On the Optimization of Multi-Cell SLIPT SystemsAmr M. Abdelhady, Osama Amin, Basem Shihada, and Mohamed-Slim Alouini

Computer Electrical, and Mathematical Science and Engineering (CEMSE) Division,King Abdullah University of Science and Technology (KAUST), Thuwal, Makkah Province, Kingdom of Saudi Arabia,

E-mail: { amr.abdelhady, osama.amin, basem.shihada, slim.alouini } @kaust.edu.sa.

Abstract—In this paper, we study the performance of simulta-neous lightwave information and power transfer (SLIPT) systemsof multi-cell indoor scenario. We aim to investigate the energyharvesting and data rate performance of multiple users whilemeeting the lightning constraints. To this end, we develop op-timization frameworks and tune the light emitting diodes averagecurrents to improve the performance of the SLIPT system. Firstly,we propose an algorithm to maximize the spectral efficiency(SE) subject to lighting and minimum harvested energy per userrequirements. The proposed algorithm can be implemented ina distributed fashion with a reduced computational burden ateach node. Then, we consider the energy harvesting maximizationproblem to investigate the maximum possible energy gain and itscorresponding SE performance. Finally, we present some extensivesimulations to explore the benefit of the optimization frameworkswith respect to standard equal allocation setting. In addition,we monitor the effect of changing several system parameters onthe two objectives and highlight the underlying trade-off betweenthem.

I. INTRODUCTION

In recent decades, the over congestion of the radio frequency(RF) spectrum, and the ever-growing users’ wireless data traffic,have thrust research efforts to exploit higher frequency bands inthe electromagnetic spectrum [1]. Visible light communication(VLC) has received lots of attention in both academia andindustry as it possesses many promising features. VLC systemsoffer large bandwidth, physical security, great potential in usingexisting lighting infrastructure, and low cost solutions. Thesefeatures have nominated VLC to be one of the candidates for5G access technologies [2].

VLC systems can offer many services besides illuminationand communications. For example, energy can be harvestedfrom light and used to support devices operating with limitedenergy sources. Energy consumption at the user equipmenthas become a very important aspect in new wireless commu-nications networks especially with the evolution of Internetof things. Thus, it is imperative to analyze and optimize theperformance of different services.

Light energy harvesting has been recently investigated forVLC systems considering different system configurations [3]–[9]. In [4], Rakia et al. considered a hybrid VLC/RF energyharvesting enabled relaying system and optimized the VLCtransmitter DC bias to maximize the average system data rate.In the context of multiple users, Zenaidi et al. studied theachievable rate region of a hybrid VLC/RF system where twotransmitters are communicating with two designated receiversthrough a relay [3]. In [5], [6], the authors investigated theresource allocation problem to maximize the spectral efficiency

(SE) of a single cell VLC downlink system with energy harvest-ing capabilities. Motivated by the aforementioned results, theauthors in [7] studied the trade-off between illumination serviceand communications service via multi-objective optimizationwhile imposing a per-user energy harvesting constraint. More-over, Liu at al. demonstrated experimentally a VLC receiverusing solar cell, which is used in both energy harvesting anddata detection [9]. The performance is measured practicallyin terms of the error probability and generated voltage ver-sus illuminance. With the increased research interest in VLCsystems with energy harvesting capabilities, Diamantoulakiset al. introduced the ”SLIPT” term and proposed differentoperation policies to balance the trade-off between the amountof harvested energy and communications quality of service fora single user single cell scenario [8].

In this paper, we study the performance optimization ofmulti-cell SLIPT system that is used to serve multiple users.The multi-cell scenario introduces interference on the servedusers, which adds a challenge on the SLIPT performanceoptimization. As such, we first optimize the LEDs averagecurrent to maximize the SE subject to both illumination andenergy harvesting constraints. In this context, we propose a low-complexity algorithm that can be implemented in a distributedway to reduce the computational burden on different LEDnodes. Then, we consider the energy harvesting maximizationproblem and propose a concave lower bound for the objectivefunction and solve it. Finally, we show the gains achieved byoptimization over simple equal allocation strategies on bothobjectives and compare the losses in SE/energy harvestingperformance when energy harvesting/SE is optimized.

II. SYSTEM MODEL

Consider a SLIPT system with K transmitters that communi-cate with K receivers simultaneously using the same frequencyband1. Thus, each user is exposed to interference from atmost K � 1 undesired transmitted streams. We assume perfectknowledge of channel state information at the transmitter LEDs.The received signal at the i-th user can be expressed as

yi

=

KX

j=1

hi,j

sj

+ ni

, (1)

1The solutions presented in this work are general enough to handle systemshaving N K receivers, with one-to-one mapping where the surplus users’links in our model can be assigned zero-channel gains.

Fig. 1: System Model

where si

is the current intensity used to transmit a symbol to thei-th user by the i-th transmitter, h

i,j

is the VLC channel gaincoefficient between the j-th transmitter and the i-th receiver,and n

i

represents the i-th receiver noise which is modeled aszero mean additive white Gaussian noise with variance �2

n

. Thedirect link that represents the intended transmission establishedbetween the transmitter and its corresponding user has the sameindices, i.e., h

i,i

.Throughout this work, we consider upper and lower bounds

on illuminance at the receivers’ plane as imposed by the lightingconstraints. We define the illuminance lower bound to be theleast possible illuminance within a cell coverage when all othersources are turned off. As for the upper bound, we defineit as the sum of the maximum illuminances of a cluster ofneighboring transmitters within their cell coverages. A clusteris defined to be a set of transmitters that are mutually separatedby less than 2dmin inter-distance, where dmin is the minimumdistance between any two transmitters in the setup. We denotethe total number of transmitter clusters by |�| in the system,with � being the set of all possible clusters in the system. Itcan be noticed that � depends mainly on the cells deploymentlayout. We assume that transmitters are placed on the ceilingin a uniform pattern, as shown in Fig. 1. Furthermore, allusers are assumed to be able to harvest energy during thewhole transmission frame while decoding operations are donein parallel [10]. We impose a constraint on the system to achievea minimum amount of harvested energy for each user. Finally,the total transmitted power by all cells is constrained to be lessthan the available power budget PM.

We assume line-of-sight existence for all links and neglectany reflected components, we employ the channel model in [11]where the channel gain h

i,j

between transmitter j and receiveri depends on the position of the receiver with respect to thetransmitter, and is given by:

hi,j

=

(m+ 1)RPDAPD

2⇡d2i,j

cos

m+1(

i,j

)rect

✓ i,j

a

◆, (2)

where m = � ln 2/ ln (cos (�a)) is the Lambertian order, �ais the semi-angle at half-power of the light source emissionpattern, APD is the effective photo-detector area, d

i,j

is thedistance between the j-th transmitter and user i,

i,j

is the

angle between the incident light ray from transmitter j andthe normal to the i-th photo-detector plane, a is the field ofview of the user’s receiver (assumed to be constant for all usedreceivers), and rect(x) is the rectangular function defined asrect(x) = 1 if |x| 1, and 0 otherwise.

III. SE VS ENERGY HARVESTING MAXIMIZATION

In this section, we study the resource allocation problemsof a multiple user SLIPT system in an interference-basedscenario where the SE and energy harvesting maximizationare of particular interest. The receivers are assumed to treatinterference as noise at detection. The exact expression for VLCchannel capacity is not yet available, consequently, we expressthe system overall SE based on VLC channels capacity lowerbound [12] with s

i

⇠ Exp(1/xi

) as

⌘SE =

1

2

KX

i=1

log2

1 +

e

2⇡

�i,i

x2i

1 +

PK

j=1,j 6=i

�i,j

x2j

!, (3)

where �i,j

is the VLC channel-to-noise ratio of the linkbetween the j-th transmitter and the i-th receiver defined as�i,j

= h2i,j

/�2n

8i 6= j, �i,i

= h2i,i

/�2n

, xi

= E {si

}.On the other hand, we evaluate the energy harvesting perfor-

mance through the total harvested power by all receivers whichcan be expressed as [4]

PH,tot =

KX

i=1

PH,i

, (4)

where, PH,i

is the total harvested power by the i-th receivercalculated as [4, Eq. 4]

PH,i

= 0.75Vt

KX

j=1

hi,j

xj

ln

0

@1 +

KX

j=1

hi,j

xj

/Io

1

A , (5)

where RPD is the photodetector responsivity, Vt is the thermalvoltage and Io is the dark saturation current of the photodetec-tor.

A. SE Maximization

The considered resource allocation problem tunes the averagecurrent intensity vector x = {x

i

}Ki=1 to maximize the total

downlink SE. The design should maintain the required illumi-nation level within range, satisfy the transmitted power budgetand maintain minimum harvested energy per user. Accordingly,we formulate the following optimization problem:

(P1) max

x

⌘SE

subject to C1 :

KX

i=1

x2i

PM

C2 :xi

⌘�

hmin/RPD � Emin 8iC3 :

X

i2Nj

xi

⌘�

hmax/RPD Emax 8j,

C4 :PH,i

� PH,th 8i,

where C1 satisfy the transmitter total radiated power budgetwith denoting the ratio between the LED electrical powerusage and the square of its driving electric current.

The constraints C2 and C3 ensure the minimum and max-imum allowable illumination levels Emin and Emax, respec-tively, with hmin and hmax being the channel gain at thefurthest/nearest point from the transmitter within cell coverage,⌘�

representing the ratio between the luminous flux emitted bythe LED and its driving current and N

l

representing the l-thtransmitters cluster in the constellation. C4 is used to guar-antee minimum harvested energy by each user. Interestingly,PH,i

is positive and monotonically increasing with respect toPK

j=1 hi,j

xj

, thus we can rewrite C4 equivalently as

KX

j=1

hi,j

xj

� g�1(PH,th) , (6)

where g�1(x) is the inverse function of g(x) =

0.75Vtx ln (1 + x/Io).To solve this problem, we employ alternate optimization

where one of the variables is tuned while the rest are kept fixed,such that the updated solution maintains the feasibility condi-tions and the overall objective function is always improved.Then, roles are changed in a cyclic order between the variablebeing optimized and the others till convergence is reached.Thus, in each iteration of the alternate optimization procedurewe need to solve a single variable optimization problem of thefollowing form:

(P2) max

xa

⌘SE (xa

)

subject to xmin,a xa

xmax,a,

where xmin,a is defined as

xmin,a = max

EminRPD

⌘�

hmin,g�1

(PH,th)�P

j 6=a

xj

ha,j

ha,a

!

(7)

while xmax,a is defined as

xmax,a = min

0

B@sPM/�

X

i 6=a

x2i

,RPDEmax

⌘�

hmax�X

i2Na,i 6=a

xi

1

CA .

(8)

The lower limit of (P2) constraint is imposed by the virtue ofC2 and C4, while the upper constraint limit is imposed by C1

and C3. As for ⌘SE(xa

), it is defined as

⌘SE(xa

) =

1

2 ln(2)

0

@KX

i=1

ln

0

@1 +

X

j 6=a

�̃i,j

x2j

+ �̃i,a

x2a

1

A

�KX

i=1,i 6=a

ln

0

@1 +

KX

j=1,j /2{i,a}

�̃i,j

x2j

+ �̃i,a

x2a

1

A

1

A , (9)

where �̃i,j

= �i,j

8i 6= j, �̃i,i

=

e

2⇡�i,i 8i.

It can be noticed that ⌘SE (xa

) is the sum of func-tions of the following form: ln

�↵+ �x2

�and � ln

�� + �x2

�

where both of them can be decomposed into differenceof two concave/convex (DC) functions of the followingforms �⇢/2x2 �

��⇢/2x2 � ln

�↵+ �x2

��and �⇢̄/2x2 ��

�⇢̄/2x2+ ln

�� + �x2

��respectively, with ⇢ � �

4↵ and⇢̄ � 2� [13]. Therefore, (P2) is a DC programming problemthat can be solved by successive convex approximation (SCA)where the following optimization problem is solved in eachSCA iteration:

(P3) max

xa

⌘̃SE (xa

)

subject to xmin,a xa

xmax,a,

where max

xa

is written as

⌘̃SE(xa

) =

KX

i=1

�⇢a,ix

2a

2

� �⇢a,i

x2a,0

2

� ln

��

a

+ �̃i,a

x2a,0

�

� ⇢a,i

xa,0 +

2�̃i,a

xa,0

�

a

+ �̃i,a

x2a,0

!(x

a

� xa,0)

!!/ (2 ln(2))

+

KX

i=1,i 6=a

� ⇢̄a,ix

2a

2

� �⇢̄a,i

x2a,0

2

+ ln

��

a,i

+ �̃i,a

x2a,0

�

� ⇢̄a,i

xa,0 �

2�̃i,a

xa,0

�

a,i

+ �̃i,a

x2a,0

!(x

a

� xa,0)

!!/ (2 ln(2)) ,

(10)

with ⇢a,i

=

�̃i,a

4�a, ⇢̄

a,i

= 2�̃i,a

, �a

= 1 +

Pj 6=a

�̃i,j

x2j

, �a,i

=

1 +

Pj 6=a,j 6=i

�̃i,j

x2j

and xa,0 is the solution obtained in the

previous SCA iteration.The solution of the previous problem can be obtained in a

closed form as

x⇤a

= max (min (xcr, xmax,a) , xmin,a) , (11)

where xcr is found to be

xcr =

xa,0

PK

i=1

⇣⇢a,i

+

2�̃i,a

�a+�̃i,ax2

a,0+ ⇢̄

a,i

� 2�̃i,a

�a,i+�̃i,ax2

a,0

⌘

PK

i=1 ⇢a,i +P

i 6=a

⇢̄a,i

.

Based on the previous discussion, our proposed solutionprocedure for (P1) proceeds as shown in Algorithm I. Theoptimization is done over two nested phases, where in theouter phase we solve a customized user-version of (P2) thatis formulated based on the solution of the previous outer phaseiterations with the aim of optimizing (P1). In the inner phaseof the solution procedure, the solution of each version of (P2)is obtained by successively solving different SCA-versions of(P3) using (11).

1) Feasibility problem: Before solving the SE maximizationproblem, we need to examine the problem feasibility. One

Algorithm I

1: Input PM, PH,th, Emin, Emax, {�i}Ki=1

2: Initialize F {x0

}, ⌘⇤SE 0

3: ifP

K

j=1 hi,j

xmaxeq,i � g�1

(PH,th) then4: F F [ x

max

eq

5: end if6: if

PK

j=1 hi,j

xmineq,i � g�1

(PH,th) then7: F F [ x

min

eq

8: end if9: for each x

init

2 F do10: Initialize x x

init

, Alt. error 1, a 1, xprev x

init

11: while Alt. error � ✏alt do12: SCA error 1

13: Initialize xa,0 x

a

14: while SCA error � ✏SCA do15: Compute x

a

using (11)16: Update SCA error |⌘SE (x

a

)� ⌘SE (xa,0)|

17: Update xa,0 x

a

18: end while19: if a = K then20: Update Alt. error |⌘SE (x

⇤)� ⌘SE (xprev)|

21: Update xprev x

⇤

22: end if23: a (a mod K) + 1

24: end while25: if ⌘SE(x⇤

) > ⌘⇤SE then26: xopt x

⇤

27: end if28: end for29: Output xopt

way to do so is to solve the following simplified optimizationproblem:

(P4) min

x

KX

i=1

x2i

subject to C2, C3, C4.

After solving (P4), it can be deduced that (P1) is infeasibleif (P4) is infeasible or the optimal value of (P4) exceedsPM. (P4) is a convex quadratic programming problem, thuswe can solve it using convex optimization subroutines such asMATLAB CVX package [14].

2) Choosing initial point: Since the algorithm performancevaries with the starting point, so we solve the problem usingthree possible initial points and take the best solution. Thepossible points are:

1) x

mineq : xmin

eq,i =E

min

R

PD

⌘�hmin

8i, which is the equal allocationassociated with the minimum illumination constraint. Thisproposed starting point gives good solution to the densecell deployment scenario.

TABLE I: Simulation Parameters.

N0

= 10�21 W/Hz Bv

= 20 MHz H = 3 mPM = 450W K = 9 E

min

= 100 luxA

PD

= 1 cm2 RPD

= 0.6A/W dmin

= 0.5 m⌘� = 7500 lumens/A = 23 W/A2 �

A

= 60�

Emax

= 3000 lux hT

= 1 m

2) x

mineq : xmax

eq,i = min

✓qP

M

K

, E

max

R

PD

⌘�hmax

|Ni|

◆8i, which

is the equal allocation associated with the maximumillumination constraint2. This initial point gives a goodsolution to the sparse cell deployment scenario.

3) x

0

: the solution of (P4), which becomes important whentwo previous solutions do not satisfy C4.

B. Energy harvesting maximization

In this study, we are interested in studying the energyharvesting performance limits of SLIPT systems in interfer-ence scenario under illumination constraints. To this end, weformulate the following problem

(P5) max

x

PH,tot

subject to C1, C2, C3.

This problem is not a convex program, consequently, wepropose using the following lower bound

˜PH,tot =

KX

i=1

ln

0

@KX

j=1

0.75hi,j

xj

Vt

1

A

+

KX

i=1

ln

ln

1 +

KX

i=1

hi,j

xj

/Io

!!

(12)

as a surrogate function for the original one and solve thefollowing optimization problem instead

(P6) max

x

˜PH,tot

subject to C1, C2, C3.

The objective function ˜PH,tot(x) is a sum of either the com-position of ln(.) or ln(ln(.)) function, which are both concavefunctions, with affine combination of the optimization variables.Thus, ˜Ph,tot(x) is a concave function, which results in a convexoptimization problem thanks to the convex set properties ofC1� C3 [15]. As a result, (P6) can be solved using any ofthe available convex programming software packages.

IV. SIMULATION RESULTS

The simulation setup consists of nine transmitters distributedover a square lattice on the ceiling of an indoor area at a heightH from the ground. It is assumed that user-cell association isdone based on nearest distance, which is obviously translated tothe square cell boundaries of side length dmin in the receivers

2|Ni| represents the cardinality of the set Ni (number of transmitters incluster i which is constant due to uniform lattice layout of transmitters andequals 4 for square grid lattice)

plane as shown inf Fig. 1. The nine users served by the systemare distributed at random such that each user is placed accordingto an uniform distribution within its corresponding transmittersquare cell boundary in the receivers plane. Moreover, thereceivers-to-ground vertical separation is assumed to be hT,with all transmitters and receivers having horizontal orientation.The average results presented in this work are calculated basedon 1000 random users’ locations realizations. The simulationparameters values are provided in Table I, unless otherwisespecified. Throughout the following simulations, we study theperformance of three allocation strategies, namely maximizedSE solution (solution of (P1)), maximized harvested energysolution (solution of (P6)), and the basic uniform allocation(xmax

eq

). We assume zero SE and energy harvesting performancefor infeasible problem realizations in average calculation ofthese objectives.

In the first simulation, we study the effect of varying thedistance between neighboring cells (which is the main controllerfor interference severity) on average optimized SE and averageoptimized harvested energy. To monitor the extreme SE andtotal harvested energy performances, we keep the per-userharvested power constraint inactive in this simulation. As dmin

increases, it can be seen in Fig. 2 that average SE performanceis improved because interference terms of the objective functiongets smaller and this improvement outweighs the performancedeterioration that could be caused as the direct links channelgains gets worsened for small dmin (probability of increasedseparation between users and their associated transmitters ascells gets larger). Thus, it can be deduced that if dmin increasesto values higher than 3.5 m, the average optimized SE perfor-mance will deteriorate and even reach zero as more realizationswill become infeasible due to minimum illumination constraint.As for the relative performance between the three solutions, itcan be noticed that the SE performance loss due to maximizingharvested energy diminishes as dmin increases. However, theSE performance gap between maximized SE solution and thetwo other solutions is significantly high in dense deploymentscenarios. On the other hand, the average total harvested powerperformance of the three considered solutions gets worse asdmin gets larger as shown in Fig. 3, which is expected sincethe receivers get further away from the transmitters so thatthe effective areas of their receivers are exposed to smallerpower densities. It can be seen that the maximized harvestedenergy solution outperforms the two other solutions, and theperformance gap between the three algorithms gets smaller asdmin increases. Interestingly, it was found that, from harvestedenergy perspective, the uniform allocation solution outperformsSE maximization for small values of dmin and the effect is re-versed for large values. It can be deduced that energy harvestingsolution tends to always satisfy C1 with equality as the PH,tot ismonotonically increasing with the power allocation. However,this is not the case for SE maximization which could easilydecrease the total transmitted power to alleviate interferenceeffect. Thus, at small dmin, the uniform allocation solutionpushes transmitters to fully use PM which makes it better

0.5 1 1.5 2 2.5 3 3.50

2

4

6

8

10

12

14Uniform allocation

Maximized SE

Maximized harvested energy

Fig. 2: Average SE vs Min. inter-cell separation distance dmin

0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

150

200

250

300

350

Uniform allocation

Maximized harvested energy

Maximized SE

Fig. 3: Average harvested power vs Min. inter-cell separationdistance dmin

than the maximized SE solution. Albeit, when dmin becomeslarge enough, the maximized SE solution exhausts PM whileallocating power in a way that considers channel asymmetrieswhich is not considered by the uniform allocation. It can be seenclearly from Fig. 2 and 3 that maximizing one of the objectivescomes at the cost of significant losses for the other, speciallyunder severe interference conditions.

In the second simulation, we study the effect of increasingthe minimum harvested power constraint on the average SEperformance for Emax = 5000 lux. It can be noticed that asPH,th increases the SE performance of optimized SE solution isnot affected initially (C4 is not active yet). As PH,th continuesincreasing, the SE performance deteriorates as the feasibilityspace gets tighter and the optimization solution satisfies C4

with equality. As PH,th keeps increasing, the probability of

0 5 10 15

0

0.5

1

1.5

2

2.5

3

3.5

Uniform allocation

Maximized SE

Fig. 4: Average SE vs PH,th

having more infeasible problems with zero contribution to theaverage SE performance increases. On the other hand, uniformallocation solution maintains SE constant as PH,th increases tillit reaches a critical value where the uniform allocation solutioninfeasibility frequency increases, hence zero SE starts to becounted for a subset of the realizations which deteriorates theaverage till it reaches zero.

V. CONCLUSION

In this paper, we considered the power allocation problemfor a multi-cell SLIPT system where interference has a non-negligible effect on the system performance. We investigatedthe performance limits of this system by maximizing two ofits design objectives, namely system overall SE, and totalharvested energy severally under lighting constraints. Moreover,we monitored the effect of optimizing each objective in termsof optimality losses in the other through extensive simulations.Furthermore, we studied the effect of adding minimum energyharvesting constraint per user on the SE performance metricand proposed a distributed algorithm to solve this problem.Simulation results highlighted the trade-off between SE andenergy harvesting whose severity explodes as cells becomesin close proximity. These results motivated studying the SE-

energy harvesting multi-objective optimization problem in orderto reach solutions that achieve balance between the two designobjectives. This approach would give SLIPT system designersthe freedom to find proper allocation that accounts for thedesired importance of each design objective.

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