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In this paper, we report for the first time on a new channel modelling technique for multi-link LiFi scenarios. By considering simplified numerical calculation, it models the links between multiple optical frontends and multiple mobile devices much faster than previous approaches. For the first two diffuse reflections, we replace ray tracing method by frequency domain channel modelling technique. For the other higher order diffuse reflections, we use a well-established model based on the integrating sphere. For validation of our new approach, we performed distributed 4x2 MIMO channel measurements. Comparison of simulation and measurement yields a relative mean square error below 5 percent for the signals with a free line-of-sight. Our new technique enables efficient modeling of mobile scenarios and analyzing statistical properties of the LiFi channels.
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An Efficient Multi-Link Channel Model for LiFi
Sreelal Maravanchery Mana, Kerolos Gabra Kamel Gabra, Sepideh Mohammadi Kouhini, Peter Hellwig, Jonas Hilt, Volker Jungnickel
Photonic Networks and Systems, Fraunhofer Heinrich Hertz Institute,
Einsteinufer 37, 10587 Berlin, Germany
sreelal.maravanchery@hhi.fraunhofer.de
AbstractIn this paper, we report for the first time on a new
channel modelling technique for multi-link LiFi scenarios. By
considering simplified numerical calculation, it models the links
between multiple optical frontends and multiple mobile devices
much faster than previous approaches. For the first two diffuse
reflections, we replace ray-tracing method by frequency domain
channel modelling technique. For the other higher order diffuse
reflections, we use a well-established model based on the
integrating sphere. For validation of our new approach, we
performed distributed 4x2 MIMO channel measurements.
Comparison of simulation and measurement yields a relative
mean square error below 5 percent for the signals with a free
line-of-sight. Our new technique enables efficient modeling of
mobile scenarios and analyzing statistical properties of the LiFi
channels.
Keywords Optical wireless communication, indoor LiFi,
MIMO, channel modelling, channel characterization.
I. INTRODUCTION
The emergence of LiFi for indoor communications opens
up new possibilities for wireless services in crowded multiuser
scenarios [1]. LiFi offers reliable, secure, high data rate
wireless links [2]. It is hard to wiretap or jam a LiFi link
because signals propagate only inside the room and in small
cells defined by the light beam, improving reliability and
security. However, the use of LiFi in indoor scenarios may be
challenging due to the line-of-sight (LOS) blockage, although
connectivity is still possible via weak diffuse reflections. A
better approach is to deploy multiple transmitters at the ceiling
and use another LOS link for resilience in case of blockage.
These techniques are also referred to as multiple-input
multiple-output (MIMO).
Channel modelling is an important step when developing
any communication system, and it is needed for performance
evaluation [3]. A comprehensive understanding of the channel
and an accurate prediction of the link are indispensable to
develop an optimal transmission scheme for LiFi.
In most indoor environments, the light is diffusely
reflected, and the resulting multi-path signals lead to inter-
symbol interference (ISI). The importance of theoretical and
experimental analyses of indoor optical wireless channels is
evident. Recently, different channel modelling methods were
introduced, which can be classified into deterministic [4]-[8]
and non-deterministic approaches [9]-[12]. Most of these
techniques have not been validated through measurements in
real scenarios. Recently, a site-specific characterization based
on non-sequential ray tracing has been introduced by using
commercial optical design software, Zemax® [13]. This
approach is capable of obtaining the channel impulse response
for any source while considering both the specular as well as
mixed specular-diffuse reflections. However, ray tracing
operates in the time domain and it follows each path until it
either absorbed or received and modelling MIMO and
mobility becomes very complex in this way. In practice, fewer
reflections are used because the LOS and first diffuse
reflections have the most noticeable effects on the achievable
data rate.
For future wireless applications, it is expected that a large
number of internet of things (IoT) devices will be connected
through LiFi systems by using distributed optical frontends
(OFEs). Due to a large number of concurrent links, the
existing channel modelling techniques for LiFi become
insufficient. A new approach is needed aiming at the so-called
system-level analysis with a large number of links including
the desired signals and their mutual interference. A feasible
channel model should provide the channel parameters of a
given indoor environment for a large number of parallel links
and support the mobility of the IoT devices as well. Only in
this way, it becomes possible to characterize the channel
quality for many devices that will communicate in parallel.
For the first time, in this paper, we introduce a simplified
channel modelling technique for large-scale LiFi
deployments. We combine the frequency domain technique
recently introduced by H. Schulze [6] with the well-known
integrating sphere model [7]. The combination of both
approaches enables efficient planning of future LiFi networks.
The main contribution of this paper is to show how both
approaches can be combined efficiently and the first
validation of this new approach is provided using the
measurements in a controlled environment. Measurements
have been conducted in a 4x2 MIMO downlink scenario, as
shown in Fig.1, with 4 OFEs and 2 mobile devices using a
direct current (DC) biased orthogonal frequency division
multiplexing (OFDM) based channel-sounding technique. For
validation, we compare measurement and simulation results.
The remainder of the paper is organized as follows.
Section II describes the efficient LiFi channel modelling
methodology and discusses the simulation environment.
Fig. 1. Measurement scenario in an empty conference room.
Transmitters and receivers are marked in red and blue color.
Section III introduces the experimental setup, the
measurement scenario and configurations of the optical
frontends. Section VI reports the simulation results as well as
measurement results. A detailed discussion of the results are
provided in section V and conclusions are given in section VI.
II. LIFI CHANNEL MODELLING METHODOLOGY
The channel modelling simulations are performed in the
frequency domain rather than in the time domain. This method
calculates channel transfer functions instead of impulse
responses. LiFi links are modelled as LOS link and NLOS
links. For LOS, we followed the widely accepted model as in
[14], which is based on the orientation and optical parameters
of Tx and Rx. For NLOS, we calculated responses for the first
two diffuse reflections using the frequency domain technique
[6] and all higher order reflections using the model based on
the integrating sphere [7]. In both LOS as well as NLOS
channel modelling scenario, we considered the same optical
parameters such as field of view (FOV) of the photodiode
(PD) and radiation pattern of the LED same as given in the
[13].
A. LOS Channel Model
The generalized LOS channel model between Tx and Rx
is given as
 
Here  is the transfer function coefficient between Tx
and Rx which can be described same as in Equation (2) in [15].
This coefficient depends on the FOV of the photodiode and
the radiation pattern of LED [14]. The variable  is the
delay time which depends on  being the distance
between Tx and Rx and which is the speed of the light [6].
B. First two diffuse reflections
The first two diffuse reflections are calculated using the
frequency domain method [6]. This method considers the
reflecting surfaces as surface elements. This allows
assembling all mutual LOS links between all surface elements
and the links between the surface elements to the Rx and Tx
in a matrix form so that higher-order reflections can be
described by consecutive matrix multiplications [6].
We assume that there are surface elements in the room.
For a single Tx to Rx scenario, as described in [6], the entire
diffuse channel model can be represented as
  
 
where is the reflection order,  is the LOS transfer
functions of the link from each surface element in the room to
the receiver,  is the LOS transfer functions for the links
from the transmitter to all surface elements, is a diagonal
 reflectivity matrix, where each diagonal element
represents the reflectivity of the  surface element. The
 matrix  is the intrinsic transfer matrix, where each
element  in this matrix represents the LOS transfer
function from  surface element to surface element. Note
that, for simplicity, we consider all reflecting surface
elements as Lambertian surfaces.
In our simulations, Equation (3) is calculated only for the
first two reflections using an iterative approach, see
section III. D in [6]. For a MIMO scenario, we followed the
same approach as given in [6] (see section III. G), where
 and  is calculated for each Tx and Rx
configuration in the room. Here, for a particular indoor
scenario, it is required only once to calculate the intrinsic
transfer function matrix . In the case of mobile MIMO
scenario, furthermore, we needed to calculate 
corresponding to the movement of users in the room.
C. Higher order diffuse reflections
From previous channel measurements, we observed that
the higher order diffuse reflections have all very similar
characteristics [16]. This is intuitive as diffuse reflections
illuminate the entire room. This motivates us to consider that
higher order diffuse reflections depend more on the
environment than on the orientation of Tx and Rx. Higher
order diffuse reflections can be modelled altogether by using
Ulbricht’s integrating sphere model, which has been adapted
to regular room dimensions in [7]. In contrast to the
microscopic approach described above, this macroscopic
model does not include any details of the room except a few
basic parameters. The generalized diffuse channel model for a
given room model is given by Equation (9) in [7]. Since the
first two diffuse reflections are calculated using the previously
mentioned frequency-domain method, here we need to
calculate only the higher-order diffuse reflections starting
from the third order onwards. Thus, the higher order diffuse
reflections can be expressed as


where is the exponential decay time which is related to room
parameters as described in [7]. The variable  is the
diffuse channel gain excluding the first two reflections and can
be expressed as
  


and it can be simplified as
  


where  is the area of the room surface,  is the area
of the receiver, is the reflectivity of the region initially
illuminated by the Tx and is the average reflectivity of the
room, see [7].
This model provides an approximate result for higher
order reflections in a given room. However, it lacks precision
at the beginning of the impulse response, particularly during
the first and second diffuse reflections, which we have
calculated for each Tx-Rx link separately. Since higher order
diffuse reflections do not dependent on Rx orientations, all
calculations have been made only once for a downlink mobile
user scenario.
Finally, the complete transfer function of the LiFi channel
can be represented as

where ranges between 0 and 1 in Equation (2). Using
Equation (6), we calculate the channel transfer function at
each frequency . Note that, in this paper, for simplicity we
considered the reflecting surfaces as Lambertian. The model
is not limited regarding the surface reflection characteristics.
It is possible to define any surfaces with any reflectance values
and characteristics (like Phong reflection model [17]).
III. LIFI CHANNEL MEASUREMENTS
MIMO channel measurements have been conducted in an
empty conference room, with the size of 5.8 m x 4.5 m x 3.1 m
as shown in Fig. 1, using a channel sounder system developed
in our lab [18]. The LiFi channel sounder is capable of
performing broadband 8×8 MIMO channel measurements at
frequencies of up to 250 MHz. The widely used multi-carrier
approach, DC biased OFDM, is used for simultaneous
measurement of MIMO LiFi channels versus frequency as
described in [18]. Each frequency response of the LiFi system
includes the response of optical frontends, wires and optical
propagation channels. All the measurement data are post-
processed using the same method reported in [19].
Particularly, frontends and cable responses were calibrated
out.
The measurements are conducted in downlink and mobile
user scenario. During the measurements, the transmitters are
kept in a 2m x 2m grid size, at 2.85 m height. The receivers
are kept at 1m height looking towards the ceiling. In the
downlink, Rx1 is kept in the center position between Tx2 and
Tx4 and Rx2 is in the middle between Tx1 and Tx3. Finally,
we considered a mobile user scenario where Rx1 moves
around in the room and Rx2 is kept fixed at the nearby center
position in the room. Measurements have been done at 40
different positions, where Rx1 is moving along the 2 m x 2 m
grid line.
IV. RESULTS
In this section, we report the measurement and simulation
results. By assuming a MATLAB based simplified room
model and considering all optical parameters the same as
reported in [13], we estimated the channel response in three
different configurations such as i) SISO, ii) 4x2 MIMO and
iii) a mobility scenario. Note that, in our simulations, we
considered only walls, ceiling, and floor of the room where the
reflectivity parameters are the same as given in [13]. At first,
to validate our new simulation method, we consider the
experimental results of the SISO scenarios that we reported in
[16]. In the same room, we performed 4x2 MIMO
measurements and compared those results with simulation
results.
A. SISO Scenario
The amplitude response of the LiFi channels in a SISO
scenario is shown in Fig. 2. As described in [13], here we
considered two configurations; LOS and NLOS with
dominant first order reflections.
Fig. 2 (a) shows the amplitude response of the LiFi
channels at different distances where Tx and Rx are looking
each other in a LOS scenario. We observe that the amplitude
response is relatively flat overall frequencies. As the
separation distance between Tx and Rx increases from 1 m to
3 m, the DC channel gain reduces. From the simulation results,
shown as dotted lines, it is clear that the simulated channel
response is in good agreement with measured results.
Fig. 2 (b) shows the amplitude response of the NLOS
channels where Tx and Rx kept in NLOS configurations at
different distances. Both Tx and Rx face towards the ceiling
as described in [13]. Here most of the dominant contribution
of the signals come from the first order reflection path. As the
separation distance increases, the possible first order
reflection reduces and higher order reflections get larger [16].
In this case, for the channels with DC channel gain more than
-35 dB, simulation results are in good agreement with the
experimental results. As distance increases, ripple effects
become noticeable at higher frequencies due to the noise,
which creates more deviation when compared to the
simulation results.
To measure the accuracy of our simulation methodology,
we calculate the mean square error (MSE) between
measurement and simulation data for both LOS and NLOS
channels (shown in Fig. 2). The calculated MSE values are
shown in Table I. It is observed that the MSE is less than 2
percentage for LOS scenarios and less than 5 percentage for
Fig. 2. Amplitude response of the LiFi channels in a SISO
scenario. (a) LOS channels, (b) NLOS channels with dominant first
order reflections [13].
TABLE I. MEAN SQUARE ERROR
Distance of
separation
between
Tx and Rx
(in meters)
MSE in percentage
LOS Scenario
1
0.1
1.5
0.3
2
0.5
2.5
0.3
3
0.1
NLOS configurations with higher channel gain. Note that, the
error is increased if the DC channel gain is decreased below -
35 dB.
B. 4X2 MIMO Scenario
The measurement and simulation results of a distributed
4x2 MIMO LiFi (see Fig. 1) are shown in Fig. 3. The channel
responses at Rx1, placed in the middle of transmitters Tx2 and
Tx4 (see Fig. 1), are shown in Fig. 3 (a). There are strong LOS
signals from Tx2 as well as from Tx4 and weak signals from
other transmitters Tx1 and Tx3. In Fig. 3, bold lines denote the
measured channel responses and dotted lines show the
simulated channel responses. Since all transmitters kept in a
2 m x 2 m grid configuration, as shown in Fig. 1, the simulated
channel responses between Rx1 to Tx2 and Rx1 to Tx4 will
be the same. In the experiment, however, due to small
differences in the optical frontends, wires and connectors, the
measured responses have minor differences from each other
and do not overlap like the simulated curves. We observed that
channel responses with respect to the transmitters Tx2 and
Tx4 have lower signal strength. So these measurement results
could be affected by the noise. That is the reason why we
observe that the measured data fluctuate more noticeably
when compared to the simulation results. To measure the
accuracy of our simulation methodology, we calculate the
relative MSE between measurement and simulation data of all
the links between each Rx and Tx. The MSE of links from
Rx1 to Tx1, followed by links to Tx2, then Tx3, and then Tx4
are 19.7%, 3.25%, 12.3%, and 0.63%, respectively. From
these results, it is obvious that channels with strong signal
strength and DC channel gain above -35 dB have lower MSE,
i.e. less than 5%.
Fig. 3 (b) shows the channel responses for Rx2, placed in
the middle between Tx1 and Tx3. It is clear that Rx2 has
strong LOS signals from Tx1 and Tx3 and weak signals from
Tx2 and Tx4. Here, in the simulated channel responses, the
links between Rx2 to Tx1 and Rx2 to Tx3 will have the same
response. Similarly, links between Rx2 to Tx2 and Rx2 to Tx4
are similar. As explained before, due to mismatch in the
optical frontends and other connectors, there will always be
minor deviations in the measurement results, which are not
identical to those in the simulations. Here MSE of links from
Rx2 to Tx1, followed by links to Tx2, then Tx3, and then Tx4
are 1.26%, 24%, 0.96%, and 36%, respectively. We observed
that MSE of the links with high channel gain is lower.
C. MIMO Mobility Scenario
In this scenario, we consider that Rx1 is moving around
the room while another receiver Rx2 is kept at a fixed position.
Fig. 4 shows the calculated heat map of the expected DC
optical power distribution in the room where Rx is kept at a
height of 1m. Positions of all Tx are marked in red color and
positions of Rx1 and Rx2 are marked in blue and green colors,
respectively. We have done measurements by moving Rx1 to
40 different positions as shown in Fig. 4.
Fig. 5. Channel gain at 5 MHz of the LiFi channels in a MIMO
mobility scenario.
Fig. 3. Amplitude response of the LiFi channels (a) at Rx1 and
(b) at Rx2 in a 4x2 MIMO scenario.
Fig. 4. Amplitude optical power distribution. All transmitters
are marked in red color. Positions of Rx1 are marked in blue color
and Rx2 position is marked in green.
To compare the experimental data with the simulations,
we calculate the channel gain at a lower frequency of 5 MHz
corresponding to each position. Fig. 5 shows the variation of
the channel gain concerning the logarithmic distance of the
separation between Tx and Rx. Channel gain is plotted for
each Tx-Rx link for all 40 positions. When the receiver is
moving far away from good illumination coverage of one of
the transmitter, then the corresponding channel gains are
reduced. In the experiment, we observed that channel gain
variation is between -15 dB to -48 dB for distance variation
from 1.85m to 3.33m. Due to mismatches in the optical
frontends, there will be negligible differences in the channel
gains at lower distances. When Rx1 is far from the
transmitters, then corresponding channel gains will be lower
and there is random variation due to noisy data.
In the simulations, since all transmitters are placed in a
2 m x 2 m grid, channel gain variations for all Tx links with
respect to Rx1 will be the same. As shown in Fig. 5, the
channel gain variations for the simulated channel gain at
5 MHz is from -15 dB to -44 dB. When compared with
experimental data, the deviation of simulated channel gain
with respect to experimental data is less at lower distances.
The difference in simulated channel gain, when compared to
experimental data is significant for higher distance where
channel gain is lower than -35 dB. This study shows that
approximate results for channel gain variations can be
estimated for a mobile device with low error. From the
numerically calculated channel, we can calculate MIMO
channel characteristics, such as statistics of singular values
and channel throughput with small error and compare them
with experimental data.
V. DISCUSSION
This study proposes an efficient channel modelling
method for LiFi channels, by combining the frequency-
domain technique in [6] with the integrating sphere approach
in [7]. Our results indicate a good agreement between
simulation results and experimental results. As principal
limitations, we have considered a simplified geometrical
model of the room to verify this technique first in a scenario
with minor complexity and characterize the new channel
modelling method in a mobile scenario in this way. Since we
are calculating the channel transfer functions, gain variations
can be calculated much faster than using ray tracing in the time
domain.
The implementation complexity of the new method
depends mostly on the performance of the selected computer.
The mobile scenario was calculated in a few minutes on a
standard laptop. Since most calculations are based on matrix
multiplications, instead of tracing each ray individually, it is
possible to speed up the calculations further by utilizing high
performance GPUs. This approach can be suitable to estimate
models especially for crowded LiFi systems with large
numbers of mobile users. It may also be helpful for estimating
how many access points are visible, how to combine signals
for optimized communication and characterize positioning in
large LiFi deployments.
Effective communication in most of the LiFi channels is
either due to LOS or first order reflections. While the user is
moving in the room, the propagation channels vary. Using our
simulation methodology, we can easily estimate approximate
results for these channel variations. We demonstrate that
simulated channel responses with gain above -35 dB have 1 to
2 dB differences when compared with experimental results.
As the gain goes below -35 dB, there is significant noise in the
experimental data and observe the significant difference of
around 2 to 4 dB when compared with simulation.
Note that, in this simulation model, as a major limitation,
accuracy of the method depends mainly on the size and
number of surface elements. As the size gets smaller, there
will be more surface elements and thus computation time gets
increases. The relation between resolution of surface element
 and time resolution  of the impulse response can be
expressed as     , where is the speed of the light.
With better time resolution, smaller i.e. more surface elements
are required, and hence the matrices in Equation (2) get larger
and simulation time will increase.
Moreover, this simulation model can be used for other
indoor scenarios including rooms filled with more obstacles.
In that case, using other algorithms, e.g. [20], possible
blockages in each link should be captured exactly and
included in the LOS as well as in frequency domain model. In
the case of diffuse reflections, the first two reflections usually
result in distinct peaks in the impulse response while all the
later diffuse reflections fold into one exponential decay (see
Fig.3 in [7]). Diffuse reflections from additional objects in the
room will be included precisely by using the frequency-
domain technique and their overall impact on the path loss and
the average time-of-flight will be captured by the sphere
model.
VI. CONCLUSION
In this paper, a simplified numerical channel modelling
method for the indoor LiFi communication channel has been
presented. The LiFi channel simulations for LOS as well as
NLOS diffuse paths are computed in the frequency domain
rather than in time domain. For NLOS diffuse channels, we
have considered the frequency domain channel modelling
technique along with the integrating sphere model.
At first, to validate our simulation method, we compared
the simulation results with the previously published SISO
measurement results. These results show that there exists a
good matching when compared with experimental data with
minimum error. To validate our simulation method in a
realistic LiFi scenario, we conducted the 4x2 distributed
MIMO measurement in an empty room. Then we compared
the measurement results with simulations results and show
that there is a good agreement between the results.
In the same MIMO configuration, we considered one Rx
at 40 different positions in the room. Measurement and
simulation results indicate that channels with a gain of more
than -35dB are in good agreement with respect to
experimental results and channels with gain less than -35 dB
have a difference of 2-4 dB. The major advantage of our new
modelling approach is the reduced computation time,
compared to the ray tracing, which allows the efficient
modelling of large LiFi scenarios with many mobile devices,
suitable for future IoT applications.
ACKNOWLEDGMENT
This research is funded by the VisIoN project, a European
Union’s H-2020 MSCA ITN program under the grant
agreement no 764461. It is also based upon work from COST
Action CA19111 NEWFOCUS, supported by COST
(European Cooperation in Science and Technology).
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