmitters jointly serve
17
Chapter 1. Introduction
multiple users. It removes the barriers between attocells and turns the previously
unwanted IAI into constructive signal components. We suggest that since multiple
LED luminaries in the same room are connected to the same power wires, PLC can
be used to serve as a backbone network to support the cooperation among multiple
VLC attocells. A VLC modem in an LED transmitter can receive data from the
very power line that provides its power through a PLC modem, while in comparison
an Ethernet backbone requires modifications in the existing indoor wiring. This co-
ordinated architecture2 can be considered as the VLC counterpart to RF CoMP in
cellular networks [49, 50]. Our numerical results for a typical VLC scenario clearly
demonstrate the improvements of receiver-side signal-to-interference-plus-noise ratio
(SINR) due to the proposed coordination.
Since 2013, considerable research efforts have been directed towards collaborative
designs for VLC systems, most of which focused on JT schemes [51, 52, 53, 54, 55,
56, 57, 58, 59]. JT is typically considered in the context of beamforming design or
frequency allocation among attocells. In [51], pseudo-inverse-based zero forcing (ZF)
and ZF dirty-paper coding were proposed for multi-user multi-input single-output
(MU-MISO) VLC systems, while a generalized-inverse-based ZF scheme was proposed
in [52] to maximize the system sum-rate. In addition, ZF block diagonalization
precoding3 schemes was considered for a multi-user multiple-input, multiple-output
(MU-MIMO) VLC system in [53]. Besides ZF, linear beamforming schemes that
are based on the minimum mean squared error (MMSE) criterion have also been
considered in [54, 55, 56, 57]. Other JT schemes that exploit frequency allocation
have been considered in [58, 59].
Despite their superior performance, the implementation of JT schemes brings two2We note that the backbone network of the coordinated architecture does not have to be PLC.3The concepts of precoding and beamforming are used interchangeably throughout the thesis.
18
Chapter 1. Introduction
major difficulties. First, JT requires tight synchronization among LED transmitters
of different attocells in order to ensure that the signals emitted from different lu-
minaires arrive at the intended user simultaneously. Second, information exchange
among different transmitters should involve not only downlink channel state informa-
tion (CSI), but also the data symbols intended for each user. JT may not be feasible
if the backbone network that interconnects the transmitters together is band-limited.
This is a particular concern considering the fact that PLC has been favored to be an
attractive solution as the backbone network for the VLC front-end [60, 61, 62, 63],
while the power line is a broadcast medium and thus the links to different VLC-
enabled luminaires need to share the PLC capacity.
In order to circumvent such difficulties, researchers have considered other CoMP
schemes that require lower coordination level among attocells to seek a compromise
between system performance and implementation complexity [64, 65, 66, 67, 68, 69,
70]. Unlike JT, those coordination schemes only require the sharing of CSI among
attocells. In addition, symbol-level synchronization among attocells is not required
as each user is served only by its assigned attocell. When the attocells are served by
single-luminaire transmitters, the coordination can be implemented via adaptively
allocating the time [64], frequency [64, 65, 66, 67, 68, 69, 70], or power resources
[68, 69, 70] among different attocells. Such allocation schemes restrain the resources
available to each attocell, and consequently, the overall data rate of the system is
reduced.
In Chapter 3, we propose a coordinated beamforming (CB) scheme for interference
mitigation in downlink multi-cell MU-MISO VLC systems, where different attocells
have multi-luminaire transmitters while each receiver has a single PD. The luminaires
in each transmitter are modulated independently of each other using separate drivers.
19
Chapter 1. Introduction
The excess degrees of freedom offered by such multiple luminaires allow forming more
directive beams towards the intended receivers while minimizing IAI. Compared with
the coordination schemes considered in [64, 65, 66, 67, 68, 69, 70], which are based
on time, frequency, or power allocation, our CB scheme exploits the spatial domain
for both multiplexing and interference mitigation purposes. In fact, our CB scheme
can be integrated with the time and frequency multiplexing techniques considered in
[64, 65, 66, 67, 68, 69, 70] to further enhance the overall system performance.
We also note that the concepts of JT and CB are not new and have been widely
studied for RF channels (see, e.g., [71, 72, 73, 74, 75, 76, 77]). However, since VLC
systems are typically modeled with the amplitude constraint on the channel input (see
Section 1.2.3), the beamforming schemes developed for RF channels are not directly
applicable to VLC transmitters.
Most research works in VLC focus on the downlink transmission, often assuming
the existence of a perfect uplink channel. To realize an uplink, both optical and RF
transmissions are potential candidates. An optical uplink suffers from problems like
energy inefficiency and device glare, and the link between the device and the fixed
uplink receiver can be poor due to user mobility and change in device orientation
[78]. Thus an RF uplink is preferred considering that most places are RF-insensitive.
One choice is a WiFi uplink, because most mobile devices have WiFi radio pre-
installed already. The integration of WiFi uplink with VLC has been discussed in a
number of research works in the literature, e.g., [45, 60, 78, 79, 80]. For VLC systems
using RF uplinks, channel reciprocity is absent and VLC transmitters need to obtain
the channel information from receivers through feedback channels. In a realistic
scenario, the channel information at the transmitter side will not be perfect due to
erroneous or outdated estimation and/or quantization. Imperfect CSI deteriorates
20
Chapter 1. Introduction
the performance of VLC systems, which requires robust designs to counteract the
performance loss. This motivates us to extend our proposed design methods to take
into account possible mismatches in channel information available to the transmitters,
which constitutes the second part of Chapter 2 and Chapter 3.
As has been mentioned in Section 1.2.1, the modulation response of the LED
transmitter is the bottleneck that impedes the capacity enhancement of VLC links.
The typical 3 dB modulation bandwidth of phosphor-based LEDs can be improved
to approximately 20 MHz with blue optical filters at the receiver side for better re-
ception, and the bandwidth is still smaller than the inverse of the maximum excess
delay of the NLoS path in most indoor environments [27]. When the transmit sig-
nal bandwidth is below the cutoff frequency of the LED, the VLC channel can be
approximated as frequency-flat, which is the assumption of both Chapters 2 and 3.
However, as the modulation bandwidth of LEDs gradually increases [28], the VLC
channel cannot be modeled as frequency-flat anymore and the multipath effect in
the VLC channel should be considered. Recently, there has been a growing interest
in applying OFDM to VLC due to its robustness to multipath dispersion, together
with its simple equalization and digital implementation. However, the high PAPR of
time-domain OFDM signals is a key challenge for VLC systems due to the limited
dynamic range of the LED, which will result in the clipping of time-domain OFDM
signal, leading to performance degradation of VLC systems.
In Chapter 4, we apply OFDM to combat the multipath dispersion of VLC signals,
instead of the single-carrier modulation which is considered in Chapters 2 and 3. In
particular, we propose in this chapter a hybrid VLC-PLC (HVP) system architecture
for the indoor downlink transmission and present the analytical framework for the
data rate analysis of the HVP system. To overcome the high PAPR problem, spa-
21
Chapter 1. Introduction
tial optical OFDM (SO-OFDM) [81] is applied across multiple luminaires, for which
we propose several subcarrier allocation schemes to exploit the frequency selectivity
of the VLC and PLC channels. Different possible and meaningful variations of the
HVP system, including the choice of optical OFDM transmission, relay and multi-
ple access schemes, are investigated and compared. The numerical results establish
achievable rates for relevant communication scenarios and highlight the advantages of
the proposed subcarrier allocation schemes in terms of rate and reduced peak power
of optical OFDM signals.
1.4 Remark on Alternating Optimization
The design tasks derived in this thesis are in the form of non-convex optimization
problems. Our main tool to solve these problems is alternating optimization [82, 83].
Throughout the thesis we apply an instance of alternating optimization that di-
vides optimization variables into two groups, and thus the alternation is between two
subproblems. For the problems considered in this thesis, the global optimum can
be found for each subproblem in the respective optimization step. This is because
the subproblems are either convex (Chapters 2 and 3) or classic integer program-
ming problems that can be solved with polynomial-time algorithms (Chapter 4) [84].
Hence, the value of the objective of the original problem improves with every it-
eration of the alternating optimization. Since furthermore the objective functions
considered in this thesis are bounded, we are assured that the objective function will
converge monotonically through alternating optimization [83, Theorem 4.5]. Despite
this structural convergence property, we also set a maximum number of iterations
when applying alternating optimization to the problems in Chapters 2–4, so as to
limit its computational complexity. Beyond this, however, our main focus in this the-
22
Chapter 1. Introduction
sis is the derivation of methods to enable performance-improved VLC transmission
and not the complexity analysis or optimization of computational methods applied
for this purpose.
1.5 Organization of the Thesis
The following chapters are organized as follows. In Chapter 2, we propose a JT
scheme for multiple connected VLC attocells and focus on the linear beamforming
design based on the MMSE criterion. The materials presented in this chapter have
been previously published in [54]. In Chapter 3, we propose a CB scheme for down-
link interference mitigation among coexisting VLC attocells utilizing multi-luminaire
transmitters. Compared to JT schemes, the proposed CB scheme places lower re-
quirements on the network in terms of backbone traffic, and is easier to implement
in a practical deployment, though at the cost of compromised performance. These
results have been submitted for publication. In Chapter 4, we propose a multi-carrier
HVP system as a potential indoor high-speed downlink solution employing the sym-
biotic relationship between PLC and VLC. To exploit the frequency selectivity of
HVP channels, as well as the multi-user and multi-transmitter diversity, we propose
several subcarrier allocation schemes with varying degrees of tradeoff among hard-
ware, computational complexity and performance for meaningful variations of the
HVP system. The materials presented in this chapter have been published in [85].
Finally, Chapter 5 summarizes the contributions of this thesis and outlines areas of
future research.
23
Chapter 2
Joint Transmission in VLC Systems
2.1 Introduction
Indoor environments generally utilize multiple wide-beam luminaires to ensure user-
friendly uniform illumination. From a communications perspective, however, the
use of wide-beam luminaries leads to increased interference levels. To mitigate the
interference across neighboring VLC attocells, this chapter proposes the joint trans-
mission of different transmitters, i.e., LED luminaries, through a backbone network.
The purpose of this coordination is to turn unwanted interference into constructive
signal components. The backbone could be realized by a wired Ethernet or power-
over-Ethernet link. Another convenient manner to realize the backbone is using
existing electrical power wiring for data communications, i.e., PLC [86]. The concept
of integrating PLC and VLC to form a hybrid system for fast data delivery to users
in indoor office buildings and homes is not new [87, 88, 89]. However, since multi-
ple LED luminaries in the same room are connected to the same power wires, PLC
can also be used to serve as a backbone network to support the cooperation among
multiple VLC attocell.
This chapter focuses on the signal processing required at the VLC transmitters
to benefit from coordination [62]. Multiple coordinated VLC emitters form a virtual
multiple-transmitter (or multiple-“antenna”) system. This is quite different from the
indoor multiple-input multiple-output (MIMO) VLC systems for point-to-point com-
24
Chapter 2. Joint Transmission in VLC Systems
munication studied in [90, 91], since we are dealing with the broadcasting of data
to multiple VLC receivers (e.g. cellular phones or tablets) employing single photo-
diode receivers here. Such MU-MISO systems have been widely studied for radio
communication systems, cf. e.g. [71, 72, 77]. However, different from RF wireless
communication, VLC uses IM and the transmitted signal must be non-negative and
constrained in mean amplitude, i.e., average optical power. These differences render
solutions developed for the RF case not directly applicable to VLC systems. We in-
vestigate the effect of different levels of coordination of luminaries in a room, leading
to different numbers of attocells and IAI scenarios. Within a coordinated VLC sys-
tem, linear MMSE precoder design is applied. This allows us to consider interference
from adjacent VLC transmitters that are not coordinated, as well as ambient light
from the sun and other non-VLC lighting devices. Furthermore, this chapter extends
the system design to the case of imperfect knowledge of the VLC transmission chan-
nel. The numerical results highlight the benefits of coordination for VLC attocell
systems by demonstrating significant gains in achievable SINR.
The remainder of the chapter is organized as follows. In Section 2.2, we propose
the JT VLC architecture with PLC as its backbone network. In Section 2.3, precoder
design strategies for VLC MU-MISO transmission with perfect CSI at the transmitter
are developed. In Section 2.4, the designs are extended to the case of imperfect CSI.
Simulation results are presented and discussed in Section 2.5, and finally we conclude
this chapter in Section 2.6.
2.2 System Model and Transmission Scheme
We consider an indoor environment with multiple LED luminaires deployed in a room,
office, laboratory or similar indoor space. The main elements of the coordinated
25
Chapter 2. Joint Transmission in VLC Systems
Figure 2.1: Illustration of indoor coordinated VLC broadcast system.
VLC broadcast system are illustrated in Figure 2.1. The luminaires function as VLC
transmitters as a secondary use, and they receive electricity and data through a PLC
backbone network. This enables some of the VLC transmitters, e.g., those connected
to the same distribution box, to operate in a coordinated fashion alike CoMP. Similar
to the definition of a CoMP-cell in the context of RF wireless systems [50], we define
a CoMP-attocell as the area covered by one VLC broadcasting system where all the
transmitters are coordinated by the PLC backbone network. In the case of multiple
CoMP-attocells in one room, there is interference from neighbouring CoMP-attocells,
which is analogous to inter-CoMP-cell interference in RF cellular systems.
2.2.1 VLC Channel
Before discussing the broadcast transmission and VLC-specific constraints, we first
briefly elaborate on channel gain and noise models applicable to the IM/DD channel
26
Chapter 2. Joint Transmission in VLC Systems
in VLC.
Each LED luminaire has NE LED elements with a Lambertian radiation pattern.
We assume that LoS propagation of visible light dominates the diffuse propagation
component and thus only the former is considered [90]. Utilizing Eq. (1.2), the
channel gain hkn between the kth user and the nth LED luminaire can be expressed
as [8]
hkn =
NE∑i=1
h(Dkni, φkni
, ψkni) , (2.1)
where Dkni, ψkni
and φkniare the distance, the angle of incidence and the angle
of irradiance between the kth user and the ith LED in the nth LED luminaire,
respectively.
The receiver-side noise term zk (see Eq. (2.7) below) can be written as
zk = ik + nk , (2.2)
where ik is the interference from neighbouring CoMP-attocells with average received
electrical power E(i2k) = σ2ik, and the VLC noise component nk comprises shot and
thermal noise. We assume that nk can be modelled as a zero-mean Gaussian variable
with variance calculated by Eq. (1.3). We observe that Ikrp is dependent on the
DC current and thus illumination level and on user location, via hkn. This renders
the optimization of broadcast transmission intractable. Therefore, we will use a
fixed upper bound for Ikrp in the following optimization. The accurate noise power is
however applied for all numerical results.
Finally, we denote the total interference and noise power at the kth user as
σ2k = E(z2
k) = σ2ik
+ σ2nk. (2.3)
27
Chapter 2. Joint Transmission in VLC Systems
2.2.2 Broadcast Transmission
In a VLC CoMP-attocell, NL LED luminaires cooperate to broadcast information
to NU single-photodiode users. OOK is applied in this work due to its popularity
in optical communications and ease of implementation4 [9]. This is accomplished by
modulating a zero-mean data signal onto the DC bias currents IDC = [I1DC, . . . , I
NLDC]T ,
which determine the brightness levels of the NL LED luminaires. In the following,
we describe the pre-processing of this data signal.
Let us denote dk ∈ {±1} the binary data symbol intended for the kth user, and
d = [d1, · · · , dNU]T is the data vector for all users with covariance matrix
Cd = I . (2.4)
The broadcast signal for VLC MU-MISO is generated through linear precoding of
the data vector with the matrix F , i.e.,
s = [s1, . . . , sNL]T = Fd . (2.5)
Finally, the transmitted current signal is given as
x = Fd+ IDC . (2.6)
We note that the conversion to a current signal and the scaling of the binary data
vector d is accomplished through matrix F . Hence, choosing dk ∈ {±1} is without
loss of generality. Furthermore, in VLC transmission, the elements of x need to be4Higher-order pulse-amplitude modulation (PAM) schemes could also be employed in the case
of high SINRs at the receivers. The precoder design would follow a similar approach as shown herefor OOK.
28
Chapter 2. Joint Transmission in VLC Systems
non-negative, which imposes constraints on F as we will discuss further below.
Collecting the channel gains hkn from Eq. (2.1) for all NU × NL links into the
channel matrix H = [h1, . . . ,hNU]T = {hkn}NU×NL
, the received signal at the kth
user can be written as
yk = hTkx+ zk = hTk fkdk + hTk∑i 6=k
fidi + zk + hTk IDC , (2.7)
where fk represents the kth column of F . The first term hTk fkdk is the desired signal,
while the second term hTk∑
i 6=k fidi represents the intra-CoMP-attocell interference.
The third term zk is the sum of inter-CoMP-attocell interference and noise as intro-
duced in Eq. (2.2). The fourth term hTk IDC is the DC photocurrent for illumination
that carries no data. It is removed via AC coupling at the receiver side, providing
the information-carrying signal at the kth receiver as
yk = yk − hTk IDC = hTk fkdk + hTk∑i 6=k
fidi + zk . (2.8)
2.2.3 Constraints on Precoding from VLC
Consider the precoding operation in Eq. (2.5), the data signal sn at the nth luminaire
satisfies
− ‖fn‖1 ≤ sn ≤ ‖fn‖1, (2.9)
where fn is the nth row vector of the precoding matrix F . After adding the DC bias,
InDC, to adjust the brightness of each LED luminaire, the electrical transmit signal
(drive current) at the nth LED luminaire is (see Eq. (2.6))
xn = sn + InDC . (2.10)
29
Chapter 2. Joint Transmission in VLC Systems
For simplicity, in the following we assume the same brightness level for every LED
luminaire, i.e.,
InDC = IDC , ∀n . (2.11)
Due to optical intensity modulation, xn ≥ 0 and thus sn ≥ −IDC from Eq. (2.10).
However, similar to the nonlinearity of RF transmitters, LEDs also have a limited
linear range [39]. While pre-distortion can be used to (approximately) linearize trans-
mission, signal clipping needs to be avoided. Furthermore, if the LED is over-driven,
not only will LED life-expectancy be reduced, but the self-heating effect will lead to
a drop in the electrical-to-optical conversion efficiency. Considering these character-
istics of LEDs, the transmit signal of each LED luminaire should satisfy
IL ≤ xn = sn + IDC ≤ IU , (2.12)
where IU > IL > 0 represent the upper and the lower bound of the LED drive current
in the linear region. Substituting this into Eq. (2.9), we get
IDC − ‖fn‖1 ≥ IL
IDC + ‖fn‖1 ≤ IU
(2.13)
and the constraint
‖fn‖1 ≤ min (IDC − IL, IU − IDC) (2.14)
for the nth row vector of the precoder matrix F . Note that, via IDC, this constraint
ties possible choices of VLC precoding matrices F to the user-selected illumination
level of the LEDs.
30
Chapter 2. Joint Transmission in VLC Systems
2.2.4 Design Objectives
Given the broadcast transmission model Eq. (2.8) and constraint Eq. (2.14), we
optimize the precoding represented by F in two ways. First, we consider the perhaps
more obvious design task of maximizing the performance of MU-MISO VLC under
illumination constraints, i.e., a given value of IDC. As an appropriate performance
measure for MU-MISO VLC we adopt the sum-MSE. Secondly, we consider a VLC
performance target represented by a given set of MSE thresholds for all users, and
find the minimal illumination level required to maintain performance. This design
provides a guaranteed VLC performance under different dimming levels. The two
design objectives are pursued in Section 2.3, assuming perfect CSI, i.e., channel gains
hkn (Eq. (2.1)), are available at the VLC transmitters. In Section 2.4, we extend
our derivations to the practically relevant case of imperfect channel knowledge at the
transmitter.
2.3 Transmitter Design with Perfect Channel
Information
As mentioned above, the performance metric for precoder design adopted in this sec-
tion is the sum MSE, which has widely been considered for precoding optimization in
RF wireless MIMO/MISO systems, e.g., [92]. In particular, we consider the modified
MSE [93] between the received signal yk at the kth user and original data dk given
by
MSEk = Edk,zk{‖cyk − dk‖2
2
}= Ed,zk{‖c(h
TkFd+ zk)− eTk d‖2
2} , (2.15)
31
Chapter 2. Joint Transmission in VLC Systems
where c is a scaling term, which does not need to be applied at the receiver but offers
a required degree of freedom in the receiver filter optimization, and ek denotes the
kth standard basis vector for the NU-dimensional space,
ek = [01×(k−1) 1 01×(NU−k)]T . (2.16)
2.3.1 Sum-MSE Minimization Problem
We first consider the sum-MSE minimization under illumination constraints. In this
case, the precoder optimization problem can be formulated as
P1 : (F ∗, c∗) = argminF ,c
NU∑k=1
MSEk
C1 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n (2.17)
Using Eq. (2.15), the objective function in P1 can be written as
f(F , c) =
NU∑k=1
MSEk = Ed,z{‖cy − d‖2
2
}. (2.18)
The optimization problem P1 is not jointly convex in precoder F and scaling factor
c. We therefore use an alternating optimization approach to, possibly suboptimally,
solve this problem. Specifically, we iteratively optimize F and c while fixing the other
variable (see Algorithm 2.1).
32
Chapter 2. Joint Transmission in VLC Systems
Fixing Receiver Gain c
We assume a fixed receiver gain c and then optimize the precoder F . In this case, it
is convenient to define
σ2sum =
NU∑k=1
σ2k (2.19)
and to write the sum-MSE as
Ed,z{‖cy − d‖2
2
}= Ed,n
{‖c(HFd+ z)− d‖2
2
}= ‖c(H ⊗ I)vec(F T )− vec(I)‖2
2 + c2σ2sum .
(2.20)
Then, defining b = vec(I), A = H ⊗ I, f = vec(F T ), and V as the NLNU ×NLNU
block-diagonal matrix of the NL×NU all-one matrix, problem P1, for a fixed gain c,
can be transformed into
P2 : (f ∗, t∗) = argminf,t
‖cAf − b‖22 + c2σ2
sum
C1 : −t � f � t ,
C2 : V t ≤ min (IDC − IL, IU − IDC) 1NU×1 , (2.21)
where vector t is a slack variable. The constraints in this optimization problem are
equivalent to the L1-norm constraint (Eq. (2.14)) resulting from the limited dynamic
range of the LED. This problem is a convex quadratic programming problem and can
be efficiently solved using, e.g., the YALMIP or CVX toolbox [94, 95, 96].
33
Chapter 2. Joint Transmission in VLC Systems
Fixing Precoder F
Now we assume the precoder matrix F as fixed and optimize for c. The optimization
problem P1 with fixed precoder F can be simplified into
P3 : c∗ = argminc‖cAf − b‖2
2 + c2σ2sum .
The optimal c∗ can now be computed as
c∗ =sym(bTAf)
‖Af‖22 + σ2
sum
, (2.22)
where
sym(X) =X +XT
2(2.23)
represents the symmetric part of a matrix X.
Algorithm 2.1 Alternating optimization algorithm for P11. Initialization:
p⇐ 0.Update H with CSI.Initialize {F }.
2. repeat3. Update c according to Eq. (2.22).4. Solve P2 and get F .5. p⇐ p+ 1.6. until ‖MSEp+1 −MSEp‖ ≤ δ (δ is a predefined threshold) or p = pmax (pmax
is a predefined maximum iteration number), where MSE =∑NU
k=1 MSEk.
34
Chapter 2. Joint Transmission in VLC Systems
2.3.2 Minimal Illumination Level Problem
We now turn to the question of what is the minimal illumination level needed to
maintain a certain VLC performance. This is important for illumination systems
with dimming, for which VLC should be supported. Illumination is proportional to
IDC, which via Eq. (2.14) affects VLC precoding. Measuring VLC performance in
terms of MSE and denoting by qk the constraint for the MSE of the kth user, the
corresponding optimization problem can be formulated as
According to the Schur complement lemma [97, 98], inequality Eq. (2.27) is equivalent
to
Θk =
√qkζ φk
φTk√qkζI
� 0 .
Thus, P4 can be reformulated as
P5 : (F ∗, ζ∗, I∗DC) = argminF ,{tk},ζ,IDC
IDC
C1 : −tk � F Tek � tk, ∀k,
C2 : 1T tk ≤ min (IDC − IL, IU − IDC) , ∀k,
C3 : Θk � 0,∀k, (2.28)
where vector tk is a slack variable. The problem is a convex semidefinite programming
problem (SDP) and can be solved efficiently numerically, e.g., [94, 95].
2.4 Robust Transmitter Design with Channel
Uncertainty
The quality of CSI at the transmitter is critical to the precoder design. While the
VLC channel is much more benign than its RF counterpart, the assumption of perfect
CSI is not necessarily practical for MU-MISO VLC. VLC systems use visible light
as the downlink medium, while the uplink medium can be RF, infrared light (IR) or
visible light [14]. In the case of VLC uplink, the uplink-downlink reciprocity will allow
CSI to be estimated at the transmitter. The more practically relevant scenario for
VLC using indoor illumination devices considered here is that an RF uplink is used.
In this case, CSI can only be estimated at the receiver and fed back to the transmitter
36
Chapter 2. Joint Transmission in VLC Systems
afterwards. Imperfect CSI can then arise from noisy and quantized channel estimation
and, perhaps more critically, the feedback of outdated estimates. The latter is the
case when the VLC channel varies due to terminal motion and/or changes in the
environment since the last channel update. As an example, Figure 2.2 illustrates a
scenario where the receiver terminal has moved from position p1, at which CSI is
reported, to position p2, at which precoded data using this CSI is received.
2.4.1 Uncertainty Models
Given the channel estimate hk, we can express the true channel gains for the kth
user as
hk = hk + δk , (2.29)
where the error vector δk represents the CSI uncertainty. According to the source of
estimation error, we consider two models for δk.
Noisy CSI
For noisy CSI, we use the stochastic error model [97]
δk ∼ N (0,Σk) , (2.30)
i.e., δk is zero-mean Gaussian distributed with covariance matrix Σk.
37
Chapter 2. Joint Transmission in VLC Systems
Figure 2.2: Illustration of outdated CSI resulting from terminal mobility in a VLCsystem.
Outdated CSI
Outdated CSI, due to e.g. a user walking with a terminal device (see Figure 2.2), is
often modelled by a bounded uncertainty model, i.e.,
‖δk‖2 ≤ εk (2.31)
for some error bound εk, which depends on the maximal changes that happened be-
tween CSI estimation and transmission using this estimation. As we show in the
following, εk should be chosen as a function of the terminal location during chan-
nel estimation, i.e., p1 in Figure 2.2. Location information could be obtained from
channel estimation itself using various positioning techniques [99, 100].
Referring to Figure 2.2, we denote L as the bound for the user movement between
two CSI updates, i.e., ‖p1−p2‖2 ≤ L. Furthermore, considering a single transmitter,
let dv and dh be the vertical and horizontal distance between transmitter and receiver,
38
Chapter 2. Joint Transmission in VLC Systems
respectively, as indicated in Figure 2.2. Then, for terminal movement in the horizontal
direction, horizontal planes at the LED transmitter and photodiode receiver, the error
bound
εk = max{ε+, ε−} (2.32)
can be obtained, where
ε+ = β(
(d2v + d2
1)−m+3
2 − (d2v + (d1 + L)2)−
m+32
), (2.33)
ε− = β(
(d2v + (d2 − L)2)−
m+32 − (d2
v + d22)−
m+32
), (2.34)
β =(m+ 1)NEsγκ
2APDdm+1v
2π sin2(ψc), (2.35)
and d1 and d2 satisfy
log
(d1
d1 + L
)=m+ 5
2log
(d2v + d2
1
d2v + (d1 + L)2
), (2.36)
log
(d2
d2 − L
)=m+ 5
2log
(d2v + d2
2
d2v + (d2 − L)2
). (2.37)
The details of the derivation of (2.32)–(2.37) are delegated to Appendix A. For the
more general case including multiple transmitters, the relationship between error
bound and physical system parameters is even more complicated than (2.32). We
thus resort to numerical analysis to obtain error bounds. As an example, Figure 2.3
shows εk as a function of the user location and the maximal location distance L. The
details of the room, illumination and VLC setup for this experiment are described in
Section 2.5.
In the following, we consider both uncertainty models to formulate robust precoder
designs. Similar to the RF wireless case, cf. e.g. [97, 98], we aim at optimizing average
performance for noisy CSI according to the stochastic model (2.30) and worst-case
39
Chapter 2. Joint Transmission in VLC Systems
−2
−1
0
1
2
−2
−1
0
1
2
0.5
1
1.5
x 10−5
x (m)y (m)
(a)
−2
−1
0
1
2
−2
−1
0
1
2
1
1.5
2
2.5
3
x 10−5
x (m)y (m)
(b)
Figure 2.3: Error bounds obtained from simulation for (a)L = 0.25 m, (b)L = 0.5 m.Illumination and VLC setup for these results are described in Section 2.5.
performance for outdated CSI with the bounded error model (2.31).
2.4.2 Sum-MSE Minimization Problem
We start with the sum-MSE minimization problem.
Robust Design with Outdated CSI
The robust broadcast precoder design for CSI uncertainty according to Eq. (2.31) is
an extension of P1 in Eq. (2.17):
P6 : (F ∗, c∗) = argminF ,c
max‖δk‖2≤εk
NU∑k=1
MSEk
C1 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n (2.38)
40
Chapter 2. Joint Transmission in VLC Systems
where
MSEk = ‖c(hTk + δTk )F − eTk ‖22 + c2σ2
k . (2.39)
Using results from [97], P6 can be transformed into
P7 : (F ∗, c∗) = argminF ,{tk},λ,µ,g,c
g2
C1 : −tk � F Tek � tk, ∀k,
C2 : 1T tk ≤ min (IDC − IL, IU − IDC) , ∀k,
C3 : Ψk � 0,∀k,
C4 : Φ � 0 , (2.40)
where
Φ =
g λT cσsum
λ gI 0
cσsum 0 g
,
Ψk =
λk − µk 0T ch
T
kF − eTk
0 µkI εkcF
(chT
kF − eTk )T εk(cF )T λkI
.
Similar to the optimization problem P1, we can obtain a local optimum of this prob-
lem by alternatively optimizing over F and c. Each problem is an SDP problem and
can be efficiently solved numerically, e.g., [94, 95].
41
Chapter 2. Joint Transmission in VLC Systems
Robust Design with Noisy CSI
As noted above, the average sum-MSE is considered. Defining
∆ = [δ1, . . . , δNU]T , (2.41)
the optimization problem can be formulated as
P8 : (F ∗, c∗) = arg minF ,c
E∆
(NU∑k=1
MSEk
)
C1 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n (2.42)
Following the steps in Eq. (2.18) and Eq. (2.20) and assuming Σk = σ2eI, we can
write the objective of P8 as
E∆ (f(F , c)) = (‖cAf − b‖22 +NUσ
2ec
2‖f‖22) + c2σ2
sum , (2.43)
where A = H⊗I, and H is the estimated channel matrix. While P8 is not a convex
optimization problem, again the application of alternating optimization for F and c
turns out to be a suitable approach. When fixing the receiver gain c, we can optimize
for F via
P9 : (f ∗, t∗) = argminf,t
(‖cAf − b‖22 +NUσ
2ec
2‖f‖22) + c2σ2
sum (2.44)
C1 : −t � f � t ,
C2 : V t � min (IDC − IL, IU − IDC) 1NU×1 .
42
Chapter 2. Joint Transmission in VLC Systems
This problem is a convex quadratic programming problem, which is solved numeri-
cally. Fixing the precoder F leads to the closed-form solution
c∗= argminc{‖cAf − b‖2
2 +NUσ2ec
2‖f‖22}+ c2σ2
sum
=sym(bT Af)
‖Af‖22 +NUσ2
e‖f‖22 + σ2
sum
.(2.45)
2.4.3 Minimal Illumination Level Problem
We finally turn to the robust design for minimizing the required illumination level
while achieving a required VLC performance.
Robust Design with Outdated CSI
To add robustness to the precoder design for minimal required brightness when CSI
is outdated, the worst-case MSE needs to satisfy the required performance qk:
max‖δk‖2≤εk
MSEk ≤ qk,∀k. (2.46)
Making use of the Schur complement lemma [97, 98] and [101, Lemma 2], Eq. (2.46)
is equivalent to ∃ λk ≥ 0,
Ψk =
√qkζ − λk vTk σk 0
vk√qkζI 0 −εkF T
σk 0√qkζ 0
0 −εkF 0 λkI
� 0,
where
vTk = (hTkF − ζeTk ) . (2.47)
43
Chapter 2. Joint Transmission in VLC Systems
Hence, we obtain the optimization problem
P10 : (F ∗, ζ∗, I∗DC) = argminF ,λ,ζ,IDC
IDC
C1 : −tk � F Tek � tk,∀k,
C2 : 1T tk ≤ min (IDC − IL, IU − IDC) , ∀k,
C3 : Ψk � 0, ∀k,
C4 : λk ≥ 0,∀k. (2.48)
This problem is an SDP and the global optimum can be obtained on the condition
that it is feasible.
Robust Design with Noisy CSI
In the case of noisy CSI, we need to replace C1 in P4 (2.24) by
Eδk(MSEk) = c2vTk vk + c2σ2e‖F ‖2
F + c2σ2k . (2.49)
Introducing auxiliary variable r and τ k = [vTk r σk], Eδk(MSEk) ≤ qk becomes
equivalent to
‖τ k‖2 ≤√qkζ
‖F ‖F ≤r
σe
(2.50)
44
Chapter 2. Joint Transmission in VLC Systems
Therefore, we can formulate the precoder design problem as
Transmitter ParametersIL 400 [mA]IU 600 [mA]Semi-angle at half power φ 1
260 [deg.]
Dimensions of LED L × W × H 3 [cm]×3 [cm]×2 [cm]LED interval 1 [cm]Number of LEDs per luminaire NE 36 (6×6)
Receiver ParametersPD area 1 cm2
Refractive index of optical concentrator κ 1.5Receiver FOV 60 [deg.]System bandwidth B 10 [MHz]Noise bandwidth factor I2 0.562Background current Ibg 5100 [µA]LED conversion factor s 0.44 [W/A]PD responsivity γ 0.30 [A/W]
ambient light from other sources such as sunlight or non-VLC enabled luminaries,
and the thermal noise is considered negligible [8].5
In the following, we assume that the VLC system transmits to NU = 4 users. For
concreteness, we further assume that the four users are centro-symmetrically located
on the plane at height z = 0.8 m, i.e., the user coordinates are (±x,±y, 0.8) m for
some x and y. We would like to emphasize that the specific system parameters, in
particular the values of NL and NU, are chosen for the sake of illustration of precoded
transmission only, and that our system design approach is applicable to any parameter5We also ran simulations assuming Ibg value of 620 µA [27]. We found that the main trends of
our results as discussed in the following are not affected by the value of the background current.
46
Chapter 2. Joint Transmission in VLC Systems
−2
−1
0
1
2
−2
−1
0
1
2
200
300
400
500
600
700
x (m)y (m)
Illu
min
an
ce (
lx)
Figure 2.4: The distribution of indoor illuminance when IDC = 500 mA.
pair (NL, NU).
In the subsequent sections, we report performance results for different transmis-
sion scenarios and precoder designs. Due to symmetry, the performance for the
NU = 4 users are identical, and thus we can drop the user index for the results. If
not stated otherwise, perfect CSI for the precoder design is assumed. For solving
the sum-MSE minimization problems via alternating optimization, the alternating
minimization will converge to a solution since the non-negative objective function
is minimized at each convex subproblem. The zero-forcing solution is used for ini-
47
Chapter 2. Joint Transmission in VLC Systems
tialization and the maximum number of iterations6 is set to 20. For solving the
convex optimization problems in this chapter, we use the YALMIP toolbox [94] in
conjunction with the MOSEK solver [103] to obtain the result numerically.
2.5.1 User Position with Joint Transmission Setup
We first investigate the achievable performance for a VLC broadcast system where
LED luminaries are fully connected by a PLC backbone network and coordinated by
a PLC controller. The users are arranged in three different setups as shown in the
first three arrangements in Fig. 2.5, where x = y = 0.5 in Setup I, x = y = 1.25 in
Setup II and x = y = 2 in Setup III, respectively. The channel matrices for these
three setups are obtained as
H I = 10−5
6.164 3.067 1.829 3.067
3.067 6.164 3.067 1.829
1.829 3.067 6.164 3.067
3.067 1.829 3.067 6.164
,
H II = 10−5
9.340 1.788 0.731 1.788
1.788 9.340 1.788 0.731
0.731 1.788 9.340 1.788
1.788 0.731 1.788 9.340
,
6The maximum number of iterations for Chapters 3 and 4 is also set to 20.
48
Chapter 2. Joint Transmission in VLC Systems
Figure 2.5: User-configurations for MU-MISO VLC are considered for numericalresults.
H III = 10−5
6.164 0.863 0.000 0.863
0.863 6.164 0.863 0.000
0.000 0.863 6.164 0.863
0.863 0.000 0.863 6.164
.
Figure 2.6 shows the results of the sum-MSE minimization problem as a function
of the DC bias IDC, i.e., the illumination level, for the three user-configurations from
Figure 2.5. Here we use the resulting optimal precoder to calculate the corresponding
SINR defined as
SINR =‖hTkwk‖2
2
‖hTk∑
i 6=k wi‖22 + σ2
k
. (2.52)
First, we observe that the system performance is symmetric with respect to IDC =
(IL + IU)/2. The SINR first increases as the DC bias IDC increases and then starts
to decrease after IDC surpasses (IL + IU)/2. This is because the electrical SINRs at
the receivers reach their maximal values when the precoded signal sn has the largest
dynamic range. Due to this symmetry property, we will only plot the results for IDC
ranging from IL to (IL + IU)/2 in the following figures. For varying positions of the
49
Chapter 2. Joint Transmission in VLC Systems
400 420 440 460 480 500 520 540 560 580 600−5
0
5
10
15
20
25
30
35
40
IDC (mA)
SIN
R (
dB
)
Setup I
Setup II
Setup III
Figure 2.6: Comparison of system performance with different user positions (as shownin Figure 2.5) as a function of illumination level. Sum-MSE minimization with perfectCSI.
50
Chapter 2. Joint Transmission in VLC Systems
four users, the setups in increasing order of SINR value are Setup I, Setup III and
Setup II. An intuitive explanation is that since the users in Setup I are closer to
each other than in Setup III, the channels are more similar and thus more difficult to
separate through precoding. Meanwhile, the distances between the LED luminaries
and users in Setup III are larger than those in Setup II, which leads to smaller channel
gains in Setup III than in Setup II.
The SINR defined in (2.52) can be used to approximate the symbol error rate
(SER) of the VLC transmission. For this, we assume that the interference is Gaussian
distributed, so that the SER can be expressed as [104]
SER = Q(√
2 SINR), (2.53)
where Q(·) is the Gaussian tail probability function. In Figure 2.7, we plot the SER
according to (2.53) as the function of DC bias IDC under Setup I. We also include the
SER results obtained from Monte Carlo simulations of the tranmission. We observe
that the two curves do not closely overlap, which speaks to the inaccuracy of the
Gaussian approximation for the VLC interference. We expect that this approxima-
tion becomes more accurate if more interferers are present as well as if high-order
modulation is used. Furthermore, as expected, we note that SER monotonically im-
proves with SINR also in the simulated SER case. Hence, we can well consider SINR
as a proxy for the SER performance.
We now highlight the benefit of coordination. To this end, we consider three
different coordination levels:
1. Joint Transmission (JT): Transmissions for all four LED luminaires are coordi-
nated.
51
Chapter 2. Joint Transmission in VLC Systems
400 405 410 41510
−6
10−5
10−4
10−3
10−2
10−1
100
IDC
(mA)
Sym
bol
Err
or
Rate
(S
ER
)
SER calculated with Equation (2.53)
SER with Monte Carlo simulation
Figure 2.7: Comparison of the SER calculation using Equation (2.53) with MonteCarlo simulation result.
52
Chapter 2. Joint Transmission in VLC Systems
(1) JT (2) PC (3) UT
LED Luminaire
CoMP-Attocell
Power Line PLC Controller
Figure 2.8: Different transmitter coordination levels in an MU-MISO VLC system.
2. Partial Coordination (PC): Transmissions for LED luminaires in the first and
the fourth quadrant and for LED luminaires in the second and the third quad-
rant are coordinated. Thus there exist two VLC CoMP-attocells in one room.
3. Uncoordinated Transmission (UT): Transmissions at the four LED luminaires
are not coordinated, which corresponds to four VLC CoMP-attocells in one
room.
The three coordination levels are illustrated in Fig. 2.8.
We consider two scenarios for user locations: Setup IV with x = 2, y = 1.25 and
Setup V with x = 0.5, y = 1.25. Figure 2.9 shows the SINR for precoder design
minimizing the sum-MSE as a function of IDC for different coordination levels and
user position scenarios. We observe that, since users are located closer to each other
and/or the neighbouring CoMP-attocell boundary in Setup V than for Setup IV, the
achievable SINR is generally higher for the latter. We can also see the significant SINR
increase due to coordination. In particular, the JT setup is clearly outperforming the
53
Chapter 2. Joint Transmission in VLC Systems
400 410 420 430 440 450 460 470 480 490 5000
5
10
15
20
25
30
35
IDC
(mA)
SIN
R (
dB
)
JT
PC
UT
Setup V
Setup IV
Figure 2.9: Comparison of system performance with different transmitter coordina-tion. Sum-MSE minimization problem with perfect CSI.
PC and UT systems, whose SINR saturates quickly due to inter-cell interference.
For Setup V, there is no performance difference for UT and PC systems, which
is due to the remaining large inter-CoMP-attocell interference in spite of the partial
coordination. In the PC system, each VLC transmitter tends to mostly communicate
to its closest receiver, which makes the PC system equivalent to a UT system.
The benefit of coordination is further demonstrated by the plots in Figure 2.10,
which show the SINR for one quadrant of the room as a function of the user’s location
(because of the symmetry of the four user’s location, the SINR plots for the other
54
Chapter 2. Joint Transmission in VLC Systems
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
x (m)
y (
m)
−5
0
5
10
15
20
25
30
35
40SINR (dB)
(a) JT system
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
x (m)
y (
m)
−5
0
5
10
15
20
25
30
35
40SINR (dB)
(b) UT system
Figure 2.10: SINR as a function of user location in one quadrant of the room andIDC = (IL + IU)/2. Sum-MSE minimization problem with perfect CSI.
quadrants are mirrored versions of those in Figure 2.10) and for IDC = (IL + IU)/2.
It can be seen that the SINR is severely IAI-limited in the UT case, and that this
problem can be overcome by coordination. In particular, the SINR for the JT system
is uniformly high in almost the entire service area. Note that the lower SINR at the
cell boundaries is an artifact of assuming centro-symmetrical user locations in our
experiments, which means that at cell boundaries users are close to each other and
thus interference is relatively high.
2.5.2 Sum-MSE Minimization with Channel Uncertainty
We now abandon the assumption of perfect CSI and consider channel uncertainty
according to the models from Section 2.4.1. For the case of outdated CSI, we consider
an assumed user location based on which we obtain a channel estimate hk. Then,
given a distance bound L, we obtain a CSI bound εk from numerical evaluation as
55
Chapter 2. Joint Transmission in VLC Systems
shown in Section 2.4.1 (see Figure 2.3). Given hk and εk, the precoder F is obtained
via P7 (2.40). Then, a set of actual channel gains h and associated SINRs (2.52) are
generated by placing users uniformly at random into the uncertainty region. For the
noisy CSI case, we use Σk = σ2eI and specify the error variance σ2
e .
Figures 2.11 and 2.12 show the SINR performance for the JT system with robust
precoder design according to the sum-MSE criterion. The results are shown as a
function of the channel uncertainty and parametrized with DC bias IDC. Setup II
from Figure 2.5 with x = 1.25 and y = 1.25 is used to calculate the channel estimate
hk and 5000 possible channel realizations hk either according to the uncertainty
bound εk or the normalized error standard deviation σe = σe/(‖vec(H)‖1/(NLNU)).
The minimum achieved SINR among channel realizations is plotted for the case of
outdated CSI, while the average SINR over channel realizations is plotted for the case
of noisy CSI. From the figures, we can see that system performance improves as the
DC bias IDC increases, until the CSI uncertainty at the transmitter limits the SINR.
Furthermore, the decline of SINR with uncertainty is less pronounced for the average
performance measure considered in Figure 2.12. The worst-case optimization for the
case of outdated CSI provides performance guarantees, which however diminish with
increasing uncertainty, as shown in Figure 2.11.
2.5.3 Minimal Illumination Level Problem
We again consider the Setup II from Figure 2.5 with x = 1.25 and y = 1.25, and
JT. Figure 2.13 shows the minimum illumination level, i.e., DC bias IDC, that is
required to meet the VLC MSE levels qk of each user terminal. The different curves
are for perfect CSI (L = 0) and outdated CSI (L > 0), and they quantify to what
extent VLC is possible when lights are dimmed. The perfect CSI case shows the best
56
Chapter 2. Joint Transmission in VLC Systems
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.515
20
25
30
35
40
L (m)
SIN
R (
dB
)
IDC = 425mA
IDC = 450mA
IDC = 475mA
IDC = 500mA
IDC
Figure 2.11: Robust sum-MSE minimization with outdated CSI. Setup II with x =1.25 and y = 1.25.
possible trade-off between illumination level and achievable performance. When CSI
uncertainty comes into play, it increases the required illumination level and even-
tually limits the achievable performance. That is, the larger the uncertainty region
(quantified by L), the earlier the problem becomes infeasible, i.e., MSE constraints
cannot be met regardless of illumination level.
2.5.4 Comparison between Robust and Non-Robust Design
Finally, we illustrate the benefits of the robust design in the case of CSI uncer-
tainty. To this end, Figure 2.14 compares the SINR performances of the robust and
57
Chapter 2. Joint Transmission in VLC Systems
10−3
10−2
10−1
100
5
10
15
20
25
30
35
40
σe
SIN
R (
dB
)
IDC = 425mA
IDC = 450mA
IDC = 475mA
IDC = 500mA
IDC
Figure 2.12: Robust sum-MSE minimization with noisy CSI. Setup II with x = 1.25and y = 1.25.
non-robust precoder designs when CSI is outdated. Similar to Figure 2.10, SINR
performance for one quadrant of the room is plotted as a function of the assumed
user location, according to which hk is obtained. The actual user location is sampled
in a circle with radius L, from which the channel gain hk follows. Figure 2.14 shows,
for each assumed location, the minimum SINR over the uncertainty region. The DC
current IDC is fixed as IDC = (IL + IU)/2.
We observe that especially for locations close to the boundaries of two cells the
robust design significantly outperforms the non-robust approach. This is due to
the possibly large mismatch between assumed and actual channel gains, which also
58
Chapter 2. Joint Transmission in VLC Systems
10−4
10−3
10−2
10−1
100
400
410
420
430
440
450
460
470
480
490
500
qk
I DC
(m
A)
L = 0.00 m
L = 0.25 m
L = 0.50 m
Figure 2.13: Robust illuminance minimization with perfect (L = 0) and outdated(L > 0) CSI. Setup II with x = 1.25 and y = 1.25.
affects the expected amount of interference, and which is not taken into account
in the non-robust design approach. For example, for the case of L = 0.25 m, the
average SINR value on the boundaries of two cells is improved from −25.99 dB to
−0.69 dB via the robust design. On the other hand, closer inspection of the results
shows that for locations further from the boundaries between cells, the precoder from
the non-robust design achieves a somewhat better SINR than the robust precoder.
For example, at the location (x, y) = (0.375, 1.000), the worst-case SINR for the
robust design is 4.4 dB, while it is 6.2 dB for the non-robust design. The reason for
this is the conservativism of the robust design, which considers the worst case for
59
Chapter 2. Joint Transmission in VLC Systems
all hypothetical gains from the bounded region Rk ={hk
∣∣∣hk=hk+δk‖δk‖2≤εk
}, even though
only a subset of these channel gains do actually occur inside the location uncertainty
region. Nevertheless, the results in Figure 2.14 demonstrate the advantage of the
robust optimization for VLC broadcasting in the case of imperfect CSI, in that the
SINR is more consistently high over the entire attocell area and when different users
are close to each other.
2.6 Conclusion
In this chapter, we have studied transmission to multiple user terminals using VLC
attocells. Considering the inter-attocell interference as a result of the broadcast na-
ture of VLC, we have proposed the coordination of transmission in different attocells.
These coordinated VLC attocells form CoMP-attocells, similar to CoMP-cells in RF
cellular networks. We have derived new linear precoding schemes that reduce intra-
CoMP-attocell interference with the objective of optimizing system performance given
an illumination level and retaining a required performance at minimal illumination
level, respectively. Our numerical results for a typical VLC scenario have clearly
demonstrated the improvements of receiver-side SINR due to the proposed coordina-
tion. As a second important contribution, we have extended the precoding methods
to include channel uncertainty, which would occur, for example, in the case of mov-
ing terminals. Simulation results have shown that these robust precoding schemes
mitigate performance drops that stale channel information causes when assumed to
be accurate.
60
Chapter 2. Joint Transmission in VLC Systems
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
x (m)
y (
m)
−15
−10
−5
0
5
10
15
20
25
30
35SINR (dB)
(a) Robust Design (L=0.25m)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
x (m)
y (
m)
−15
−10
−5
0
5
10
15
20
25
30
35SINR (dB)
(b) Non-Robust Design (L=0.25m)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
x (m)
y (
m)
−15
−10
−5
0
5
10
15
20
25
30
35SINR (dB)
(c) Robust Design (L=0.5m)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
x (m)
y (
m)
−15
−10
−5
0
5
10
15
20
25
30
35SINR (dB)
(d) Non-Robust Design (L=0.5m)
Figure 2.14: Comparison between robust and non-robust design for sum-MSE mini-mization problem with outdated CSI.
61
Chapter 3
Coordinated Beamforming in VLC
Systems
3.1 Introduction
As we can see from the previous chapter, uncoordinated VLC attocells will strongly
interfere with each other. In fact, it has been shown that the degradation in SINR for
users at the edge of the attocell can be as severe as 30 dB. The proposed JT scheme
can greatly enhance the user performance through transmitter cooperation. However,
both the global user data and channel state information need to be exchanged among
transmitters of different attocells in the JT scheme, which puts a high requirement
on the backbone network. What is more, in order to ensure that signals emitted from
different transmitters arrive at the receiver at the same time, tight synchronization
is required among the scattered VLC transmitters. In this chapter, we propose the
CB scheme for downlink interference mitigation among coexisting VLC attocells uti-
lizing multi-luminaire transmitters. Compared to the JT scheme, the proposed CB
scheme places lower requirements on the network in terms of backbone traffic, and
is easier to implement in a practical deployment, though at the cost of compromised
performance. In this chapter, we investigate the downlink transmission of coordi-
nated VLC attocells and focus on its transmitter design. We adopt the weighted sum
mean square error (WSMSE) as the performance metric to take into consideration
62
Chapter 3. Coordinated Beamforming in VLC Systems
interference, noise, and fairness among users in system optimization. We consider
the WSMSE minimization problem with linear beamforming restricted by amplitude
constraints. Such constraints arise from dynamic range limitations in typical LEDs.
Moreover, similar to Chapter 2, we extend our design method to take into account
possible mismatches in channel information available to the transmitters. We provide
numerical examples to illustrate the performance of the proposed CB scheme in typi-
cal VLC scenarios. We also quantify the performance gap among several coordination
schemes including JT and CB.
The remainder of the chapter is organized as follows. We introduce the system
model and transmission scheme in Section 3.2. In Section 3.3, the design algorithms
for CB are proposed assuming perfect downlink CSI at VLC transmitters. In Section
3.4, the design for CB is extended to the case of imperfect CSI. Numerical results
and discussions are provided in Section 3.5, and finally, we conclude the chapter in
Section 3.6.
3.2 System Model and Transmission Scheme
In this section, we first describe the system model and transmission scheme for the
considered multi-cell VLC system. We then specify the constraints imposed on the
linear beamformer to satisfy the amplitude constraints on the transmitted signal.
3.2.1 System Model
We consider a downlink VLC system composed of NA coordinated attocells that can
exchange information with each other through a band-limited backbone network (see
Figure 3.1). Each attocell is composed of one VLC transmitter that employs NL
LED luminaires, and each luminaire has NE LED bulbs. Such luminaires can be
63
Chapter 3. Coordinated Beamforming in VLC Systems
Centralized Controller
NA VLC attocells
Backbone
Network
Multi-luminaire VLC transmitter LED luminaire Single-photodiode VLC user
NL Luminaires per
Transmitter
Figure 3.1: Illustration of the CB structure.
modulated independently of each other using separate drivers. Each attocell serves
NU single-PD users, and each user is served by a single attocell. Therefore, we have
a multi-cell MU-MISO scenario.
3.2.2 Transmission Scheme
We considerM -ary pulse amplitude modulation (M -PAM) as the modulation scheme,
with M = 2, 4, 8, 16, . . . . Let dik ∈ {−1, 3−MM−1
, 5−MM−1
, . . . , 1}, i = 1, . . . , NA, k =
1, . . . , NU, denote the data symbol intended for the kth user in the ith attocell, and
let di = [di1 , . . . , diNU]T denote the vector of data symbols intended for all the users in
the ith attocell. Note that the entries of di are independent, and thus the covariance
64
Chapter 3. Coordinated Beamforming in VLC Systems
matrix of di is η2I, where I represents the identity matrix and
η =
√M + 1
3(M − 1). (3.1)
Using linear beamforming, the transmitted signal vector at the ith attocell is con-
structed as
xi = F idi + I iDC , (3.2)
where F i ∈ RNL×NU is the beamforming matrix, and I iDC = [I i1DC, Ii2DC, · · · , I
iNLDC ]T is
a DC term that sets the illumination level. Note that the zero-mean nature of the
data vector di ensures that the illumination level is unaffected by data transmission.
For the kth user in the ith attocell uik , the received signal can be decomposed into
three parts:
1) Intra-attocell Signal: We use yintraik
to represent the signal component generated
within the ith attocell and it is given by
yintraik
= hTikixi = hTikifki dik + hTiki
NU∑m=1,m 6=k
fmi dim + hTikiIiDC , (3.3)
where hikj ∈ RNL×1 denotes the channel gain vector between uik and the VLC trans-
mitter of the jth attocell, and fki is the kth column vector of F i.
2) Inter-attocell Interference: Besides the intra-attocell signal, user uik also re-
ceives interfering signals from neighboring attocells. The total interfering signal from
all the other attocells yinterik
can be expressed as
yinterik
=
NA∑j=1,j 6=i
hTikjxj =
NA∑j=1,j 6=i
NU∑m=1
hTikjfmj djm +
NA∑j=1,j 6=i
hTikjIjDC . (3.4)
65
Chapter 3. Coordinated Beamforming in VLC Systems
3) Receiver noise: The dominant noise at user uik , denoted as nik , can be modelled
as a zero-mean Gaussian variable with variance calculated by Eq. (1.3), where the
average current due to the useful received signal at the user uik , Iik (Irp in Eq. (1.3)),
can be calculated by
Iik =
NA∑j=1
hTikjIjDC . (3.5)
The total received signal yik at user uik is the sum of the three components mentioned
above, and can be expressed as
yik = yintraik
+ yinterik
+ nik (3.6)
= hTikifki dik︸ ︷︷ ︸
desired signal
+ hTiki
NU∑m=1,m 6=k
fmi dim︸ ︷︷ ︸intra-attocell interference
+
NA∑j=1,j 6=i
NU∑m=1
hTikjfmj djm︸ ︷︷ ︸
inter-attocell interference
+
NA∑j=1
hTikjIjDC︸ ︷︷ ︸
DC photocurrent
+ nik︸︷︷︸noise
.
At the receiver, the DC component∑NA
j=1 hTikjIjDC is removed via AC coupling, leaving
the information-carrying signal at uik as
yik = yik −NA∑j=1
hTikjIjDC . (3.7)
3.2.3 Design Constraints
For the illumination uniformity of the indoor environment, we shall assume that all
the LEDs are driven by an equal DC bias, i.e.,
I ikDC = IDC, ∀i, k. (3.8)
66
Chapter 3. Coordinated Beamforming in VLC Systems
For typical current-driven LEDs, though the nonlinear characteristic for current-
light conversion can be compensated by pre-distorters installed before the LED, the
dynamic range of LEDs is still inherently limited. Thus, the current signal should
satisfy a certain amplitude constraint to avoid signal clipping. To ensure that the
LED operates within its physical limits, the beamforming matrix F i should satisfy
the constraint (2.14):
‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k, (3.9)
where fki represents the kth row in F i, and IU > IL > 0 represent the upper and the
lower bound of the LED drive current in the linear region.
3.3 Transmitter Design with Perfect Channel
Information
Similar to Chapter 2, we consider MMSE beamforming design in this chapter. Linear
beamformers can achieve reasonable throughput performance with considerably lower
complexity relative to their nonlinear counterparts. Two major linear beamforming
techniques are ZF beamforming and MMSE beamforming. ZF beamforming cancels
out multi-user interference through channel inversion. However, ZF is infeasible when
the number of luminaries in each attocell is less than the total number of users of all
the coordinated attocells [74]. Furthermore, ZF has relatively poor performance in
low SNR regions [105]. In comparison, MMSE beamforming has less strict require-
ments on the number of luminaires per attocell, and outperforms ZF beamforming
in noise-limited scenarios as it also takes into account the receiver noise in design
optimization [106].
67
Chapter 3. Coordinated Beamforming in VLC Systems
We consider a linear receiver at the VLC user, so the estimated received signal
dik at uik can be expressed as
dik = cikyik , (3.10)
where the scaling factor cik is the receive filter for user uik . Then the mean square
error (MSE) for user uik can be calculated as
MSEik = Ed,n‖dik − dik‖22 (3.11)
= η2‖cikhTikiF i − eTk ‖2
2 + η2
NA∑j=1,j 6=i
‖cikhTikjF j‖2
2 + c2ikσ2ik,
where ek is the kth standard basis vector for the NU-dimensional space and is ex-
pressed in (2.16). Note that the second term results from the inter-attocell interfer-
ence and is absent in the MSE expression of JT (See Eq. (2.25)). In this section,
we aim at optimizing the system performance subject to the LED dynamic range
constraint (3.9) assuming the availability of perfect CSI at the transmitters. We use
the WSMSE as the performance measure so that the possibly different priorities of
different users can be considered in system design. More specifically,
WSMSE =
NA∑i=1
WSMSEi =
NA∑i=1
NU∑k=1
wikMSEik , (3.12)
where WSMSEi represents the WSMSE of the ith attocell, and wik > 0 denotes
the priority (weight) of user uik at the current scheduling slot according to some
criteria. Considering the constraint (3.9) on the beamforming matrix, the WSMSE
68
Chapter 3. Coordinated Beamforming in VLC Systems
minimization problem can be formulated as
P1 : min{F i},{cik}
WSMSE (3.13)
C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k .
When wik = 1 ∀i, k, P1 degenerates to the sum-MSE optimization problem which
may impose unfairness across users. More generally, the weights wik can be updated
over time to maintain fairness among terminals. Designing the optimal weights for
the system is outside the scope of the chapter. Instead, we focus on obtaining the
solution to the optimization problem for a given set of weights. The objective function
in optimization problem P1 is biconvex in terms of beamforming matrices {F i} and
scaling factors {cik} [83]. Fixing either of these two groups of variables will result in
a (convex) quadratic optimization problem. Here we use the alternating optimization
method to, possibly suboptimally, solve the problem. Fixing beamforming matrices
{F i}, we can obtain the closed-form expression for the optimal MMSE receiving filter
c∗ik =η2hTikif
ki
η2∑NA
j=1
∑NU
m=1 ‖hTikj
fmj ‖22 + σ2
ik
,∀i, k. (3.14)
We also need to acquire the optimal beamforming matrices {F i} given fixed scaling
factors {cik}. For notational simplicity, we define
H ij = [hi1j,hi2j, . . . ,hiNUj]T ,
Ci = diag([ci1 , ci2 , · · · , ciNU]T ),
W i = diag([√wi1 ,√wi2 , · · · ,
√wiNU
]T ),
ni = [ni1 , ni2 , . . . , niNU]T .
69
Chapter 3. Coordinated Beamforming in VLC Systems
Then WSMSEi can be expressed as
WSMSEi =
NU∑k=1
wikMSEik = Ed,ni
{∥∥W i
(Ci
( NA∑j=1
H ijF jdj + ni)− di
)∥∥2
2
}(3.15)
= η2∥∥((W iCiH ii)⊗ I) vec
(F Ti
)− vec (W i)
∥∥2
2
+ η2
NA∑j=1,j 6=i
∥∥((W iCiH ij)⊗ I) vec(F Tj
)∥∥2
2+
NU∑k=1
w2ikc2ikσ2ik.
Define wi = vec (W i), Aij = (W iCiH ij)⊗I, f j = vec(F Tj
), and V as the NLNU×
NUNL block-diagonal matrix of the NL × NU all-one matrix. With fixed {cik}, P1
can be transformed into
P2 : min{f i}
NA∑i=1
(η2 ‖Aiif i −wi‖2
2 + η2
NA∑j=1,j 6=i
∥∥Aijf j∥∥2
2+
NU∑k=1
w2ikc2ikσ2ik
)C1:− ti ≤ f i ≤ ti, ∀i ,
C2: V ti ≤ min (IDC − IL, IU − IDC) 1NLNU×1, ∀i .
P2 is a convex quadratic programming problem and can be efficiently solved by the
MOSEK solver [103]. Once P2 is solved, the optimal beamforming matrices F j can
be retrieved from vector f j.
For the suboptimal alternating optimization, the ZF beamformer can be used as
the initialization point to secure a satisfactory solution. Define the concatenation of
all channel matrices as
H = [HT11, . . . ,H
TNA1, . . . ,H
T1NA
, . . . ,HTNANA
].
When NL ≥ NANU, the general form for the transmit ZF beamformer of the ith
70
Chapter 3. Coordinated Beamforming in VLC Systems
attocell can be expressed as [74]:
F ZFi =
( NA∑j=1
NA∑m=1
NU∑k=1
hjkmhTjkm
)−HT
ii diag(Λi) =(HHT
)−HT
ii diag(Λi) , (3.16)
where Λi = [Λi1 ,Λi2 , . . . ,ΛiNU]T and
(HHT
)−=(HHT
)†+(I−(HHT
)†(HHT
)U i
).
Λik > 0 represents the symbol gain for dik , and U i is an arbitrary matrix. Then we
have
HjiFZFi =
0 i 6= j ,
diag(Λi) i = j .
In this chapter, we set
U i =(HHT
)†(HHT
),
Λi =min (IDC − IL, IU − IDC)
maxm
(∑NU
k=1
∣∣∣∣((HHT)†HT
ii
)m,k
∣∣∣∣)1NU×1 ,
and we get
F ZFi =
(HHT
)†HT
ii diag(Λi) . (3.17)
Such a ZF beamforming matrix satisfies the constraint of P1 and can be used as
the initialization point for the alternating optimization algorithm. We note that
when NL < NANU, the inter-attocell and intra-attocell interference cannot be fully
canceled with the beamforming matrix (3.17). However, (3.17) still remains a wise
choice for the initialization purpose [74]. The algorithm for solving P1 is summarized
in Algorithm 3.1.
71
Chapter 3. Coordinated Beamforming in VLC Systems
Algorithm 3.1 Alternating optimization algorithm for P11. Initialization:
p⇐ 0.Update H ij with CSI.Initialize {F i}.
2. repeat3. Update {cik} according to Eq. (3.14).4. Update {Aij} with {cik}.5. Solve P2 and get {F i}.6. p⇐ p+ 1.7. until ‖WSMSEp+1 −WSMSEp‖ ≤ δ (δ is a predefined threshold) or p = pmax
(pmax is a predefined maximum iteration number).
3.4 Robust Transmitter Design with Channel
Uncertainty
The linear beamforming design in the previous section is based on the premise of
perfect CSI. In practice, however, CSI at the transmitter side is usually contaminated
due to various factors like quantization, erroneous channel estimation or outdated
feedback. Assuming an additive channel uncertainty model, the actual channel gain
can be expressed as
hikj = hikj + δikj , (3.18)
where hikj represents the channel estimate, and δikj represents the error vector re-
sulting from channel uncertainty. As a result, the MSE for user uik can be expressed
72
Chapter 3. Coordinated Beamforming in VLC Systems
as
MSEik = η2‖cik(hT
iki+ δTiki)F i − eTk ‖2
2 + η2
NA∑j=1,j 6=i
‖cik(hT
ikj+ δTikj)F j‖2
2 + c2ikσ2ik.
Typically, there are two classes of models to characterize δikj: the deterministic
model and the stochastic model. For the deterministic model, we assume the actual
channel gain vector, although not exactly known, lies within a certain region with
the estimated nominal value at the center of the region. In this chapter, we assume
‖δikj‖ ≤ ε, where ε is some known constant and represents the level of uncertainty7.
The goal of robust design with the deterministic model is to guarantee a certain
performance level for every possible channel realization, which is achieved through
optimizing the worst-case performance by solving a min-max optimization problem
[97, 107]. For the stochastic model, we model the elements of error vector δikj as
Gaussian distributed random variables. Particularly in this chapter, we assume δikj is
zero-mean Gaussian distributed with covariance matrix σ2eI, where σe is some known
constant. With the stochastic model, we aim at optimizing the average performance
[97, 107].
3.4.1 Robust Design with the Deterministic Model
In this subsection, we apply the deterministic model to characterize the CSI imper-
fection and aim at ensuring worst-case robustness through beamforming design. P17 We assume the same level of CSI uncertainty for each user in this chapter.
73
Chapter 3. Coordinated Beamforming in VLC Systems
is modified to the min-max optimization problem
P3 : min{F i},{cik}
max‖δikj‖2≤ε
WSMSE =
NA∑i=1
NU∑k=1
wikMSEik (3.19)
C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k ,
Using the Schur complement lemma [108] and [101, Lemma 2], P3 can be transformed
into
P4 : min{F i},{ci},{λikj},{tikj},{gik}
z2 (3.20)
C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k ,
C2 : Ψikj � 0, ∀i, j, k ,
C3 : Φik � 0, ∀i, k ,
C4 : λikj ≥ 0, ∀i, j, k ,
C5 : κ � 0,
74
Chapter 3. Coordinated Beamforming in VLC Systems
where
Ψikj =
tiki − λiki η(cikh
T
ikiF i − eTk ) 0
η(cik(hT
ikiF i)
T − ek) tikiI εηcikFTi
0 εηcikF i λikiI
i = j ,
tikj − λikj ηcikh
T
ikjF j 0
ηcik(hT
ikjF j)
T tikjI εηcikFTj
0 εηcikF j λikjI
i 6= j .
(3.21)
κ=
z ωT
ω zI
,
Φik =
gik tik1 . . . tikNAcikσik
tik1
... gikI
tikNA
cikσik
,
ω = [w11g11 , . . . , w1NUg1NU
, . . . , wNANUgNANU
]T .
Similar to Algorithm 3.1 for P1, a local optimum of P4 can be obtained through
alternatively optimizing over {F i} and {ci}. Each problem is an SDP and can be
solved numerically.
75
Chapter 3. Coordinated Beamforming in VLC Systems
3.4.2 Robust Design with the Stochastic Model
For the stochastic error model, we would like to secure the average system perfor-
mance in the robust design. The optimization problem can be formulated as
P5 : min{F i},{cik}
E (WSMSE) =
NA∑i=1
NU∑k=1
wikE (MSEik) (3.22)
C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k .
Alternating optimization can also be used to solve P5 which is a non-convex opti-
mization problem. Fixing {cik}, P5 can be transformed into
P6 : min{F i}
NA∑i=1
(η2∥∥∥Aiif i −wi
∥∥∥2
2+
NA∑j=1,j 6=i
η2∥∥∥Aijf j
∥∥∥2
2+ Tr(W 2
iC2i )η
2σ2e
NA∑j=1
∥∥f j∥∥2
2
+
NU∑k=1
w2ikc2ikσ2nik
)C1:− ti � f i � ti, ∀i ,
C2: V ti ≤ min (IDC − IL, IU − IDC) 1NLNU×1, ∀i ,
where Aij =(W iCiH ij
)⊗ I and H ij =
[hi1j, hi2j, . . . , hiNU
j
]T. P6 is a convex
quadratic programming problem and can be solved numerically. Fixing {F i}, we
have
c∗ik =η2h
T
ikifki
η2∑NA
m=1
∑NU
j=1(‖hTikmf jm‖22 + σ2
e‖fjm‖2
2) + σ2ik
,∀i, k.
76
Chapter 3. Coordinated Beamforming in VLC Systems
3.5 Numerical Results and Discussions
In this section, we present our simulation results to demonstrate the performance of
the proposed CB scheme. First, we compare the performance of VLC systems under
different coordination schemes. Then we show that a careful choice of the weighting
vector can significantly improve fairness among users. Finally, we demonstrate the
performance gain of the adopted robust beamforming design given imperfect CSI.
3.5.1 Simulation Setup
We consider OOK as the modulation scheme for the simulation, i.e., M = 2, and
thus η = 1. This is perhaps the most practical transmission scheme for IM systems
because of simplicity and immunity to nonlinear distortion. We consider an indoor
environment illustrated in Figure 3.2a for our simulation purposes. The coordinate
system and the area planning8 are both shown in Figure 3.2b. The room dimensions
are 10×5×3 m3. Two multi-luminaire VLC transmitters (NA = 2) are installed in the
ceiling and are interconnected through a backbone network. Simulation parameters
for VLC transmitters and receivers are listed in Table 3.1. We consider two lighting
setups, where NL = 2, NE = 64 for Lighting Setup I (LS-I) and NL = 4, NE = 36 for
Lighting Setup II (LS-II). The coordinates of LED luminaires in each setup are listed
in Table 3.2.
As the primary function of VLC transmitters is illumination, we first investigate
the illumination performance of the two lighting setups. The illuminance distribution
with LS-I and LS-II are shown in Figure 3.3a and Figure 3.3b when IDC = 500 mA,8According to the DIN EN 12464-1 standard [38] for the planning and design of lighting instal-
lations, the area planning for indoor workplaces defines both task area and immediate surroundingarea. The task area is defined as the area in which the visual task is carried out. The immediatesurrounding area is defined as a band surrounding the task area within the field of vision with aminimum width of 0.5 m.
77
Chapter 3. Coordinated Beamforming in VLC Systems
Table 3.1: Simulation parameters
Transmitter ParametersIL 300 [mA]IU 700 [mA]Lambertian order m 1LED conversion factor s 0.44 [W/A]System Bandwidth B 10 [MHz]
Receiver ParametersPD area APD 1 [cm2]Concentrator refractive index κ 1.5Receiver FoV ψc 60 [deg.]Noise bandwidth factor I2 0.562Background current Ibg 100 [µA]PD responsivity γ 0.30 [A/W]
respectively. The corresponding average illuminance and uniformity of the task area
and the immediate surrounding area under both lighting setups are shown in Ta-
ble 3.3. According to the DIN EN 12464-1 standard [38], the illuminance and uni-
formity of both setups satisfy the requirements for office work and study. In this
section, we use the SINR as expressed in Eq. (3.23) as the metric for performance
comparison.
SINRik =η2‖hTikif
ki ‖2
η2∑NU
j=1,j 6=k ‖hTiki
f ji ‖2 + η2∑NA
j=1,j 6=i∑NU
m=1 ‖hTikj
fmj ‖2 + σ2ik
(3.23)
If not stated otherwise, we assume NU = 2 in the following. Note that the specific
values of the system parameters M , NU, NA and NL chosen in this section are solely
for the purpose of simulation illustration, and the system design can be applied to
any values of M , NU, NA and NL.
78
Chapter 3. Coordinated Beamforming in VLC Systems
(a) Room Illustration.
10 m
5 m
y
x
z
a
b
b
a
b
b
a
a
(b) Illustration of office areas. The yellow zone is the immediate surrounding area, andthe red area is the task area. b = 0.5 m. Illuminance calculations can ignore a marginalstrip extending a = 0.5 m from the walls according to [38].
Figure 3.2: Room Setup.
79
Chapter 3. Coordinated Beamforming in VLC Systems
Table 3.2: Luminaire coordinates of LS-I and LS-II
and orthogonal frequency-division multiple access (OFDMA). SA of multi-user
HVP systems is a non-trivial task due to the coupling of subcarrier pairing,
relay selection and user selection, and the limited number of subcarriers per
LED luminaire set by SO-OFDM. To reduce the computational complexity of
SA, we investigate the performance of chunk-based SA [113] and propose several
suboptimal polynomial-time SA algorithms. We note that the contribution of
our work is not dependent on any specific OFDM signal format employed by
the VLC link. We adopt two variations of OFDM signal formats as the VLC
multicarrier solutions in this chapter due to their popularity. However, the
proposed optimization framework can be easily extended to any other OFDM
signal formats in SO-OFDM-based HVP systems.
The remainder of the chapter is organized as follows. In Section 4.2, we introduce
the SO-OFDM-based HVP system, and present the channel and noise models for
the PLC and VLC links. In Section 4.3, different optical OFDM formats and relay
protocols are investigated for the HVP system, and the corresponding achievable rate
expressions are presented. In Section 4.4, computationally efficient SA algorithms,
with and without SP, are proposed for the two multi-access schemes. Simulation
results for different variations of HVP systems are presented and discussed in Sec-
tion 4.5. Finally, the conclusions are drawn in Section 4.6.
93
Chapter 4. The Hybrid VLC-PLC System
4.2 System Model
4.2.1 Problem Scenario
We propose an SO-OFDM-based HVP system for downlink transmission to NU users
located in the same room and served via the cooperation of NL LED luminaires,
and each luminaire consists of NE LEDs. Figure 4.1 illustrates the system structure
showing a single user. The power line acts as the backbone network that feeds data
to and coordinates cooperation among the multiple VLC-equipped LED luminaires,
which in turn operate as full-duplex relays which process the received PLC signal and
forward it via VLC to indoor users. Applying SO-OFDM across multiple luminaires,
each luminaire only emits a subset of the data symbols from the received PLC OFDM
signal. The VLC signals from multiple LED luminaires superpose at the photo-diode
detectors of the users, where a conventional OFDM receiver can be used to decode the
information. To achieve this, accurate time and frequency synchronization is required
for the VLC hop. Since both VLC and PLC OFDM are baseband modulated, carrier
frequency offset is absent and only timing needs to be taken care of. To resolve the
time synchronization problem resulting from the time difference of arrivals of users’
signal at the luminaires, we can ensure that the cyclic prefix length of the OFDM
symbol is longer than the time difference of arrivals. Further considering the fact
that the LoS link plays the major role in VLC systems [8], and the inter-luminaire
distances between VLC transmitters in the indoor environment are relatively small,
the situation here is relatively simpler compared to CoMP systems with RF imple-
mentation [114]. In the rest of the chapter, we assume VLC transmitters are perfectly
synchronized. For the HVP uplink, one preferred choice is WiFi uplink (see Section
1.3). The WiFi uplink, for the HVP system specifically, can be implemented through
94
Chapter 4. The Hybrid VLC-PLC System
LED Luminary 1
WiFi Uplink
PLC
modem
OFDM
Demodulation
Subcarrier
Selection
Subcarrier
Permutation
OFDM
Modulation
LED Luminary 2
OFDM
Demodulation
Subcarrier
Selection
Subcarrier
Permutation
OFDM
Modulation
OFDM
Demodulation
Subcarrier
Selection
Subcarrier
Permutation
OFDM
Modulation
LED Luminary NL
PLC-WiFi
integrated
modem
PLC
Network
...
Figure 4.1: Block diagram of the HVP system.
a PLC-WiFi integrated modem (which could act as the coordinator point), as illus-
trated in Figure 4.1. Such an uplink would provide the CSI about the VLC links to
the coordinator point for system optimization.
4.2.2 Transmitter and Receiver Model
Figure 4.2 shows a detailed block diagram of the SO-OFDM HVP system with respect
to a specific luminaire relay. We note that the baseband OFDM signals transmit-
ted over the PLC and VLC links satisfy the Hermitian symmetry property in the
frequency domain, and in the following, we will only describe the processing for the
independent information-carrying subcarrier sets (Pinfo and Vinfo in Section 4.3).
In the PLC hop, the PLC modem broadcasts the same wideband OFDM signal
to every LED luminaire containing Np independent information-carrying subcarriers.
In the VLC hop, SO-OFDM is applied, and the kth luminaire re-modulates Nk of the
received PLC data symbols onto Nk of Nv available VLC subcarriers. The Nv −Nk
unused subcarriers are set to zero. The subcarrier subsets across different luminaires
95
Chapter 4. The Hybrid VLC-PLC System
are disjoint and we have∑NL
k=1Nk = Np. At each LED luminaire, we consider a
subcarrier pairing approach which adaptively matches incoming with outgoing sub-
carriers to fully exploit the frequency diversity of both PLC and VLC channels. The
number of subcarriers Nk and thus subcarrier pairs assigned to the kth luminaire
cannot exceed an upper limit in order to limit the PAPR of the OFDM signal at each
LED luminaire.
We consider two operating modes for the LED luminaire relay, namely amplify-
and-forward (AF) and decode-and-forward (DF). An AF-mode VLC relay demodu-
lates the PLC signal, scales the selected subcarrier signals, and re-modulates them
applying subcarrier pairing. In addition to this, a DF-mode relay also decodes the re-
ceived signal. Only if decoding is deemed successful, based on an outer error-detection
code, the DF-mode relay will re-encode and re-modulate the data, and then forward
it to the destination.
At the user side, the VLC analog front-end (AFE) consists of a photo-diode
detector to convert the optical to an electrical received signal and an AC coupler to
remove the DC signal component, which is responsible for the primary illumination
function of the LED luminaires. This is followed by a conventional OFDM receiver.
4.2.3 Channel and Noise Model
Power Line Communication
To faithfully model the signal transfer over the low-voltage power line network, we
apply the bottom-up approach based on transmission-line theory as presented in
[115, 116] and implemented in a simulator in [117], which leads to a distinctive PLC
channel for each LED luminaire based on the cable characteristics of its corresponding
power line branch. The noise in PLC systems consists of colored background noise,
96
Chapter 4. The Hybrid VLC-PLC System
Cyclic prefix
removalFFT
QAM
Modulation
Data
input Hermitian
symmetry
InsertionIFFT
PLC
AFE
Cyclic prefix
insertion
PLC
AFE
PLC
Channel
PLC noise
S/P P/S
S/PP/SDemodulationDecode
Encode
S/P
Modulation
Subcarrier
PairingIFFT P/S
Cyclic prefix
insertion
Power
scalingClipping D/A
DC bias
VLC AFE
VLC
Channel
VLC noise
Cyclic prefix
removalFFT
VLC
AFES/PP/SDemodulationDecode
Data
output
PLC Transmitter
LED Luminary
VLC Receiver
Subcarrier
Selection
Figure 4.2: Detailed block diagram of the SO-OFDM HVP downlink system for oneluminaire and one user. Blocks with dashed lines are not present in LED luminairesoperating in amplify-and-forward mode.
narrowband disturbance, and impulsive noise [111]. We model the first two terms
through the combined power spectral density (PSD) of the shape as in [118, Eq.
(4)], as also adopted in the IEEE 1901 standard [119, Annex F.3.5.2]. Impulse noise
is modeled as a non-stationary random process. For the purpose of mathematical
tractability, we disregard the impulse noise in the rate optimization. This is justified
as the impulse noise events occur with relatively low probability (see. e.g. [120]) and
if significant lead to outage events. Furthermore, one of the major components of
impulse noise in the low-voltage power line is random aperiodic impulse noise. In this
case, rate optimization considering the aperiodic noise for the purpose of adaptive
transmission is ineffective. Note that in all the numerical results presented in Section
4.5, we will consider the impulse noise for the purpose of simulation accuracy, and we
apply the two-state approximation as in [121, Eq. (19)] to calculate the achievable
97
Chapter 4. The Hybrid VLC-PLC System
rate. To enable the reproducibility of the numerical results, we have made the PLC
noise simulator available online [122].
Visible Light Communication
The VLC channel is frequency selective due to the low-pass characteristics of the
LED emission and the multipath dispersion of the VLC signal. The latter starts
to play a role when the transmitted signal is broadband [27], which is the case for
the considered HVP system. In this chapter, we take both the LoS link and NLoS
link (reflections) into consideration for the VLC channel modeling. We assume that
propagation from either the LED source or a reflection point on the walls follows the
Lambertian radiation pattern. The channel gain h between the receiver (the user or a
reflection point on the walls) and the light source (the LED source or a reflection point
on the walls) can then be expressed using Eq. (1.2). Based on Eq. (1.2), we apply
the modified Monte Carlo method presented in [34] to obtain the frequency-domain
channel gain HCL(f) in our simulations, and our source code written in MATLAB
is available at [123]. The first three reflections are taken into account as they carry
most of the VLC signal power. Together with the frequency response for the LED
emissions which can be approximated by [124]
HLED(f) =1
1 + j ffLED
, (4.1)
with fLED representing the 3 dB cutoff frequency of the LED low-pass characteristics,
the overall VLC channel gain can be expressed as
Hv(f) = HLED(f)HCL(f). (4.2)
98
Chapter 4. The Hybrid VLC-PLC System
The noise in VLC systems comprises shot noise, which is induced by ambient light,
and thermal noise. The variance of the total VLC noise can be modeled as a zero-
mean Gaussian random variable with variance σ2vn calculated by Eq. (1.3).
4.3 Rate Analysis of the HVP System
In this section, we derive the expressions for the achievable rates for downlink trans-
mission with the HVP system using different relaying strategies. More specifically,
we consider the rate associated with a single OFDM subcarrier pair of the PLC-VLC
link to a single user. Since different subcarriers are orthogonal and users are multi-
plexed over orthogonal subcarriers or time slots, rate expressions of the total HVP
system follow then immediately.
4.3.1 Signal at the PLC Hop
The baseband PLC OFDM signal uses the set Pinfo of information-carrying subcarri-
ers, where |Pinfo| = Np. Denoting the PLC frequency-domain transmitted symbol at
subcarrier l as Xp(l), and with the usual assumptions about sufficient cyclic-prefix
length, synchronization, and channel time-invariance, the PLC frequency-domain sig-
nal Y kp (l) at subcarrier l received by the kth LED luminaire can be expressed as
Y kp (l) = Hk
p(l)Xp(l) +Nkp (l) , (4.3)
where Hkp(l) and Nk
p (l) are the PLC channel gain and noise for subcarrier l at the
kth LED luminaire, respectively. The corresponding SNR is
SNRkp(l) =
∣∣Hkp(l)∣∣2σ2
p
σ2pn,k(l)
, (4.4)
99
Chapter 4. The Hybrid VLC-PLC System
where σ2p = E
[|Xp(l)|2
]and σ2
pn,k(l) = E[∣∣Nk
p (l)∣∣2].
4.3.2 Signal at the VLC Hop
The kth VLC transmitter modulates Nk subcarriers from the set Vinfo of active
information-carrying subcarriers, and |Vinfo| = Nv. Denoting the frequency-domain
transmitted symbol over subcarrier l as Xkv (l) and the size of the discrete Fourier
transform applied for VLC as Nvfft, the time-domain samples at each element of the
kth luminaire can be expressed as
xkv,info(n) =1√Nv
fft
Nvfft−1∑l=0
Xkv (l)exp
(j2πnl
Nvfft
), (4.5)
where Hermitian symmetry Xkv (l) =
(Xk
v (Nvfft − l)
)∗ holds, and only 2Nk out of Nvfft
Xkv (l) are non-zero due to SO-OFDM (see Section 4.2.2). The signal xkv,info(n) is
used to modulate the intensity of the LED luminaire. To make the signal compatible
with the IM/DD channel, in the following we consider both DCO-OFDM and ACO-
OFDM, which are the two popular forms of intensity-modulated optical OFDM [43,
44].
Since an LED as a transmitter has a limited dynamic range, the time-domain
OFDM signal may be clipped due to a high PAPR [39]. Let IL and IU represent the
lower and upper bound of the LED forward current, respectively, and IDC be the DC
bias current. Then, the clipped signal can be expressed as
xkv,clip(n) = FCLIP(xkv,info(n)) , (4.6)
100
Chapter 4. The Hybrid VLC-PLC System
where [40]
FCLIP(x) =
b, x ≤ b ,
t, x ≥ t ,
x, otherwise ,
(4.7)
and t = IU−IDC, b = IL−IDC for DCO-OFDM, and t = IU−IDC, b = max(IL−IDC, 0)
for ACO-OFDM. Neglecting possible differences among LEDs located at the same
luminaire, we obtain the equivalent transmitted signal of the kth LED luminaire as
xkv,sum(n) = NE
(xkv,clip(n) + IDC
). (4.8)
We note that the level of the bias current, which together with clipping ensures the
non-negativity of the transmit signal, is determined by the illumination requirement
on the luminaire.
To proceed with formulating the received signal after the VLC link, we need
to distinguish between the OFDM modalities used at the VLC transmitter (DCO-
OFDM or ACO-OFDM) and the relaying methods (DF or AF) to obtain Xkv (l).
This is done in the next subsection, where we derive the associated expressions for
achievable rates for a single subcarrier pair of the HVP system.
4.3.3 Achievable Rate Expression for Each Subcarrier Pair
DCO-OFDM
For DCO-OFDM, Vinfo = {1, 2, . . . , Nv}. According to Bussgang’s theorem [125], the
clipped signal at the kth luminaire can be modeled as an attenuation of the original
101
Chapter 4. The Hybrid VLC-PLC System
signal plus a non-Gaussian uncorrelated noise component [126]:
xkv,clip(n) = Akxkv,info(n) + nkc(n) , (4.9)
where nkc(n) is the non-Gaussian clipping noise term with variance σ2clip,k and Ak
is the attenuation factor. Given the electrical power of the VLC signal P kv =∑Nv
fft−1
l=0 E[|Xk
v (l)|2]/Nv
fft and the constants from the clipping function (4.7), and
defining the normalized clipping levels bk = b/√P k
v and tk = t/√P k
v , we have
[40, 127]
Ak = Q(bk)−Q
(tk), (4.10)
and
σ2clip,k =P k
v
(Ak −
(φ(bk)− φ(tk) + (1−Q(bk)
)bk +Q(tk)tk)2 − (Ak)2
+(1−Q(bk)
)(bk)2 +Q(tk)(tk)2 + φ(bk)bk − φ(tk)tk
), (4.11)
where Q(·) and φ(·) are the tail probability function and the probability density
function of the standard normal distribution.
Substituting (4.9) into (4.8) gives the output signal at the kth LED luminaire as
xkv,sum(n) = NEAkxkv,info(n) +NEn
kc(n) +NEIDC . (4.12)
Correspondingly, we can write for the frequency-domain signal at the lth subcarrier
Xkv,sum(l) = NEA
kXkv (l) +NEN
kclip(l) , (4.13)
where the DC component NEIDC is not present for l ∈ Vinfo and Nkclip is the discrete
102
Chapter 4. The Hybrid VLC-PLC System
Fourier transform of nkc . According to the central limit theorem (CLT), Nkclip can
be modeled as an additive complex-valued Gaussian variable with zero mean and
variance of σ2clip,k [40]. We now consider the two relaying schemes.
DF Scheme In DF, the relay will only forward the message if it was detected
correctly as verified by an outer error-detection code. Then, we will have Xkv (l) =
αXp(m), where subcarrier m ∈ Pinfo from the PLC link is paired with subcarrier l ∈
Vinfo for the VLC link, and the factor α adjusts the VLC signal strength. The pairing
will be discussed in more detail in Section 4.4. The received signal on subcarrier l at
user u when served from luminaire k follows as
Y k,uv (l) = Hk,u
v (l)Xkv,sum(l) +Nu
v (l) (4.14)
= NEαAkHk,u
v (l)Xp(m) +NEHk,uv (l)Nk
clip(l) +Nuv (l) ,
where Hk,uv (l) is the VLC channel gain for subcarrier l between the kth luminaire
and user u, and Nuv (l) is the VLC noise on subcarrier l at user u. The corresponding
subcarrier SNR is
SNRk,uv (l) =
|NEαAkHk,u
v (l)|2σ2p
|NEHk,uv (l)|2σ2
clip,k + σ2vn,u
, (4.15)
where σ2vn,u = E
[|Nu
v (l)|2]. As both clipping and VLC receiver noise can be approxi-
mated as i.i.d. Gaussian noise when Nk ≥ 64 [126], the corresponding per-subcarrier
rate can be calculated as (in bit per use)9 [128]
Rk,u(l,m) = min(log2(1 + SNRk
p(m)), log2(1 + SNRk,uv (l))
).
9Both Eq. (4.16) and Eq. (4.18) can be derived from [128, Eq. (15)] and [128, Eq. (12)], respec-tively, via setting the direct link channel gain to 0. The absence of the coefficient 1
2 is due to thefull-duplex property of the luminaire relay.
103
Chapter 4. The Hybrid VLC-PLC System
AF Scheme For AF, we have Xkv (l) = βYp(m), where β is the amplification factor
for the AF scheme. Similar to (4.14), Y k,uv (l) can be expressed as
Y k,uv (l) = NEA
kβHk,uv (l)Hk
p(m)Xp(m) +NEAkβHk,u
v (l)Nkp (m) (4.16)
+NEHk,uv (l)Nk
clip(l) +Nuv (l) ,
and the corresponding SNR at user u is given by
SNRk,uv (l,m) =
∣∣NEAkβHk,u
v (l)Hkp(m)
∣∣2 σ2p∣∣∣NEAkβH
k,uv (l)
∣∣∣2 σ2pn,k(m) +
∣∣∣NEHk,uv (l)
∣∣∣2 σ2clip,k + σ2
vn,u
. (4.17)
Using again the fact that the total noise is Gaussian, the achievable rate follows as
Rk,u(l,m) = log2
(1 + SNRk,u
v (l,m)). (4.18)
ACO-OFDM
Different than DCO-OFDM, only odd subcarriers in ACO-OFDM carry information,
i.e., Vinfo = {1, 3, . . . , 2Nv − 1}, which allows for zero-level clipping and reduces the
minimum level of DC bias at the cost of reduced bandwidth efficiency [43]. The
where U(·) is the Heaviside step function [129] and the variance of the clipping noise
nkc(n) is [40]
σ2clip,k = P k
v
(Ak((bk)2 + 1
)− 2(Ak)2 − bk
(φ(bk)− φ(tk)
)− φ(tk)(tk − bk) +Q(tk)(tk − bk)2
). (4.20)
With this, the expression for the frequency-domain signal at the lth subcarrier for
l ∈ Vinfo is the same as in Eq. (4.13). Accordingly, the SNR expressions for DF
relaying in (4.15) and AF relaying in (4.17) also apply to ACO-OFDM and can be
used in the rate expression (4.16) and (4.18), respectively, to obtain the associated
achievable rate.
4.4 Subcarrier Allocation in HVP Systems
We now use the rate expressions from the previous section to optimize the rate of the
overall HVP system. Since multiple users compete for resources, we integrate a notion
of fairness into the rate optimization. In particular, we introduce a weight variable wu
that represents the priority of user u. For example, in the case of a proportional fair
(PF) scheduling policy that prioritizes the user with the lowest average data-rate, we
have wu = 1/Ruavg(n) for long-term fairness consideration, where Ru
avg(n) is computed
as
Ruavg(n) =
(1− 1
Nres
)Ru
avg(n− 1) +1
Nres
Ru(n− 1) , (4.21)
and Ru(n) is the data rate at instance n and Nres is the response time of the low-pass
filter [130]. We note that the optimization framework presented in this section is
105
Chapter 4. The Hybrid VLC-PLC System
independent of the specific scheduling policy that is applied.
The optimization of the achievable rate of the HVP system is accomplished
through SA schemes, for which we propose two variants. The first variant, which
we refer to as SA without subcarrier permutation (SP), retains the subcarrier as-
signment when transitioning from PLC to VLC link. Assuming for simplicity and
without loss of generality that Nv = Np, we have Pinfo = Vinfo and thus l = m in
(4.16) and (4.18) for DCO-OFDM. Since Vinfo = {1, 3, . . . , 2Nv−1} for ACO-OFDM,
we have l = 2m − 1, m ∈ Pinfo, in this case. The second scheme applies subcarrier
permutation at the relays, and we refer to it as SA with SP. It makes use of the fact
that the per-subcarrier link qualities of the PLC and VLC hop are independent of
each other.
Since the number of subcarriers in broadband HVP systems can be very large, an
SA scheme considering each individual subcarrier will not only have large computa-
tional complexity, but also requires significant signaling overhead. To mitigate the
computational and coordination complexity, a chunk-based SA scheme can be applied
[113]. This means that a set of Ns adjacent subcarriers is grouped into a chunk, and
the chunk is used as the minimum unit in SA. Hence, in the following we consider
that Nc chunks are available in total, where Np = Nv = NsNc, of which Ck chunks
are assigned to kth luminaire, i.e., Nk = NsCk. Obviously, Ns = 1 is the special case
of single-subcarrier-based allocation. Given that a codebook of size Sc (Sc = 2q) is
employed for the channel gain vector space Huv(l) = [H1,u
v (l), H2,uv (l), . . . , HNL,u
v (l)],
qNc bits of CSI feedback are required for one OFDM block per VLC user. We define
the binary variable xk,ui,j ∈ {0, 1}, i, j ∈ {1, 2, . . . , Nc}, with xk,ui,j = 1 indicating that
ith chunk in the PLC hop together with the jth chunk in the VLC hop are assigned
to user u with the assistance of the kth VLC-enabled luminaire. Furthermore, we will
106
Chapter 4. The Hybrid VLC-PLC System
need in the following xu = [xk,ui,j ]i,j=1,...,Nc, k=1,...,NLas the Nc ×Nc ×NL SA tensor for
user u and x = [x1, . . . ,xNU] as the Nc×Nc×NLNU tensor for SA across all users, and
we will use the sets Nc = {1, 2, . . . , Nc}, NL = {1, 2, . . . , NL} and NU = {1, . . . , NU}
in the following, where Nc, NL and NU are the sets of chunk indices, luminaire indices
and user indices, respectively.
Next, we present the SA methods first for HVP with OFDM-TDMA and then for
HVP with OFDMA.
4.4.1 OFDM-TDMA
With OFDM-TDMA, the whole frequency spectrum is owned exclusively by the user
with the highest priority weight wu in a certain time slot. Hence, SA is performed
for one user only at a time.
SA without SP
For SA without SP, we have xk,ui,j = 0 for i 6= j, and the rate maximization problem
can be formulated as
P1 : x∗u = argmax{xu}
∑i∈Nc
∑k∈NL
xk,ui,i Rk,ui,i (4.22)
C1 :∑k∈NL
xk,ui,i = 1,∀i ∈ Nc,
C2 :∑i∈Nc
xk,ui,i = Ck,∀k ∈ NL,
C3 : xk,ui,i ∈ {0, 1}, ∀i ∈ Nc, ∀k ∈ NL ,
where Rk,ui,j represents the rate of the chunk pair (i, j) for user u and PLC-VLC relay
k. Constraint C1 guarantees that each subcarrier pair is assigned to one and only one
107
Chapter 4. The Hybrid VLC-PLC System
relay, and C2 ensures the number of subcarriers pairs allocated to each relay. P1 can
be categorized as a linear semi-assignment problem and can be solved with a time
complexity of O(N2cNL) [131]. For the simulation results in the next section, we use
the YALMIP [94] toolbox in conjunction with the MOSEK solver [103] to obtain a
solution numerically.
SA with SP
Here we generalize P1 and allow subcarrier permutation at the relays. In this case,
the optimization problem for user u can be formulated as
P2 : x∗u = argmax{xu}
∑i∈Nc
∑j∈Nc
∑k∈NL
xk,ui,j Rk,ui,j (4.23)
C1 :∑j∈Nc
∑k∈NL
xk,ui,j = 1,∀i ∈ Nc ,
C2 :∑i∈Nc
∑k∈NL
xk,ui,j = 1,∀j ∈ Nc ,
C3 :∑i∈Nc
∑j∈Nc
xk,ui,j = Ck,∀k ∈ NL ,
C4 : xk,ui,j ∈ {0, 1},∀i, j ∈ Nc, ∀k ∈ NL ,
where C1 and C2 guarantee that each subcarrier is assigned to exactly one relay for
the PLC and VLC hop, respectively, and C3 controls the number of assigned subcar-
rier pairs per relay. P2 can be categorized as a constrained linear 0-1 programming
problem, which is NP-hard. We therefore apply a heuristic alternating optimization
method to solve P2 suboptimally within polynomial time [132]. To this end, we
108
Chapter 4. The Hybrid VLC-PLC System
introduce vectors {yui,j} and {zk,ui } with x
k,ui,j = yui,jz
k,ui , and P2 is transformed into
P2.1 : (y∗u, z∗u) = argmax
{yu,zu}
∑i∈Nc
∑j∈Nc
∑k∈NL
yui,jzk,ui Rk,u
i,j
C1 :∑j∈Nc
yui,j = 1,∀i ∈ Nc,
C2 :∑i∈Nc
yui,j = 1,∀j ∈ Nc,
C3 :∑k∈NL
zk,ui = 1,∀i ∈ Nc,
C4 :∑i∈Nc
zk,ui = Ck,∀k ∈ NL,
C5 : yui,j, zk,ui ∈ {0, 1},∀i, j ∈ Nc, ∀k ∈ NL ,
where yu = [yui,j]i,j∈Nc and zu = [zk,ui ]i∈Nc,k∈NL. P2.1 is a bilinear 0-1 programming
problem, and we obtain a suboptimal solution by alternately optimizing on yu and
zu. When yu is fixed, we can ignore constraints C1 and C2, and P2.1 will degenerate
to P1 with Rk,ui,i replaced by T k,ui =
∑j∈Nc
yui,jRk,ui,j , which will be referred to as P2.2.
When zu is fixed, we define Sui,j =∑
k∈NLzk,ui Rk,u
i,j and P2.1 becomes
P2.3 : y∗u = argmax{yu}
∑i∈Nc
∑j∈Nc
yui,jSui,j
C1 :∑j∈Nc
yui,j = 1,∀i ∈ Nc,
C2 :∑i∈Nc
yui,j = 1, ∀j ∈ Nc,
C3 : yui,j ∈ {0, 1},∀i, j ∈ Nc ,
which is a classic assignment problem and can be solved by the Hungarian algorithm
with a computational complexity of O(N3c ) [133, 134]. The algorithm of the alter-
109
Chapter 4. The Hybrid VLC-PLC System
nating optimization for P2 is summarized in Algorithm 4.1 and the time complexity
is O(N3c +N2
cNL).
Algorithm 4.1 Alternating Optimization for P21. Initialization:
u∗ = argmaxu∈NU{wu}.
Calculate {Rk,u∗
i,j }.y0u∗ ⇐ INc×Nc , p⇐ 0.
2. repeat3. Update {T k,u
∗
i } with ypu∗ .4. Solve P2.2 according to [131] and get zpu∗ .5. Update {Su∗i,j} with z
pu∗ .
6. Solve P2.3 and get yp+1u∗ .
7. p⇐ p+ 1.8. until ‖yp+1
u∗ − ypu∗‖ ≤ δ (δ is a predefined threshold)
9. Compute xu∗ according to xk,u∗
i,j = yu∗i,jz
k,u∗
i .10. Update {wu}u∈NU
according to rate update (4.21).
4.4.2 OFDMA
OFDMA accomplishes multiple access by assigning different subcarriers to different
users. This allows for a more flexible SA scheme that can exploit multi-user diversity.
110
Chapter 4. The Hybrid VLC-PLC System
SA without SP
Without SP at the relays, again xk,ui,j = 0 for i 6= j, and the maximization problem
for the weighted sum rate is
P3 : x∗ = argmax{x}
∑u∈NU
wu∑i∈Nc
∑k∈NL
xk,ui,i Rk,ui,i (4.24)
C1 :∑u∈NU
∑k∈NL
xk,ui,i = 1,∀i ∈ Nc,
C2 :∑u∈NU
∑i∈Nc
xk,ui,i = Ck,∀k ∈ NL ,
C3 : xk,ui,i ∈ {0, 1},∀i ∈ Nc, k ∈ NL, u ∈ NU .
Similar to problem P2, we introduce vectors {ai,u} and {bi,k} with xk,ui,i = ai,ubi,k, and
suboptimally solve P3 with alternating optimization based on the transformation into
P3.1 : (a∗, b∗) = argmax{a,b}
∑u∈NU
wu∑i∈Nc
∑k∈NL
ai,ubi,kRk,ui,i
C1 :∑u∈NU
ai,u = 1,∀i ∈ Nc ,
C2 :∑k∈NL
bi,k = 1,∀i ∈ Nc ,
C3 :∑i∈Nc
bi,k = Ck, ∀k ∈ NL ,
C4 : ai,u, bi,k ∈ {0, 1}, ∀i ∈ Nc, k ∈ NL, u ∈ NU ,
where a = [ai,u]i∈Nc,u∈NUand b = [bi,k]i∈Nc,k∈NL
. Let Eui =
∑k∈NL
bi,kRk,ui,i , F k
i =∑u∈NU
ai,uwuRk,u
i,i , and function u∗i = argmaxu∈NU{wuEu
i }. We observe that the
optimal solution of P3.1 with b fixed is a vector a∗ with ai,u∗i = 1 and zero otherwise.
When a is fixed, we can ignore constraints C1 in P3.1, and P3.1 will degenerate to P1
111
Chapter 4. The Hybrid VLC-PLC System
with Rk,ui,i replaced by F k
i and xk,ui,i replaced by bi,k, which will be referred to as P3.2.
The algorithm of the alternating optimization for P3 is summarized in Algorithm 4.2,
and the time complexity is O(N2cNL +NcNUNL).
Algorithm 4.2 Alternating Optimization for P31. Initialization:
Calculate {Rk,ui,i }.
a0 ⇐ INc×NU, p⇐ 0.
2. repeat3. Update {F k
i } with ap.4. Solve P3.2 according to [131] and get bp.5. Update {Eu
i } with bp.6. Find u∗i and obtain ap+1.7. p⇐ p+ 1.8. until ‖ap+1 − ap‖ ≤ δ (δ is a predefined threshold)9. Compute x according to xk,ui,i = ai,ubi,k.10. Update {wu}u∈NU
according to rate update in (4.21).
SA with SP
Allowing subcarrier permutation at the relays, the weighted sum rate maximization
problem can be expressed as
P4 : x∗ = argmax{x}
∑u∈NU
wu∑i∈Nc
∑j∈Nc
∑k∈NL
xk,ui,j Rk,ui,j
C1 :∑u∈NU
∑j∈Nc
∑k∈NL
xk,ui,j = 1,∀i ∈ Nc ,
C2 :∑u∈NU
∑i∈Nc
∑k∈NL
xk,ui,j = 1,∀j ∈ Nc ,
C3 :∑u∈NU
∑i∈Nc
∑j∈Nc
xk,ui,j = Ck, ∀k ∈ NL ,
C4 : xk,ui,j ∈ {0, 1}, ∀i, j ∈ Nc, k ∈ NL, u ∈ NU .
112
Chapter 4. The Hybrid VLC-PLC System
P4 is a constrained linear 0-1 programming problem, which is NP-hard. Here we
propose a heuristic subcarrier offloading algorithm that can solve the problem sub-
optimally within polynomial time. First we relax the constraints of P4 and consider
P4 without C3, which will be referred to as P4.1. P4.1 can be solved with the al-
gorithm proposed in [135] within a polynomial time of O(NLNUN2c + N3
c ), and the
solution is denoted as {xk,ui,j }. Define NL1 and NL2 as the sets of luminaires that
do and do not exceed the assigned value Ck, respectively, with NL1 = {k|ck > Ck},
NL2 = {k|ck < Ck}, where ck =∑
u∈NU
∑i∈Nc
∑j∈Nc
xk,ui,j . Define Rk,ui,j = wuRk,u
i,j
and set R = {Rk,ui,j |x
k,ui,j = 1, k ∈ NL1}. Then we can execute the subcarrier offload-
ing algorithm summarized in Algorithm 4.3 and obtain the solution x∗ to P4. The
time complexity of Algorithm 4.3 is O(NcNLNU + Nc log(Nc)). So the total time
complexity of solving P4 will be O(NLNUN2c +N3
c ).
Algorithm 4.3 Subcarrier Offloading Algorithm1. Sort R in increasing order and store it in array AR2. for Rk,u
i,j in AR3. Initialize Rmax
i,j ⇐ 0, (k∗, u∗)⇐ (0, 0)
4. for k′ ∈ NL2, u′ ∈ NU
5. if Rk′,u′
i,j > Rmaxi,j
6. Rmaxi,j ⇐ Rk′,u′
i,j , (k∗, u∗)⇐ (k′, u′)
7. end if8. end for9. xk,ui,j ⇐ 0, xk
∗,u∗
i,j ⇐ 1, update ck, NL1 and NL2.10. if NL1 = ∅11. break12. end if13. end for14. update {xk,ui,j } ⇐ {x
k,ui,j }.
113
Chapter 4. The Hybrid VLC-PLC System
4.5 Numerical Results and Discussions
We now evaluate the performance of the proposed SO-OFDM-based HVP system.
We consider an example setup of a 5 m × 5 m room with NL = 4 coordinated
VLC-enabled LED luminaires, each of which contains NE = 36 LEDs. The setup
of the HVP system and the applied coordinate system are illustrated in Figure 4.3.
Denoting the length of the power line connecting the ith luminaire and the PLC
modem as li, we consider an example setup where l1 = 7 m, l2 = 8 m, l3 = 9 m,
l4 = 10 m. The LEDs have an operating range of IL = 300 mA to IU = 700 mA, with
a 3 dB bandwidth WLED = 10 MHz with blue filtering [102]. The DC bias is set to
IDC = (IL + IU)/2 = 500 mA, which provides a sufficient illumination for office work
and study with this system setup [54].
The HVP system has Np = 1024 independent information-carrying subcarriers,
and we set Ck = 256, k = 1, . . . , 4. For the PLC link, the minimum subcarrier fre-
quency is 2.026 MHz and the subcarrier spacing is 24.4 kHz [119]. For the VLC link,
we adopt the same subcarrier spacing as the PLC link, but the first data carrying
subcarrier is at frequency 24.4 kHz. The PLC transmit PSD is set to -50 dBm/Hz ac-
cording to the HomePlug AV standard [136] so that conducted and radiated emission
limits are met. The PLC noise in the simulation includes background, narrowband,
and impulse noise, where the PSDs and the corresponding measurement-based param-
eters of the former two are described in [137] and [118], respectively. For the impulse
noise, we adopt the model from the IEEE 1901 standard [119, Annex F.3.5.2], which
includes periodic synchronous, periodic asynchronous and aperiodic noise compo-
nents, and we apply the parameters from measurements provided in [138]. The PLC
noise simulator we developed and used here is available online [122]. For simulation
accuracy, we apply the two-state approximation as in [121, Eq. (19)] to calculate
114
Chapter 4. The Hybrid VLC-PLC System
the average achievable rate, which takes into account all of colored background noise,
narrowband disturbance and impulsive noise. The average achievable rate can be cal-
culated as the weighted sum of the achievable rates of the system with and without
impulse noise:
Ravg = (1− p)Rwithout_imp + pRwith_imp , (4.25)
where Ravg denotes the average achievable rate, Rwithout_imp denotes the achievable
rate of the system when impulse noise is absent and only colored background noise
and narrowband disturbance are considered, and Rwith_imp denotes the achievable
rate of the system when impulse noise is present. p denotes the probability of im-
pulse noise occurrence, and we let p = 0.01 in the simulation based on the PLC
noise measurement [120]. According to the measurement, p < 0.01 in even heavily
disturbed power line environment, thus our simulation results can be considered as a
lower bound of the average achievable rate. Further system parameters are listed in
Table 4.1.
4.5.1 Single-User System
We first consider the single-user scenario and focus on analyzing the system perfor-
mance with different optical OFDM, relay and SA schemes. In the following, we use
DF-DCO, DF-ACO, AF-DCO and AF-ACO to identify the cases where DF or AF
relaying at the luminaires is used together with DCO-OFDM or ACO-OFDM for the
optical OFDM scheme, respectively.
Figure 4.4 compares the achievable rates of the four transmission schemes as a
function of the user location in the x-y plane. The user height is assumed to be
z = 0.8 m. We observe that for all four schemes, the system achieves the highest rate
VLC ParametersLambertian order m 1PD area APD 1 [cm2]Concentrator refractive index κ 1.5Receiver FOV ψc 85 [deg.]Noise bandwidth factor I2 0.562Background current Ibg 100 [µA]LED conversion factor s 0.44 [W/A]PD responsivity γ 0.30 [A/W]
when the user is near the center of the room and rate decreases as the user moves
closer to the walls. SA without SP and SA with SP can improve the achievable
rate notably across the room compared with a random SA at the luminaire relays,
which we refer to as Random SA. In Figure 4.4, we also notice that the DCO-OFDM
scheme achieves a higher system rate than ACO-OFDM. This is due to the fact
that ACO-OFDM only utilizes odd subcarriers for data transmission, which makes
it less bandwidth-efficient than DCO-OFDM. In particular, for the same number
of information-carrying subcarriers in DCO-OFDM and ACO-OFDM, ACO-OFDM
uses a broader frequency spectrum and thus suffers from stronger channel attenuation
at higher frequencies. For the results in Figure 4.4, we set α =√
10 and β = 10,
which is a reasonable choice as will be discussed next.
For the results in Figure 4.5 and Figure 4.6, we fix the user location to x = −0.5 m,
y = 1.5 m, and z = 0.8 m. In Figure 4.5, we show the achievable rate as a function
of the relay gain α and β, respectively. When the relay gain is small and thus the
116
Chapter 4. The Hybrid VLC-PLC System
transmission power for the VLC hop is relatively low, the system performance is VLC-
noise limited. Increasing the relay gain will increase the SNR, but at some point LED
clipping distortion becomes the dominant noise source and curbs further performance
improvements. Hence, there is an optimal relay gain for each of the four transmissions
schemes, which depends on the magnitude of VLC noise, VLC channel (e.g., receiver
orientation, etc). Figure 4.6 compares the performance of Random SA, SA without SP
and SA with SP as a function of chunk size Ns. We can observe that SA without SP
and SA with SP can greatly enhance the system performance compared with Random
SA. Note that for SA without SP in the AF-DCO system, modulation/demodulation,
FFT/IFFT and encode/decode blocks shown in Figure 4.2 are not required, and the
signal transition between PLC and VLC can be done in the analogue domain. Based
on the results, a chunk size of Ns = 16 seems to provide close to optimal performance,
while providing computational complexity savings when solving the SA optimization
problem.
We next investigate whether the PLC or the VLC hop is limiting the performance
of the HVP system, for which we focus on the DF-mode and SA with SP. Since the
PLC and VLC channels are frequency selective, we count the number NVLC_BL of
subcarrier pairs for which the VLC hop is the bottleneck link when the maximum
achievable rate is attained. Figure 4.7 plots the NVLC_BL as a function of the user
location in the x-y plane with z = 0.8 m for both DF-DCO and DF-ACO. The 3 dB
bandwidth of WLED = 10 MHz used for the results in Figure 4.7a corresponds to the
current system setup with a blue filter at the photodiode, and WLED = 2 MHz for
the results in Figure 4.7b corresponds to a photodiode receiver without blue filtering
[139]. We observe that NVLC_BL of DF-DCO is generally smaller than that of DF-
ACO due to the stronger channel attenuation of ACO-OFDM at higher frequencies.
117
Chapter 4. The Hybrid VLC-PLC System
In Figure 4.7a, NVLC_BL is typically less than 60 out of Np = 1024 subcarrier pairs
for both DF-DCO and DF-ACO, which shows that the PLC link is the main bottle-
neck for the end-to-end performance of the HVP system. This changes notably and
especially for the system operating in the DF-ACO mode when the LED bandwidth
is reduced to 2 MHz. Here, the VLC hop limits the system performance, as shown
in Figure 4.7b.
4.5.2 Multi-User System
We now consider the scenario of multiple VLC users. We perform simulations for
both OFDM-TDMA and OFDMA to evaluate the corresponding achievable rate and
user fairness. In this section, we use AF-ACO as the example transmission scheme.
Figure 4.8 shows the average sum achievable rate against the number of VLC users.
For a given value of NU, a set of sum achievable rates are calculated and averaged by
distributing NU users uniformly at random over the indoor environment. For a fixed
location of NU users, we evaluate the average sum achievable rate over 100 time slots,
and the weights {wu} in schemes with PF scheduling are updated with Nres = 20 in
(4.21). For schemes without PF, OFDM-TDMA without PF represents an OFDM-
TDMA scheme with wu set to 1 and the user scheduling degrades to a Round-Robin
(RR) scheme. OFDMA without PF represents an OFDMA scheme with wu set to 1,
and the user scheduling degrades to a sum-rate maximizing scheduling and fairness
across users is neglected. From Figure 4.8, we can see that as NU increases, the sum
achievable rates of OFDMA schemes grow monotonically while the sum achievable
rates of OFDM-TDMA remain almost unchanged. OFDMA outperforms OFDM-
TDMA since it exploits the multi-user diversity. Not imposing the PF constraint
provides further gains due to the increased multi-user diversity.
118
Chapter 4. The Hybrid VLC-PLC System
The benefit of schemes with PF is illustrated in Figure 4.9. We consider a fixed
location profile forNU = 4 users and plot the average achievable rate for each user over
100 time slots (we assume that users remain static during this time period). We can
see that PF can improve the data rate fairness across users for both OFDM-TDMA
and OFDMA schemes, and PF is significantly important for OFDMA scheme. For
the setup in Figure 4.9, due to the poor channel conditions, no subcarrier is allocated
to User 4 in the OFDMA scheme without PF. Unlike RF wireless communication,
there is no multipath fading for indoor VLC channels due to the large photodiode size
compared with the optical wavelength. The deterministic nature of the VLC channel
will fix users in low SNR channels to become complete neglected in user scheduling
if PF scheduling is not applied. As expected, although PF results in lower overall
rate, it is a desirable feature to ensure some level of fairness among the users of the
proposed HVP system.
4.6 Conclusion
In this chapter, we have proposed a multicarrier HVP system as a potential indoor
high-speed downlink solution employing the symbiotic relationship between PLC and
VLC. Compared with traditional multicarrier-based VLC-PLC integration, the pro-
posed HVP system alleviates the PAPR problem for VLC transmitters and elim-
inates the inter-luminaire interference through the cooperation of LED luminaires
piggybacked on the powerline backbone. We have considered the HVP system as a
two-hop relay system and investigated different approaches of signal transition be-
tween PLC and VLC systems. To exploit the frequency selectivity of HVP channels,
as well as the multi-user and multi-transmitter diversity, we have proposed several
subcarrier allocation schemes with varying degrees of tradeoff among hardware, com-
119
Chapter 4. The Hybrid VLC-PLC System
putational complexity and performance for meaningful variations of the HVP sys-
tem. As another important contribution, we have investigated and compared two
multi-access schemes for the HVP system, i.e., OFDMA and OFDM-TDMA. Several
polynomial-time SA algorithms are proposed correspondingly. At the cost of higher
computational complexity, OFDMA has been shown to outperform OFDM-TDMA
for the HVP system in multi-user situations. For future work, power and bit loading
for the SO-OFDM-based HVP system can be investigated, where the linear period-
ically time varying (LPTV) properties of PLC channels can be exploited to reduce
the complexity of implementation [140].
120
Chapter 4. The Hybrid VLC-PLC System
LED luminary
Access
Network
VLC User PLC modem
12
3
4
Powerline
zx
y
Figure 4.3: The setup of HVP system.
121
Chapter 4. The Hybrid VLC-PLC System
0
2.5
5
0
2.5
5120
140
160
180
x (m)
(a) AF−DCO
y (m)
Ach
ievab
le r
ate
(M
bit
s/s)
0
2.5
5
0
2.5
580
100
120
140
160
x (m)
(b) AF−ACO
y (m)
Ach
ievab
le r
ate
(M
bit
s/s)
0
2.5
5
0
2.5
5100
150
200
x (m)
(d) DF−ACO
y (m)
Ach
ievab
le r
ate
(M
bit
s/s)
SA with SP
SA without SP
Random SA
0
2.5
5
0
2.5
5160
170
180
190
200
x (m)
(c) DF−DCO
y (m)
Ach
ievab
le r
ate
(M
bit
s/s)
Figure 4.4: Achievable rate as a function of user location. Nc = 16, α =√
10, β = 10.
122
Chapter 4. The Hybrid VLC-PLC System
100
101
102
60
80
100
120
140
160
180
β
Ach
ievab
le r
ate
(M
bit
s/s)
(a) AF−DCO
100
101
102
20
40
60
80
100
120
140
160
β
Ach
ievab
le r
ate
(M
bit
s/s)
(b) AF−ACO
100
101
102
80
100
120
140
160
180
200
α
Ach
ievab
le r
ate
(M
bit
s/s)
(c) DF−DCO
SA with SP
SA without SP
Random SA
100
101
102
80
100
120
140
160
180
200
α
Ach
ievab
le r
ate
(M
bit
s/s)
(d) DF−ACO
Figure 4.5: Achievable rate versus relay gain (α or β). Nc = 16. User location isx = −0.5 m, y = 1.5 m, z = 0.8 m.
123
Chapter 4. The Hybrid VLC-PLC System
Figure 4.6: Comparison of different SA schemes with different chunk size Ns. α =√10, β = 10. User location is x = −0.5 m, y = 1.5 m, z = 0.8 m.
124
Chapter 4. The Hybrid VLC-PLC System
0
2.5
5
0
2.5
5
0
10
20
30
40
50
60
70
80
DF−DCO
NV
LC
_B
L
0
2.5
5
0
2.5
5
0
20
40
60
80
100
120
DF−ACO
NV
LC
_B
L
(a) WLED = 10 MHz.
0
2.5
5
0
2.5
5
0
20
40
60
80
100
120
140
DF−DCO
NV
LC
_B
L
0
2.5
5
0
2.5
5
0
100
200
300
400
500
600
700
800
DF−ACO
NV
LC
_B
L
(b) WLED = 2 MHz.
Figure 4.7: NVLC_BL as a function of user location. Nc = 16. NVLC_BL is the numberof subcarrier pairs for which the VLC hop is the bottleneck link when the maximumachievable rate is attained. 125
Chapter 4. The Hybrid VLC-PLC System
Nu = 1 Nu = 2 Nu = 3 Nu = 4 Nu = 5145
150
155
160
165
170
175
180
Number of users
Ach
iev
ab
le r
ate
(M
bit
s/s)
OFDM−TDMA without PF
OFDM−TDMA with PF
OFDMA without PF
OFDMA with PF
OFDM−TDMA
OFDMA
Figure 4.8: Achievable rate versus the number of users NU. SA with SP and AF-ACOare applied. β = 10, Nc = 16.
126
Chapter 4. The Hybrid VLC-PLC System
User 1 User 2 User 3 User 40
10
20
30
40
50
(a) OFDM−TDMA without PF
Ach
iev
ab
le r
ate
(M
bit
s/s)
User 1 User 2 User 3 User 40
5
10
15
20
25
30
35
40
(b) OFDM−TDMA with PF
Ach
iev
ab
le r
ate
(M
bit
s/s)
User 1 User 2 User 3 User 40
10
20
30
40
50
60
70
80
(c) OFDMA without PF
Ach
iev
ab
le r
ate
(M
bit
s/s)
User 1 User 2 User 3 User 40
10
20
30
40
50
(d) OFDMA with PF
Ach
iev
ab
le r
ate
(M
bit
s/s)
Figure 4.9: Comparison of multi-access schemes with and without PF for NU = 4.The example locations are (x = −1.25, y = 1.25, z = 0.8) m, (x = −1.25, y =−1.25, z = 0.8) m, (x = 1.25, y = 1.25, z = 0.8) m and (x = 2.5, y = 2.5, z = 0.8) mfor User 1, User 2, User 3 and User 4, respectively. SA with SP and AF-ACO areapplied. Nc = 16, β = 10.
127
Chapter 5
Conclusion
5.1 Summary
Most research in physical-layer VLC transmission schemes focus on point-to-point
communication, however, typical rooms are usually equipped with multiple LED
luminaires instead of just one to ensure the uniformity of indoor illumination level.
Multiple independent point-to-point links will lead to strong interference among users
as the illumination footprints of neighboring LED luminaires usually have significant
overlap. To mitigate the co-channel interference, the simplest method is traditional
frequency planning that assigns different sub-bands to neighbouring attocells. An-
other method is to position VLC luminaires separately to avoid overlapping foot-
prints, and the gap between attocells is covered by RF base stations. In comparison
with frequency planning, this hybrid RF-VLC scheme allows full frequency reuse
among VLC attocells.
Different from the previous methods, the research work in this thesis presented an
alternative approach which achieves interference mitigation through coordination of
different VLC attocells. The thesis focused on developing transmission schemes for
coordinated VLC attocells. We considered three different coordinated architectures
for VLC downlink transmission. Chapter 2 proposed the full cooperation among
VLC attocells and the multiple coordinated VLC emitters form a virtual multiple-
transmitter system. The system design in Chapter 2 focused on the MMSE precoder
128
Chapter 5. Conclusion
design subject to lighting constraint. Chapter 3 extends the work in Chapter 2 by
considering looser coordination among neighboring attocells with multiple luminaires
each, which puts less requirement on the inter-attocell communication and synchro-
nization, though at the cost of compromised system performance. Numerical results
show that the coordination scheme proposed in Chapter 3 provides a good tradeoff
between system performance and complexity. While Chapter 2 and 3 assumed the
existence of backbone network for VLC transmitter, Chapter 4 delved deeper into the
power line backbone network for the proposed hybrid VLC-PLC system. In addition,
SO-OFDM was applied across multiple neighboring VLC transmitters to alleviate the
PAPR problem for each VLC transmitter, and several subcarrier allocation schemes
are proposed to exploit the frequency selectivity of the VLC and PLC channels. Dif-
ferent possible and meaningful variations of the HVP system, including the choice of
optical OFDM transmission, relay and multiple access schemes, are investigated and
compared.
5.2 Future Work
In Chapter 2 and Chapter 3, we focus on developing the spatial multiplexing tech-
niques at the transmitter side to serve multiple indoor VLC users simultaneously. It
will be interesting to investigate the joint optimization of user scheduling and beam-
forming to enhance the system performance when the number of users exceeds that
of VLC-enabled LED luminaires. What’s more, the designs proposed by Chapter 2
and Chapter 3 only apply to the single-carrier modulation, more specifically, PAM.
The optimal multi-carrier beamforming designs for both JT and CB, to the author’s
knowledge, have yet to be studied.
In fact, our ultimate goal is to build a Cloud VLC Access Network (C-VAN) which
129
Chapter 5. Conclusion
is similar to its counterpart Cloud Radio Access Network (C-RAN) in RF systems
[141]. Individual signal processing units for different VLC attocells are replaced by
a centralized unit. The LED luminaires operate as access points for the users, and
are connected to the centralized unit which coordinates the transmission for all the
attocells. The advantages of deploying C-VAN for indoor VLC systems are multi-fold.
First, smoother handover across different VLC attocells can be realized. Second, C-
VAN increases system adaptability to non-uniform indoor traffic by dynamic resource
allocation at the centralized unit. Third, C-VAN reduces the deployment cost for
VLC-enabled luminaires since luminaires in C-VAN require no baseband processing
module. Last, and most importantly, C-VAN can achieve higher system capacity
and lower IAI through collaboration among VLC transmitters. The research work
in this thesis is the first step towards a practical C-VAN system. In this thesis, we
focus on the (robust) precoder design and various resource allocation algorithms, and
assume perfect synchronization, unlimited backbone capacity and negligible delay for
coordinated VLC systems, which is not the case in reality. Factors, like time and
frequency synchronization across different VLC transmitters, backbone requirement
for a predefined VLC data rate and the effect of delay in the backbone network are
vital to the successful implementation of a working system. Future research is needed
to address these issues.
130
Bibliography
[1] Cisco Systems Inc., Cisco Visual Networking Index: Global Mobile Data TrafficForecast Update, 2016-2021 White Paper, accessed on April 5, 2017. [On-line]. Available: http://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/mobile-white-paper-c11-520862.pdf
[2] P. Rost, C. J. Bernardos, A. De Domenico, M. Di Girolamo, M. Lalam,A. Maeder, D. Sabella, and D. Wübben, “Cloud technologies for flexible 5Gradio access networks,” IEEE Commun. Mag., vol. 52, no. 5, pp. 68–76, May2014.
[3] Huawei Technologies Co. Ltd, Global Connectivity Index, 2016 White Paper,accessed on June 10, 2017. [Online]. Available: http://www.huawei.com/minisite/gci/pdfs/Global_Connectivity_Index_2016_whitepaper.0614.pdf
[4] Federal Communications Commission, The National Broadband Plan, accessedon May 19, 2016. [Online]. Available: https://transition.fcc.gov/national-broadband-plan/national-broadband-plan.pdf
[5] McKinsey & Company, Lighting the Way: Perspectives onthe Global Lighting Market, 2nd ed., accessed on Dec.25, 2016. [Online]. Available: https://www.mckinsey.de/files/Lighting_the_way_Perspectives_on_global_lighting_market_2012.pdf
[6] Cisco Systems Inc., Digital Building Solution., accessed on Dec. 25,2016. [Online]. Available: http://www.cisco.com/c/en/us/solutions/workforce-experience/digital-building/index.html
[8] T. Komine and M. Nakagawa, “Fundamental analysis for visible-light commu-nication system using LED lights,” IEEE Trans. Consum. Electron., vol. 50,no. 1, pp. 100–107, Feb. 2004.
[9] “IEEE standard for local and metropolitan area networks–Part 15.7: Short-range wireless optical communication using visible light,” IEEE Std 802.15.7-2011, pp. 1–309, Sept. 2011.
[10] J. Vucic, C. Kottke, S. Nerreter, K.-D. Langer, and J. W. Walewski, “513 Mbit/svisible light communications link based on DMT-modulation of a white LED,”J. Lightw. Technol., vol. 28, no. 24, pp. 3512–3518, Dec. 2010.
[11] D. Tsonev, H. Chun, S. Rajbhandari, J. J. McKendry, S. Videv, E. Gu, M. Haji,S. Watson, A. E. Kelly, G. Faulkner, M. Dawson, H. Haas, and D. O’Brien, “A3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride,”IEEE Photon. Technol. Lett., vol. 26, no. 7, pp. 637–640, Apr. 2014.
[12] pureLiFi, Li-Fi: High-Speed Communication via LED Modulation, accessed onJune. 10, 2017. [Online]. Available: http://www.archlighting.com/technology/li-fi-high-speed-communication-via-led-modulation_o
[13] Y. Wang, X. Huang, L. Tao, J. Shi, and N. Chi, “4.5-Gb/s RGB-LED basedWDM visible light communication system employing CAP modulation and RLSbased adaptive equalization,” Optics express, vol. 23, no. 10, pp. 13 626–13 633,May 2015.
[14] D. Tsonev, S. Videv, and H. Haas, “Light fidelity (Li-Fi): Towards all-opticalnetworking,” in Proc. SPIE, vol. 9007, Dec. 2013, pp. 900 702–900 702.
[15] H. Haas, “High-speed wireless networking using visible light,” SPIE Newsroom,Apr. 2013.
[16] C.-X. Wang, F. Haider, X. Gao, X.-H. You, Y. Yang, D. Yuan, H. Aggoune,H. Haas, S. Fletcher, and E. Hepsaydir, “Cellular architecture and key technolo-gies for 5G wireless communication networks,” IEEE Commun. Mag., vol. 52,no. 2, pp. 122–130, Feb. 2014.
[17] H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” J. Lightw. Technol.,vol. 34, no. 6, pp. 1533–1544, Mar. 2016.
[18] MarketsandMarkets, Location-Based Services (LBS) and Real Time LocationSystems (RTLS) Market by Location (Indoor and Outdoor), Technology(Context Aware, UWB, BT/BLE, Beacons, A-GPS), Software, Hardware,Service and Application Area - Global Forecast to 2021, accessed on Jan.11, 2017. [Online]. Available: http://www.marketsandmarkets.com/Market-Reports/location-based-service-market-96994431.html
[19] H. Liu, Y. Gan, J. Yang, S. Sidhom, Y. Wang, Y. Chen, and F. Ye, “Push thelimit of WiFi based localization for smartphones,” in Proceedings of the 18thAnnual International Conference on Mobile Computing and Networking, Aug.2012, pp. 305–316.
[20] M. Kavehrad, M. Chowdhury, and Z. Zhou, “Indoor positioning methods usingVLC LEDs,” Short-Range Optical Wireless: Theory and Applications, pp. 225–262, Oct. 2015.
[21] T.-H. Do and M. Yoo, “An in-depth survey of visible light communication basedpositioning systems,” Sensors, vol. 16, no. 5, p. 678, May 2016.
[22] T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh,T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based vis-ible light communication for automotive applications,” IEEE Commun. Mag.,vol. 52, no. 7, pp. 88–97, July 2014.
[23] A. Cailean and M. Dimian, “Current challenges for visible light communicationsusage in vehicle applications: A survey,” IEEE Commun. Surveys Tuts., vol. PP,no. 99, pp. 1–1, 2017.
[24] E. F. Schubert, T. Gessmann, and J. K. Kim, Light Emitting Diodes. WileyOnline Library, 2005.
[25] H. Le Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, andE. Won, “100-Mb/s NRZ visible light communications using a postequalizedwhite LED,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1063–1065, Aug.2009.
[26] S. Rajbhandari, H. Chun, G. Faulkner, K. Cameron, A. V. Jalajakumari,R. Henderson, D. Tsonev, M. Ijaz, Z. Chen, H. Haas, E. Xie, J. McKendry,J. Herrnsdorf, E. Gu, M. Dawson, and D. O’Brien, “High-speed integrated visi-ble light communication system: Device constraints and design considerations,”IEEE J. Sel. Areas Commun., vol. 33, no. 9, pp. 1750–1757, Sept 2015.
[27] J. Grubor, S. Randel, K. Langer, and J. Walewski, “Broadband informationbroadcasting using LED-based interior lighting,” J. Lightw. Technol., vol. 26,no. 24, pp. 3883–3892, Dec. 2008.
[28] J. J. McKendry, D. Massoubre, S. Zhang, B. R. Rae, R. P. Green, E. Gu, R. K.Henderson, A. Kelly, and M. D. Dawson, “Visible-light communications us-ing a CMOS-controlled micro-light-emitting-diode array,” J. Lightw. Technol.,vol. 30, no. 1, pp. 61–67, Jan. 2012.
[29] C. Danakis, M. Afgani, G. Povey, I. Underwood, and H. Haas, “Using a CMOScamera sensor for visible light communication,” in IEEE Globecom Workshops(GC Wkshps), Dec 2012, pp. 1244–1248.
[30] F. Gfeller and U. Bapst, “Wireless in-house data communication via diffuseinfrared radiation,” Proceedings of the IEEE, vol. 67, no. 11, pp. 1474–1486,Nov. 1979.
133
Bibliography
[31] V. Jungnickel, V. Pohl, S. Nonnig, and C. Von Helmolt, “A physical model ofthe wireless infrared communication channel,” IEEE J. Sel. Areas Commun.,vol. 20, no. 3, pp. 631–640, Apr. 2002.
[32] J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt,“Simulation of multipath impulse response for indoor wireless optical channels,”IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367–379, Apr. 1993.
[33] F. Lopez-Hernandez, R. Perez-Jimeniz, and A. Santamaria, “Monte Carlo cal-culation of impulse response on diffuse IR wireless indoor channels,” ElectronicsLetters, vol. 34, no. 12, pp. 1260–1262, June 1998.
[34] F. J. Lo, R. Pe et al., “Ray-tracing algorithms for fast calculation of the channelimpulse response on diffuse IR wireless indoor channels,” Optical engineering,vol. 39, no. 10, pp. 2775–2780, Oct. 2000.
[35] S. D. Personick, “Receiver design for digital fiber optic communication systems,Part I and II,” Bell system technical journal, vol. 52, pp. 843–886, July-Aug.1973.
[36] T. Hong, “A close look at the china design standard for energy efficiency ofpublic buildings,” Energy and Buildings, vol. 41, no. 4, pp. 426–435, Apr. 2009.
[37] ISO, ISO 8995-1: 2002 (CIE S 008/E: 2001) Lighting of Indoor Work Places,2002.
[38] European Norm (EN) 12464-1, “Light and lighting - lighting of work places,Part 1: Indoor work places,” 2011.
[39] H. Elgala, R. Mesleh, and H. Haas, “An LED model for intensity-modulatedoptical communication systems,” IEEE Photon. Technol. Lett., vol. 22, no. 11,pp. 835–837, June 2010.
[40] S. D. Dimitrov, “Analysis of OFDM-based intensity modulation techniques foroptical wireless communications,” Ph.D. dissertation, University of Edinburgh,Jul. 2013.
[41] E. Monteiro and S. Hranilovic, “Design and implementation of color-shift keyingfor visible light communications,” J. Lightw. Technol., vol. 32, no. 10, pp. 2053–2060, May 2014.
[42] J. Armstrong, “OFDM for optical communications,” J. Lightw. Technol.,vol. 27, no. 3, pp. 189–204, Feb. 2009.
[43] J. Armstrong and A. Lowery, “Power efficient optical OFDM,” IET ElectronicsLetters, vol. 42, no. 6, pp. 370–372, Mar. 2006.
134
Bibliography
[44] J. Armstrong and B. J. Schmidt, “Comparison of asymmetrically clipped opti-cal OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett.,vol. 12, no. 5, pp. 343–345, May 2008.
[45] M. B. Rahaim, A. M. Vegni, and T. D. Little, “A hybrid radio frequency andbroadcast visible light communication system,” in IEEE GLOBECOM Work-shops (GC Wkshps), Dec. 2011, pp. 792–796.
[46] F. Jin, R. Zhang, and L. Hanzo, “Resource allocation under delay-guaranteeconstraints for heterogeneous visible-light and RF femtocell,” IEEE Trans.Wireless Commun., vol. 14, no. 2, pp. 1020–1034, Feb. 2015.
[47] X. Li, R. Zhang, and L. Hanzo, “Cooperative load balancing in hybrid visiblelight communications and WiFi,” IEEE Trans. Commun., vol. 63, no. 4, pp.1319–1329, Apr. 2015.
[48] Y. Wang, D. A. Basnayaka, X. Wu, and H. Haas, “Optimization of load balanc-ing in hybrid LiFi/RF networks,” IEEE Trans. Commun., vol. 65, no. 4, pp.1708–1720, Apr. 2017.
[49] D. Lee, H. Seo, B. Clerckx, E. Hardouin, D. Mazzarese, S. Nagata, andK. Sayana, “Coordinated multipoint transmission and reception in LTE-advanced: deployment scenarios and operational challenges,” IEEE Commun.Mag., vol. 50, no. 2, pp. 148–155, Feb. 2012.
[50] R. Irmer, H. Droste, P. Marsch, M. Grieger, G. Fettweis, S. Brueck, H. P. Mayer,L. Thiele, and V. Jungnickel, “Coordinated multipoint: concepts, performance,and field trial results,” IEEE Commun. Mag., vol. 49, no. 2, pp. 102–111, Feb.2011.
[51] Z. Yu, R. J. Baxley, and G. T. Zhou, “Multi-user MISO broadcasting for indoorvisible light communication,” in IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP), May 2013.
[52] T. Pham, H. Le Minh, and A. Pham, “Multi-user visible light communica-tion broadcast channels with zero-forcing precoding,” IEEE Trans. Commun.,vol. 65, no. 6, pp. 2509–2521, June 2017.
[53] Y. Hong, J. Chen, Z. Wang, and C. Yu, “Performance of a precoding MIMOsystem for decentralized multiuser indoor visible light communications,” IEEEPhoton. J., vol. 5, no. 4, pp. 7 800 211–7 800 211, Aug. 2013.
[54] H. Ma, L. Lampe, and S. Hranilovic, “Coordinated broadcasting for multiuserindoor visible light communication systems,” IEEE Trans. Commun., vol. 63,no. 9, pp. 3313–3324, Sept. 2015.
135
Bibliography
[55] ——, “Robust MMSE linear precoding for visible light communication broad-casting systems,” in IEEE Globecom Workshops, Dec. 2013, pp. 1081–1086.
[56] K. Ying, H. Qian, R. J. Baxley, and S. Yao, “Joint optimization of precoderand equalizer in MIMO VLC systems,” IEEE J. Sel. Areas Commun., vol. 33,no. 9, pp. 1949–1958, Sept. 2015.
[57] B. Li, J. Wang, R. Zhang, H. Shen, C. Zhao, and L. Hanzo, “Multiuser MISOtransceiver design for indoor downlink visible light communication under per-LED optical power constraints,” IEEE Photon. J., vol. 7, no. 4, pp. 1–15, Aug.2015.
[58] C. Chen, D. Tsonev, and H. Haas, “Joint transmission in indoor visible lightcommunication downlink cellular networks,” in IEEE Globecom Workshops (GCWkshps), Dec. 2013, pp. 1127–1132.
[59] D. Bykhovsky and S. Arnon, “Multiple access resource allocation in visible lightcommunication systems,” J. Lightw. Technol., vol. 32, no. 8, pp. 1594–1600,Apr. 2014.
[60] P. Hu, P. H. Pathak, A. K. Das, Z. Yang, and P. Mohapatra, “PLiFi: HybridWiFi-VLC networking using power lines,” in Proceedings of the 3rd Workshopon Visible Light Communication Systems, Aug. 2016, pp. 31–36.
[61] T. Komine, S. Haruyama, and M. Nakagawa, “Performance evaluation of nar-rowband OFDM on integrated system of power line communication and visiblelight wireless communication,” in International Symposium on Wireless Perva-sive Computing, Jan. 2006, pp. 6–11.
[62] H. Ma, L. Lampe, and S. Hranilovic, “Integration of indoor visible light andpower line communication systems,” in IEEE International Symposium onPower Line Communications and Its Applications (ISPLC), Mar. 2013, pp.291–296.
[63] A. Ndjiongue, H. C. Ferreira, K. Ouahada, and A. H. Vinckz, “Low-complexitySOCPBFSK-OOK interface between PLC and VLC channels for low data ratetransmission applications,” in IEEE International Symposium on Power LineCommunications and its Applications (ISPLC), Mar. 2014, pp. 226–231.
[64] B. Ghimire and H. Haas, “Self-organising interference coordination in opticalwireless networks,” EURASIP Journal on Wireless Communications and Net-working, vol. 2012, no. 1, pp. 1–15, Apr. 2012.
[65] H.-S. Kim, D.-R. Kim, S.-H. Yang, Y.-H. Son, and S.-K. Han, “Mitigation ofinter-cell interference utilizing carrier allocation in visible light communicationsystem,” IEEE Commun. Lett., vol. 16, no. 4, pp. 526–529, Apr. 2012.
136
Bibliography
[66] S.-Y. Jung, D.-H. Kwon, S.-H. Yang, and S.-K. Han, “Reduction of inter-cellinterference in asynchronous multi-cellular VLC by using OFDMA-based cellpartitioning,” in 18th IEEE International Conference on Transparent OpticalNetworks (ICTON), July 2016, pp. 1–4.
[67] R. Bai, H. Tian, B. Fan, and S. Liang, “Coordinated transmission based in-terference mitigation in VLC network,” in IEEE 82nd Vehicular TechnologyConference (VTC Fall), Sept. 2015, pp. 1–5.
[68] M. Kashef, M. Abdallah, K. Qaraqe, H. Haas, and M. Uysal, “Coordinatedinterference management for visible light communication systems,” IEEE J.Opt. Commun. Netw., vol. 7, no. 11, pp. 1098–1108, Nov. 2015.
[69] K. Zhou, C. Gong, Q. Gao, and Z. Xu, “Inter-cell interference coordination formulti-color visible light communication networks,” in IEEE Global Conferenceon Signal and Information Processing (GlobalSIP), Dec. 2016, pp. 6–10.
[70] X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocationfor NOMA visible light communication multi-cell networks,” IEEE Commun.Lett., vol. 21, no. 4, pp. 777–780, Apr. 2017.
[71] S. Serbetli and A. Yener, “Transceiver optimization for multiuser MIMO sys-tems,” IEEE Trans. Signal Process., vol. 52, no. 1, pp. 214–226, Jan. 2004.
[72] V. Stankovic and M. Haardt, “Generalized design of multi-user MIMO precod-ing matrices,” IEEE Trans. Wireless Commun., vol. 7, no. 3, pp. 953–961, Mar.2008.
[73] A. Tajer, N. Prasad, and X. Wang, “Robust linear precoder design for multi-cell downlink transmission,” IEEE Trans. Signal Process., vol. 59, no. 1, pp.235–251, Jan. 2011.
[74] L. Venturino, N. Prasad, and X. Wang, “Coordinated linear beamforming indownlink multi-cell wireless networks,” IEEE Trans. Wireless Commun., vol. 9,no. 4, pp. 1451–1461, Apr. 2010.
[75] W. Yu, T. Kwon, and C. Shin, “Multicell coordination via joint scheduling,beamforming, and power spectrum adaptation,” IEEE Trans. Wireless Com-mun., vol. 12, no. 7, pp. 1–14, July 2013.
[76] R. Zakhour and D. Gesbert, “Distributed multicell-MISO precoding using thelayered virtual SINR framework,” IEEE Trans. Wireless Commun., vol. 9, no. 8,pp. 2444–2448, Aug. 2010.
137
Bibliography
[77] H. Huh, H. C. Papadopoulos, and G. Caire, “Multiuser MISO transmitter op-timization for intercell interference mitigation,” IEEE Trans. Signal Process.,vol. 58, no. 8, pp. 4272–4285, Aug. 2010.
[78] S. Shao, A. Khreishah, M. Ayyash, M. B. Rahaim, H. Elgala, V. Jungnickel,D. Schulz, T. D. Little, J. Hilt, and R. Freund, “Design and analysis of avisible-light-communication enhanced WiFi system,” Journal of Optical Com-munications and Networking, vol. 7, no. 10, pp. 960–973, Oct. 2015.
[79] A. Jovicic, J. Li, and T. Richardson, “Visible light communication: Opportuni-ties, challenges and the path to market,” IEEE Commun. Mag., vol. 51, no. 12,pp. 26–32, Dec. 2013.
[80] S. Shao, A. Khreishah, M. B. Rahaim, H. Elgala, M. Ayyash, T. D. Little, andJ. Wu, “An indoor hybrid WiFi-VLC Internet access system,” in IEEE 11thInternational Conference on Mobile Ad Hoc and Sensor Systems (MASS), Oct.2014, pp. 569–574.
[81] M. S. Mossaad, S. Hranilovic, and L. Lampe, “Visible light communicationsusing OFDM and multiple LEDs,” IEEE Trans. Commun., vol. 63, no. 11, pp.4304–4313, Nov. 2015.
[82] J. C. Bezdek and R. J. Hathaway, “Some notes on alternating optimization,”Advances in Fuzzy Sets and System, vol. 2, pp. 288–300, 2002.
[83] J. Gorski, F. Pfeuffer, and K. Klamroth, “Biconvex sets and optimization withbiconvex functions: A survey and extensions,” Mathematical Methods of Oper-ations Research, vol. 66, no. 3, pp. 373–407, 2007.
[84] D. W. Pentico, “Assignment problems: A golden anniversary survey,” EuropeanJournal of Operational Research, vol. 176, no. 2, pp. 774–793, 2007.
[85] H. Ma, L. Lampe, and S. Hranilovic, “Hybrid visible light and power line com-munication for indoor multiuser downlink,” Journal of Optical Communicationsand Networking, vol. 9, no. 8, pp. 635–647, Aug. 2017.
[86] H. C. Ferreira, L. Lampe, J. Newbury, and T. G. Swart, Eds., Power Line Com-munications: Theory and Applications for Narrowband and Broadband Commu-nications over Power Lines. John Wiley & Sons Ltd, 2010.
[87] T. Komine and M. Nakagawa, “Integrated system of white LED visible-lightcommunication and power-line communication,” IEEE Trans. Consum. Elec-tron., vol. 49, no. 1, pp. 71–79, Feb. 2003.
138
Bibliography
[88] P. Amirshahi and M. Kavehrad, “Broadband access over medium and low volt-age power-lines and use of white light emitting diodes for indoor communi-cations,” in IEEE Consumer Communications & Networking Conference, LasVegas, Nevada, USA, 2006.
[89] A. Tonello, P. Siohan, A. Zeddam, and X. Mongaboure, “Challenges for 1 Gbpspower line communications in home networks,” in IEEE International Sympo-sium on Personal, Indoor and Mobile Radio Communications (PIMRC), Sep.2008, pp. 1–6.
[90] L. Zeng, D. O’Brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, andE. Won, “High data rate multiple input multiple output (MIMO) optical wire-less communications using white LED lighting,” IEEE J. Sel. Areas Commun.,vol. 27, no. 9, pp. 1654–1662, Dec. 2009.
[91] T. Fath and H. Haas, “Performance comparison of MIMO techniques for opti-cal wireless communications in indoor environments,” IEEE Trans. Commun.,vol. 61, no. 2, pp. 733–742, Feb. 2013.
[92] C. W. Tan, M. Chiang, and R. Srikant, “Maximizing sum rate and minimizingMSE on multiuser downlink: Optimality, fast algorithms and equivalence viamax-min SINR,” IEEE Trans. Signal Process., vol. 59, no. 12, pp. 6127–6143,Dec. 2011.
[93] M. Joham, K. Kusume, M. H. Gzara, W. Utschick, and J. Nossek, “TransmitWiener filter for the downlink of TDDDS-CDMA systems,” in IEEE Seventh In-ternational Symposium on Spread Spectrum Techniques and Applications, vol. 1,Sept. 2002, pp. 9–13.
[94] J. Lofberg, “YALMIP: A toolbox for modeling and optimization in MATLAB,”in IEEE International Symposium on Computer Aided Control Systems Design,Sept. 2004, pp. 284–289.
[95] M. Grant and S. Boyd, “Graph implementations for nonsmooth convex pro-grams,” in Recent Advances in Learning and Control, ser. Lecture Notes inControl and Information Sciences, V. Blondel, S. Boyd, and H. Kimura,Eds. Springer-Verlag Limited, 2008, pp. 95–110, http://stanford.edu/~boyd/graph_dcp.html.
[96] ——, “CVX: Matlab software for disciplined convex programming, version 2.1,”http://cvxr.com/cvx, Mar. 2014.
[97] M. Shenouda and T. N. Davidson, “On the design of linear transceivers formultiuser systems with channel uncertainty,” IEEE J. Sel. Areas Commun.,vol. 26, no. 6, pp. 1015–1024, Aug. 2008.
[98] N. Vucic, H. Boche, and S. Shi, “Robust MSE-constrained downlink precodingin multiuser MIMO systems with channel uncertainty,” in 45th Annual AllertonConference on Communication, Control, and Computing, Sept. 2007.
[99] W. Zhang and M. Kavehrad, “Comparison of VLC-based indoor positioningtechniques,” Proc. SPIE, vol. 8645, pp. 86 450M–86 450M–6, Jan. 2013.
[100] J. Armstrong, Y. Sekercioglu, and A. Neild, “Visible light positioning: aroadmap for international standardization,” IEEE Commun. Mag., vol. 51,no. 12, pp. 68–73, Dec. 2013.
[101] Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, “Robust mean-squared error es-timation in the presence of model uncertainties,” IEEE Trans. Signal Process.,vol. 53, no. 1, pp. 168–181, Jan.
[104] M. K. Simon and M.-S. Alouini, Digital communication over fading channels.John Wiley & Sons, 2005, vol. 95.
[105] C. B. Peel, B. M. Hochwald, and A. L. Swindlehurst, “A vector-perturbationtechnique for near-capacity multiantenna multiuser communication-Part I:Channel inversion and regularization,” vol. 53, no. 1, pp. 195–202, Jan. 2005.
[106] E. Bjornson, M. Bengtsson, and B. Ottersten, “Optimal multiuser transmitbeamforming: A difficult problem with a simple solution structure [lecturenotes],” IEEE Signal Process. Mag., vol. 31, no. 4, pp. 142–148, June 2014.
[107] J. Wang and D. P. Palomar, “Worst-case robust MIMO transmission with im-perfect channel knowledge,” vol. 57, no. 8, pp. 3086–3100, Aug. 2009.
[108] R. A. Horn and C. R. Johnson, “Matrix anlysis.” Cambridge University Press,1985.
[109] W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “Ahybrid power line and visible light communication system for indoor hospitalapplications,” Computers in Industry, vol. 68, pp. 170–178, Feb. 2015.
[110] A. Familua, A. Ndjiongue, K. Ogunyanda, L. Cheng, H. Ferreira, and T. Swart,“A semi-hidden markov modeling of a low complexity FSK-OOK in-house PLCand VLC integration,” in IEEE International Symposium on Power Line Com-munications and Its Applications (ISPLC), 2015, pp. 199–204.
[111] H. Ferreira, L. Lampe, J. Newbury, and T. Swart, Power Line Communications:Theory and Applications for Narrowband and Broadband Communications overPower Lines. John Wiley & Sons, 2011.
[112] H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs andOFDM,” IEEE Trans. Consum. Electron., vol. 55, no. 3, pp. 1127–1134, Aug.2009.
[113] M. Herdin, “A chunk based OFDM amplify-and-forward relaying scheme for4G mobile radio systems,” in International Conference on Communications,vol. 10, June 2006, pp. 4507–4512.
[114] P. Marsch and G. P. Fettweis, Coordinated Multi-Point in Mobile Communica-tions: From Theory to Practice. Cambridge University Press, 2011.
[115] A. M. Tonello and F. Versolatto, “Bottom-up statistical PLC channel modeling-Part I: Random topology model and efficient transfer function computation,”IEEE Trans. Power Del., vol. 26, no. 2, pp. 891–898, Apr. 2011.
[116] ——, “Bottom-up statistical PLC channel modeling-Part II: inferring the statis-tics,” IEEE Trans. Power Del., vol. 25, no. 4, pp. 2356–2363, Oct. 2010.
[117] G. Marrocco, D. Statovci, and S. Trautmann, “A PLC broadband channel simu-lator for indoor communications,” in IEEE International Symposium on PowerLine Communications and Its Applications (ISPLC), Mar. 2013, pp. 321–326.
[118] D. Benyoucef, “A new statistical model of the noise power density spectrum forpowerline communication,” in International Symposium on Power Line Com-munications and Its Applications (ISPLC), 2003, pp. 136–141.
[119] IEEE Std 1901-2010, “IEEE standard for broadband over power line networks:Medium access control and physical layer specifications,” 2010.
[120] M. Zimmermann and K. Dostert, “Analysis and modeling of impulsive noisein broadband powerline communications,” IEEE Trans. Electromagn. Compat.,vol. 44, no. 1, pp. 249–258, Feb 2002.
[121] L. Di Bert, P. Caldera, D. Schwingshackl, and A. M. Tonello, “On noise mod-eling for power line communications,” in IEEE International Symposium onPower Line Communications and Its Applications (ISPLC), Apr. 2011, pp.283–288.
[122] G. Prasad, H. Ma, M. Rahman, F. Aalamifar, and L. Lampe, A CumulativePower Line Noise Generator, accessed on Dec. 25, 2016. [Online]. Available:http://www.ece.ubc.ca/~gauthamp/PLCnoise
[123] H. Ma, Indoor VLC ray-tracing, accessed on Mar. 10, 2016. [Online]. Available:https://github.com/mhrex/Indoor_VLC_Ray_Tracing.git
[124] L. Grobe and K.-D. Langer, “Block-based PAM with frequency domain equal-ization in visible light communications,” in IEEE Globecom Workshops, Dec.2013, pp. 1070–1075.
[125] J. J. Bussgang, “Crosscorrelation functions of amplitude-distorted Gaussiansignals,” Technical report, MIT Research Laboratory of Electronics, Mar. 1952.
[126] D. Dardari, V. Tralli, and A. Vaccari, “A theoretical characterization of non-linear distortion effects in OFDM systems,” IEEE Trans. Commun., vol. 48,no. 10, pp. 1755–1764, Oct. 2000.
[127] S. Randel, F. Breyer, S. C. Lee, and J. W. Walewski, “Advanced modulationschemes for short-range optical communications,” IEEE J. Sel. Topics QuantumElectron., vol. 16, no. 5, pp. 1280–1289, Sep.-Oct. 2010.
[128] J. N. Laneman, D. N. Tse, and G. W. Wornell, “Cooperative diversity in wirelessnetworks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory,vol. 50, no. 12, pp. 3062–3080, Dec. 2004.
[129] E. W. Weisstein, “Heaviside step function,” From MathWorld–A Wolfram WebResource. http://mathworld. wolfram. com/HeavisideStepFunction.html, 2008.
[130] C. Wengerter, J. Ohlhorst, V. Elbwart, and A. G. Edler, “Fairness and through-put analysis for generalized proportional fair frequency scheduling in OFDMA,”in IEEE 61st Vehicular Technology Conference, vol. 3, May 2005, pp. 1903–1907.
[131] J. Kennington and Z. Wang, “A shortest augmenting path algorithm for thesemi-assignment problem,” Operations Research, vol. 40, no. 1, pp. 178–187,Jan.âĂŞFeb. 1992.
[132] A. M. Frieze, “A bilinear programming formulation of the 3-dimensional as-signment problem,” Mathematical Programming, vol. 7, no. 1, pp. 376–379,Dec. 1974.
[133] H. W. Kuhn, “The Hungarian method for the assignment problem,” Naval Re-search Logistics Quarterly, vol. 2, no. 1-2, pp. 83–97, Mar. 1955.
[134] J. Munkres, “Algorithms for the assignment and transportation problems,”Journal of the Society for Industrial & Applied Mathematics, vol. 5, no. 1,pp. 32–38, Mar. 1957.
[135] Y. Liu and M. Tao, “Optimal channel and relay assignment in OFDM-basedmulti-relay multi-pair two-way communication networks,” IEEE Trans. Com-mun., vol. 60, no. 2, pp. 317–321, Feb. 2012.
[136] H. A. Latchman, S. Katar, L. Yonge, and S. Gavette, “Homeplug AV and IEEE1901: A handbook for PLC designers and users.” Wiley-IEEE Press, 2013.
[137] T. Esmailian, F. R. Kschischang, and P. Glenn Gulak, “In-building power linesas high-speed communication channels: channel characterization and a testchannel ensemble,” International Journal of Communication Systems, vol. 16,no. 5, pp. 381–400, May 2003.
[138] J. A. Cortés, L. Diez, F. J. Cañete, and J. J. Sánchez-Martínez, “Analysis ofthe indoor broadband power-line noise scenario,” IEEE Trans. Electromagn.Compat., vol. 52, no. 4, pp. 849–858, Nov. 2010.
[139] H. Le Minh, Z. Ghassemlooy, D. O’Brien, and G. Faulkner, “Indoor gigabitoptical wireless communications: Challenges and possibilities,” in 12th Inter-national Conference on Transparent Optical Networks (ICTON), June 2010.
[140] M. Tunc, E. Perrins, and L. Lampe, “Optimal LPTV-aware bit loading in broad-band PLC,” IEEE Trans. Commun., vol. 61, no. 12, pp. 5152–5162, Dec. 2013.
[141] A. Checko, H. L. Christiansen, Y. Yan, L. Scolari, G. Kardaras, M. S. Berger,and L. Dittmann, “Cloud RAN for mobile networks-a technology overview,”IEEE Commun. Surveys Tuts., vol. 17, no. 1, pp. 405–426, Firstquarter 2015.
143
Appendix A
Proof of Outdated CSI Bound
For the terminal movement in the horizontal direction, the terminal can either move
away from or towards the VLC transmitter. In the former case, the resulting differ-
ence in the scalar channel gain between two consecutive CSI updates can be expressed
as a function of dh and calculated according to Equation (1.2):
ε+(dh) = hp1− hp2
(A.1)
=(m+ 1)NEsγκ
2APD
2π(d2v + d2
h)
(dv√d2v + d2
h
)m+1
− (m+ 1)NEsγκ2APD
2π(d2v + (dh + L)2)
(dv√
d2v + (dh + L)2
)m+1
= β
((d2v + d2
h
)−m+32 −
(d2v + (dh + L)2)−m+3
2
),
where
β =(m+ 1)NEsγκ
2APDdm+1v
2π sin2(ψc). (A.2)
Based on the three facts:
1. ε+(0) > 0 ,
2. d ε+(dh)d dh
∣∣∣dh=0
> 0 ,
3. limdh→+∞ ε+(dh)→ 0 ,
144
Appendix A. Proof of Outdated CSI Bound
it can be deduced that there exists one maximum in (0, +∞). Therefore, there exists
at least one d1 ∈ (0,+∞) that satisfies d ε+(dh)d dh
∣∣∣dh=d1
= 0, and one of those d1 is
corresponding to the maximum. To obtain d1, we calculate the derivative of equation
(A.1):
d ε+(dh)
d dh
∣∣∣∣dh=d1
= 0
⇒ log
(d1
L+ d1
)=m+ 5
2log
(d2v + d2
1
d2v + (L+ d1)2
). (A.3)
So the maximum channel gain difference between two consecutive CSI updates when
the user terminal moves away from the VLC transmitter is
ε+ = maxdh
ε+(dh) = β(
(d2v + d2
1)−m+3
2 − (d2v + (d1 + L)2)−
m+32
), (A.4)
where d1 satisfies (A.3). Similarly, if the user terminal moves towards the VLC trans-
mitter, the maximum difference in the scalar channel gain between two consecutive
CSI updates can be expressed as
ε− = β(
(d2v + (d2 − L)2)−
m+32 − (d2
v + d22)−
m+32
), (A.5)
where d2 satisfies
log
(d2
d2 − L
)=m+ 5
2log
(d2v + d2
2
d2v + (d2 − L)2
). (A.6)
So the error bound for the kth user can be expressed as εk = max{ε+, ε−}, together