Available via license: CC BY 4.0
Content may be subject to copyright.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
1
LED Half-power Angle Optimization for Ultra-Dense Indoor Visible
Light Communication Network Deployment
Jiaojiao Xu, Chen Gong, Jianghua Luo, and Zhengyuan Xu
Due to limited interference range, the advantage of visible light communication (VLC) over wireless fidelity (WiFi) lies more in
the unit-area transmission rate rather than the single-link transmission rate. To characterize the achievable transmission rate per
unit area, we consider an indoor downlink VLC network with dense attocell configuration for the transmitters with single-color
light-emitting diode (LED) and multi-color LEDs, assuming binomial distributed users. We divide each attocell into central region
and boundary region, and propose the transmission protocols based on such attocell division. We optimize the LED half-power
angle to maximize the mean achievable transmission rate per unit area. More specifically, we investigate the rates of cell-center
and cell-boundary users under fairness consideration for the single LED transmitter system. We characterize the mean achievable
transmission rate per unit area under the white light constraints in the multiple LEDs transmitter system. The performance of the
proposed transmission protocols is evaluated by numerical results.
Index Terms—Dense coverage, Multi-color LED, Unit-area achievable transmission rate, VLC.
I. INT ROD UC TI ON S
Future wireless communication will expand the spectrum to
higher frequency region to meet the demand for massive access
and high communication rates. With the advancement of the
green lighting and rapid development of high-power light-
emitting diodes (LEDs), one promising solution is to adopt op-
tical wireless communication, including infrared spectrum [1],
visible light spectrum [2], and ultra-violet spectrum [3], [4].
In a typical visible light communication (VLC) system, low-
cost LEDs and photodiodes (PDs) are widely employed for the
transmitter and the receiver, respectively [5]. Compared with
other communication methods, VLC can potentially offer high
modulation bandwidth with pre-/post-equalizers, high trans-
mission rate, and enhanced security. It is attracting extensive
research interests from both academia and industrial areas [6]–
[9].
Due to limited transmission range and interference range,
one advantage of VLC lies in the deployment of dense
attocells [10]–[12], where the mean unit-area achievable trans-
mission rate can be significantly enhanced, at the cost of
more complicated network infrastructure. Work [10] presents
an analytical model for the coverage analysis of multiuser
VLC networks considering the cooperation among access
points (APs) to reduce the inter-cell interference and enhance
the useful signal power. In work [11], a new mathematical
framework for the coverage probability analysis of multiuser
VLC networks taking into account the idle probability of
access points (APs) that are not associated with any users is p-
resented. It also indicates that the evaluation of the distribution
This work was supported by National Key Research and Development
Program of China (Grant No. 2018YFB1801904), Key Program of National
Natural Science Foundation of China (Grant No. 61631018), Key Research
Program of Frontier Sciences of CAS (Grant No. QYZDY-SSW-JSC003).
Jiaojiao Xu, Chen Gong, and Zhengyuan Xu are with Key Laboratory of
Wireless-Optical Communications, Chinese Academy of Sciences, School of
Information Science and Technology, University of Science and Technol-
ogy of China, Hefei, China. Email: xjj1224@mail.ustc.edu.cn, {cgong821,
xuzy}@ustc.edu.cn.
J. Luo is with National Mobile Communications Research Laboratory,
Southeast University, Nanjing 210096, China. He is also with Zhongshan
Zhongchuang Technology Research Institute of Opto-electronics Industry,
Zhongshan 528415, China. Email: luojh@chinavlc.org.
function of the signal-to-interference-plus-noise ratio (SINR)
is more challenging in VLC networks than in radio frequency-
based cellular networks, which is also our research point.
Work [12] also reveals that the dense deployment of multiple
APs can achieve seamless coverage and meet high throughput
demand through adopting the cooperative transmission in the
VLC network. The VLC network communication coverage
has been investigated in [10], [11] via adopting a stochastic
geometry model. Moreover, it can be potentially deployed in
the fourth industrial revolution (Industry 4.0) and industrial
internet areas with data exchange in industrial production units
and densely distributed terminals [13]. This requires reliable
data transmission to guarantee smooth operations for densely
distributed terminals.
Based on the aforementioned advantage of dense attocells
deployment, we consider dense indoor optical attocell cover-
age in this work, and adopt mean achievable transmission rate
per unit receiver area as a performance metric, rather than the
network throughput [14] or the achievable transmission rate
for a single-link adopted in most existing research works [15],
[16]. Work [14] mainly considers an indoor VLC network,
which can support flexible access and resource allocation
of multiple mobile users in the ultra-dense attocell layout.
Furthermore, for the transmission rate fairness of different
region users, we divide each attocell into central and boundary
regions rather than simply using square attocells, and propose
transmission protocols based on such attocell division. Mean-
while, we also consider the square attocells without region
division as the comparison.
Work [17] shows the average received optical power increas-
es with the semi-angle reduced, which could further influence
the transmission rate. In this work, we optimize the LED half-
power angle to maximize the mean achievable transmission
rate per unit area given fairness consideration for single LED
system, and investigate the mean achievable rates of cell-
center and cell-boundary users. Moreover, we determine the
optimal value of LED half-power angle, which provides higher
transmission rate under illumination constraints. From the
numerical results, it is observed that the mean achievable rate
per unit area first increases and then decreases with the LED
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
2
half-power angle. We also propose two protocols, where two
adjacent cells are transmitting in a time-division manner or
simultaneously. Besides, we also introduce 3-color multiple
LED transmitter system including red (R), green (G), blue
(B), which constitutes the 3-color VLC system [18]–[21]. We
propose to optimize the half-power angle of the boundary and
central LEDs, under white light illumination constraint and
receiving color light requirements.
The remainder of this paper is organized as follows. Sec-
tion II introduces the indoor VLC attocell system architecture
and outlines the problem to be solved. Section III proposes
the protocol design and optimization for single-color LED
system. Section IV proposes the protocol design and optimiza-
tion for multi-color LED system. Section V and Section VI
analyzes the numerical results. Finally, conclusion is made in
Section VII.
II. IN DO OR VLC ATTOCELL MODEL
A. System Model
Consider an indoor attocell VLC network composed of
squared layout attocells, with edge length Dfor each square.
The LEDs in the attocell network serve for both illumina-
tion and communication, and are placed at the cell center.
Such dense LED coverage can well model the ultra-dense
VLC transmitter deployment in aircraft carbin or underground
garages/workshops.
We consider both single-color and multi-color transmission
within indoor dense attocells, which adopt a single white
LED and three red/green/blue (R/G/B) LEDs in one attocell,
respectively. The LED layout is shown in Figure 1.
Fig. 1. The attocell/LED layout and receiver distribution for the indoor VLC
network.
Assume that the users are standing on the ground and
employing the PD/APD to receive the VLC signal, the re-
ceivers are densely distributed in the attocells, where each
user is served by the LED of its attocell. Assume that the
user distribution obeys Binomial Point Process (BPP) with
user density λ[11], i.e., the number of users in any area obeys
binomial distribution and the mean number of users per unit
area is λ. Such BPP can be approximated by an M×M
grid of layout for independent and identically distributed user
positions for certain large M, where the probability that an
user exists on a position in the grid is λ/M2.
Assume that the LED transmission direction is strictly
downwards, and the user receiving direction is strictly upwards
in the industrial scenario, for example, the receiver is a vehicle-
mounted terminal in the underground parking lot. The received
signals consist of the desired signal from its attocell and the
interference from the adjacent attocell LEDs. In this work, in
contrast to optimizing the single-link achievable transmission
rate, we focus on optimizing the mean achievable transmission
rate per unit area.
B. Lambertian Model for Optical Attocell
We assume that each transmitting LED has a Lambertian ra-
diation pattern [22]–[24]. Since the NLOS (non-line-of-sight)
components in the received signal are few, we only consider
the LOS information in the following analysis. Letting ϕ1/2
denote the semi-angle at half transmission power, the channel
DC gain is given by HDC ,
HDC =(m+ 1)A
2πDd2cosm(ϕ)Ts(ψ)cos(ψ),(1)
where m,-1/log(cos(ϕ1/2)) denotes the Lambertian index; A
denotes the detector area; Dddenotes the distance between the
transmitter and the receiver; ϕdenotes the radiation angle from
the transmitter; ψdenotes the incidence angle at the receiver;
and Ts(ψ)denotes the optical filter gain.
Assume the same modulation depth for all transmitting
LEDs, i.e., the same ratio of the AC component over the
DC component. In the output electric-domain signal of the
photoelectric conversion, the AC component is extracted for
the signal detection. The received electric signal component
PScan be expressed as follows,
PS=γ2PrSignal2,(2)
where coefficient γcharacterizes overall responsiveness as the
combination of modulation depth and receiver response, which
is a scalar independent of any geometries, and PrSignal is the
optical power of the desirable received signal.
The receiver receives optical interference from neighboring
cells, leading to interference power PIin the electric domain.
Assume additive white Gaussian noise (AWGN) with variance
PNcontributed by shot noise and thermal noise, given by,
PN=σ2
shot +σ2
thermal,(3)
where σ2
shot and σ2
thermal denote the shot noise variance and
thermal noise variance, respectively. The shot noise variance
is given by,
σ2
shot = 2qγB(PrS ignal +PrI CI )+2qIbgI2B, (4)
where PrICI is the interference power in the optical do-
main, including not only inter-cell interference for single-
color transmitter, but also weak intra-cell interference for
multi-color transmitter. Note that PrICI is different from the
interference power PIin the electric domain. We adopt the
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
3
same response coefficient for different colors due to the slight
coefficient difference for different colors. In Equation (4), q
is the elementary charge; Bis equivalent noise bandwidth;
Ibg is background current; and I2= 0.562 is the typical noise
bandwidth factor [24]. Assuming a p-i-n/field effect transistor
(FET) transimpedance receiver [25], [26], with negligible gate
leakage current and 1/f noise, the thermal noise variance is
given by,
σ2
thermal =8πK Tk
GηAI2B2+16π2KTkΓ
gm
η2A2I3B3,(5)
where Kis Boltzmann constant; Tkis absolute temperature;
Gis the open-loop voltage gain; ηis the fixed capacitance
of photo detector per unit area; Γis the FET channel noise
factor; gmis the FET transconductance; and I3= 0.0868.
The Shannon capacity in Gaussian channel is adopted as an
approximation on the downlink transmission rate for AWGN
VLC channel. Gaussian channel capacity is adopted as an
approximation on the achievable downlink transmission rate,
which is tight for medium-to-high signal to interference and
noise ratio (SINR), as the typical scenario for the indoor VLC.
According to references [27]–[29], it is given by
R=1
2log2(1 + PS
PN+PI
).(6)
where coefficient 1
2before log(·) function stems from the
Gaussian channel capacity per transmission bandwidth and the
real channel for VLC. Note that the values of PrSignal ,PrI CI ,
and PIdepend on the specific transmission protocols. Signal
or interference is artificially divided according to different
protocols, so Gaussian approximation is applicable.
C. Problem Statement
The mean achievable transmission rate per unit area, denot-
ed as Fu, is the mean achievable transmission rate per user
multiplied by the mean number of users per unit area, given
by
Fu=λEN
n=1 Rn
N,(7)
where Nis the number of users in an attocell; Rnrepresents
the achievable rate of user n; and the expectation is taken over
all attocells and BPP realizations of users.
Note that the definition of Fuis virtually equivalent to the
area spectral efficiency given in [30]. The transmission rate is
given by B∗Fu, where Bis the signal bandwidth involved in
Equation (4). However, since in this work we also investigate
the mean rate for cell boundary/center users and the related
fairness, the form shown in Equation (7) is adopted.
III. THE TR AN SM IS SI ON PROTOC OL F OR SI NG LE -CO LO R
LED
A. Central-Boundary Area Division
Based on the LED Lambertian radiation model, we divide
each cell into the center region with radius rand the remaining
boundary region, as shown in Figure 2. Since the attocell has
a maximum radius of 1
2Das the largest inscribed circle, we
Fig. 2. The division of cell center and cell boundary regions.
have r∈[0,1
2D]. The transmission protocols are given as
follows.
•For the attocell center users, all LEDs transmit signals
simultaneously with normalized time slot division τto
the entire slot, 0≤τ≤1, where the center users within
a specific attocell are served in a time-division manner;
•For the attocell boundary users, we propose two proto-
cols:
P rotocol a)We divide the squared-layout attocells into
two sets like white and black lattices in a chess board,
where any two adjacent attocells belong to two different
sets. The attocell division is shown in “2TDM Roof” in
Figure 2. The two different sets are served in a time-
division manner, with two non-overlapping duration (1 −
τ)/2and also non-overlappling with the serving time of
cell-center users.
P rotocol b)We propose that all attocells serve the
boundary users simultaneously in the remaining 1−τ
slot duration, and the users within a specific attocell
boundary area are served in a time-division manner. The
interference from other attocells is treated as additive
noise.
For the above transmission protocols, let Kdenote the
number of attocells, R(i)
ndenote the achievable transmission
rate of user nin attocell i. Then, for both cell-center users
and cell-boundary users in attocell i, the received DC signal
optical power PrSignal involved in Equation (2), denoted as
P(i)
rSignal, can be expressed by
P(i)
rSignal =H(i)
DC Pt,(8)
where H(i)
DC denotes the link gain from attocell i;Ptis the
LED transmission optical power for each attocell. For the cell-
center users in cell i, the received DC optical signal power
PrICI involved in Equation (4), denoted as P(i)
rI CI , is given
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
4
by
P(i)
rICI =
K
j=1,j̸=i
H(j)
DC Pt.(9)
The interference power in the electric domain P(i)
Ican be
expressed by
P(i)
I=
j∈SiγH (j)
DC Pt2,(10)
where Siis the set of attocells serving simultaneously with
attocell i. Note that Si={j: 1 ≤j≤K, j ̸=i}for cell-
center users and cell-edges for protocol b; and Sidenotes the
set with the same black/white lattices attocell for protocol a,
which means jis the attocell in the same odd/even diagonal
with attocell iin the LED layout.
Let c(i)denote the number of cell-center users in attocell
i, and N(i)−c(i)denote the number of boundary users. The
mean transmission rate of attocell center users, denoted as Rc,
is given by,
Rc=λE1
K
i=1 c(i)
K
i=1
τ(R(i)
1+... +R(i)
c(i))
c(i);(11)
and the mean transmission rate of attocell boundary users,
denoted as Rb, is given in Equation (12). Then, the mean
achievable transmission rate per unit area Fuis given in
Equation (13), where the expectation is taken over the BPP
realization assuming that all LEDs are transmitting not only a
DC but also an AC signal.
Rb=
λE1
K
i=1(N(i)−c(i))
K
i=1
1−τ
2(R(i)
c(i)+1 +... +R(i)
N(i))
N(i)−c(i), for protocol a;
λE1
K
i=1(N(i)−c(i))
K
i=1
(1 −τ)(R(i)
c(i)+1 +... +R(i)
N(i))
N(i)−c(i), for protocol b.
(12)
B. Illuminance Constraint
We characterize the illuminance variation constraint, via an
upper bound Uth on the ratio of the maximum optical power
Prmax(ϕ1/2)over the minimum one Prmin(ϕ1/2)from all
LEDs, given by
Prmax ϕ1/2
Prmin ϕ1/2≤Uth,(14)
which can reflect the optical power uniformity from illumina-
tion in the VLC attocell.
C. Attocell Transmission Parameter Optimization
The Lambertian half-power angle ϕ1/2and slot division
parameter τneed to be optimized. A large value of half-
power angle ϕ1/2may cause strong inter-attocell interference
to degrade the achievable transmission rate of adjacent attocell
boundary users, while a small value of ϕ1/2may degrade the
achievable transmission rate of its own attocell users. Given
parameter τ, we aim to search the optimal ϕ1/2to maximize
Fu, shown as follows,
max
ϕ1/2
Fu(ϕ1/2, τ).(15)
Due to larger inter-cell interference for protocol binvolved in
Equation (13), the optimal half-power angle to maximize Fu
tends to be lower than that for protocol a.
Moreover, since uniform illumination is desirable for human
eye comfort in the receiving attocell, half-power angle ϕ1/2
cannot be too small, which will lead to observable light spot
on the ground. Ratio Uth in the corner and edge attocells
tends to be larger under the same half-power angle ϕ1/2due
to less uniform illumination intensity distribution. We can
maximize the transmission rate Fufor different thresholds Uth
for protocol aand protocol b, shown as follows,
max
ϕ1/2
Fu(ϕ1/2, τ), s.t. (14),(16)
where lower half-power angle leads to higher Uth according to
the Equation (14). Moreover, as Uth → ∞, the maximization
in (16) almost converges to (15).
On the other hand, adjusting time-sharing τlinearly adjusts
the rate of center and boundary users, leading to a fairness
consideration Rcand Rb. Moreover, to characterize the fair-
ness between the two types of users, we define ∆R,Rb−Rc
as the discrepancy between the rate of cell boundary users and
cell center users. We aim to investigate the achievable region
of Fuand ∆R, via searching through all feasible values of
system parameters. We can maximize Fu(ϕ1/2, τ )given an
upper bound on Uth.
IV. THE TR AN SM IS SI ON PROTOCOL FOR MULTI -CO LO R
LED
A. Chromaticity Diagram for White Light Illumination
Consider a multi-color communication network, with 3
LEDs of R/G/B colors in each unit area attocell. For color i,
1≤i≤3, let Si(ξ)denote its spectral response to the stimulus
of unit transmission power over a wide-range of wavelengths
on wavelength ξ. Let p˙ıbe the transmission power on color
i. Then, the power spectral density (PSD), denoted as C(ξ),
is given by
C(ξ) =
3
i=1
piSi(ξ).(17)
The retina in the human eye contains three types of cones–
short (S), medium (M) and long (L) responsible for color
vision, whose spectral responses are denoted by βX(ξ), βY(ξ),
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
5
Fu=
λE1
K
i=1 N(i)
K
i=1 τ(R(i)
1+... +R(i)
c(i))
c(i)+(1 −τ)(R(i)
c(i)+1 +... +R(i)
N(i))
2(N(i)−c(i)) , for protocol a;
λE1
K
i=1 N(i)
K
i=1 τ(R(i)
1+... +R(i)
c(i))
c(i)+(1 −τ)(R(i)
c(i)+1 +... +R(i)
N(i))
N(i)−c(i), for protocol b.
(13)
and βZ(ξ), respectively. Since the flickering rate is much high-
er than the perception rate of human eyes, the DC components
reflect the human eye observation, given by the following
expectations E[pi][31] for 1≤i≤3,
X=3
i=1
E[pi]Si(ξ)βX(ξ)dξ,
Y=3
i=1
E[pi]Si(ξ)βY(ξ)dξ,
Z=3
i=1
E[pi]Si(ξ)βZ(ξ)dξ,
(18)
where the expectation denotes the time-average over instanta-
neous power pi. The human eye color vision is the projection
of (X, Y, Z)onto plane x+y+z= 1, given as follows,
x=X
X+Y+Z, y =Y
X+Y+Z, z =Z
X+Y+Z.
(19)
Since for each position, the link gains for different colors
may be different due to different half-power angles, the colors
at different positions are not exactly the same. In the CIE
1931 chromaticity diagram, there is no significant change of
chromaticity as the coordinates of chromaticity vary within a
small range, characterized by MacAdam ellipse [32], [33]. We
need to find the set of feasible half-power angles for cell-center
and cell-boundary colors, such that the colors at all positions
belong to certain MacAdam ellipse centered at the white color
point.
B. Central-Boundary Area Division
Assume multi-color LEDs as the system transmitter, where
each color is the smallest resource allocation block that can be
allocated for cell-center and cell-boundary areas. Define rcb as
the area ratio of the two regions, given by
rcb =πr2
D2−πr2.(20)
Considering there are R/G/B LED transmitters and more
central region users in actual scenarios, we adopt two colors
for the cell-center area and one color for the cell-boundary
area. Thus, rcb = 2 and radius r=2/(3π)D.
Assume the same half-power angle for the two LEDs for
the central region, where each LED serves half of the central
region users selected randomly, which follows the idea of
fractional frequency reuse (FFR) [27]. Meanwhile, we adopt
different color allocations of the boundary region between
adjacent attocells to reduce the inter-cell interference. Define
△ϕ1/2as the half-power angle difference between the LEDs
serving the central and boundary regions, which is still a
parameter to be designed. In the color allocation, we adopt
the same color on the main diagonal direction of the layout,
as shown in Figure 3.
Fig. 3. The LED color division of cell center and cell boundary regions.
To mitigate the cross-color interference, three ideal optical
filters with cutoff wavelengths [300nm, 520nm], [520nm,
600nm], and [600nm, 800nm] are employed for R, G, and
B colors, respectively, which means the responses inside and
outside the pass band are 1and 0, respectively. The same
approach can be applied if the optical filters are not ideal. The
3×3optical filter gain matrix Fis given according to [31]:
F=
0.99 0.09 0
0.01 0.91 0
0 0.01 0.99
.(21)
For user nin cell i, denote the set of R/G/B LEDs as
LEDn. Denote the set of one serving LED as LEDS
n, which
is allocated as the transmission source LED according to the
transmission protocol. The other two are treated as interfering
LEDs, denoted as LEDn\LEDS
n, the ”\” denotes set minus.
The received interference signal also includes the optical signal
from the three R/G/B LEDs set in adjacent attocells. Thus, for
user nin cell i, the optical power, denoted as P(i)
rSignal,n, can
be expressed by,
P(i)
rSignal,n =H(i)
nl (0) ·Pt,l ·Fll, l ∈LEDS
n,(22)
where H(i)
nl (0) represents the DC gain from the transmitter
to the user n;Pt,l represents the optical power of the color
lunder white lighting constraint; Fll represents the diagonal
element of color l.
Then, for user nin cell i, the received optical interfer-
ence power, denoted as P(i)
rICI,n, including the main inter-
cell interference and weak intra-cell interference, is given in
Equation (23). Moreover, the received interference power in
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
6
P(i)
rICI,n =
p∈LEDS
n
l∈LEDn\LEDS
n
H(i)
nl (0) ·Pt,l ·Fpl +
1≤j≤K
j̸=i
p∈LEDS
n
1≤l≤3
H(j)
nl (0) ·Pt,l ·Fpl (23)
P(i)
I,n =
p∈LEDS
n
l∈LEDn\LEDS
n
γ·H(i)
nl (0) ·Pt,l ·Fpl2+
1≤j≤K
j̸=i
p∈LEDS
n
1≤l≤3
γ·H(j)
nl (0) ·Pt,l ·Fpl2
(24)
Rc=λE1
K
i=1 c(i)
K
i=1 (R(i)
1+... +R(i)
⌈c(i)/2⌉)
⌈c(i)/2⌉+
(R(i)
⌈c(i)
2⌉+1 +... +R(i)
c(i))
c(i)− ⌈c(i)/2⌉ (25)
Rb=λE1
K
i=1(N(i)−c(i))
K
i=1
(R(i)
c(i)+1 +... +R(i)
N(i))
N(i)−c(i).(26)
Fu=λE1
K
i=1 N(i)
K
i=1 (R(i)
1+... +R(i)
⌈c(i)/2⌉)
⌈c(i)/2⌉+
(R(i)
⌈c(i)
2⌉+1 +... +R(i)
c(i))
c(i)− ⌈c(i)/2⌉+(R(i)
c(i)+1 +... +R(i)
N(i))
N(i)−c(i) (27)
the electric domain, denoted as P(i)
I,n , can be expressed by
Equation (24).
Similarly, the mean transmission rate of the cell-center users
is given in Equation (25), where ⌈c(i)/2⌉is the approximate
half of the number of the users in the central region randomly
served by one of the two cell-center color. Such approxima-
tion is needed, since the number of users served by each
cell-center color must be an integer. The mean achievable
transmission rate of the cell-boundary users Rbis given by
Equation (26). Thus, the mean achievable transmission rate
for each user based on the SINR in the electric domain is
adopted for performance evaluation, given by Fu, as shown
in Equation (27). More strict white light requirement leads to
tighter half-power angle for the same △ϕ1/2, which decreases
the mean achievable transmission rate Fu.
C. Illuminance Power Constraint
For the illuminance power constraint, we still adopt Uth
as an upper bound on the ratio between the maximum opti-
cal power and minimum optical power. Letting Pr(ϕR
1/2, L),
Pr(ϕG
1/2, L)and Pr(ϕB
1/2, L)denote the optical power at
position L(two-dimensional position on the same height of
a user) of red, green and blue colors, respectively, we have
the following constraint
maxLPr(ϕR
1/2, L) + Pr(ϕG
1/2, L) + Pr(ϕB
1/2, L)
minLPr(ϕR
1/2, L) + Pr(ϕG
1/2, L) + Pr(ϕB
1/2, L)≤Uth.(28)
Similarly, ratio Uth in corner and edge attocells would be
larger under the same half-power angle ϕ1/2and △ϕ1/2due
to less uniform illumination intensity distribution.
Given threshold Uth, the range of half-power angle ϕ1/2and
half-power angle difference of the central and boundary LEDs
△ϕ1/2can be specified. We can optimize the transmission rate
Fuwith respect to threshold Uth.
D. Attocell Transmission Parameter Optimization
We optimize the Lambertian half-power angles for two
central LEDs and one boundary LED, to maximize the unit-
area mean achievable transmission rate under white lighting
constraints. We allow a certain offset for the chromaticity
points, for example within the circle with (0.43, 0.405) and
(0.344, 0.353) as both end points of the diameter, as shown in
Figure 4. Let Rdenote such region of (x, y).
Fig. 4. The user chromaticity points offset at the receiver in the CIE 1931
color space.
The transmission configuration optimization based on the
brute-force search mainly consists of two steps. We find the set
of system parameters such that the lighting and minimum rate
constraint is satisfied for all positions in the attocell network,
and maximize the mean unit-area achievable transmission rate,
formulated as follows,
max
ϕ1/2,∆ϕ1/2
Fu(ϕ1/2,△ϕ1/2),
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
7
s.t. (x, y)∈ R for all points and (28).
V. NUMERICAL RESULTS FO R SIN GL E-C OL OR LED
A. System Parameter Configuration
The default system parameters of single LED transmitter for
the indoor VLC attocell communication system are listed in
Table I, including the room size, the transmitting LED layout,
and the PD parameters of the receiver. The system parameters
obey the default settings unless explicitly stated. Assume that
25 LEDs are installed on the ceiling at a height of 3.0m from
the floor, where each optical attocell of an LED covers an unit
area attocell, i.e., D= 1m. Thus, the max half-power angle is
given by
ϕ1/2max = arctan(√2∗D2/2
3),(29)
which means the half power occurs at the corner of the square
attocell and can be treated as an upper bound on the half-power
angle. From the numerical results, it is seen that the optimal
half-power angle is lower than that upper bound. Moreover,
ϕ1/2max would be larger as Dincreases, i.e., ϕ1/2max would
be larger with sparser LEDs layout. The transmission power
of each LED is set to be 1W. Each user is served by the LED
of its own attocell, treating the signals from other attocells as
interference.
Assume that the detector area of PD is 1cm2, the gain of
an optical filter is 1.0, and the responsiveness (O/E conversion
efficiency) of PD is 0.54A/W , according to the parameter
setting in [24]. We adopt binomial approximation to approach
the BPP of users, via defining M×Muser locations per
unit area and probability λ/M2that there is a user in each
point. A large value of Mand a medium value of λlead to
more accurate approximation of BPP. Typical values of other
parameters [24], [34] involved in Equation (5) are: Tk= 295K,
γ= 0.54A/W, G= 10, gm= 30mS, Γ= 1.5, η= 112pF/cm2,
and B= 100MHz. Note that such bandwidth can be achieved
by the transmitter-side pre-equalizers and amplifiers.
TABLE I
SIM ULATI ON PAR AM ETE R SE TTI NG F OR SI NG LE LE D TR ANS MIT TE R
SY STE M.
Parameter Value
Room size 5.0m×5.0m×3.0m
The number of LEDs 25
The distance between LEDs 1m
The optical transmission power per LED: Pt1W
The physical detection area of PD : A1cm2
The gain of optical filter Ts(ψ)1.0
The responsiveness of PD : γ0.54A/W
For a certain transmission protocol, the mean achievable
transmission rate per unit area Fuis determined by parameters
r,ϕ1/2and τ. Parameter rspecifies the division of the cell-
center and cell-boundary regions at the receiver. We investigate
mean rate Fuwith respect to half-power angle ϕ1/2and
transmission time slot τ, and the criterion on selecting the
parameters. Moreover, we investigate the achievable region of
Fuand ∆Rto characterize the overall mean rate and fairness
between the attocell-center and attocell-boundary users. The
expectation over BPP is taken over 200 realizations based on
the binomial approximation, which suffice to provide a smooth
result.
B. Numerical Simulation Results
1) Protocol a
We consider constraints r∈[0,0.5],ϕ1/2∈[0, ϕ1/2max]
and τ∈[0,1]. We first consider the case of no region division
in one attocell, i.e., r= 0 and τ= 0, which can be seen as
the performance comparison benchmark. Figure 5 shows the
mean transmission rate per unit area Fuwith respect to half-
power angle ϕ1/2for no region division, where ϕ1/2starts
from 0.2to ϕ1/2max with step size 0.2. It can be seen that Fu
first increases and then decreases with ϕ1/2, and the optimal
ϕ1/2to maximize Fuis about 5.4degrees.
0 5 10 15
1/2(deg)
0
2
4
6
8
Fu(bit/m2)
r=0, =0
Fig. 5. The mean achievable rate per unit area with respect to LED half-power
angle ϕ1/2for no region division.
Figure 6 shows the mean transmission rate per unit area
Fuwith respect to half-power angle ϕ1/2for different values
of time sharing τand radius r. We show the results for τ=
0.1,0.3,0.5,0.7,0.9. Similarly, we can know that given τ,Fu
firstly increases and then decreases with ϕ1/2, and the optimal
ϕ1/2to maximize Fuis about 5degrees, which is not sensitive
to radius r. It is consistent with the intuition that the radius r
only defines the grouping of central and boundary users. Note
that under the cases τ= 0.7 and 0.9, the optimal ϕ1/2has
an obvious difference with r= 0.1, which is a very unfair
parameter combination situation and should be avoided in the
system design. Moreover, it can be seen that the largest Fu
on the case of central-boundary region division is higher than
that of no region division, which is also the motivation of our
research.
Figure 7 shows the mean transmission rate Rcand Rbwith
respect to half-power angle ϕ1/2for time sharing τand radius
r= 0.1. Slot τis selected from 0.1to 1with step size 0.1.
We show the results for τ= 0.1,0.3,0.5,0.7,0.9. It can be
seen that the optimal half-power angle for Rcis lower than
that for Rb. Moreover, slot τcannot be too large due to the
transmission rate fairness between the central and boundary
users.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
8
0 5 10
1/2(deg)
0
5
10
Fu(bit/m2)
=0.1
r=0.1
r=0.2
r=0.3
r=0.4
r=0.5
0 5 10
1/2(deg)
0
5
10
Fu(bit/m2)
=0.3
0 5 10
1/2(deg)
0
5
10
15
Fu(bit/m2)
=0.5
0 5 10
1/2(deg)
0
5
10
15
20
Fu(bit/m2)
=0.7
0 5 10
1/2(deg)
0
5
10
15
20
Fu(bit/m2)
=0.9
Fig. 6. The mean achievable rate per unit area with respect to LED half-power
angle ϕ1/2for different time sharing τ.
0 5 10
1/2(deg)
0
2
4
6
8
Rc or Rb (bit/m2)
=0.1
0 5 10
1/2(deg)
0
2
4
6
8
Rc or Rb (bit/m2)
=0.3
0 5 10
1/2(deg)
0
5
10
Rc or Rb (bit/m2)
=0.5
0 5 10
1/2(deg)
0
5
10
15
20
Rc or Rb (bit/m2)
=0.7
0 5 10
1/2(deg)
0
5
10
15
20
Rc or Rb (bit/m2)
=0.9
Rc
Rb
Fig. 7. Mean transmission rates Rcand Rbwith respect to LED half-power
angle ϕ1/2for different time sharing τ.
Figure 8 shows the achievable region of Fuand ∆Rwith
respect to all possible combination of half-power angle ϕ1/2
and time sharing τ, for different attocell-center radii r. It is
observed that as rincreases, given fixed Fu, e.g., Fu= 10,
lower minimum |∆R|can be achieved. It is seen that the
maximum Fugrows linearly with the absolute value of ∆R.
Note that as rincreases, the area and number of users in
the cell-center and boundary regions get closer, such that Rc
is closer to Rb. Meanwhile, the interference of the adjacent
attocell becomes larger as radius rincreases, resulting in a
decrease of Fu, while it is more fair for different region users.
For different central region radii rand cell-center user
serving time slot τ, we optimize half-power angle ϕ1/2, with
-10 -5 0
R
0
5
10
15
20
25
Fu(bit/m2)
r=0.1
-2 -1 0
R
0
5
10
15
20
25
Fu(bit/m2)
r=0.2
-2 -1 0
R
0
5
10
15
20
25
Fu(bit/m2)
r=0.3
-0.4-0.2 0 0.2
R
0
5
10
15
20
25
Fu(bit/m2)
r=0.4
-0.4-0.2 0 0.2
R
0
5
10
15
20
25
Fu(bit/m2)
r=0.5
Fig. 8. The relationship between Fuand certain ∆Rwith respect to all
combinations of half-power angle ϕ1/2for time sharing τ.
step size 0.2from 4degrees to 6degrees. The optimal half-
power angle ϕ1/2considering the cell-center and boundary rate
fairness is shown in Table II. Larger rimplies larger attocell-
center regions, which leads to larger time-sharing τand lower
ϕ1/2with more concentrated LED beam. However, the optimal
ϕ1/2is not sensitive to r.
TABLE II
THE O PT IMA L ϕ1/2WIT H RE SP ECT T O DIFF ER ENT rA ND τF OR
PROT OCO L a.
r0 0.1 0.2 0.3 0.4 0.5
τ0 0.015 0.05 0.13 0.3 0.62
Rc\8.3283 7.0257 7.1863 8.3184 9.3674
Rb7.2685 7.3106 7.5688 7.9406 8.2762 7.9355
optimal ϕ1/25.4 5.4 5.4 5.4 5.2 5.0
Fu7.2685 7.3393 7.4998 7.7307 8.2941 9.0296
2) Protocol b
The system parameters in protocol b, such as the central
region radius r, half-power angle ϕ1/2and time slot τ, take
the same values as those for protocol a. Simulation results
also show the same trend of the mean achievable transmission
rate Fuwith half-power angle ϕ1/2, as shown in Figure 9,
Figure 10 and Figure 11. It is seen that the optimal half-
power angle is about 4.0degrees, which is lower than that
of 5.4degrees of protocol a. Also, the largest Fuon the case
of central-boundary region division is higher than that of no
region division.
Table III lists the optimal time slot and half-power angle
under the minimum ∆Rbetween central and boundary users
under different radii r. It can be seen that to ensure the
minimum ∆R, the optimal half-power angle is lower than the
corresponding one in Table II. For the boundary region users,
since the overall interference is larger due to more interfering
attocells, the access interference needs to be reduced by
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
9
0 2 4 6 8 10 12 14
1/2(deg)
0
2
4
6
8
10
12
Fu(bit/m2)
r=0, =0
Fig. 9. The mean achievable rate per unit area with respect to LED half-power
angle ϕ1/2for no region division.
0 5 10
1/2(deg)
0
5
10
15
Fu(bit/m2)
=0.1
0 5 10
1/2(deg)
0
5
10
15
Fu(bit/m2)
=0.3
0 5 10
1/2(deg)
0
5
10
15
Fu(bit/m2)
=0.5
0 5 10
1/2(deg)
0
5
10
15
20
Fu(bit/m2)
=0.7
0 5 10
1/2(deg)
0
5
10
15
20
Fu(bit/m2)
=0.9
0 5 10
1/2(deg)
0
5
10
15
20
Fu(bit/m2)
=1
Fig. 10. The mean achievable rate per unit area with respect to LED half-
power angle ϕ1/2with r=0.1 for different time sharing τ.
shrinking the half-power angle of the LEDs, thereby reducing
the mean transmission rate difference ∆R.
TABLE III
THE O PT IMA L ϕ1/2WI TH RE SP ECT T O DI FFER ENT rAND τF OR
PROT OCO L b.
r0 0.1 0.2 0.3 0.4 0.5
τ0 0.016 0.061 0.14 0.275 0.53
Rc\9.9852 9.9162 9.5299 9.3337 9.4863
Rb11.5351 11.4568 11.1437 10.4613 9.3034 8.7385
optimal ϕ1/23.9 4 4 4 4 4
Fu11.5351 11.4062 10.9902 10.2012 9.3147 9.3083
We investigate the relationship between the LED half-power
angle and the ratio of the maximum optical power over
the minimum optical power. We divide the cells into three
categories, corner cell, edge cell and center cell, referring to
the 4cells at the corner, the 12 cells on the edge but not at the
corner, and 9cells in the center areas, respectively, as shown
0 5 10
1/2(deg)
0
5
10
Rc or Rb(bit/m2)
=0.1
0 5 10
1/2(deg)
0
2
4
6
8
Rc or Rb(bit/m2)
=0.3
0 5 10
1/2(deg)
0
5
10
Rc or Rb(bit/m2)
=0.5
0 5 10
1/2(deg)
0
5
10
15
20
Rc or Rb(bit/m2)
=0.7
0 5 10
1/2(deg)
0
5
10
15
20
Rc or Rb(bit/m2)
=0.9
Rc
Rb
0
Fig. 11. Mean transmission rates Rcand Rbwith respect to LED half-power
angle ϕ1/2with r=0.1 for different time sharing τ.
in Figure 12. The results on log10 Uth for corner, edge and
center attocells are shown in the Figure 13. It can be seen that
the ratio of the corner attocell is the largest under the same
half-power angle ϕ1/2.
Fig. 12. The 25 LEDs optical transmitter cells.
Based on the half-power angle acquired by the above pro-
tocols, we can obtain Uth = 72 corresponding to ϕ1/2= 5.4
degree for protocol a, and Uth = 2303 corresponding to
ϕ1/2= 4.0degree for protocol b. We can set different levels of
Uth to explore the half-power angle, for example, ϕ1/2>5.2
degree for Uth <100,ϕ1/2>6.0degree for Uth <32.6,
and ϕ1/2>7.4degree for Uth <10. The corresponding half-
power angle range can be obtained via setting different Uth
thresholds, based on which we can optimize the transmission
rate Fuwith respect to Uth for protocol aand protocol b,
as shown in Figure 14. It can be seen that for higher Uth,
since the half-power angle can be lower, protocol bwill show
higher Fucompared with protocol a. Moreover, lower Uth
is required for more uniform illumination, while higher Uth
can be allowed under unmanned working environments, which
leads to higher Fu.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
10
2 4 6 8 10 12 14
1/2 (deg)
0
10
20
30
40
50
60
10*log10(Uth) (dB)
white LED, 10*log10(Uth) ~ 1/2
corner
edge
center
1/2= 4.0 deg
1/2= 5.4 deg
Uth= 100
Uth= 32.6
Uth= 10
Fig. 13. The indoor illumination uniformity Uth with respect to LED half-power angle ϕ1/2.
0 10 20 30 40 50 60
10*log10(Uth) (dB)
0
2
4
6
8
10
12
Fu (bit/m2)
white LED, Fu ~ 10*log10(Uth)
protocol a
protocol b
Fig. 14. The transmission rate Fuwith respect to Uth for protocol aand
protocol b.
VI. NU ME RI CA L RES ULTS F OR MU LTI -CO LOR LEDS
A. System Parameter Configuration
We denote the half-power angle of boundary region LED
as ϕ1/2, and the half-power angle of central region LEDs
is ϕ1/2− △ϕ1/2. The default system parameters of 3-color
multiple LEDs transmitter are the same as the single LED
transmitter system, as listed in Table I. There are totally 75
R/G/B LEDs installed on the ceiling at a height of 3.0m
from the floor, where each optical attocell of R/G/B LED
covers an unit area attocell. The white light illumination
constraint leads to different optical transmission power of
the R/G/B LED placed at the center. According to the fixed
white point (0.387,0.379) adopted in the chromaticity dia-
gram, the corresponding R/G/B LED transmission power is
PR= 0.3741W, PG= 1.0W, and PB= 0.4451W.
Due to the static central-boundary area division, we mainly
investigate the mean achievable transmission rate per unit area
Fuwith respect to the half-power angle of the boundary LED
ϕ1/2and the half-power angle difference △ϕ1/2. Again, we
utilize 200 realizations based on the binomial approximation
to provide a smooth result.
B. Numerical Simulation Results
We investigate half-power angle range under the condition
that the white light illumination requirement are satisfied.
Similar to white LED layout, we divide the 25 R/G/B LEDs
attocells into corner cells, edge cells and center cells, as shown
in Figure 15.
Fig. 15. The 25 R/G/B LEDs optical transmitter cells.
Take the corner attocell as an example. The transmis-
sion power of R/G/B LEDs corresponds to the white point
(0.387,0.379) on the chromaticity diagram. The half-power
angle difference △ϕ1/2is set to 0.2deg. The half-power angle
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
11
of the boundary LED ϕ1/2is set from 4.4deg to 5.2deg with
0.2deg step size. The chromaticity point offset of the receiver
is shown in Figure 16. It can be seen that given a constant
△ϕ1/2, larger ϕ1/2leads to lower offset from the chromaticity
point.
0 0.5
x
0
0.2
0.4
0.6
0.8
y
1/2=4.4 deg
0 0.5
x
0
0.2
0.4
0.6
0.8
y
1/2=4.6 deg
0 0.5
x
0
0.2
0.4
0.6
0.8
y
1/2=4.8 deg
0 0.5
x
0
0.2
0.4
0.6
0.8
y
1/2=5 deg
corner attocell, 1/2= 0.2 deg
0 0.5
x
0
0.2
0.4
0.6
0.8
y
1/2=5.2 deg
receiving users
chromaticity point
(0.387,0.379)
0.3 0.4
0.35
0.4
0.45
Fig. 16. The chromaticity point offset of the receiving users relative to the
point (0.387,0.379).
Considering 25 indoor R/G/B LEDs optical cells, the half-
power angle constraint results are obtained, as shown in
Table IV. It is required that the half-power angle range is
applicable to all 25 optical cells. Taking △ϕ1/2= 0.2deg
as an example, the minimum half-power angle of boundary
LED ϕ1/2min should be 4.5deg. Then, the half-power angle
of boundary LED for all cells is ϕ1/2∈[4.5, ϕ1/2max], for
certain maximum angle ϕ1/2max.
TABLE IV
THE MINIMUM HALF-POW ER AN GL E FOR 3D IFFE RE NT CL AS SES O PT ICA L
CE LLS .
△ϕ1/2(deg) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ϕ1/2(deg)
corner 3.6 4.5 5.1 5.5 5.9 6.2 6.5 6.8 7.1 7.3
edge 3.6 4.4 4.9 5.3 5.6 5.9 6.2 6.4 6.6 6.7
center 3.0 3.7 4.1 4.5 4.8 5.1 5.3 5.5 5.7 5.9
Based on the chromaticity point offset of the receiver
discussed above, we want to explore the trend of Fuwith
respect to half-power angle of the boundary LED ϕ1/2and
half-power angle difference △ϕ1/2considering the white light
illumination constraint in multi-color transmission system.
Figure 17 shows the mean achievable transmission rate per unit
area Fuwith respect to ϕ1/2and half-power angle difference
△ϕ1/2, under constraints ϕ1/2∈[ϕ1/2min, ϕ1/2max ]for
sufficiently high ϕ1/2max. It is seen that for △ϕ1/2= 0.1
deg, Fuhas a peak at ϕ1/2= 4.2deg. While under other
values of △ϕ1/2,Fuis monotonically decreasing with ϕ1/2,
due to white light requirement resulting in a tight range of half-
power angle, which is different with that of the single-color
transmission system. Actually, the results show that the white
light illumination is the primary constraint for parameters
optimization in multi-color system.
5 10
1/2
0
5
10
15
20
25
Fu (bit/m2)
1/2min= 4.5
1/2= 0.2
5 10 15
1/2
0
5
10
15
20
Fu (bit/m2)
1/2min= 5.1
1/2= 0.3
5 10 15
1/2
0
5
10
15
20
Fu (bit/m2)
1/2min= 5.5
1/2= 0.4
5 10 15
1/2
0
5
10
15
20
Fu (bit/m2)
1/2min= 5.9
1/2= 0.5
5 10
1/2
0
5
10
15
20
Fu (bit/m2)
1/2min= 6.2
1/2= 0.6
5 10
1/2
0
5
10
15
20
25
Fu (bit/m2)
1/2min= 3.6
1/2= 0.1
Fig. 17. The relationship between transmission rate Fuand the half-power
angle of the boundary LED ϕ1/2and the half-power angle difference △ϕ1/2.
Moreover, similar to single-color system, we explore the
illumination uniformity considering lighting color constraint.
The ratio of the maximum optical power over the minimum
one with respect to LED half-power angle ϕ1/2and difference
△ϕ1/2for the 3classes attocells is shown in Figure 18. Again,
the corner attocell shows the largest ratio from Figure 18 (a),
which obviously shows the 3D height difference of Uth with
respect to ϕ1/2and △ϕ1/2in different regions. Figure 18 (b)
more clearly illustrates the numerical depth of Uth. It can be
seen that such ratio is not sensitive to △ϕ1/2as ϕ1/2is con-
stant, and decreases monotonically with ϕ1/2, and this can be
seen more clearly from Figure 19 for corner attocell. Similar
to the single white LED system, the corresponding ϕ1/2and
△ϕ1/2can be obtained via setting different thresholds Uth,
based on which we can optimize the transmission rate Fuwith
respect to Uth for R/G/B LED transmitter system, as shown
in Figure 20.
Figure 20 shows the maximum mean rate Fuwith respect
to the maximum power ratio Uth, under different values of
∆ϕ1/2representing different levels of chromatic deviation.
It is seen that given the maximum power ratio Uth,Fu
is not sensitive to ∆ϕ1/2, which means that we can also
optimize ϕ1/2to increase Fuin multi-color LED system.
Higher Fuand lower Uth can be observed in the R/G/B LED
transmitter system compared to those in white LED system
in Figure 14, which reveals that we can choose a multi-
color system instead of a single-color system without harsh
constraints. Note that the black dot-dash line rectangle is the
area of interest for illumination, where Uth is lower with
better illumination uniformity. In the blue dotted rectangle
area, higher Uth corresponds to lower ϕ1/2, which implies
pencil beams and needs to be avoided for practical application.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
12
(a) The 3D height of Uth .
4.709
4.709
4.709
4.709
9.418
9.418
0 5 10
1/2 (deg)
0.5
1
1.5
2
2.5
3
1/2 (deg)
corner
3color LED, 10*log10(Uth) ~ 1/2 & 1/2
4.4629
4.4629
8.9258
8.9258
0 5 10
1/2 (deg)
0.5
1
1.5
2
2.5
3
1/2 (deg)
edge
6.226
6.226
6.226
12.4521
0 5 10
1/2 (deg)
0.5
1
1.5
2
2.5
3
1/2 (deg)
center
(b) The depth graph of Uth .
Fig. 18. Power ratio Uth with respect to LED half-power angle ϕ1/2and half-power angle difference △ϕ1/2.
2 4 6 8 10 12 14
1/2 (deg)
5
10
15
20
25
30
35
40
45
10*log10(Uth) (dB)
3color LED, 10*log10(Uth) ~ 1/2 & 1/2
1/2=0.1 deg
1/2=0.4 deg
1/2=0.7 deg
1/2=1.0 deg
1/2=1.3 deg
1/2=1.6 deg
1/2=1.9 deg
1/2=2.2 deg
1/2=2.5 deg
1/2=2.8 deg
Fig. 19. Power ratio Uth with respect to LED half-power angle ϕ1/2for the corner attocell.
Moreover, Table V lists the minimum ϕ1/2under different
values of △ϕ1/2for Uth = 10. Again, the minimum ϕ1/2is
not sensitive to △ϕ1/2, while ϕ1/2is the primary factor.
TABLE V
THE M INI MU M HAL F-P OWER A NG LE FO R CO RNE R ATTO CEL L WI TH
Uth ≤10 FO R DI FFER ENT △ϕ1/2.
△ϕ1/2(deg) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
ϕ1/2(deg) — 3.6 4.5 5.1 5.5 5.9 6.2 6.5 6.8 7.1 7.3
Uth ≤10 7.4 7.5 7.5 7.7 7.7 7.8 7.7 7.8 7.9 7.9
VII. CO NC LU SI ON
We have considered an indoor downlink VLC network with
dense attocell layout and BPP distributed users for single LED
transmitter system and multi-color LEDs transmitter system.
We have divided each attocell into central region and boundary
region, and proposed the transmission protocols for single-
color and multi-color transmitters based on the attocell divi-
sion. We have proposed protocols to optimize the LED half-
power angle to maximize the mean achievable transmission
rate per unit area, and investigated the rates of cell-center and
cell-boundary users. For the single LED transmitter system,
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
13
5 10 15 20 25 30 35 40 45
10*log10(Uth) (dB)
0
5
10
15
20
25
Fu (bit/m2)
3color LED, Fu ~ 10*log10(Uth)
1/2=0.1 deg
1/2=0.4 deg
1/2=0.7 deg
1/2=1.0 deg
1/2=1.3 deg
1/2=1.6 deg
1/2=1.9 deg
1/2=2.2 deg
1/2=2.5 deg
1/2=2.8 deg
5 10 15
4
6
8
10
Fig. 20. Transmission rate Fuwith respect to Uth for R/G/B LED transmitter system.
it is observed that the mean achievable transmission rate first
increases and then decreases with the LED half-power angle.
For the multi-color LEDs transmitter system, it is observed
that the mean achievable transmission rate decreases with the
LED half-power angle monotonically due to strong white light
constraint except for extremely small △ϕ1/2= 0.1deg. It
is seen that via the cell center and boundary division, larger
overall rate can be achieved compared with that without cell
division.
REF ER EN CE S
[1] K. Wang, Z. Yuan, E. Wong, K. Alameh, H. Li, K. Sithamparanathan,
and E. Skafidas, “Experimental demonstration of indoor infrared optical
wireless communications with a silicon photonic integrated circuit,”
IEEE Journal of Lightwave Technology, vol. 37, no. 2, pp. 619–626,
Feb. 2018.
[2] H. Alshaer and H. Haas, “Bidirectional lifi attocell access point slicing
scheme,” IEEE Transactions on Network and Service Management,
vol. 15, no. 3, pp. 909–922, May 2018.
[3] Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and
state-of-the-art,” IEEE Communications Magazine, vol. 46, no. 5, p-
p. 67–73, May 2008.
[4] H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communi-
cation: potential and state-of-the-art,” IEEE Communications Magazine,
vol. 49, no. 9, pp. 56–62, Sept. 2011.
[5] A. Jovicic, J. Li, and T. Richardson, “Visible light communication:
opportunities, challenges and the path to market,” IEEE Communications
Magazine, vol. 51, no. 12, pp. 26–32, Dec. 2013.
[6] L. Grobe, A. Paraskevopoulos, J. Hilt, D. Schulz, F. Lassak, F. Hartlieb,
C. Kottke, V. Jungnickel, and K.-D. Langer, “High-speed visible light
communication systems,” IEEE Communications Magazine, vol. 51,
no. 12, pp. 60–66, Dec. 2013.
[7] Q. Wang, Z. Wang, and L. Dai, “Asymmetrical hybrid optical OFDM
for visible light communications with dimming control,” IEEE Photonics
Technology Letters, vol. 27, no. 9, pp. 974–977, Sept. 2015.
[8] Q. Wang, Z. Wang, L. Dai, and J. Quan, “Dimmable visible light com-
munications based on multilayer aco-ofdm,” IEEE Photonics Journal,
vol. 8, no. 3, pp. 1–11, Aug. 2016.
[9] Q. Wang, C. Qian, X. Guo, Z. Wang, D. G. Cunningham, and I. H.
White, “Layered ACO-OFDM for intensity-modulated direct-detection
optical wireless transmission,” Optics Express, vol. 23, no. 9, pp. 12382–
12393, 2015.
[10] L. Yin and H. Haas, “A tractable approach to joint transmission in
multiuser visible light communication networks,” IEEE Transactions on
Mobile Computing, Oct. 2018.
[11] L. Yin and H. Haas, “Coverage analysis of multiuser visible light com-
munication networks,” IEEE Transactions on Wireless Communications,
vol. 17, no. 3, pp. 1630–1643, Mar. 2018.
[12] J. Deng, X. Jin, X. Ma, M. Jin, C. Gong, and Z. Xu, “Graph-based
scheduling for cooperative transmission in indoor VLC systems,” in
2019 IEEE International Conference on Communications Workshops
(ICC Workshops), pp. 1–6, IEEE, 2019.
[13] P. W. Berenguer, D. Schulz, J. Hilt, P. Hellwig, G. Kleinpeter, J. K.
Fischer, and V. Jungnickel, “Optical wireless MIMO experiments in an
industrial environment,” IEEE Journal on Selected Areas in Communi-
cations, vol. 36, no. 1, pp. 185–193, Jan. 2018.
[14] M. Zeng, K. Zhou, C. Gong, S. Lou, X. Jin, and Z. Xu, “Design and
demonstration of an indoor visible light communication network with
dynamic user access and resource allocation,” in 2017 9th International
Conference on Wireless Communications and Signal Processing (WC-
SP), pp. 1–6, Oct 2017.
[15] X. Tan, H. Zhang, and J. Hu, “Achievable transmission rate of the
secondary user in cognitive radio networks with hybrid spectrum access
strategy,” IEEE Communications Letters, vol. 17, no. 11, pp. 2088–2091,
Sept. 2013.
[16] G. Zheng, C. Gong, and Z. Xu, “Constrained partial group decoding with
max-min fairness for multi-color multi-user visible light communica-
tion,” IEEE Transactions on Communications, vol. 67, no. 12, pp. 8573–
8584, Dec. 2019.
[17] K. Saxena, R. Raj, and A. Dixit, “A novel optimization approach for
transmitter semi-angle and multiple transmitter configurations in indoor
visible light communication links,” in 2018 9th International Conference
on Computing, Communication and Networking Technologies (ICCCN-
T), pp. 1–7, IEEE, 2018.
[18] G. Cossu, A. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “3.4
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/OJCOMS.2020.3005421, IEEE Open
Journal of the Communications Society
14
gbit/s visible optical wireless transmission based on RGB LED,” Optics
Express, vol. 20, no. 26, pp. B501–B506, 2012.
[19] K. Cui, J. Quan, and Z. Xu, “Performance of indoor optical femtocell by
visible light communication,” Optics Communications, vol. 298, pp. 59–
66, 2013.
[20] P. Ge, X. Liang, J. Wang, C. Zhao, X. Gao, and Z. Ding, “Optical filter
designs for multi-color visible light communication,” IEEE Transactions
on Communications, vol. 67, no. 3, pp. 2173–2187, Mar. 2018.
[21] Y. Xiao and Y.-J. Zhu, “Chromaticity-adaptive generalized spatial modu-
lation for MIMO VLC with multi-color LEDs,” IEEE Photonics Journal,
vol. 11, no. 4, pp. 1–12, Aug. 2019.
[22] F. R. Gfeller and U. Bapst, “Wireless in-house data communication via
diffuse infrared radiation,” Proceedings of the IEEE, vol. 67, no. 11,
pp. 1474–1486, Nov. 1979.
[23] J. M. Kahn and J. R. Barry, “Wireless infrared communications,”
Proceedings of the IEEE, vol. 85, no. 2, pp. 265–298, Feb. 1997.
[24] T. Komine and M. Nakagawa, “Fundamental analysis for visible-light
communication system using LED lights,” IEEE Transactions on Con-
sumer Electronics, vol. 50, no. 1, pp. 100–107, Jun. 2004.
[25] S. D. Personick, “Receiver design for digital fiber optic communication
systems, i,” Bell System Technical Journal, vol. 52, no. 6, pp. 843–874,
1973.
[26] R. Smith and S. Personick, “Receiver design for optical fiber communi-
cation systems,” in Semiconductor Devices for Optical Communication,
pp. 89–160, Springer, 1980.
[27] K. Zhou, C. Gong, and Z. Xu, “Color planning and intercell interference
coordination for multicolor visible light communication networks,” IEEE
Journal of Lightwave Technology, vol. 35, no. 22, pp. 4980–4993, Nov.
2017.
[28] D. A. Basnayaka and H. Haas, “Hybrid RF and VLC systems: Improving
user data rate performance of VLC systems,” in 2015 IEEE 81st
Vehicular Technology Conference (VTC Spring), pp. 1–5, 2015.
[29] H. Tabassum and E. Hossain, “Coverage and rate analysis for co-existing
RF/VLC downlink cellular networks,” IEEE Transactions on Wireless
Communications, vol. 17, no. 4, pp. 2588–2601, Feb. 2018.
[30] I. Stefan, H. Burchardt, and H. Haas, “Area spectral efficiency perfor-
mance comparison between VLC and RF femtocell networks,” in 2013
IEEE international conference on communications (ICC), pp. 3825–
3829, IEEE, 2013.
[31] C. Gong, S. Li, Q. Gao, and Z. Xu, “Power and rate optimization
for visible light communication system with lighting constraints,” IEEE
Transactions on Signal Processing, vol. 63, no. 16, pp. 4245–4256, Aug.
2015.
[32] P. M. Butala, J. C. Chau, and T. D. Little, “Metameric modulation for
diffuse visible light communications with constant ambient lighting,”
in 2012 International Workshop on Optical Wireless Communications
(IWOW), pp. 1–3, IEEE, 2012.
[33] D. L. MacAdam, “Visual sensitivities to color differences in daylight,”
Journal of the Optical Society of America, vol. 32, no. 5, pp. 247–274,
1942.
[34] A. P. Tang, J. M. Kahn, and K.-P. Ho, “Wireless infrared commu-
nication links using multi-beam transmitters and imaging receivers,”
in Proceedings of ICC/SUPERCOMM’96-International Conference on
Communications, vol. 1, pp. 180–186, IEEE, 1996.
