# Channel Modelling and Error Performance Investigation for Reading Lights
Based In-flight LiFi

Anil Yesilkaya, and Harald Haas Manuscript received July xx, 2021; revised
December xx, 2021.Authors are with LiFi Research and Development Center
(LRDC), Department of Electronic and Electrical Engineering, University of
Strathclyde, Glasgow G1 1RD, UK. This research has been supported in part by
Zodiac Inflight Innovations (TriaGnoSys GmbH), EPSRC under Established Career
Fellowship Grant EP/R007101/1, Wolfson Foundation and European Commission’s
Horizon 2020 research and innovation program under grant agreement 871428,
5G-CLARITY project.

###### Abstract

The new generation of communication technologies are constantly being pushed
to meet a diverse range of user requirements such as high data rate, low power
consumption, very low latency, very high reliability and broad availability.
To address all these demands, fifth generation (5G) radio access technologies
have been extended into a wide range of new services. However, there are still
only a limited number of applications for radio frequency (RF) based wireless
communications inside aircraft cabins that comply with the 5G vision.
Potential interference and safety issues in on-board wireless communications
pose significant deployment challenges. By transforming each reading light
into an optical wireless access point (AP), light-fidelity (LiFi), could
provide seamless on-board connectivity in dense cabin environments without RF
interference. Furthermore, the utilization of available reading lights allows
for a relatively simple, cost-effective deployment with the high energy and
spectral efficiency. To successfully implement the aeronautical cabin LiFi
applications, comprehensive optical channel characterization is required. In
this paper, we propose a novel Monte Carlo ray-tracing (MCRT) channel
modelling technique to capture the details of in-flight LiFi links.
Accordingly, a realistic channel simulator, which takes the cabin models,
interior elements and measurement based optical source, receiver, surface
material characteristics into account is developed. The effect of the
operation wavelength, cabin model accuracy and user terminal mobility on the
optical channel conditions is also investigated. As a final step, the on-board
direct-current biased optical orthogonal frequency division multiplexing (DCO-
OFDM) performance is evaluated by using obtained in-flight LiFi channels.
Numerical results show that the location of a mobile terminal and accurate
aircraft cabin modelling yield as much as $12$ and $2$ dB performance
difference, respectively.

###### Index Terms:

In-flight communications (IFC), LiFi, Monte-Carlo Ray Tracing (MCRT), channel
modelling, DC-biased optical OFDM (DCO-OFDM), bit-error-ratio (BER)

††publicationid: pubid: © 2022 IEEE. Digital Object Identifier
10.1109/TVT.2022.3148796

##  I Introduction

The rapid paradigm shift from the voice oriented circuit-switched domain to
the data centric packet-switched network has emerged as a major driver of
innovation in wireless communication technologies. The user demand for high
speed video streaming and online gaming services, augmented reality
(AR)/virtual reality (VR) applications, wearable devices and internet-of-
things (IoT) create a data greedy ecosystem. Recent forecasts by Cisco showed
that monthly data traffic will reach more than $77$ exabytes by 2022, with
$93\%$ of this emerging due to smart phones and tablets [1]. However,
industrial automation, autonomous cars, remote controlling and tactile
internet require strict reliability and low latency features instead of high
data rates. Furthermore, machine type communications (MTC), which is based on
sensor networks, requires low data rate, power consumption and high user
density to build smart entities. In order to cope with these diverse and ever
increasing demands, services in fifth generation (5G) new radio (NR) networks
are categorized into three main categories; enhanced mobile broadband (eMBB),
ultra-reliable and low-latency communications (uRLLC) and massive MTC (mMTC).

As a natural extension of the digital revolution and 5G NR targets, aircraft
infotainment and broadband internet access became one of the most important
revenue sources for the airline industry. Accordingly, the market potential
forecasts show that the revenue for in-flight broadband enabled passenger
services for the years 2028 and 2035 are expected to be more than 36 and 63
billion US dollars, respectively [2]. Although the majority of airline
companies are already providing various on-board connectivity solutions,
passengers are still obligated to keep their cellular connections off during
flight. Nonetheless, the responses taken from passenger surveys show that
$92\%$ of passengers are interested in using their own devices for on-board
infotainment [3]. Extreme user density, approximately
$3.03~{}\text{passengers}/\text{m}^{2}$ for a narrow-body aircraft, and
potential interference issues in small confined areas such as aircraft cabins,
pose significant challenges. Specifically, safety concerns and related
regulations in the aviation industry prevents the wide adoption of on-board
radio frequency (RF) cellular networks.

One of the key enablers of 5G NR to meet the user demand is the utilization of
the higher frequency portion (e.g. Sub-6 and millimetre wave) of the spectrum
along with the existing bands to provide additional capacity. To comply with
5G NR innovations, light-fidelity (LiFi), which is a bi-directional and
seamless optical wireless broadband networking solution, could overcome the
challenges mentioned above. The non-interfering nature of the light with RF
and the unregulated spectrum, which is 2600 times larger than the entire RF
band [4, 5], are the main advantages of LiFi to realize small cells and high
frequency reuse. Moreover, the deployment, energy, cost efficiency and
enhanced security aspects of LiFi could also be harvested via the utilization
of the pre-existing in-built reading lights in the cabin as broadband in-
flight wireless access points (APs). To achieve mentioned goals, accurate
channel modelling plays an important role in designing highly efficient LiFi
networks. Unlike RF channels with slow, fast fading and shadowing effects,
indoor LiFi applications have relatively more deterministic channel
characteristics due to the intrinsic nature of intensity-modulation and
direct-detection (IM/DD) transmission [6]. However, due to the high geometric
and spectral dependency of the on-board optical channels, each specific
application requires it’s own modelling procedure. Furthermore, both the
analytical line-of-sight (LoS) and recursive channel modelling approaches in
the literature do not always yield accurate results, as some of the optical
characteristics are omitted for calculation simplicity. To capture details of
the in-flight optical wireless communications (IFOWC) channels and provide
deeper time and frequency-domain analyses, a comprehensive in-flight channel
modelling approach is proposed in this paper. Accordingly, both infra-red (IR)
and visible light (VL) spectrum channels are characterized by using realistic
source, receiver, cabin, seating and coating material models within a Monte
Carlo ray-tracing (MCRT) simulation environment.

The contributions of this work can be summarised as follows:

  * •

A novel optical channel modelling toolkit for broadband in-flight LiFi is
proposed. Accordingly, realistic geometry of the aircraft cabin and the
auxiliary parts; seats and overhead luggage compartment are designed first.
Then, geometrical, spatial, angular and spectral profiles of the front-end
optics and surface materials are modelled and inputted into the toolkit. The
MCRT based simulations are conducted both in the IR and VL bands for the
realistic and simplified aircraft cabin structures and for various user
equipment (UE) locations.

  * •

The time dispersive in-flight LiFi channels are characterized by calculating
the channel impulse response (CIR), channel frequency response (CFR), direct-
current (DC) gain, mean delay, root-mean-squared (RMS) delay spread and
flatness factor parameters. Moreover, the bandwidth properties of the channels
are also devised by frequency domain analyses of the MCRT based channel data.

  * •

Lastly, a practical on-board LiFi system performance under both the multipath
optical channel and non-linear transmit light emitting diode (LED) clipping
effects are presented. The analytical bit error ratio (BER) expression for DC
biased optical orthogonal frequency division multiplexing (DCO-OFDM) under the
mentioned channel impairments are obtained and compared with the computer
simulation results. The importance of the accuracy of the aircraft cabin
modelling, transmission wavelength and the location of the UE on a practical
system performance are also investigated.

The reminder of the paper is organized as follows. In Section II, a
comprehensive IFOWC channel modelling literature review is provided. In
Section III, the details of the proposed MCRT based LiFi channel modelling
environment is presented. In Section IV, the mathematical background of the
channel simulations and characterization along with the time and frequency
domain analyses are provided and discussed. In Section V, the analytical
expression and computer simulations based BER performance curves of DCO-OFDM
obtained under the frequency selectivity and non-linear LED clipping noise are
also presented. Finally, the conclusions are drawn in Section VI.

_Notation_ : Throughout the paper, vectors are in bold lowercase letters. The
$x$, $y$ and $z$ axes elements of the vector
$\mathbf{a}=[a_{x},~{}a_{y},~{}~{}a_{z}]$ are given by $a_{x}$, $a_{y}$ and
$a_{z}$, respectively. The Dirac delta, inverse tangent and limit functions
are expressed by $\delta(\cdot)$, $\arctan(\cdot)$ and $\lim\\{\cdot\\}$,
respectively. The magnitude of a complex number $z$, logarithm of a number to
base $b$, statistical expectation, circular convolution, element-wise
multiplication and ceiling operations are also denoted by $\lvert z\rvert$,
$\log_{b}\left(\cdot\right)$, $\text{E}\\{\cdot\\}$, $\circledast$, $\circ$
and $\lceil\cdot\rceil$, respectively. The real-valued normal distribution
with mean, $\mu$, and variance, $\sigma^{2}$, is given by
$\mathcal{N}(\mu,\sigma^{2})$. The Q-function is defined by
$Q(x)=\frac{1}{\sqrt{2\pi}}\int_{x}^{\infty}e^{-u^{2}/2}\text{d}u$.

##  II Multi-bounce IFOWC Channel Modelling Literature

In this section, a literature review for multi-bounce IFOWC channel modelling
techniques, which includes LoS and non-LoS (NLoS) components, will be
presented. The path loss (PL) and RMS delay spread characteristics of the
multi-bounce optical channel for ceiling (wash) light-based IR links is
investigated in [7]. Accordingly, the MCRT analysis inside a simplified Boeing
777 cabin model is presented. Similarly, in [8], an IFOWC system with IR-laser
diode (LD) based ceiling lights is considered where the data is envisaged to
be delivered to seat backs within a cellular deployment, which covers 5 seats.
Moreover, multipath CIR is obtained by MCRT for a simplified cabin model and
results are validated by mock-up cabin measurements. Another ceiling light
based channel characterization for the IR band IFOWC is proposed in [9] and
[10]. Accordingly, the multi-bounce MCRT channel model for a simplified cabin
model is utilized to estimate the parameters of PL and shadowing. Moreover,
the cell edge and centre signal-to-interference-ratio (SIR) maps are also
obtained. Note that the omni-directional transmitter (TX)-receiver (RX) pair
is designed in [9, 10] to show that the RF PL model (Friis’ formula) with
shadowing (slow fading) effects can also be modelled in incoherent optical
wireless communications (OWC). Furthermore, the effect of frequency reuse (FR)
schemes on the SIR distribution is also investigated in [10]. The ceiling
mounted passive retro-reflector based communication between passenger service
units (PSUs) via IR directed links is proposed in [11]. However, only a single
bounce, $\kappa\in\\{0,1\\}$, CIR with a simplified cabin model is calculated
by using the method in [12]. Note that the parameter $\kappa$ will be used to
refer the light rays after the $\kappa^{\text{th}}$ order reflections, where
$0\leq\kappa\leq\kappa_{\text{max}}$. The parameter $\kappa_{\text{max}}$ is
the maximum number of reflections considered within the system. Furthermore,
$0^{\text{th}}$ bounce corresponds to the LoS component of the channel. In
[13], an MCRT based IFOWC channel modelling technique, which is able to
encounter up to $10$-bounces, is used to obtain SIR and signal-to-noise-ratio
(SNR) maps. Accordingly, VL and IR band sources in uplink (UL) and downlink
(DL) directions, respectively, are employed. However, a very primitive cabin
and aircraft interior model is presented in [13], where the details of the
optical channels are also neglected. In the same work, a hardware
implementation of the IFOWC network and user side adapter prototypes are also
presented. Another ray tracing based VL band IFOWC CIR modelling method for a
realistic Boeing 737-900 cabin and seating scenario is given by [14]. In the
paper, both the BER spatial distributions and respective outage probability
values are also obtained. The signal-to-interference-plus-noise-ratio (SINR)
maps for a simplified Boeing 737 cabin and seat models is presented for both
phosphorescence and red-green-blue based white LEDs in [15]. The modified MCRT
method is used in order to trace a million rays up to $5$-bounce while
Lambertian and Phong radiation patterns are assumed for the LEDs. Similarly,
in [16], $5$-bounce, $0\leq\kappa\leq 5$, ray tracing simulations for a
simplified Boeing 727 cabin model and seating is obtained to simulate UL IR
band IFOWC. The effect of passenger movements on the channel and system
performance is also investigated, where it has been reported that $10$ Mbit/s
can be supported by UL IFOWC. A modified MCRT method to obtain VL band reading
light based DL IFOWC CIR is presented with a realistic Boeing 737 cabin model
and seating in [17]. Specifically, various sources with different beam angles
and solar radiation coming from the windows are taken into consideration in
the SINR calculations. The same approach to obtain the CIR is also adopted for
a simplified Airbus A320-200 cabin and seat models in [18]. The investigation
of an IR band IFOWC inside the cockpit, which aims to provide bidirectional
connectivity between the ceiling unit and the pilot headset, is given by [19].
Moreover, a Lambertian bidirectional reflectance distribution function, source
semi-angles, realistic pilot body models and the effect of users head movement
are investigated in [19]. The same approach is enhanced in [20] to capture the
effect that both body and head movements have on the IR band CIR.

##  III In-flight LiFi Channel Modelling Methodology

The signal propagation in the IR and VL spectrum is highly dependent on
geometry and the surface structure of the considered environment/scenario due
to the weak penetration characteristics of electromagnetic (EM) waves. Thus,
it is very important to ensure that geometry and optical characteristics of
both the interior and exterior elements of an aeronautical cabin environment
are captured accurately as possible for comprehensive channel modelling.
However, it is emphasized by the previous section that the existing channel
modelling approaches are unable to provide realistic TX, RX, cabin
geometry/interior, coating material and reflection/refraction characteristics
as a whole. Furthermore, deeper analyses on important channel parameters;
frequency response, coherence time/bandwidth, flatness and mobility effects
are also omitted. Therefore, in this section, we propose a non-sequential ray
tracing (NSRT) based in-flight LiFi channel modelling approach, which is able
to encompass a complete set of TX, RX and environment parameters. Accordingly,
the shortcomings of the MCRT based CIR modelling technique, which is given in
[21, 22, 23, 24], are resolved by the proposed method. Hence, a complete
optical channel modelling capability in realistic aircraft environments are
supported in the proposed technique by including the RX spectral, angular and
spatial characterization.

The proposed MCRT simulations are performed with the aid of optical design
software tool, Zemax OpticStudio version 20.2 [25]. The benefit of using a
commercial solution is the generation of reproducible, replicable and
repeatable results, as the packages and libraries are standard and independent
of application. The adopted software is able to perform both sequential ray
tracing (SRT) or NSRT depending on the application. In NSRT, the generated
rays hit the surfaces merely based on the physical positions and the optical
properties of the objects by considering the direction of the rays. Whereas,
in SRT, the rays are obliged to propagate in a predefined sequence of surfaces
or objects, which is very important in imaging optics. Since the primary
purpose of LiFi systems is not only communication, but also illumination
(mostly diffuse) via reading and wash lighting, the NSRT method is adopted in
this research. For our simulations, the realistic aircraft cabin environment
is created by the generation of computer-aided-design (CAD) models. Then, the
measurement based source and material characteristics are imported into the
simulation environment. To obtain the CIRs, a ray database (RDB) file needs to
be generated via NSRT, which contains the extensive optical and geometrical
information for every single ray traced. Lastly, powerful data processing
tools are employed to extract and analyse properties of the optical channel.
The block diagram of the proposed MCRT based channel modelling methodology is
depicted in Fig. 1.

Figure 1: Block diagram for proposed MCRT based optical channel modelling
method.

###  III-A Generation of the Aircraft Cabin Environment

(a)

(b)

Figure 2: Isometric view of the realistic (left) and simplified (right) CAD
cabin models (units are in cm). The yellow point represents the local origin
of the adopted cabin models. Figure 3: The geometrical details of the
realistic (black) and simplified (red) narrow-body cabin models (units are in
cm). Figure 4: Top view of the seating layout (units are in cm).

To model the aeronautical cabin environment accurately, the global positions
and orientations for the cabin and interior objects must be defined first. For
the sake of clarity, the geometric parameters of the objects will be given in
vector notation, which is defined with respect to (w.r.t.) the global
coordinate system. The origin of the global coordinate system is defined as
the vector $O(0,~{}0,~{}0)$. The position orientation of each object within
the simulation environment is defined by $3\times 1$ location and orientation
vectors $\mathbf{v}=(v_{x},~{}v_{y},~{}v_{z})$ and
$\mathbf{o}=(o_{x},~{}o_{y},~{}o_{z})$, where the $x$, $y$ and $z$ axes
coordinates and rotation with respect to the $x$, $y$ and $z$ axes are given
by $v_{x}$, $v_{y}$, $v_{z}$ and $o_{x}$, $o_{y}$, $o_{z}$, respectively. As
can be inferred from previous section, the majority of works in the literature
assumed a simplified aircraft cabin, where the curvatures and fine details of
the geometry are approximated as flat surfaces. In our work, two types of
cabin structures, namely realistic and simplified models, will be considered
to investigate the effect of geometrical simplification on the accuracy of the
channel parameters. Accordingly, a narrow-body type Airbus A320 is adopted as
the main cabin structure for our realistic ray-tracing simulations. Technical
details of the narrow-body A320 fuselage were obtained from [26] and the three
dimensional model is regenerated using CAD software. Then, the complex faces
of the CAD object are replaced with flat surfaces to obtain a simplified cabin
model similar to [9] and [10]. The technical drawings and dimensions of both
cabin models are depicted for isometric and cross-sectional views in Figs. 2
and 3, respectively. As shown in Fig. 2, the cabin structure is symmetric
along the $+z$-axis, where only a section of the whole cabin is sufficient to
generalize the obtained results. Thus, a portion of the cabin fuselage with
the length of $7.6$ m will be employed in this research. Furthermore, only the
reading lights based power contributions are considered in our optical
channels, where the window shades are designed to be closed in our three
dimensional cabin models. However, the variable ambient noise effect will be
considered as an electrical domain shot noise at the RX in our practical error
performance simulations.

(a)

(b)

Figure 5: Side (left) and front (right) views of the (a) real/measured (b)
recreated seats (units are in cm). The local origin of the generated seat
model is given by the yellow point.

####  III-A1 The Cabin Interior

The majority of commercial airliners utilize narrow-beam reading lights on-
board [27]. Thus, the coverage of a reading light would not be wider than a
single row of seats, where both the seats and passengers will serve as a
natural barrier between the seat rows. Due to the symmetric structure of the
cabin environment, the left hand-side, $+x$ direction, of a 6-abreast, 3-3
formation, seating will be considered to create the generalized model.
Moreover, the reflection contributions from the neighbouring rows are also
evaluated by taking both front and back triple seats into account. For the
sake of simplicity, the rows and seats will be labelled as 29, 30, 31 and A,
B, C, respectively. Details of the seating structure and dimensions are given
in Fig. 4.

The seat pitch is another important parameter for cabin design, which is
defined as the distance between any arbitrary point on one seat and the exact
same point in the seats directly in front or behind it. To maximize the number
of passengers on-board, aircraft companies tend to minimize the seat pitch,
which can be as low as $28$ inches. However, it has been reported in [28] that
passenger well-being and comfort is strongly correlated to how far back the
seat can recline. Furthermore, any seat pitch enlargements after $32$ inches
are also reported not to have a significant affect on the passenger comfort,
where the practical values lie between $30$ and $34$ inches for the economy
class. Hence, the seat pitch is chosen to be $81$ cm ($\approx 32$ inches) in
our simulation environment, which falls within the standard economy class
range.

####  III-A2 Passenger Seating

The design of the seats is another important issue for passenger comfort,
especially in medium and long-haul flights. The passenger seat dimensions, and
further details on the seating layout, are obtained via measurements on Weber
Aircraft LLC, more recently known as Safran Passenger Innovations, aircraft
seating. Then, the geometrically simplified CAD models are generated and
implemented in the simulation environment. The photos of the actual seating
and the technical drawings of the CAD software generated seat models are
depicted in Figs. 5(a) and 5(b), respectively. Note that the local origin of
the obtained seat model is depicted by the yellow point in Fig. 5(b).

###  III-B Sources, Receivers and Coating Materials

Figure 6: Typical directional reading light structure where the base is an
array of OSRAM GW QSSPA1.EM high power LED chips. Figure 7: The technical
drawings of the VL band OSRAM GW QSSPA1.EM (left) and IR band OSRAM SFH 4253
(right) LED chips used in the reading light design (units are in mm).

The implementation of in-flight connectivity (IFC) and/or in-flight
entertainment (IFE) systems, which require the airframe or cabin interior to
be redesigned, could introduce significant costs to the current global airline
industry. On the contrary, in-flight LiFi offers the great advantage of using
the existing cabin lighting structure, while only requiring very minor
modifications. Accordingly, the practical implementation of on-board LiFi
mainly includes the utilization of two types of sources; reading and wash
lights. The reading lights could be utilized to provide broadband data to the
seats via either the PSUs or directly to the passenger’s portable electronic
devices (PEDs). Similarly, the wash lights could serve for low/mid data rate
applications such as sensory, IoT, device-to-device (D2D) communications
infrastructure etc. as well as on-board payment systems. Note that cabin
illumination must be dimmed in the critical phases of flight, namely take-off
and landing, for safety purposes. For overnight flights, dimming, or even
turning the cabin lights off completely, should be considered for passenger
comfort. More importantly, the $800-1000$ nm band is reported to be the most
suitable PHY layer common mode signal region for the LiFi applications by
“IEEE 802.11bb Standardization Task Group on Light Communications”. In
addition, the VL band spectra is remained as an optional PHY mode in IEEE
802.11bb standardization process [29]. Therefore, in this research, both the
VL and IR bands will be used interchangeably in the DL direction to comply
with the Federal Aviation Administration (FAA) dimming regulations as well as
IEEE 802.11bb Light Communications standards. It is also important to note
that the IR band is almost always preferential for the uplink transmission for
the purpose of maintaining passenger eye safety and comfort. In the following,
a realistic reading light design and associated surface material
characterization will be detailed to address the raised safety and
communication regulations.

(a) OSRAM GW QSSPA1.EM

(b) OSRAM SFH 4253

Figure 8: Source directivity plots of the VL (left) and IR (right) band LED
chips for the azimuthal angles $[0~{}45~{}90~{}135]$.

####  III-B1 Reading Lights

In the aircraft interior lighting market, there are two main reading light
structures based on their beam profile; highly directional and dispersed [27].
Generally, to provide the best conditions for reading, highly directional
lights, consisting of an LED array as a base, a concave mirror and a lens,
which could be Fresnel or bi/double-convex, are preferred. Hence, effectively
a collimated beam is created as depicted in Fig. 6, which is directed towards
the vicinity of the tray table. On the other hand, dispersed light sources
contain only the LED array base to achieve a wider spread for illumination
purposes [30]. As mentioned in the previous chapter, the contribution of the
NLoS paths are strictly required to design a robust communication system.
Therefore, in this research, the optoelectronic characteristics of the
dispersed reading lights will be investigated as potential sources for in-
flight LiFi applications.

The non-imaging optical transmit front-end structure is adopted in our study
to model the reading lights, each of which will serve as a LiFi AP in the
given system design. Accordingly, a $4\times 4$ LED chip array is designed to
form the base of the reading lights in the simulation environment which is
given in Fig. 6. The origin point of the reading light element is chosen as
the centre point of the LED. For simplicity in the optical calculations, each
LED chip unit is assumed to be outputting $1$ W optical power that yields $16$
W power per reading light. In the designed array, off-the-shelf OSRAM GW
QSSPA1.EM High Power White LED [31] and OSRAM SFH 4253 High Power IR LED [32]
chip specifications are used to model the realistic VL and IR band emitters,
respectively. The separation between each LED chip within the array is chosen
as $4$ mm, refer to Fig. 6, for both sources based on their surface-mounted
device (SMD) packagings. The technical drawings and the detailed dimensions of
the SMD epoxy packaging for both sources are depicted in Fig. 7.

(a) OSRAM GW QSSPA1.EM

(b) OSRAM SFH 4253

Figure 9: Relative radiometric colour spectrum of; (a) VL
$[0.382~{}0.780]~{}\mu\text{m}$ and (b) IR $[0.770~{}0.920]~{}\mu\text{m}$
band LED chips used in the MCRT simulations.

To create an accurate model of the non-imaging light structure; (i) spatial,
(ii) angular and (iii) spectral characterization and respective parameters are
needed. The realistic spatio-angular characteristics of the sources are
ensured by the manufacturer provided ray files which have been inputted into
the simulation environment. The ray files contain a large number of emitted
ray recordings, up to 5 million, to project source characteristics without
requiring complex internal parameters. The emission patterns of the chosen
sources are given by the source directivity plots provided in Fig. 8.
Accordingly, the angle axis shows the polar angle for a source located in the
$+z$ direction and the colours represent different azimuthal angle scans,
$0^{\circ}$, $45^{\circ}$, $90^{\circ}$ and $135^{\circ}$, for the spherical
coordinate system. As can be seen from the figure, both sources have a
Lambertian-like emission pattern with strong axial symmetry, which corresponds
to full width at half maximum (FWHM) of $120^{\circ}$, in other words, half
power semi angle of $\Phi_{\text{h}}=60^{\circ}$. However, note that the ideal
diffuse (Lambertian) emitter model assumes a point source, whereas our
realistic modelling contains spatial information about the source emitting
profiles.

As our channel modelling technique operates in the granularity level of a
“light ray”, non-monochromatic sources must be broken into discrete
wavelengths to encounter refraction, reflection, diffraction and absorption
effects. The radiometric spectral characteristics of the sources could be
defined in the simulation environment by spectrum (SPCD) files. Accordingly,
the SPCD file format in OpticStudio contains the relative spectral
distribution coefficients with their corresponding wavelengths. The values in
the spectral file will be used to determine the relative frequency of the rays
with the associated spectra. Hence, a higher relative weight will increase the
likelihood that the emergence of a ray with a given wavelength in MCRT. Since
each ray carries a fraction of the total power of the source in MCRT, the
higher weight would result in a larger optical power in the given wavelength,
which is also the case in real life measurements. The relative radiometric
colour spectrum plots for the adopted sources are provided in Fig. 9. As can
be seen from figure, the relative spectral distribution function of the
adopted white (visible band) LED, $f_{\text{v}}(\lambda)$, against wavelength
$\lambda$, consists of two local maximums; at the
$\lambda_{S}^{\text{blue}}=450$ nm and $\lambda_{S}^{\text{yellow}}=604$ nm,
due to the blue base and yellow phosphor coating. The spectral
characterization of the white source is defined by $66$ and $136$ measurement
based data points for blue and yellow spectra, respectively. Furthermore, in
our realistic model, the correlated colour temperature (CCT) of the white LEDs
is chosen to be 3000 K. Similarly, the relative radiometric spectral
distribution for the adopted IR source is given by Fig. 9(b). The relative
spectral distribution function of the IR LED, $f_{\text{i}}(\lambda)$, has a
global maxima at the $\lambda_{S}^{\text{IR}}=860$ nm. The spectral
characterization of the IR source is also ensured by the $76$ spectral data
points, where the further resolution is obtained by spline interpolation if
needed.

(a) OSRAM SFH 2716

(b) OSRAM SFH 2704

Figure 10: Relative angular responsivity characteristic plots for the adopted
VL (left) and IR (right) band detectors. The ideal cosine responsivity curve
is given by black dotted line as a benchmark.

(a) OSRAM SFH 2716 with $\lambda_{R}^{\text{VL}}=620$ nm (solid blue)

(b) OSRAM SFH 2704 with $\lambda_{R}^{\text{IR}}=900$ nm (solid blue)

Figure 11: The relative spectral response curves for the adopted detectors,
$g_{\text{v}}(\lambda)$ and $g_{\text{i}}(\lambda)$ (solid blue) with the
relative spectral distributions for the OSRAM GW QSSPA1.EM,
$f_{\text{v}}(\lambda)$ (solid magenta) and OSRAM SFH 4253,
$f_{\text{i}}(\lambda)$ (solid green). Figure 12: The coating materials used
in the cabin interior design; white opaque plastic (left), blue ripstop nylon
fabric (middle) and black polyester pile carpet (right) [33].

(a)

(b)

(c)

Figure 13: Relative spectral reflectivity values of the coating materials with
respect to the adopted VL and IR band source characteristics. The
$f_{\text{v}}(\lambda)$ and $f_{\text{i}}(\lambda)$ are depicted as magenta
and green solid lines, respectively. The resultant characteristics after
multiplication of relative spectral reflectivity of the coating materials and
relative spectral distributions of the sources are given by black dotted lines
under the respective curves.

####  III-B2 Receivers

Our MCRT approach is capable of generating a complete optical channel analysis
by taking the realistic receiver characteristics into consideration. Similar
to the source modelling, spatial, angular and spectral specifications are also
required for realistic detector design. As discussed in the previous
subsection, the VL and IR band emission characteristics are adopted at the TX.
Thus, the utilization of two detectors is also required in order to match the
spectral responsivity characteristics between the photo-diodes (PDs) and their
intended sources. In our simulations, two silicone PIN PDs; OSRAM SFH 2716
with the peak sensitivity at $\lambda_{R}^{\text{VL}}=620$ nm and OSRAM SFH
2704 with the peak sensitivity at $\lambda_{R}^{\text{IR}}=900$ nm are adopted
as the VL and IR band detectors, respectively. Accordingly, rectangular shaped
bare (without an optical filter) PDs with a $1~{}\text{cm}^{2}$ active area
are created in the simulation environment. The relative angular responsivity
curves of the OSRAM SFH 2716 and OSRAM SFH 2704 are depicted in Figs. 10(a)
and 10(b), respectively. In figures, the ideal cosine responsivity curve for a
bare detector, in [6], is also given as the benchmark. It can be inferred from
Figs. 10(a) and 10(b) that the angular responsivity of our adopted IR band
detectors follow a slightly modified cosine profile. Note that the angular
characteristics of both receive PDs are defined by $100$ measurement based
samples. Without loss of generality, the spectral and angular detection
profile of the PDs are assumed to be homogeneous w.r.t. the spatial domain.
Finally, the obtained profiles are inputted to our simulation environment to
model the spatio-angular characteristics of the detector elements.

Similar to source spectra, the detector spectral characteristics are also fed
into the simulation environment for the chosen detection devices. The relative
spectral responsivity functions for OSRAM SFH 2716, $g_{\text{v}}(\lambda)$,
and OSRAM SFH 2704, $g_{\text{i}}(\lambda)$, detectors, which are represented
by $84$ and $136$ measured data points, are plotted in Figs. 11(a) and 11(b),
respectively. The solid blue lines in Figs. 11(a) and 11(b) depict the
respective detector characteristics. Moreover, magenta and green lines
represent the OSRAM GW QSSPA1.EM and OSRAM SFH 4253 relative spectral
distribution functions which are denoted by $f_{\text{v}}(\lambda)$ and
$f_{\text{i}}(\lambda)$, respectively. The overall spectral response of the VL
and IR band detectors w.r.t. the VL and IR band sources are calculated by
$f_{\text{v}}(\lambda)g_{\text{v}}(\lambda)$,
$f_{\text{i}}(\lambda)g_{\text{i}}(\lambda)$ and
$f_{\text{i}}(\lambda)g_{\text{v}}(\lambda)$,
$f_{\text{i}}(\lambda)g_{\text{i}}(\lambda)$, respectively and also plotted by
the dotted black lines under the magenta and green curves. As can be seen from
Figs. 11(a) and 11(b), each source requires its matching/tuned detector at the
RX to harvest the highest collected power. Consequently, in our simulations
VL, $\lambda_{S}^{\text{blue}}=450$ nm and $\lambda_{S}^{\text{yellow}}=604$
nm, and IR, $\lambda_{S}^{\text{IR}}=860$ nm, band sources are matched with
their corresponding detectors with the peak wavelengths of
$\lambda_{R}^{\text{VL}}=620$ nm and $\lambda_{R}^{\text{IR}}=900$ nm,
respectively.

####  III-B3 Coating Materials

The NLoS path contributions within dense and complex environments play an
important role in the overall channel conditions. In the IFOWC literature, the
majority of the research has been dedicated to the IR spectrum sources and
their relative reflection characteristics. However, the spectral profiles
between the VL and IR band source-detector pair differ significantly in
practice, which is depicted in Fig. 11. Specifically, the reflectivity of the
coating materials within the IR band become almost flat due to the inherent
narrow-band characteristics of the IR sources, where the optical power is
concentrated in the vicinity of a single wavelength. However, the optical
power of the VL sources are spread across multiple wavelengths, generally blue
and yellow or red, green and blue, which makes them wide-band sources. Hence,
the effective optical properties of the interior surfaces w.r.t. the VL and IR
bands must be modelled accurately.

(a)

(b)

Figure 14: Details of the reading light based CIR simulations; front (left)
and side (right) views of the cabin (units are in cm). Green circles and red
squares represent the centre point for the upper section of the seats and CIR
measurement points in each seat, respectively.

To capture the characteristics of realistic cabin interior coatings, the
spectral reflectance measurement data is used in our simulations. Accordingly,
the reflection and absorption characteristics of the aeronautical cabin
interior coating profiles are obtained from the United States Geological
Survey (USGS) High Resolution Spectral Library Version 7 [33]. The main
surface coating for the cabin interior, including the side walls, ceiling and
head luggage compartments, is typically chosen to be fiber reinforced plastic
(FRP) in real world applications to meet the flammability requirements. In our
simulations, the light coloured plastic, depicted in Fig. 12, is adopted to
accurately imitate the characteristics of the main interior surfaces of the
cabin. Thus, the white opaque plastic material and its optical properties are
imported into the simulation environment. Note that the interior faces of both
the realistic and simplified cabin models are assumed to be coated with the
same material. Secondly, a blue coloured nylon ripstop fabric coating has been
imported to model the real passenger seat dress covering, which is shown in
Fig. 5(a). Lastly, the cabin flooring is chosen to be made out of black
polyester pile carpet, to accurately model a real world commercial airline
interior. The visual representations of the adopted coating materials and
their spectral reflectivity characteristics are given in Figs. 12 and 13,
respectively. In Fig. 13, the portion of the reflectivity spectrum that
corresponds to the adopted source spectral distributions,
$f_{\text{v}}(\lambda)$ and $f_{\text{i}}(\lambda)$, are given for the chosen
materials separately. Similar to the source spectral plots, the result of a
multiplication between the source characterization and the coating material
reflectivity functions is plotted by dotted black lines under the respective
source curve. It can easily be inferred from Fig. 13 that the reflectivity
characteristics of the white opaque plastic is almost flat for both VL and IR
wavelength regions. Conversely, the reflectivity profiles of the blue ripstop
nylon fabric and black polyester pile carpet are highly absorbent in the VL
band as opposed to the IR band. Moreover, the effect of the coating materials
on the overall response is also different from each other, as anticipated,
since the source profiles are significantly contrasting. Note that the
representation of coating characteristics by an average reflectance value, as
vastly practised in the literature, would introduce a recursive error in the
channel modelling. Explicitly, the error will be amplified in each reflection
of a light ray during CIR calculations. In our simulations, the coating
materials are represented by $519$ data points, for the $0.382-0.780$ $\mu$m
region to match the spectra of adopted VL and IR band sources.

##  IV MCRT Simulations for In-flight LiFi Channels

In this section, details of the MCRT based channel simulation methodology will
be provided. Then, a comprehensive time and frequency domain analyses on the
obtained optical channels and the inferred results will be presented for
different wavelengths, cabin models and UE locations. The MCRT simulations
will be conducted for a practical in-flight LiFi communications scenario,
where the data bearing optical power is transferred from the reading lights to
the PED. Accordingly, a three dimensional simulation environment with aircraft
cabin, auxiliary interior elements, sources, receivers and coating material
models, as detailed in the previous section, are utilized in MCRT simulations.
The detailed illustration of the simulation environment and arrangement of the
components is given in Fig. 14. As can be seen from Figs. 2 and 14, both cabin
models are centred along the $x$ and $y$-axes in simulations such that the
simplified cabin represents the rough approximation of the complex geometric
curvatures in the realistic model. Three reading lights, $r_{1}$, $r_{2}$ and
$r_{3}$, are assumed to be mounted on the PSU with a $3$ cm between them in
the $x$-axis. To maximize the delivered optical power to their intended seats,
the reading lamps are directed towards the centre of mass for the upper
section of the seat, where the centre point is depicted as a green circle in
Figs. 14(a) and 14(b). Depending on the manufacturer and cabin model type, the
reading light adjustment could be an option. However, due to space
limitations, only the fixed adjustment is simulated in this work without loss
of generality. To deliver the maximum optical power within each individual
seating area for the fixed case, the selection of initial $z$-axis rotation
values $\alpha_{1}$, $\alpha_{2}$ and $\alpha_{3}$, which are introduced to
the $r_{1}$, $r_{2}$ and $r_{3}$, respectively, can be given by

$\displaystyle\alpha_{1}$
$\displaystyle\geq-\arctan(53/84)\approx-32.25^{\circ},$
$\displaystyle\alpha_{2}$ $\displaystyle=\arctan(0/84)=0^{\circ},$
$\displaystyle\alpha_{3}$ $\displaystyle\leq\arctan(53/84)\approx
32.25^{\circ}.$ (1)

As can be seen from the expression above, the main objective of the reading
lights is to provide sufficient illumination in the vicinity of the passenger
tray table. To achieve that goal, we aim to deliver the maximum optical power
to the centre point of an imaginary line which intersects the seats from top
to bottom (refer to green circles in Fig. 14). For the sake of implementation
simplicity, initial rotation angles of $\alpha_{1}=-33^{\circ}$,
$\alpha_{2}=0^{\circ}$ and $\alpha_{3}=33^{\circ}$ are adopted in our MCRT
simulations by choosing the least integer angle greater than or equal to the
given limits. The elevation of the receiver elements, depicted as red squares
in Figs. 14(a) and 14(b), is chosen with the aid of human models to represent
the average height of the hand-held PEDs. A total of three mobile terminal
locations, C1, B2 and A3, are chosen to investigate the LoS and/or NLoS
channel effects as well as cell centre and edge performances. Unlike the
imaging ray tracing applications, where the generated rays hit each surface
only once in a premeditated sequence, non-imaging NSRT is the main technique
used in our simulations. The reason behind this is the illumination purposes
of the reading lamps and unordered reflections from complex surface geometries
with various reflectivity profiles. Also, the interior surfaces are designed
to introduce spectrally dependent reflectivity and scattering if a ray strikes
a surface. In every bounce of the light ray, the specular components of the
reflections receive zero energy, which means the total energy is set to be
equally divided among $\nu_{\text{s}}$ scattered rays. Thus, the number of
total rays must be traced after $\kappa^{\text{th}}$ order reflection becomes,
$n_{\text{R}}=(\nu_{\text{s}})^{\kappa}$. In the last iteration, the maximum
number of rays that are traced by the simulator is calculated by,
$n_{\text{R,max}}=(\nu_{\text{s}})^{\kappa_{\text{max}}}$. In our simulations,
$\nu_{\text{s}}=5$ is chosen to accurately represent purely diffuse
reflections in a computationally efficient manner. Another important MCRT
parameter is the “minimum relative ray intensity”, which decides when to
terminate the iteration of tracing a particular ray. Thus, it terminates a
trace when the ray intensity is below or equal to a fraction of the initial
intensity. In our simulations, the “minimum relative ray intensity” is chosen
as $10^{-4}$ and $10^{-5}$ for IR and VL spectra simulations, respectively.
Note that the overall reflectivity of the coating materials in the VL band is
significantly lower compared to the IR, thus, a lower minimum relative ray
intensity value must be chosen to capture the details of the VL channel.
Therefore, the maximum number of reflections captured by our MCRT simulations,
$\kappa_{\text{max}}$, becomes $4$ and $6$ for IR and VL bands, respectively.
Lastly, the number of rays generated per LED chip is chosen to be $5$ million
in our simulations, which yields to a total of $80$ million rays per reading
light in IR band simulations. Since the generation of white light requires
yellow and blue components, where each of which are chosen to be represented
by $5$ million rays. Hence, the total of $160$ million rays are generated per
white LED based reading light.

###  IV-A Optical Channel Characterization

The multiple-bounce (multipath) CIR between the source $S$ and the receiver
$R$ could be expressed by our MCRT simulation results as follows:

$\displaystyle h(t;S,R)=\sum_{i=1}^{i_{\text{hit}}}P_{i}\delta(t-t_{i}),$ (2)

where $P_{i}$, $i_{\text{hit}}$ and $t_{i}$ denote the received incoherent
irradiance, total number of rays that hit the receiver and the elapsed time
for $i^{\text{th}}$ ray to reach the receiver, respectively. It is important
to note that all the incoming rays that strike the detector surface with
different irradiance values and time delays. In order to reduce the individual
rays related observation errors and to obtain meaningful information from the
ray scatter, data binning/clustering on $h(t;S,R)$ is applied, which yields
the discrete-time optical (physical) CIR as follows:

$\displaystyle
h[n;S,R]=\sum_{n=0}^{N_{\text{b}}-1}\widetilde{P}_{n}\delta(n-t_{n}),\quad\text{for
}n\in\\{0,1,\cdots,N_{\text{b}}-1\\}.$ (3)

Accordingly, the number of bins is given by

$\displaystyle N_{\text{b}}=\left\lceil\frac{t_{\text{L}}-t_{1}}{\Delta
w}\right\rceil,$ (4)

where the time of arrival for the first and last rays are denoted by $t_{1}$
and $t_{\text{L}}$, respectively. In addition, $\Delta w$ is width of the
bins. Hence, the bin edge for the $n^{\text{th}}$ bin could also be given by
$t_{n}=t_{1}+n\Delta w$. Moreover, the cumulated irradiance value within the
given bin interval is calculated by $\widetilde{P}_{n}=\sum\limits_{\forall
i}P_{i}$, where $\forall i\in\left[t_{n}~{}t_{n+1}\right]$, if
$n=N_{\text{b}}-1$ and $\forall i\in\left[t_{n}~{}t_{n+1}\right)$, otherwise.
After obtaining the discrete-time CIR, the important parameters for channel
characterization could be devised. The optical CFR is described in terms of
the CIR obtained in (3) as follows:

$\displaystyle H(f;S,R)=\int\limits_{-\infty}^{\infty}h(t;S,R)e^{-j2\pi
ft}\text{d}t\approx\sum\limits_{n=0}^{N_{\text{b}}-1}h[n;S,R]e^{-j\frac{2\pi
kn}{N}},$ (5)

where the sampling frequency could be calculated as $\Delta f=1/\Delta w$.
Hence, the frequency axis of the discrete Fourier transform (DFT), becomes
$k\in\frac{\Delta
f}{N}\circ\left\\{-\frac{N}{2},-\frac{N}{2}+1,\cdots,\frac{N}{2}-1\right\\}$.
The number of subcarriers in the DFT operation could also be found by
$N=2^{\lceil\log_{2}\left(N_{\text{b}}\right)\rceil}$. It is also important to
note from the above expressions that the temporal domain accuracy is directly
related to the bin width, $\Delta w$, where the resulting discrete-time CIR
closely approximates the actual channel when the bin width approaches zero,
$\lim\limits_{\Delta w\rightarrow 0}h[n;S,R]\approx h(t;S,R)$. Another
important parameter, the DC channel gain or total optical power of the impulse
response can also be calculated by using (5),

$\displaystyle H(0;S,R)$
$\displaystyle=\int_{-\infty}^{\infty}h(t;S,R)\text{d}t$
$\displaystyle\approx\sum_{n=-\infty}^{\infty}h[n;S,R]=\sum\limits_{n=0}^{N_{\text{b}}-1}\sum\limits_{\kappa=0}^{\kappa_{\text{max}}}h^{(\kappa)}[n;S,R].$
(6)

By using the above expression, the average transmitted and received optical
powers could be linked by using the DC channel gain as follows:
$P_{R}=H(0;S,R)P_{S}$, which yields the path loss of

$\displaystyle\text{PL}=-10\log_{10}H(0;S,R)\quad\text{in dB}.$ (7)

The RMS delay spread and mean delay are two important measures to define the
multipath richness of the channel, which also shows the impact of inter-symbol
interference (ISI) on the system performance. Hence, the RMS delay spread
could be calculated by using the second and zeroth moments of $h[n;S,R]$ as
follows:

$\displaystyle\tau_{\text{RMS}}=\sqrt{\frac{\int\limits_{-\infty}^{\infty}(t-\bar{\tau})^{2}h^{2}(t;S,R)\text{d}t}{\int\limits_{-\infty}^{\infty}h^{2}(t;S,R)\text{d}t}}=\sqrt{\frac{\sum\limits_{n=0}^{N_{\text{b}}-1}(n-\bar{\tau})^{2}h^{2}[n;S,R]}{\sum\limits_{n=0}^{N_{\text{b}}-1}h^{2}[n;S,R]}},$
(8)

where the mean delay is given in terms of the zeroth and first raw moments of
$h[n;S,R]$ by

$\displaystyle\bar{\tau}=\frac{\int\limits_{-\infty}^{\infty}th^{2}(t;S,R)\text{d}t}{\int\limits_{-\infty}^{\infty}h^{2}(t;S,R)\text{d}t}=\frac{\sum\limits_{n=0}^{N_{\text{b}}-1}nh^{2}[n;S,R]}{\sum\limits_{n=0}^{N_{\text{b}}-1}h^{2}[n;S,R]}$
(9)

Lastly, the dominance of the LoS link is also an important factor to evaluate
the contribution of LoS and NLoS paths, which indicates how flat the channel
is. Accordingly, the “flatness factor” is calculated as the ratio between LoS
and NLoS channel powers as follows:

$\displaystyle\rho$
$\displaystyle=\frac{P_{\text{LoS}}}{P_{\text{LoS}}+P_{\text{NLoS}}}=\frac{\int\limits_{-\infty}^{\infty}h^{(0)}(t;S,R)\text{d}t}{\sum\limits_{\kappa=0}^{\kappa_{\text{max}}}\int_{-\infty}^{\infty}h^{(\kappa)}(t;S,R)\text{d}t}=\frac{\sum\limits_{n=0}^{N_{\text{b}}-1}h^{(0)}[n;S,R]}{H(0;S,R)}.$
(10)

Cabin Models |  | A320 simplified
---
A320 realistic
Cabin Model Positions (cm) |  | $\mathbf{p}_{\text{simp}}=(0,~{}0,~{}0)$
---
$\mathbf{p}_{\text{real}}=(6.577,~{}0,~{}0)$
Seat Model Positions (cm) |  | $\mathbf{p}_{\text{31C}}=(215.199,~{}42.643,~{}270)$
---
$\mathbf{p}_{\text{31B}}=(268.199,~{}42.643,~{}270)$
$\mathbf{p}_{\text{31A}}=(321.199,~{}42.643,~{}270)$
$\mathbf{p}_{\text{30C}}=(215.199,~{}42.643,~{}351)$
$\mathbf{p}_{\text{30B}}=(268.199,~{}42.643,~{}351)$
$\mathbf{p}_{\text{30A}}=(321.199,~{}42.643,~{}351)$
$\mathbf{p}_{\text{29C}}=(215.199,~{}42.643,~{}432)$
$\mathbf{p}_{\text{29B}}=(268.199,~{}42.643,~{}432)$
$\mathbf{p}_{\text{29A}}=(321.199,~{}42.643,~{}432)$
Reading Light Positions (cm) |  | $\mathbf{p}_{r_{1}}=(289.199,~{}167.643,~{}408)$
---
$\mathbf{p}_{r_{2}}=(292.199,~{}167.643,~{}408)$
$\mathbf{p}_{r_{3}}=(295.199,~{}167.643,~{}408)$
Reading Light $z$-axis Orientations |  | $\alpha_{1}=-33^{\circ}$
---
$\alpha_{3}=33^{\circ}$
Number of Chips per Reading Light |  $16$ ($4\times 4$)
| Number of Generated Rays per
---
LED Chip / Reading Light
| VL Band: $10\times 10^{6}$ / $160\times 10^{6}$
---
IR Band: $5\times 10^{6}$ / $80\times 10^{6}$
Power per Reading Light ($P_{\text{t}}$) |  $16$ W
Model of the LED Chips |  | VL Band: OSRAM GW QSSPA1.EM
---
IR Band: OSRAM SFH 4253
FWHM of the LED Chips | $120^{\circ}$
PD Positions (cm) |  | $\mathbf{p}_{\text{C1}}=(221.699,~{}100.443,~{}408)$
---
$\mathbf{p}_{\text{C2}}=(239.199,~{}100.443,~{}408)$
$\mathbf{p}_{\text{C3}}=(256.699,~{}100.443,~{}408)$
$\mathbf{p}_{\text{B1}}=(274.699,~{}100.443,~{}408)$
$\mathbf{p}_{\text{B2}}=(292.199,~{}100.443,~{}408)$
$\mathbf{p}_{\text{B3}}=(309.699,~{}100.443,~{}408)$
$\mathbf{p}_{\text{A1}}=(327.699,~{}100.443,~{}408)$
$\mathbf{p}_{\text{A2}}=(345.199,~{}100.443,~{}408)$
$\mathbf{p}_{\text{A3}}=(362.699,~{}100.443,~{}408)$
Model of the PDs |  | VL Band: OSRAM SFH 2716
---
IR Band: OSRAM SFH 2704
Effective Area of the PDs | $1~{}\text{cm}^{2}$
FWHM of the PDs |  | OSRAM SFH 2716: $120^{\circ}$
---
OSRAM SFH 2704: $132^{\circ}$
Coating Materials |  | White Opaque Plastic ($\nu_{\text{s}}=5$)
---
Blue Ripstop Nylon ($\nu_{\text{s}}=5$)
Black Polyester Pile Carpet ($\nu_{\text{s}}=5$)
Time Resolution/ Bin Width ($\Delta w$) |  $0.2$ ns

TABLE I: Details of the parameters used in the MCRT simulations.

###  IV-B MCRT Simulation Results

In this subsection, the proposed MCRT simulation results will be presented for
both IR and VL spectra. The complete set of parameters used in these
simulations are provided in Table I.

####  IV-B1 IR Band Results

The IR band CIR and CFR plots for both realistic and simplified cabin models
including the passenger seating are given in Fig. 15. The rows in $2\times 3$
subplot matrix represent the domain of the plot e.g., time or frequency, where
the columns are the three measurement points for seats A, B and C. Moreover,
the channel characterization parameters are also obtained and presented in
Table II in conjunction with the figures, where the number of rays that hit
each PDs is given by $i_{\text{hit}}$. The time and frequency domain
simulation results for the adopted cabin models are presented and compared
with LoS analytical model in Figs. 15(a)-(f). Accordingly, up to $4$-bounce,
$0\leq\kappa\leq 4$, CIR simulation results, $h(t;r_{1},\text{C1})$,
$h(t;r_{2},\text{B2})$ and $h(t;r_{3},\text{A3})$, are presented for adopted
UE locations C1, B2 and A3, respectively. Moreover, the frequency response
plots are obtained for fast Fourier transform (FFT) size of $N=512$ for the
channel bandwidth of $B_{\text{CH}}=5$ GHz. Note that the Figs. 15(d)-(f) are
only presented for the frequency range of $f~{}\in[0~{}B_{\text{CH}}/2]$,
since the frequency response of the LiFi data signals are conjugate symmetric
due to the IM/DD technique.

(a) $h(t;r_{1},\text{C1})$

(b) $h(t;r_{2},\text{B2})$

(c) $h(t;r_{3},\text{A3})$

(d) $\lvert H(f;r_{1},\text{C1})\rvert$

(e) $\lvert H(f;r_{2},\text{B2})\rvert$

(f) $\lvert H(f;r_{3},\text{A3})\rvert$

Figure 15: IR band in-flight LiFi CIR and CFR simulation results obtained by
proposed MCRT based method for seated simplified cabin model () and seated
realistic cabin model (). The analytical LoS channel () is presented as a
benchmark.

| Simplified Cabin (IR Band) | Realistic Cabin (IR Band)
---|---|---
$S,R$ | $i_{\text{hit}}$ | $H[0;S,R]$ |  $\tau_{\text{RMS}}$ (ns) | $\rho$ | $i_{\text{hit}}$ |  $H[0;S,R]$ (W) |  $\tau_{\text{RMS}}$ (ns) | $\rho$
$r_{1},\text{C1}$ | $101430$ | $2.405\text{E}^{-5}$ | $0.084$ | $0.859$ | $102793$ | $2.369\text{E}^{-5}$ | $0.094$ | $0.872$
$r_{2},\text{B2}$ | $192648$ | $7.503\text{E}^{-5}$ | $0.055$ | $0.924$ | $197009$ | $7.545\text{E}^{-5}$ | $0.053$ | $0.919$
$r_{3},\text{A3}$ | $272609$ | $3.052\text{E}^{-5}$ | $0.241$ | $0.638$ | $318557$ | $3.543\text{E}^{-5}$ | $0.252$ | $0.549$

TABLE II: The proposed MCRT simulation results to characterize the $4$-bounce
IR channels for both the simplified and realistic cabin models.

In Figs. 15(a) and (d), the MCRT based CIR and CFR results are given for both
cabin models along with the LoS analytical model as a benchmark. For the UE
location C1, the magnitude of only the LoS component obtained by the MCRT
simulations for simplified and realistic cabins become approximately
$2.12\times 10^{-5}$ and $2.07\times 10^{-5}$, respectively. In comparison
with the LoS analytical channel model, simplified and realistic cabin models
based simulation results yield $12.60\%$ and $14.63\%$ less LoS magnitude,
respectively. The reason for this is the angular and spectral characteristics
of both the optical front-end and interior coating in simulations, which are
omitted in the analytical model. Specifically, the angle of emergence and
incidence values are significantly larger for points C1 and A3 compared to B2.
Note that a small time difference, around $0.07$ ns, between the analytical
LoS model and the simulations occurs due to the simulated real world
imperfections in the MCRT. Furthermore, the effect of higher order
reflections, $\kappa>0$, to the channel characteristics could also be assessed
by using the flatness factor. Hence, the $\rho$ for simplified and realistic
cabins based simulation results becomes $0.859$ and $0.872$, which is $14.1\%$
and $12.79\%$ less compared to the LoS analytical model, respectively.
Therefore, it can be inferred that both the analytical model and simplified
cabin are able to capture the details of the channel when the NLoS components
are not as significant. This is also confirmed by the frequency response plot
in Fig. 15(d), where the mean magnitude response difference of $0.58$ and
$0.69$ dB is observed between the simplified and realistic cabin simulations
with the LoS analytical model, respectively. Also, the peak-to-peak magnitude
response difference for simplified and realistic cabin simulations is given by
$0.64$ and $0.66$ dB, respectively. It can be inferred both from both the time
and frequency domain results that the effect of higher order reflections are
quite minor in seat C due to the large physical distance from the reflector
surfaces e.g., side wall, which yields a LoS dominated link characteristics.

In Figs. 15(b) and (e), the MCRT based CIR and CFR results are obtained for
the UE location B2, respectively. Accordingly, LoS components of the
simulation results becomes approximately $6.93\times 10^{-5}$ for both cabin
models. This means that the LoS component for the simulation results are
$1.62\%$ less for both cabin models compared to the LoS analytical model.
However, the DC channel gain of simplified and realistic cabin models
increased by $67.95\%$ and $68.60\%$, respectively, compared to the UE
location C1. The main reason behind this significant increase is the decreased
source-receiver distance, where it becomes the minimum for the TX-RX pair of
$r_{2}-\text{B2}$ among all UE locations. Another important set of factors to
note is the spectral dependencies of the optical front-end and coating as well
as the angles of emergence and incidence. However, compared to C1, where the
effect of an imperfect angular response is significant, both the emergence and
incidence angles are almost zero in B2. Thus, we can conclude that the
magnitude difference between the LoS component of the simulation results and
the analytical model is mainly caused by the spectral dependencies. Moreover,
the increase in the flatness factor from C1 to B2 is also significant.
Accordingly, the flatness factor increases by $7.57\%$ and $5.39\%$ for
simplified and realistic cabin models, respectively. Although the optical
power that comes from the side-wall reflections is increased in B2 compared to
C1, the dominant LoS component makes the NLoS contributions negligible. Also,
we can observe that the mean magnitude response of the simplified and
realistic cabin simulations become approximately $0.07$ dB less than the
analytical LoS channel model. The peak-to-peak magnitude response difference
for simplified and realistic cabin simulations is given by $0.41$ and $0.44$
dB, respectively. Therefore, we can conclude that the received optical power
for the simulation point B2 is going to be the highest among all the other
points due to the minimum source-receiver separation, which effectively means
a higher communications capacity. In addition, the frequency flat/LoS channel
assumption for seat B is also accurate due to the weak NLoS contribution.

(a) $h(t;r_{1},\text{C1})$

(b) $h(t;r_{2},\text{B2})$

(c) $h(t;r_{3},\text{A3})$

(d) $\lvert H(f;r_{1},\text{C1})\rvert$

(e) $\lvert H(f;r_{2},\text{B2})\rvert$

(f) $\lvert H(f;r_{3},\text{A3})\rvert$

Figure 16: VL band in-flight LiFi CIR and CFR simulation results obtained by
proposed MCRT based method for seated simplified cabin model () and seated
realistic cabin model (). The analytical LoS channel () is presented as a
benchmark.

| Simplified Cabin (VL Band) | Realistic Cabin (VL Band)
---|---|---
$S,R$ | $i_{\text{hit}}$ | $H[0;S,R]$ |  $\tau_{\text{RMS}}$ (ns) | $\rho$ | $i_{\text{hit}}$ |  $H[0;S,R]$ (W) |  $\tau_{\text{RMS}}$ (ns) | $\rho$
$r_{1},\text{C1}$ | $271763$ | $1.619\text{E}^{-5}$ | $0.021$ | $0.929$ | $277731$ | $1.608\text{E}^{-5}$ | $0.031$ | $0.937$
$r_{2},\text{B2}$ | $542237$ | $6.242\text{E}^{-5}$ | $0.015$ | $0.979$ | $535559$ | $6.265\text{E}^{-5}$ | $0.014$ | $0.976$
$r_{3},\text{A3}$ | $1075022$ | $2.155\text{E}^{-5}$ | $0.150$ | $0.709$ | $1060614$ | $2.519\text{E}^{-5}$ | $0.191$ | $0.607$

TABLE III: The proposed MCRT simulation results to characterize the $6$-bounce
VL channels for both the simplified and realistic cabin models.

In Figs. 15(c) and (f), the simulation results are obtained by using both the
simplified and realistic cabin models and compared with the benchmark for
point A3. Similar to C1 results, the LoS component magnitudes for the
simplified and realistic cabin simulations become $2.01\times 10^{-5}$ and
$1.98\times 10^{-5}$, respectively. This means that the simplified and
realistic LoS simulation components are $17.08\%$ and $18.37\%$ lower compared
to the analytical model. This biggest difference among all points also stems
from the combination of imperfect angular and spectral profiles of the
elements. Furthermore, it can clearly be seen that the secondary reflection
for both simplified and realistic CIR emerged after $3.8$ ns. Note that
compared to point B2, the RMS delay spread has increased by $338.18\%$ and
$375.47\%$ for simplified and realistic cabin simulations, respectively.
Similarly, the flatness factor in point A3 becomes approximately $30.95\%$ and
$40.26\%$ for simplified and realistic cabin simulation results, respectively.
From Fig. 15(f), the mean magnitude response for both the simplified and
realistic cabin simulations becomes $0.81$ and $0.88$ dB less than the LoS
analytical model, respectively. Furthermore, the peak-to-peak magnitude
response difference for simplified and realistic cabin simulation results
become $2.41$ and $4.18$ dB, respectively. More importantly, the $3$ dB cut-
off frequency for the IR band LiFi optical channel in realistic cabin becomes
$498$ MHz. Consequently, it can be said that the location of the UE impacts
two of the most important parameters of the communication channel; (i)
received signal power and, (ii) the effective bandwidth in such complex
environments.

####  IV-B2 VL Band Results

The time and frequency domain analysis of the in-flight LiFi channel for the
VL band source and receiver pair are given for the adopted cabin models and UE
locations in Figs. 16(a)-(f). Unlike the IR band results, the VL band LiFi
channels are simulated up to $6$-bounces, $0\leq\kappa\leq 6$, and the
detailed parameters are presented in Table III. The higher order reflections
compared to the IR band simulations were required as the absorption rate of
the coating materials are higher in the VL spectra. It is also important to
note that the LoS analytical channel expression, given in [6], is independent
of the operation wavelength, which will be granting a convenient direct
comparison between IR and VL band results.

The CIR and CFR comparisons for the UE location C1 are depicted in Figs. 16(a)
and (d), respectively. As can be seen from figures, the LoS channel components
of $1.54\times 10^{-5}$ and $1.51\times 10^{-5}$ are obtained by simplified
and realistic cabin simulations, respectively. Thus, these numbers yield
$36.27\%$ and $37.74\%$ smaller LoS component for simplified and realistic
cabin simulations compared to analytical model, respectively. The underlying
reason for this difference is also realistic spectral and angular
characteristics which are taken into consideration in our simulations. Even
though point C1 is furthest from the side wall, the NLoS components still
comprises approximately $7.1\%$ and $6.3\%$ of the total received optical
power for simplified and realistic cabin simulations, respectively. In the
frequency domain, the mean value of the magnitude responses for both the
simplified and realistic cabin simulations become $1.96$ and $2.06$ dB smaller
compared to analytical benchmark, respectively. Moreover, the peak-to-peak
magnitude response difference of $0.25$ and $0.36$ dB are obtained by
simplified and realistic simulation results, respectively. Therefore, we can
infer from the obtained results that, due to the higher optical imperfections
presented in VL band simulations, the received signal power differs from the
analytical expectation more than that of the IR band results.

In Figs. 16(b) and (e), both the impulse and frequency response results and
comparisons are given for both cabin models along with the LoS analytical
expression for the UE location of B2. Accordingly, the simplified and
realistic simulation results yield a LoS component of $6.11\times 10^{-5}$ and
$6.12\times 10^{-5}$, respectively. Hence, the presented values yield a
$13.32\%$ and $13.23\%$ smaller LoS component in comparison with the
benchmark, respectively. As can be seen from Table III, the NLoS contribution
to total received optical power is $2.1\%$ and $2.4\%$ for simplified and
realistic cabin simulation results, respectively. The mean magnitude response
difference between simulations against the benchmark becomes $0.62$ dB for
both cabin models. Furthermore, the peak-to-peak magnitude response difference
for simplified and realistic cabin simulations is given by $0.11$ and $0.12$
dB, respectively. Again, the UE location in seat B yields the highest
achievable received optical signal power compared to other two seats.

Lastly, in Figs. 16(c) and (f), both the time and frequency domain results and
comparisons are given for both cabin models when the UE is located in point
A3. The LoS components obtained by simplified and realistic cabin simulations
is given by $1.59\times 10^{-5}$ and $1.56\times 10^{-5}$, respectively. Thus,
the simplified and realistic cabin simulation results yield $34.33\%$ and
$35.52\%$ lower LoS component compared to the benchmark, respectively. It is
important to note that the contribution of the spectral characteristics of the
source, receiver and coating is higher in the VL band as the detector
introduces an almost ideal cosine profile. It has been shown by narrow-band IR
results that the realistic source and receivers do not match closely with the
flat spectral profile. Therefore, the VL band sources, whose power is spread
over a wider spectral range, present a greater mismatch. In terms of RMS delay
spread, the simplified and realistic simulations yield $900\%$ and $1264\%$
increase for the simulation point A3 compared to B2, respectively. Also, the
portion of the NLoS channel contribution became almost $30\%$ and $40\%$ in
the simplified and realistic cabin applications, respectively. In the
frequency domain, the difference of the mean magnitude response between the
simplified and realistic simulations with the benchmark becomes $1.83$ and
$1.91$ dB, respectively. Also, the peak-to-peak magnitude response values for
simplified and realistic simulation results also given by $1.89$ and $3.92$
dB, respectively. Note that the $3$ dB cut-off frequency for the VL band LiFi
optical channel in realistic cabin becomes $566$ MHz.

##  V Performance of DCO-OFDM Under The Channel Impairments

In this section, the performance of the practical in-flight LiFi systems are
evaluated by employing a widely adopted multi-carrier optical transmission
technique, DCO-OFDM [34]. Accordingly, the BER performance of DCO-OFDM is
investigated under both optical domain multipath propagation and LED non-
linearity based clipping.

TABLE IV: The set of parameters used in the BER simulations.

Parameter | Description | Value
---|---|---
$B_{\text{CH}}$ | The channel bandwidth |  $5$ GHz
$N$ | Number of subcarriers | $512$
$M$ | Order of the QAM constellation |  $4$ and $64$
$\beta_{\text{dB}}$ | DC bias value |  $19.19$ dB
$L$ | Number of channel taps | $7$
$N_{\text{CP}}$ | Length of the CP | $7$
$I_{\textrm{min}}$ | The lower limit for the $I_{\textrm{f}}$ |  $100$ mA [31, 32]
$I_{\textrm{max}}$ | The upper limit for the $I_{\textrm{f}}$ |  $700$ mA [31, 32]

As a first step in DCO-OFDM, the binary user data vector, which contains the
information to be transmitted, is parsed into $(N-2)\log_{2}(M)$ elements. The
parameter $M$ denotes the order of the quadrature amplitude modulation (QAM)
modulation. Then, each element is one-to-one mapped into a complex valued
$M$-QAM symbol, $X[k]$, where $k\in\\{1,2,\cdots,\frac{N}{2}-1\\}$. Please
note that in order to obtain a real valued signal after the inverse FFT (IFFT)
operation, Hermitian symmetry must be imposed on the frequency domain symbols,
$X[N-k]=X[k]^{\ast},~{}\forall k\in\\{0,1,\cdots,N-1\\}$, where
$X[0]=X[N/2]=0$. Hence, only $\frac{N}{2}-1$ subcarriers carry useful
information in DCO-OFDM. For $N>64$, the time domain signal after the IFFT,
will follow independent identically distributed (i.i.d.) Gaussian
distribution, $x[n]\sim\mathcal{N}\left(0,\sigma^{2}\right),~{}\forall
n\in\\{0,1,\cdots,N-1\\}$ according to the central limit theorem. Since, we
have adopted the standard definitions of the IFFT/FFT pair at the TX and RX,
respectively, $\sigma^{2}=\frac{1}{N}$.

The main transmission technique in LiFi systems is referred to as IM/DD, where
the information is carried via the instantaneous light intensity. Thus, a DC
bias, $\beta$, must be introduced prior to transmission as the light intensity
cannot take a negative value. Furthermore, double-sided clipping is also
needed to make the transmit signal compliant with the dynamic range of the
LEDs. Hence, the resultant truncated Gaussian distributed time-domain signal
could be expressed by

$\displaystyle\hat{x}[n]=\big{[}x[n]+\beta\big{]}^{I_{\text{max}}}_{I_{\text{min}}}=\left\\{\begin{array}[]{ll}I_{\text{min}},&\text{if
}x[n]<I_{\text{min}}-\beta\\\ I_{\text{max}},&\text{if
}x[n]>I_{\text{max}}-\beta\\\ x[n]+\beta,&\text{otherwise}\end{array}\right.,$
(14)

where $I_{\text{min}}\leq\beta\leq I_{\text{max}}$ and $\beta=r\sigma$. The
parameter $r$ denotes the bias proportionality factor, which adjusts the
amount of bias in terms of the standard deviation of the unbiased and
unclipped $x[n]$. After the DC bias addition, the time domain shifted signal
follows the distribution
$x[n]+\beta\sim\mathcal{N}\left(r\sigma,(r^{2}+1)\sigma\right)$. In
literature, the DC bias in decibels is also defined by
$\beta_{\text{dB}}=10\log_{10}\left(r^{2}+1\right)$. To simulate the realistic
transmit LED front-end electrical properties of the adopted VL (OSRAM GW
QSSPA1.EM) and IR (OSRAM SFH 4253) band sources, the forward current value is
constrained to be within the
$I_{f}\in\left[I_{\text{min}}~{}I_{\text{max}}\right]=[100~{}700]$ mA range
[31, 32]. Moreover, in order to locate the time domain signal at the middle of
the dynamic range and minimize the non-linear clipping effect of the LEDs,
$\beta=400$ mA ($\beta_{\text{dB}}=19.19$ dB) is adopted in our simulations.

It is important to note that the non-linear and memoryless LED clipping effect
could be represented as a linear process with a deterministic attenuation
factor, $A$, and a random time domain additive clipping noise, $c[n]$, by
Bussgang’s theorem as follows [35, 36]:

$\displaystyle z[n]=\hat{x}[n]-\beta=Ax[n]+c[n],$ (15)

where $\text{E}\\{z[n]\\}=\text{E}\\{c[n]\\}=\mu_{z}=P_{\text{opt}}-\beta$.
The optical power of the biased and double sided clipped signal could be
calculated by

$\displaystyle P_{\text{opt}}$
$\displaystyle=\text{E}\\{\hat{x}[n]\\}=\frac{\sigma}{\sqrt{2\pi}}\left(e^{-(I_{\text{min}}-\beta)^{2}/2\sigma^{2}}-e^{-(I_{\text{max}}-\beta)^{2}/2\sigma^{2}}\right)$
$\displaystyle+\left(I_{\text{max}}-\beta\right)Q\left(\frac{I_{\text{max}}-\beta}{\sigma}\right)+\left(\beta-
I_{\text{min}}\right)Q\left(\frac{I_{\text{min}}-\beta}{\sigma}\right)+I_{\text{min}}.$
(16)

If we subtract $\mu_{z}$ from both sides of (15),

$\displaystyle z^{\prime}[n]=z[n]-\mu_{z}=Ax[n]+c^{\prime}[n],$ (17)

where $z^{\prime}[n]$, $c^{\prime}[n]$ and $x[n]$ are all zero-mean random
variables. Thus, the value of $A$ could be deduced from the above expressions
by

$\displaystyle
A=\frac{\text{E}\\{x[n]y^{\prime}[n]\\}}{\sigma}=Q\left(\frac{I_{\text{min}}-\beta}{\sigma}\right)-Q\left(\frac{I_{\text{max}}-\beta}{\sigma}\right).$
(18)

As can be seen from the above expression, the attenuation factor could simply
be represented as the area under the unclipped portion of the biased time
domain signal $x[n]+\beta$. It is important to note that any DC bias
introduced at the TX and/or RX won’t effect the frequency domain symbols since
it will fall on to the unused $0^{\text{th}}$ subcarrier. Therefore, the
electrical power of the time-domain clipping noise could be represented by

$\displaystyle
P_{c}=\sigma_{c}^{2}=P_{\text{elec}}-P_{\text{opt}}^{2}-A^{2}\sigma^{2},$ (19)

where the electrical power of the biased and double-sided clipped signal could
be expressed as follows:

$\displaystyle P_{\text{elec}}=\text{E}\\{\hat{x}[n]^{2}\\}=$
$\displaystyle\frac{\sigma}{\sqrt{2\pi}}\left(\left(I_{\text{min}}+\beta\right)e^{-(I_{\text{min}}-\beta)^{2}/2\sigma^{2}}-\left(I_{\text{max}}+\beta\right)e^{-(I_{\text{max}}-\beta)^{2}/2\sigma^{2}}\right)$
$\displaystyle+\left(\beta^{2}+\sigma^{2}-I_{\text{min}}^{2}\right)Q\left(\frac{I_{\text{min}}-\beta}{\sigma}\right)$
$\displaystyle+\left(I_{\text{max}}^{2}-\beta^{2}-\sigma^{2}\right)Q\left(\frac{I_{\text{max}}-\beta}{\sigma}\right)+I_{\text{min}}^{2}.$
(20)

At the receiver, the multipath optical wireless channel distorted signal is
received by a PD. Furthermore, the additive white Gaussian noise (AWGN) also
plays a role in the electrical domain signal,
$y[n]=h[n]\circledast\hat{x}[n]+w[n]$, obtained after the cyclic prefix (CP)
removal. Note that the effective noise term at the RX, $w[n]$, consists of the
addition of shot and thermal noises, where the shot noise emerges as a result
of ambient light sources and information bearing signal itself. In the case
where high ambient light power at the PD is significantly larger than the
transmit signal power, the shot noise becomes signal independent. Therefore,
the high intensity shot noise at the RX could be modelled as a summation of
independent low power Poisson processes, which could be approximated as a zero
mean Gaussian distribution. Consequently, the effective noise could be
modelled as AWGN, $w[n]\sim\mathcal{N}\left(0,\sigma_{w}^{2}\right)$, where
$\sigma_{w}^{2}=\sigma_{\text{shot}}^{2}+\sigma_{\text{thermal}}^{2}$.
Independent from the shot noise, the thermal noise emerges due to the random
motions of the electrons in the front-end circuitry.

(a) IR band

(b) VL band

Figure 17: Relative optical power, $P_{\text{opt}}~{}(\%)$, for the CIR when
$1\leq L\leq 7$ larger magnitude taps are chosen. The CIRs are given for both
simplified, $h_{s}$, and realistic, $h_{r}$, cabin models for (a) IR band and
(b) VL band sources.

In practical wireless communication systems, the number of channel taps are
limited in the time domain since they follow an exponential decay profile. To
find the effective number of channel taps ($L$) for our simulations, the
fractional optical power analysis depicted in Fig. 17 is used. As illustrated
in Fig. 17, the relative optical power, $P_{\text{opt}}\%$, represents the
portion of optical power when first $L$ largest taps are picked from the CIR
as the effective channel. From the figure, it can be inferred that $L=7$ taps
yield at least $80\%$ of the optical power of the initial CIRs for all the UE
locations and both spectral regions. Consequently, the $7$ highest taps based
CIRs are obtained from MCRT simulation results, are utilized in our BER versus
effective-SNR-per-bit plots. The CP length in the DCO-OFDM system must be
$N_{\text{CP}}\geq L$, to avoid ISI as a rule of thumb. Hence, the CP length
of $N_{\text{CP}}=L$ is adopted in our simulations. By using (15), we can
obtain the frequency-domain signal at the RX after the CP addition and removal
at the TX and RX, respectively as well as FFT operation by

$\displaystyle Y[k]=H[k]\big{(}AX[k]+C[k]\big{)}+W[k],\quad\text{for
}k\in\\{1,2,\cdots,\frac{N}{2}-1\\},$ (21)

where the FFT of $h[n]$, $x[n]$, $c[n]$ and noise term $w[n]$ are denoted by
$H[k]$, $X[k]$, $C[k]$ and $W[k]$, respectively for the $k^{\text{th}}$
subcarrier. It is important to note that the electrical domain frequency
response characteristics of the front-end opto-electronic elements,
$H_{\text{elec}}[k]$, could also be lumped into the channel model if
necessary. Hence, the effective channel becomes,
$H_{\text{eff}}[k]=H[k]H_{\text{elec}}[k]$. In this work, the electrical
domain channel impairments, the analogue/digital and electrical/optical domain
conversions are assumed to be ideal without loss of generality. Thus, the
analytical average BER expression for DCO-OFDM under double-sided clipping and
frequency selective channel effects could be calculated by using [37],

$\displaystyle\text{BER}_{\text{theo}}$
$\displaystyle=\frac{2}{N-2}\sum_{k=1}^{(N/2)-1}\frac{4M_{k,1}M_{k,2}-2\left(M_{k,1}+M_{k,2}\right)}{M_{k,1}M_{k,2}\log_{2}\left(M_{k,1}M_{k,2}\right)}$
$\displaystyle\times
Q\left(\sqrt{\frac{6\gamma_{k}\log_{2}\left(M_{k,1}M_{k,2}\right)}{M_{k,1}^{2}+M_{k,2}^{2}-2}}\right),$
(22)

where $M_{k}=M_{k,1}\times M_{k,2}$ denotes $M$ for $k^{\text{th}}$
subcarrier. The electrical domain effective-SNR-per-bit for the
$k^{\text{th}}$ subcarrier after the zero-forcing (ZF) channel equalization
could also be calculated by

$\displaystyle\gamma_{k}=\frac{BA^{2}\text{E}\\{\lvert
X[k]\rvert^{2}\\}}{R_{k}N\left(\sigma_{c}^{2}+\sigma_{w}^{2}/\lvert
H[k]\rvert^{2}\right)},$ (23)

where the orthogonal frequency division multiplexing (OFDM) signal bandwidth
is given by $B$. Also, the bit rate for the $k^{\text{th}}$ subcarrier could
be calculated by

$\displaystyle
R_{k}=B\log_{2}\left(M_{k}\right)\left(\frac{N-2}{N}\right)\left(\frac{N}{N+N_{\text{CP}}}\right)\quad\text{bits/sec.}$
(24)

By using the above equation, the spectral efficiency of the $k^{\text{th}}$
subcarrier of DCO-OFDM could also be calculated by $\eta_{k}=R_{k}/2B$
bits/sec/Hz.

(a) IR band, $M=4$ ($1~{}\text{bit/sec/Hz}$)

(b) IR band, $M=64$ ($3~{}\text{bits/sec/Hz}$)

Figure 18: BER vs. effective SNR-per-bit performance curves for a DCO-OFDM
system under the MCRT channel dispersion and double-sided clipping
impairments. The simulation results for realistic and simplified cabin models
are given by dashed and solid lines, respectively. The theoretical results are
presented by markers.

(a) VL band, $M=4$ ($1~{}\text{bit/sec/Hz}$)

(b) VL band, $M=64$ ($3~{}\text{bits/sec/Hz}$ )

Figure 19: BER vs. effective SNR-per-bit performance curves for a DCO-OFDM
system under the MCRT channel dispersion and double-sided clipping
impairments. The simulation results for realistic and simplified cabin models
are given by dashed and solid lines, respectively. The theoretical results are
presented by markers.

In our BER simulations, all the subcarriers are modulated by using the same
normalized QAM modulation which yields, $M_{k}=M,~{}\forall k$ and
$\text{E}\\{\lvert X[k]\rvert^{2}\\}=1$. Since the magnitude of the channel
taps, $\lvert H[k]\rvert$, are in the order of $10^{-5}$, in MCRT results, the
electrical PL at the RX becomes $-100$ dB. Therefore, the BER plots are
presented w.r.t. the _received_ electrical-SNR-per-bit value, which could be
calculated by
$\underline{E_{\text{b,elec}}/N_{0}}=E_{\text{b,elec}}/N_{0}-100$ [38]. The
rest of DCO-OFDM system parameters and their descriptions, which are used in
the error performance simulations are given in Table IV.

The BER vs. $\underline{E_{\text{b,elec}}/N_{0}}$ plots of DCO-OFDM for
average spectral efficiency of $1$ and $3$ bits/sec/Hz are given in Figs. 18
and 19, respectively. The circle and square markers represent the computer
simulation results for IR and VL bands, respectively, where the lines are the
theoretical results obtained by using (22). Furthermore the different colours
among each plot depicts the various locations of the UE as explained at the
beginning of the section. As illustrated in Fig. 18, the error performance of
seat B in the IR band outperforms seats C and A result at least $10$ dB in
both low and mid/high spectral efficiency regions. A similar trend can also be
seen in VL band, as depicted in Fig. 19, where the error performance
difference between seat B with seats C and A becomes at least $12$ dB for both
spectral efficiency values. The main reason behind this error performance in
point B2 is the very high received SNR as well as a lack of multipath
dispersion compared to other measurement points. For the UE location A3, DCO-
OFDM error performance under both the IR and VL band channels with simplified
cabin model outperformed the realistic cabin as much as $2$ dB in both
spectral efficiency regions. This difference is also important as it shows the
importance of cabin geometry on the practical system performance.

##  VI Conclusion

In this paper, a reading lights based broadband in-flight LiFi system is
investigated. Accordingly, an MCRT based realistic DL on-board LiFi channel
modelling technique for both IR and VL bands is presented. Accordingly, two
narrow-body aircraft cabin models, one with accurate dimensions, surface
geometry and curvatures, and another with planar surfaces are generated.
Moreover, economy class cabin interior seating is also considered in our
simulations. To model the source, receiver and surface coating optical
characteristics, measurement based spatio-angular and spectral properties are
used. Results show that the location of the UE and cabin simplification have a
significant impact on the channel parameters. The analytical expression and
computer simulations based BER curves obtained for DCO-OFDM also confirmed the
MCRT results for a practical system performance. Consequently, favourable
propagation characteristics and high link budget properties makes in-flight
LiFi a highly suitable candidate for on-board broadband 5G NR applications.

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|  Anil Yesilkaya (Member, IEEE) received the B.Sc. (Hons.) and M.Sc. degrees
in electronics engineering from Kadir Has University, Istanbul, Turkey, in
2014 and 2016, respectively. He received the PhD. degree in digital
communications from the University of Edinburgh, Edinburgh, U.K., in 2021. He
is currently working as a postdoctoral research associate in Horizon 2020
project 5G-CLARITY at the LiFi Research and Development Centre, University of
Strathclyde. He was a recipient of the Best Paper Award from the IEEE
International Conference on Communications (ICC) Optical Networks and Systems
(ONS) Symposium in 2018.
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|  Harald Haas (Fellow, IEEE) received the Ph.D. degree from The University of
Edinburgh in 2001. He is a Distinguished Professor of Mobile Communications at
The University of Strathclyde/Glasgow, Visiting Professor at the University of
Edinburgh and the Director of the LiFi Research and Development Centre. Prof
Haas set up and co-founded pureLiFi. He currently is the Chief Scientific
Officer. He has co-authored more than 600 conference and journal papers. He
has been among the Clarivate/Web of Science highly cited researchers between
2017-2021. Haas’ main research interests are in optical wireless
communications and spatial modulation which he first introduced in 2006. In
2016, he received the Outstanding Achievement Award from the International
Solid State Lighting Alliance. He was the recipient of IEEE Vehicular Society
James Evans Avant Garde Award in 2019. In 2017 he received a Royal Society
Wolfson Research Merit Award. He was the recipient of the Enginuity The
Connect Places Innovation Award in 2021. He is a Fellow of the IEEE, the Royal
Academy of Engineering (RAEng), the Royal Society of Edinburgh (RSE) as well
as the Institution of Engineering and Technology (IET).
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