Towards Terabit LiFi Networking

Ahmad Adnan Qidan, Taisir El-Gorashi1 and Jaafar M. H. Elmirghani

School of Electronic and Electrical Engineering, University of Leeds, LS2 9JT, U.K.

Keywords:

Optical Wireless Communication, Infrared Lasers, Interference Management, Load Balancing, Optimization,

Hybrid Networks.

Abstract:

Light Fidelity (Li-Fi) is a networked version of optical wireless communication (OWC), which is a strong

candidate to fulﬁll the unprecedented increase in user-trafﬁc expected in the near future. In OWC, a high

number of optical access points (APs) is usually deployed on the ceiling of an indoor environment to serve

multiple users with different demands. Despite the high data rates of OWC networks, due to the use of the

optical band for data transmission, they cannot replace current radio frequency (RF) wireless networks where

OWC has several issues including the small converge area of an optical AP, the lack of uplink transmission

and high blockage probabilities. However, OWC has the potential to support the requirements in the next

generation (6G) of wireless communications. In this context, heterogeneous optical/RF networks can be con-

sidered to overcome the limitations of OWC and RF systems, while providing a high quality of service in terms

of achievable data rates and coverage. In this work, infrared lasers, vertical-cavity surface-emitting(VCSEL)

lasers, are used as the key elements of optical APs for serving multiple users. Then, transmission schemes such

as zero forcing (ZF) and blind interference alignment (BIA) are introduced to manage multi-user interference

and maximize the sum rate of users. Moreover, a WiFi system is considered to provide uplink transmission

and serve users that experience a low signal to noise ratio (SNR) from the optical system. To use the re-

sources of the heterogeneous optical/RF network efﬁciently, we derive a utility-based objective function that

aims to maximize the overall sum rate of the network. This complex problem can be solved using distributed

algorithms to provide sub-optimal solutions with low complexity. The results show that the sum rate of the

proposed hybrid network is higher than the standalone optical network, using different transmission schemes.

1 INTRODUCTION

In the last decade, radio frequency (RF) wireless net-

works have suffered from trafﬁc congestion due to the

massive use of the Internet in different ﬁelds. There-

fore, complementary wireless networks are highly

required to ofﬂoad the trafﬁc of RF wireless net-

works, while providing high data rates, low latency,

low power consumption and high security, etc. Re-

cently, optical wireless communication (OWC) us-

ing license-free optical bandwidth have been inves-

tigated to support high communication speeds com-

pared to RF networks. In (Li et al., 2014; Wang

et al., 2014), light-emitting diodes (LEDs) are used

for illumination and data transmission, achieving high

aggregate data rates. Thus, LED-based OWC sys-

tems have low cost infrastructure as sending infor-

mation occurs while LEDs are already on for provid-

ing illumination. In contrast to incandescent bulbs,

LEDs are characterized by their small size, long life-

time, high energy efﬁciency and low cost. How-

ever, LEDs have relatively low modulation speeds,

which may cause limitations in terms of the achiev-

able data rates of OWC systems. In (Adnan-Qidan

et al., 2021; Alazwary et al., 2021), vertical-cavity

surface-emitting(VCSEL) lasers are proposed for use

as transmitters to serve users. It is shown that clus-

ters of VCSELs have the potential to provide Tbps

data rates due to their high modulation speeds. How-

ever, the transmitted power of VCSEL must obey eye

safety regulations.

Interference management is a crucial issue in

wireless networks. In particular, an OWC system re-

quires a high number of optical APs to ensure cover-

age for multiple users distributed in an indoor envi-

ronment. Therefore, muti-user interference must be

addressed to maximize the multiplexing gain of the

network. Orthogonal transmission schemes such as

time division multiple access (TDMA) (Abdelhady

et al., 2019), code division multiple access (CDMA)

(Qiu et al., 2018) and orthogonal frequency division

multiple access (OFDMA) (Bawazir et al., 2018) can

Qidan, A., El-Gorashi, T. and Elmirghani, J.

Towards Terabit LiFi Networking.

DOI: 10.5220/0010955000003121

In Proceedings of the 10th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2022), pages 203-212

ISBN: 978-989-758-554-8; ISSN: 2184-4364

203

be implemented for assigning exclusive resources to

each user, which results in a low spectral efﬁciency.

Transmit precoding (TPC) such as minimizing the

mean square error (MMSE) (Sifaou et al., 2017),

zero-forcing (ZF) (Marshoud et al., 2015), or inter-

ference alignment (IA) (Pham et al., 2017), are imple-

mented for optical wireless networks to serve all users

simultaneously. However, TPC schemes are derived

originally for RF networks, and therefore, they must

be modiﬁed prior to considering their implementation

in optical wireless networks. In other words, the per-

formance of TPC schemes is subject to the unique

characteristics of the optical signal. For instance, the

transmitted signal must be strictly non-negative, and

therefore, a DC current bias is applied to eliminate

the negative values of the transmitted signal, which

might cause distortion for useful information. In addi-

tion, TPC schemes require channel state information

(CSI) at optical transmitters in order to align the in-

terference among users, which is challenging to pro-

vide such information in wireless networks (Adnan-

Qidan et al., 2019). Recently, blind interference align-

ment (BIA) has been applied for optical wireless net-

works to align multi-user interference without CSI at

transmitters (Morales-C

espedes et al., 2017; Adnan-

Qidan et al., 2019; Qidan et al., 2021b). Particularly,

in (Morales-C

espedes et al., 2017), a special optical

receiver called reconﬁgurable detector is proposed to

enable the implementation of BIA in optical wireless

networks, where each user must have the ability to

switch its channel state following a predeﬁned pat-

tern of BIA. It is shown that BIA overcomes the lim-

itations of the optical signal as its precoding matrix

is given by positive values. Besides, BIA avoids the

need for CSI at transmitters, achieving high user rates

compared to other transmission schemes including or-

thogonal and TPC schemes. However, BIA requires

large channel coherence time to guarantee that the op-

tical channel remains static during the transmission of

information to multiple users (Gou et al., 2011), and

therefore, each user can decode its information with

minimum error maximizing the DoF of a network.

A Heterogeneous optical/RF wireless network can

provide a wide connectivity area for Mobil users in

an indoor environment. It is worth mentioning that

each optical AP illuminates a small and conﬁned area

referred to as attocell, and therefore, users might ex-

perience high inter-cell interference that results in low

SNR. Additionally, uplink transmissions in OWC sys-

tems are usually implemented using different optical

frequency bands. Therefore, hybrid optical/RF net-

works can overcome these challenges. At this point,

resource management and user association must be

taken into account due to the fact that optical and RF

systems differ in terms of coverage and available re-

sources. In (Wang et al., 2017), load balancing is ad-

dressed in a hybrid optical/WiFi network to maximize

the overall sum rate of the network. In (Adnan-Qidan

et al., 2020) an optimization problem is formulated in

a BIA-based hybrid optical and WiFi network to re-

lax the limitations of BIA while providing high data

rates. In (Qidan et al., 2018), a load balancing ap-

proach is proposed, in which a WiFi system plays the

role of serving users that experience degraded opti-

cal system performance. It is worth mentioning that

the problems of resource management and user asso-

ciation are usually deﬁned as Mixed integer nonlin-

ear programming (MINLP) problems that have high

complexity. In (Qidan et al., 2021a) distributed al-

gorithms via Lagrangian multipliers are proposed for

solving these problems while providing sub-optimal

solutions with low complexity, where the main prob-

lem is divided into sub-problems that can be solved

separately.

In this work, a laser-based optical wireless system

is considered, coexisting of a WiFi system for serv-

ing multiple users. We ﬁrst deﬁne our system model,

which is composed of multiple optical APs deployed

on the ceiling providing downlink transmission and a

WiFi AP that provides uplink transmission and serves

users blocked from receiving a high optical power.

Then, the achievable user rate is derived taking into

consideration the implementation of different trans-

mission schemes, ZF and BIA. Finally, an optimiza-

tion problem is formulated to manage the resources of

the hybrid network jointly with user association. This

problem can be solved directly providing an optimal

solution with high computational time. Therefore, a

distributed algorithm is proposed to obtain a solution

considerably close to the optimal one with low com-

plexity. The results show that the sum rate of the hy-

brid network is higher than the standalone optical sys-

tem.

2 SYSTEM MODEL

We consider a number of optical APs deployed on the

ceiling given by L, l = {1, ...,L}, and each optical AP

consists of a certain number of VCSELs, L

, as shown

in Fig. 1. This optical wireless system serves K,

k = {1, ...,K}, users randomly distributed on the re-

ceiving plane. To provide a wide ﬁeld of view (FoV),

each user is equipped with a reconﬁgurable detector

composed of M photodiodes, which point to differ-

ent directions providing linear independent channel

responses, as shown in Fig. 2. Focusing on a generic

user k, k ∈ K, connected to optical AP l at time n, the

OWC-SP 2022 - Workshop on Optical Wireless Communications: Status and Perspectives

204

AP 1

AP 𝑙

AP 𝐿

User 1

User

WiFi AP

IR reconfigurable detector

Receiving plane

Ceiling

Floor

Figure 1: System model of a hybrid network composed of

multiple optical APs and a WiFi system.

signal received at its photodiode m, m ∈ M, is

[k,l]

[n] = h

[k,l]

[n])

x[n] + z

[k,l]

[n], (1)

where h

[k,l]

[n])

∈ R

×1

, m

[k,l]

[n] is the mode

of photodiode m at time slot n, x is the transmitted

signal and z

[k,l]

is real valued additive white Gaussian

noise with zero mean and variance given by the sum

of shot noise, thermal noise and the intensity noise of

the laser, i.e.,

= σ

∑

+ RIN

∑

6=l

[k,l

]

t,l

)

B, (2)

where σ

∑

is the sum of shot noise and thermal noise,

and RIN is the relative intensity noise of the VCSEL

transmitter (Adnan-Qidan et al., 2021). Note that,

[k,l

]

is the interference channel between user k and

adjacent optical AP l

, δ

is the responsivity of pho-

todiode m, P

t,l

is the optical power of AP l

and B is

the single-sided bandwidth of the system.

In this work, a WiFi AP is considered to pro-

vide uplink transmission and serve users that receive

low optical power from the optical APs. In this con-

text, the optical and WiFi systems are connected to

a central unit that controls user association and the

resources of the network such that load balancing be-

tween the systems is achieved (Adnan-Qidan et al.,

2020). Moreover, the central unit has information on

the distribution of the users, in addition to some infor-

mation that varies based on the transmission scheme

considered for managing the interference among the

users in the hybrid network. In particular, orthogonal

transmission is considered for the WiFi system, while

ZF or BIA is applied for the optical system.

2.1 Optical Transmitter

The optical channel is usually given by Line-of-Sight

(LoS) and diffuse components. That is, the optical

channel between AP l and user k at photodiode m is

[k,l]

(m) = h

[k,l]

LoS

(m) + h

diff

( f )e

−j2π f ∆T

, (3)

where h

[k,l]

LoS

(m) corresponds to the LoS link, h

diff

are

non-LoS components and ∆T is the delay between

them. Note that, a reconﬁgurable detector is con-

sidered in this work, and therefore, each user has a

wide FoV receiver, which results in detecting a large

portion of the optical power radiated from LoS links.

Given this point, non-LoS components can be ne-

glected for the sake of simplicity (Adnan-Qidan et al.,

2021).

The power distribution of the VCSEL-based op-

tical AP follows a Gaussian function of multiple

modes. In this context, the transmitted power of the

optical AP is determined by the beam waist W

, the

wavelength λ and the distance d from the ceiling to

the receiving plane. Thus, the beam radius of the laser

at distance d is

= W

1 +





1/2

, (4)

where d

is the Rayleigh range given by

πW

, (5)

where n = 1 is the refractive index of air. Moreover,

the intensity spatial distribution of the laser over the

transverse plane at distance d can be expressed as

I(r,d) =

πW

exp



−



, (6)

where r is the radial distance from the center of the

beam spot and the distance d.

Considering that the detection area of the recon-

ﬁgurable detector is A

rec

, all the photodiodes of the

reconﬁgurable detector have the same size and detec-

tion area. Thus, the detection area of photodiode m is

given by A

rec

, m ∈ M. In this case, the received

power of user k at photodiode m from optical AP l is

given by

m,l

/2π

I(r,d)2πrdr

= P

t,l

1 −exp

−2



2πW



(7)

Towards Terabit LiFi Networking

205

BIA-

Signal

processing

Signal

Selector

Decoding

Data

Photodiode

𝑀

. . . .

𝜑

𝑙

𝑘

(𝑀)𝜑

𝑙

𝑘

(1)

Figure 2: Reconﬁgurable optical detector.

2.2 Reconﬁgurable Detector

The receiver considered in this work is composed of

M photodiodes that provide channel responses lin-

early independent following an angle diversity ar-

rangement (Morales-C

espedes et al., 2017). As

shown in Fig. 2, all the photodiodes are connected to a

single signal processing chain through a selector, min-

imizing the power consumption of the receiver. Each

photodiode m has a unique orientation given by its

polar and azimuth angles, which are denoted as θ

[k,m]

and α

[k,m]

, respectively. Thus, the orientation vector

of photodiode m of user k is given by

[k,m]

sin



[k,m]



cos



[k,m]



sin



[k,m]



sin



[k,m]



, cos



[k,m]

i

(8)

Moreover, the irradiance and incidence angles are

determined by

[k]

= arccos

·v

[k]

kkv

[k]

(9)

[k]

(m) = arccos

[k,m]

·v

[k]

[k,m]

kkv

[k]

(10)

respectively, where

is the normal orientation vec-

tor of optical AP l and v

[k]

is the vector from optical

AP l to user k . Note that, each optical AP points to

the ﬂoor, and hence, the normal orientation vector is

n = [0,0,−1]. It is worth mentioning that the photo-

diodes arrangement of a reconﬁgurable detector can

follow different geometrical patterns including pyra-

midal, hemispherical or random receiving orientation

angle (ROA) distributions such that providing distinct

and linearly independent channel responses is guaran-

teed.

At this point, the channel matrix of user k con-

nected for example to L optical APs is given by

[k]







[k]

(1)

[k]

(1)

... h

[k]

(1)

[k]

(2)

[k]

(2)

... h

[k]

(2)

[k]

(M)

[k]

(M)

... h

[k]

(M)







(11)

where h

[k]

(m) is the channel response between optical

AP l and user k at the photodiode m of the reconﬁg-

urable detector. Note that, the reconﬁgurable detector

must consist of at least M = L photodiodes in order to

ensure that H

[k]

is a full-rank matrix.

2.3 Uplink Transmission

A WiFi system is considered in the hybrid network

to provide uplink transmission. In this context, each

user has an RF interface to communicate with the

WiFi system, and the power allocated to that RF in-

terface is denoted by P

. The WiFi system devotes

resources for the uplink transmission, allocating

[k]

= e

/K resources for each user. Note that, the

power consumption at the RF interface of each user

must be taken into account due to battery limitations.

Hence, denoting ρ as power ampliﬁer efﬁciency, the

power consumption equals to P

/ρ. It is worth point-

ing out that ensuring power consumption within the

limit requires the deﬁnition of three constraints for the

maximum power allocated to the RF interface of the

user, the battery power constraint of the user and the

minimum rate of the uplink transmission.

3 MULTIPLE ACCESS SCHEMES

In general, optical wireless systems are composed

of a high number of optical transmitters that serve

multiple users. In such high density wireless net-

works, multi-user interference is a crucial issue that

must be managed efﬁciently to achieve a high spec-

tral efﬁciency. In this context, low complexity or-

thogonal transmission schemes such as TDMA (Ab-

delhady et al., 2019) and OFDMA (Bawazir et al.,

2018) are implemented for this purpose where ex-

clusive time or frequency slots are allocated to each

user. In addition, WDMA can be implemented for

avoiding multi-user interference by allocating a cer-

tain wavelength to each user while using optical ﬁlters

on the user side to eliminate the other wavelengths.

OWC-SP 2022 - Workshop on Optical Wireless Communications: Status and Perspectives

206

Despite the low complexity of the orthogonal trans-

mission schemes, the utilization of the network re-

sources might be minimized. In the following, ad-

vanced transmission schemes are introduced to serve

multiple users simultaneously. Note that, the equa-

tions below are derived for a simple full connectivity

optical wireless system where L APs serve K users.

However, they can be simply extended for our system

model in Section 2.

3.0.1 Precoding Transmission Schemes

TPC schemes, such as ZF in (Marshoud et al., 2015),

are proposed for interference management in optical

wireless networks assuming prefect CSI at transmit-

ters as well as cooperation among optical APs.

Let us consider linear transmit precoding to man-

age muti-user interference, and then, derive the

achievable user rate. Focussing on user k, its precod-

ing vector is denoted as w

[k]

∈ R

L×1

, and its received

signal is given by

[k]

= h

[k]

+ h

[k]

∑

6=k

]

+ z

[k]

, (12)

where the ﬁrst term is the useful information intended

to user k and the second term is the interference re-

ceived due to transmission to the other users, k

6= k.

Moreover, s

[k]

is the symbol transmitted to user k.

Note that, On–off keying (OOK) can be used in op-

tical wireless communication for the sake of avoid-

ing complexity. The interference term in equation

(12) can be canceled using the precoding of the ZF

scheme. Furthermore, the channel matrix for the sce-

nario considered in this section, K users connected to

L AP, is given by

H =

[1]

,.. .,h

[k]

,.. .,h

[K]

, (13)

where H ∈ R

K×L

, and the precoding matrix is given

W =

[1]

,.. .,w

[k]

,.. .,w

[K]

, (14)

where W ∈R

L×K

. Thus, HW = diag(

√

), where g

is the channel gain of user k after the ZF precoding. In

(Marshoud et al., 2015), the lower band user capacity

is derived taking into consideration the implementa-

tion of the ZF scheme. It is expressed as

[k]

≥

log





1 +

2 | h

[k]

πe



∑

6=k

| h

[k]

]

+σ







(15)

Therefore, the achievable user rate of ZF, r

[k]

, can be

written as follows

[k]

log





1 +

2 | h

[k]

πe



∑

6=k

| h

[k]

]

+σ







(16)

and the sum rate is given by R

∑

k=1

[k]

. It is

worth mentioning that the pseudo-inverse is H

†

(HH

)

−1

, which obeys the ZF criterion to obtain

interference-free signals at users.

In addition to the requirement of TPC schemes

in terms of the need for CSI at transmitters, the use

of TPC schemes in optical wireless networks is sub-

ject to limitations due to the optical signal charac-

teristics such as the non-negativity of the transmit-

ted signal and the high correlation among the chan-

nel responses of users (Morales-C

espedes et al., 2017;

Adnan-Qidan et al., 2019; Qidan et al., 2021b). It is

shown that these schemes achieve low data rates com-

pared to their performance in RF networks. There-

fore, the following points must be taken into consid-

eration prior to considering TPC schemes for interfer-

ence management.

• The need for prefect CSI at optical transmitters.

• Cooperation among optical APs is required.

• The precoding matrix for determining the trans-

mitted signal contains negative and positive val-

ues, and therefore, a DC bias current must be ap-

plied to guarantee the non negativity of the trans-

mitted signal.

• The performance of TPC schemes is subject to

correlation among the channel responses of users.

3.0.2 Blind Interference Alignment

Following (Gou et al., 2011), in this section, the

methodology of BIA is introduced in detail in

a multiple-input multiple-output broadcast channel

(MISO BC) scenario where L APs serve K users. The

key idea of BIA is aligning the useful information in-

tended to each user into a full rank matrix, while hav-

ing the interfering signals contained into a matrix that

has at least one dimension less. Basically, BIA allo-

cates a number of alignment blocks determined in ac-

cordance with the size of the network, i.e., the number

of transmitters and users, to each user simultaneously.

During an alignment block of user k, k ∈ K, the chan-

nel state of that user changes among L distinct preset

modes, while the channel states of all other users re-

main constant, as shown in Fig. 3. Note that, the re-

conﬁgurable photodetector derived in Section 2 gives

the user the ability to vary its channel state among

Towards Terabit LiFi Networking

207

BIA for the MISO BC

User 1

h(1)

h(2)

…

h(L

-1)

h(1)

…

h(L

-1)

h(1)

…

h(L

-1)

⌠…⌡

h(L

)

h(L

)

h(L)

…

h(1)

h(2)

h(L

-1)

User k

h(1)

…

h(1)

h(2)

…

h(2)

h(L

-1)

…

h(L

-1)

⌠…⌡

h(1)

h(2)

h(L-1)

…

h(L)

h(L

)

h(L)

group

groupgroup group

Block 1

simultaneous transmission

Block 2

orthogonal transmission

alignment block

user k

user k '

[ k ]

[ k ']

(L − 1)

K −1

(L − 1)

K −1

K × (L − 1)

K −1

(L − 1)

Figure 3: The transmission block of BIA. Each color represents a preset mode.

the symbol extensions, i.e., the time slots, of its align-

ment block. Denoting a symbol transmitted to user k

as u

[k]

, where ` th is the index of an alignment block

allocated to user k , BIA guarantees the linear indepen-

dence of the symbols u

[k]

= {u

[k]

`,1

,.. .,u

[k]

`,L

} received

from L transmitters over alignment block `. Addi-

tionally, the independence among multiple alignment

blocks allocated to each user must be ensured during

the entire transmission block. To satisfy this condi-

tion, the alignment blocks of each user must be trans-

mitted in orthogonal fashion such that any pair of

alignment blocks allocated to the same user do not

contain any symbol in common, giving each user the

ability to decode the information transmitted over its

alignment blocks.

Once the independence among the desired sym-

bols of user k is ensured, the interference received

due to transmission to all other users, for example u

]

transmitted to user k

, k

6= k, can be aligned into a ma-

trix that has less dimensions than the data streams u

[k]

intended to user k during each of its alignment blocks.

Given this point, the interference can be measured and

subtracted, and L DoF carried by u

[k]

can be decoded

by user k.

To guarantee the methodology mentioned above,

the transmission block of BIA is divided into Block

1 and Block 2, comprising (L −1)

+ K(L −1)

−1

time slots in total. As a result, (L −1)

K−1

alignment

blocks are allocated to each user. Referring to Fig. 3,

the contractions of Block 1 and Block 2, as well as

the length of each block, are described as follows. In

Block 1, transmissions to all users occur simultane-

ously, causing severe interference among them. On

the other hand, each user is served in orthogonal fash-

ion over Block 2 in order to give users enough di-

mensions to measure and cancel the interference re-

ceived during Block 1, i.e., user k measures the sym-

bols transmitted to all other users u

]

, k

6= k, during

Block 2, and subtracts it afterwards from the signal

received at Block 1. Therefore, the ﬁrst (L −1) slots

of each alignment block must belong to Block 1 form-

ing a group, while the last time slot of each alignment

block is provided over Block 2. As a result, the length

of Block 1 is given by (L−1)

time slots, while Block

2 comprises K(L −1)

K−1

time slots.

At this point, the signal received by user k from L

transmitters during an alignment block after interfer-

ence subtraction can be written as

[k]

= H

[k]

, (17)

where

[k]

∈ R

L×1

is the signal received during the L

time slots of alignment block `. Moreover, in (17),

[k]



[k]

(1) ... h

[k]

(L)



∈ R

L×1

, (18)

is the channel matrix of user k that contains L linearly

independent channel responses, i.e., H

[k]

is a full rank

matrix, and

[k,c]

is real valued additive white Gaus-

sian noise with zero mean and variance given by the

sum of thermal noise, shot noise and noise that re-

sults from interference subtraction, which is deﬁned

as a covariance matrix as follows

˜z



L−1

L−1,1

1,L−1



. (19)

It is worth mentioning that the performance of BIA

is limited in a high density network due to increase

in subtraction noise as the number of users increases.

Moreover, the requirements of large channel coher-

ence time become more difﬁcult to guarantee in such

high density networks. In BIA, the achievable user

rate can be written as

[k]

bia

[k]

bia

×E

log

det



+ P

str

[k]

−1

i

(20)

where e

[k]

bia

L+K−1

is the ratio of the number of

alignment blocks allocated to user k to the length of

the BIA transmission block, P

str

is the power allocated

to the data stream and R

[k]

is the covariance matrix of

noise.

OWC-SP 2022 - Workshop on Optical Wireless Communications: Status and Perspectives

208

Table 1: Simulation Parameters.

Optical system parameters Value

Bandwidth of VCSEL laser 5 GHz

Wavelength of VCSEL laser 830 nm

VCSEL beam waist 5 −30 µm

Physical area of the photodiode 15 mm

Receiver FOV 45 deg

Detector responsivity 0.53 A/W

Gain of optical ﬁlter 1.0

Laser noise −155 dB/Hz

WiFi parameters Value

OFDM subcarrier number 108

Transmitted power for Wi-Fi AP 20 dBm

Bandwidth for WiFi AP 40 MHz

Noise power of WiFi -63 dBm

4 OPTIMIZATION PROBLEM

The resources of the optical wireless system must be

managed among users taking into consideration the

existence of the complementary WiFi system to max-

imize the sum rate of the hybrid optical/RF network.

Speciﬁcally, an optimization problem is formulated

in this section with an objective function that jointly

ﬁnds the optimal user assignment and resource allo-

cation for multiple users. In previous works on het-

erogeneous networks, SNR maximization is consid-

ered for user assignment to avoid complexity where

users simply connect to a wireless system that pro-

vides high SNR. However, this approach is not ef-

ﬁcient when optical and RF systems work together

due to the fact that an optical AP illuminates a small

area compared to an RF AP, and therefore, consider-

ing SNR maximization might lead to overloading one

of these systems (Adnan-Qidan et al., 2020). Con-

sequently, resource management in such hybrid opti-

cal/RF networks must be based on rate maximization

where users connect to the system that has more avail-

able resources than the other.

Let us deﬁne a new notation L ,l = {1,.. . ,L },

that contains all the available APs, i.e., optical and

WiFi APs, in the indoor environment, as shown in Fig

1. Moreover, an expression for the achievable user-

rate regardless of the optical and WiFi systems can be

written as

[k,l]

= e

[k,l]

, (21)

where r

[k,l]

is the achievable user rate of a generic user

k connected to optical or WiFi APs, and e

[k,l]

denotes

the fraction of the resources allocated to user k from

AP l. Note that, the achievable user rate for the opti-

cal system is given by equations (20) or (16) based on

the transmission scheme considered, BIA or ZF, re-

spectively. On the other hand, the achievable user rate

of the WiFi system can be easily derived considering

orthogonal frequency-division multiplexing (OFDM)

with multiple subcarriers, which are allocated in or-

thogonal fashion to the users connected to the WiFi

system avoiding multi-user interference as in (Adnan-

Qidan et al., 2020).

The overall achievable rate of a generic user k is

given by

[k]

∑

l∈L

[k,l]

, (22)

where x

[k,l]

is a variable that determines user associa-

tion. In this context, the variable x

[k,c]

= 1 if user k is

connected to AP l, otherwise the variable x

[k,c]

= 0.

At this point, our aim is to formulate an optimiza-

tion problem that maximizes the sum rate of all the

users by assigning each user to an AP that provides

a high user-rate. In this context, we deﬁne a utility

function of the overall user rate in equation (22) un-

der several constraints that ensure the maximization

of the hybrid network overall sum rate. That is

max

x,e

∑

k∈K

∑

l∈L

[k,l]

(23)

s.t.

∑

l∈L

[k,l]

= 1 ∀k ∈ K

∑

k∈K

[k,l]

≤ 1 ∀l ∈L

0 ≤ e

[k,l]

≤ 1, x

[k,l]

∈

{

0,1

}

, ∀l ∈ L , ∀k ∈ K,

where ϕ(.) is a strictly concave function that achieves

some levels of fairness among the users of the net-

work if it is considered in its logarithmic form, i.e.,

ϕ(.) = log(.) (Adnan-Qidan et al., 2020; Qidan et al.,

2021a). The ﬁrst constraint in (23) ensures that each

user connects to only one AP, i.e., one of the optical

APs or the WiFi system. The second constraint guar-

antees that the portion of the transmission resources

employed for each optical AP or the WiFi system is

less than 1. Moreover, the last constraint considers the

feasible region of the optimization variables, where

[k,l]

and e

[k,l]

are binary and real variables between 0

and 1, respectively.

The problem in (23) is MINLP in which two vari-

ables, x

[k,l]

and e

[k,l]

, are coupled, and therefore, it

is not easy to solve. In this sense, a decentralized

algorithm via Lagrangian multipliers can be used to

provide an effective solution with low computational

time. In particular, the Lagrangian function of the

main problem in (23) is formulated as

Towards Terabit LiFi Networking

209

10 11 12 13 14 15 16 17 18 19 20

Number of users

Sum rate [bits/s/Hz]

Hybrid network, W0=15 micro

Hybrid network, W0=10 micro

Standalone optical network, W0=15 micro

Standalone optical network, W0=10 micro

Figure 4: Sum rates of hybrid optical/RF and standalone optical networks versus the number of users, considering BIA for

data transmission.

0 10 20 30 40 50 60 70 80 90

Sum rate [bits/s/Hz]

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CDF

Hybrid network, W0=15 micro, BIA

Standalone optical network, W0=15 micro, BIA

Hybrid network, W0=15 micro, ZF

Standalone optical network, W0=15 micro, ZF

Figure 5: CDF of the sum rate for hybrid optical/RF and standalone optical networks.

f (x,k,µ) =

∑

k∈k

∑

l∈L

[k,l]



log(r

[k,l]

) −µ



| {z }

s(x,µ

)

∑

l∈L

(µ

−log(K

))

| {z }

g(k,µ

)

(24)

considering

∑

k∈K

[k,l]

= K

is the load on AP l and

uniform resource allocation among K

users, i.e.,

[k,l]

. Note that, µ

is a Lagrangian multiplier that

works as a message between AP l and users sending

requests to connect to that AP. The problem in (24)

can be divided into sub-problems, s(x,µ

) and g(k, µ

)

that can be solved on the user side and the AP side,

respectively, more details are in (Adnan-Qidan et al.,

2020)

5 PERFORMANCE EVALUATION

An indoor environment is considered with dimensions

5m × 5m × 3m. On the ceiling, L = 16 optical APs

are deployed to serve K users distributed on the re-

ceiving plane. Moreover, a WiFi AP is considered to

provide uplink transmission as well as serving users

who penalize the sum rate of the optical wireless sys-

tem. In this work, each user is equipped with a recon-

ﬁgurable detector that contains multiple photodiodes

in order to provide linearly independent channel re-

sponses from the whole set of the transmitters. In ad-

dition, each user has an RF antenna given the fact that

some users might be served by the WiFi AP in accor-

dance to the solution of the optimization problem in

(23). The rest of the simulation parameters are listed

in Table I.

In Fig.4, the sum rate of the hybrid network is

shown versus the number of users considering differ-

ent values of the laser beam waist. Recall that the

OWC-SP 2022 - Workshop on Optical Wireless Communications: Status and Perspectives

210

optimization problem formulated in this work can be

solved directly considering equation (24), i.e., a de-

centralized algorithm, due to its practicality where a

sub-optimal solution close to the solution of the cen-

tralized algorithm can be obtained with low complex-

ity. The ﬁgure shows that the sum rate increases

with the number of users where each user experi-

ences a different channel gain. Note that, the hy-

brid network achieves higher sum rate compared with

the standalone optical wireless network, in which the

WiFi AP provides only uplink transmission, and it is

not considered in the optimization problem that max-

imizes the sum rate of the users in downlink transmis-

sion. Furthermore, the sum rates of all the scenarios

increase with increase in the beam waist of the laser

due to the fact that the received power of each user in-

creases considerably with the beam waist W

as more

power is focused towards the users.

Finally, Fig. 5 shows the cumulative distribu-

tion function (CDF) of the sum rate in the hybrid

network implementing BIA or ZF schemes to align

multi-user interference. It is shown that BIA is su-

perior to ZF and more suitable for the optical wire-

less system due to the fact that BIA naturally satisﬁes

the non-negativity of the optical signal, and therefore,

it helps in avoiding the need for applying a DC bias

current to the optical signal, which might cause clip-

ping distortion to useful information. It is worth men-

tioning that BIA suffers data rate degradation as the

number of users increases in the network due to chan-

nel coherence requirements and noise enhancement.

However, in the case of the hybrid network, some of

the users negatively impacting the sum rate within the

coverage of each optical AP can be moved to the WiFi

system such that the overall sum rate of the hybrid

network is maximized.

6 CONCLUSIONS

In this paper, the performance of an optical wireless

system using IR lasers is evaluated taking into con-

sideration the existence of a WiFi system. First, the

system model composed of multiple IR lasers on the

ceiling serving multiple users is deﬁned. In addition,

a WiFi system is considered to provide uplink trans-

mission and serve users that overload the optical wire-

less system. Then, two transmission schemes are de-

ﬁned for the optical wireless system, ZF and BIA, to

derive the achievable user rates. After that, an op-

timization problem is formulated to jointly ﬁnd the

optimal user association and resource allocation that

maximize the overall sum rate of the hybrid network.

The optimization problem is a MINLP complex prob-

lem, which is difﬁcult to solve. Therefore, a decen-

tralized algorithm is proposed via Lagrangian mul-

tipliers where the main problem is divided into sub-

problems that can be solved separately. The results

show signiﬁcant enhancement in the sum rate of the

hybrid optical/RF network after performing the op-

timization problem that considers all the APs in the

environment including the WiFi system.

7 FUTURE DIRECTIONS

IR laser-based optical wireless communication can

unlock data rate speeds in a range of Tbps. How-

ever, crucial wireless communication issues ranging

from the physical layer, the data link layer and the net-

work layer must be addressed including transmitter

and receiver designs, developing highly efﬁcient in-

terference management schemes and optimal resource

allocation approaches and backhaul network designs,

etc. In general, these issues might lead to formulat-

ing complex optimization problems that are difﬁcult

to solve. Note that, some optimization tools are avail-

able to solve such complex optimization problems.

However, practical algorithms are highly required es-

pecially when real-time scenarios are concerned.

In recent years, machine learning (ML) techniques

have been studied for solving NP-hard optimization

problems with different contexts (Sun et al., 2019;

Zhu et al., 2020). For instance, some of the previ-

ous works in the literature related to the optimiza-

tion problem formulated in this paper (Elgamal et al.,

2021; Shrivastava et al., 2020; Ahmad et al., 2020)

consider the implementation of reinforcement learn-

ing (RL) to solve various optimization problems in

optical and RF systems where RL can interact with

an environment to learn an optimal policy that makes

right decisions. Speciﬁcally, in (Elgamal et al., 2021),

reinforcement learning is used for assigning each user

to an exclusive wavelength in a WDMA-based opti-

cal wireless network. In (Shrivastava et al., 2020),

a deep Q-network (DQN) learning-based algorithm

is proposed for solving an optimization problem that

aims to maximize the sum rate of a hybrid optical/RF

network through allocating power and bandwidth in

addition to user association. In (Ahmad et al., 2020),

a RL-based load balancing approach is proposed for

maximizing the sum rate of users in a hybrid LiFi/

WiFi network. It is shown that ML techniques can

provide sub-optimal solutions while avoiding com-

plexity. However, conventional ML techniques are

not suitable in terms of providing immediate solu-

tions in large size optical wireless networks. As fu-

ture work, deep learning can be used for solving var-

Towards Terabit LiFi Networking

211

ious optimization problems as it is expected to be su-

perior to ML techniques where a learning process is

preformed over a data set generated in an ofﬂine phase

to provide sub-optimal solutions in a real time phase.

ACKNOWLEDGEMENTS

This work has been supported in by the Engineer-

ing and Physical Sciences Research Council (EP-

SRC), in part by the INTERNET project under Grant

EP/H040536/1, and in part by the STAR project under

Grant EP/K016873/1 and in part by the TOWS project

under Grant EP/S016570/1. All data are provided in

full in the results section of this paper.

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