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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

Abstract—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.

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

NLOS Scenario

1

0.1

0.1

1.5

0.3

0.4

2

0.5

1.5

2.5

0.3

3.8

3

0.1

6.7

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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