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JOURNAL OF SCIENCE AND TECHNOLOGY: ISSUE ON INFORMATION AND COMMUNICATIONS TECHNOLOGY, VOL. 2, NO. 1, AUGUST 2016 9

Resource Allocation for Wireless Networkswith Energy Harvesting Constraints Over

Fading ChannelsMohammed Baljon and Lian Zhao

Abstract—This paper considers the utilize of energy harvesters, instead of conventional time-invariant energy sources, inwireless communication. For the purpose of exposition, we study the traditional two-hop communication system for delaylimited (DL) and delay tolerant (DT) relaying networks over fading channels, in which the source node transmits with powerdrawn from energy harvesting (EH) sources and the relay transmits with conventional non-EH sources. We address thethroughput maximization problem for the proposed system model for DL and DT cases. We find that the optimal powerallocation algorithm for the single-hop communication system with EH constraints, namely, recursive geometric water-filling(RGWF), can be utilized as a guideline for the design of the two-hop system. We first introduce RGWF algorithm and we showthe advantages of the geometric approach in eliminating the complexity of the Karush-Kuhn-Tucker (KKT) condition as well asproviding a closed-form and exact solutions to the proposed problem. Based on the RGWF algorithm, we propose offline jointpower allocation and transmission time scheduling schemes for DL relaying network and DT relaying network. We alsopropose efficient online resource allocation schemes for both relays’ cases. The performance of the proposed schemes isevaluated via simulation and the results demonstrate that a network with delay tolerant ability provides better performance interm of throughput.

Index Terms—energy harvesting technology, delay limited networks,delay tolerant networks, fading channels, optimisation,relay networks (telecommunication), resource allocation, telecommunication power management, telecommunicationscheduling.

F

1. IntroductionWith increasing demand and explosion growth in wire-less communication in recent years, energy conservationbecomes more desirable to save the world’s energy con-sumption. Today’s number of communication devices,such as smartphones and sensor nodes will be dou-bled or tripled by 2050 [1]. According to InternationalEnergy Agency [1], due to huge demand of energy onall fields by 2050, investments on energy preservationcould decrease the waste of energy by one-third. Greencommunication is the key solution of many problemsthat related to the wasting energy due to radio transmis-sions [2]. Green Radio (GR) basically can be representedas the relationship between energy harvested from theenvironment along with efficient techniques to utilizethe energy wisely. As a matter of fact, scavenging am-bient energy and utilizing the available energy wiselylead to maximizing the throughput [3], [4].

Another advantage of utilizing green communica-tion is to maximize the radio communication tasks’ life-time. Operation of traditional communication systemscan not surpass battery size or power constraint of thepower supply. In contrast, nodes with energy harvesting

Mohammed Baljon and Lian Zhao are with Electrical and ComputerEngineering Department, Ryerson University, ON, Canada (Email:[email protected], [email protected]).

Manuscript received June 2016; accepted for publication August 2016.

capability in wireless communication systems are ableto harvest energy from the environment, such as sun,wind, vibration etc,. Therefore, we can say, EH nodesare a potential technique that defeats the limitation ofnetwork longevity by recharging the nodes with thesufficient power opportunistically from nature as shownin [5]–[7].

Although the lifetime of communication systemswill be prolonged due to the energy replenishment fromnature, optimizing the resource allocation and designparameters are mandatory. Along with this motivation,designing an algorithm that provides optimum allo-cated power for green wireless communication is sig-nificant. Resource allocation in green wireless commu-nication has been studied under various system mod-els with various performance metrics. Several optimaltransmission policies have been presented for a single-hop transmission and many other transmission typeswith EH constraints in recent open literature.

Transmission polices for EH communication systemsto maximize throughput have been well investigated re-cently. Throughput maximization problem for a single-hop with EH constraints over a fading channel has beeninvestigated in [8] and [9]. Authors in [10] revisit theproblem in [8], [9] and a novel approach: a RecursiveGeometric Water-Filling (RGWF) algorithm, is proposedas an optimal transmission policy.

On the other hand, multi-hop transmission is used inISSN 1859-1531

10 JOURNAL OF SCIENCE AND TECHNOLOGY: ISSUE ON INFORMATION AND COMMUNICATIONS TECHNOLOGY, VOL. 2, NO. 1, AUGUST 2016

order to expand the network size geographically usingrelays, thereby increasing the communication transmis-sion range. Besides, multi-hop transmission is utilizedto enhance the energy efficiency of the network. Manyresearchers have proposed new algorithms and trans-mission policy in order to gain an efficient energy wire-less relaying system. Two-hop communication systemswith EH constraints have been studied recently, but onlyfor some special cases. Authors in [11] propose an opti-mal transmission policy for the two-hop system modelin case of multiple EH packets arriving at the relay. In[12], throughput maximization problem for the two-hopcommunication system in case of an EH source withtwo energy arrivals has been solved using cumulativecurve algorithm. In [13], a Recursive Geometric Water-Filling (RGWF) algorithm, which is used to obtain op-timum power allocation for a single-hop transmission,was adopted to gain an efficient transmission policyfor a two-hop communication with EH Source (EH-S)and conventional Non-EH Relay (NEH-R) over a fadingchannel for a delay-limited network.

In this paper, we investigate optimal and sub-optimal transmission policy of the same system modelin [13] for DL relaying network as well as DT relayingnetwork under deterministic (offline) and online settingbased on RGWF algorithm. By comparing our workwith the existing results, the contributions of this workare summarized as follows:

• We present novel solutions to tackle the through-put maximization problem for the system modelwith EH-S and half-duplex NEH-R network overa fading channel, which has not been consideredin the literature.

• The low-complexity RGWF algorithm is modi-fied and extended into a two-hop network sce-nario in such that optimize the offline resourceallocation that maximizes the end-to-end systemthroughput for DL and DT relaying networks.

• For DL and DT cases, we propose several onlinelow-complexity approaches that provide reason-able performance.

The remainder of this paper is organized as follows.General tools and background work are presented inSection II and III, respectively. Section IV presents thesystem model and introduces the transmission policyadopted in this paper. In Section V, we formulate thethroughput maximization problem and we propose thedeveloped algorithms for the DL case. The formulationof the throughput maximization problem and the pro-posed algorithms for the DL case are discussed in Sec-tion IV, followed by numerical results and conclusionsin Sections V and VI, respectively.

2. General ToolsEH communication is an advanced wireless communi-cation technique that has attracted enormous researchattention. Radio resources, such as power and band-width, have to be well utilized and it can be classifiedas a Radio Resource Management (RRM) problem. Re-

cently, various tools are accomplished and establishedfor solving RRM problems. Water-Filling (WF) is a well-known information theory technique and it is a usefultool for RRM problem in wireless communication sys-tems. Specifically, WF is widely utilized to determinepower allocation strategy that maximizes point-to-pointchannel capacity by assigning more power to the chan-nel with higher gains. As a result, the overall channelcapacity is maximized. In the following, we introducethe water-filling problem, which can be formulated intothe following problem: given P > 0, as the total poweror volume of the water, find that

max{pi

}K

i=1

PKi=1

Li

2 · log(1 + hipi)subject to: 0 pi, 8i,PK

i=1 pi = P

(1)

where K is the total number of channels. Let Li,hi and pi denote the time duration, the channel fadinggain and the transmission power of the ith channel,respectively. Since the constraints are that (i) the allo-cated power to be nonnegative, and (ii) the sum of thepower equals P , the problem (1) is called the water-filling (problem) with sum power constraint.

By interpreting the observed properties of the opti-mal power allocation scheme as a water-filling scheme,pi units of water is filled into a rectangle container withbottom width as L

i

2 , (i=1,. . . , K). For unifying parameternotation, through a change of variables, we can obtainan equivalent target problem as follows:

max{pi

}K

i=1

PKi=1 ⌧i · log(1 + hipi)

subject to: 0 pi, 8i,PKi=1 pi = P

(2)

where ⌧i Li

2 , hi hi

Li

and pi Lipi. Note that thesymbol is the assignment operator.

In this section, two water-filling approaches are pre-sented that solve the water-filling (problem) with sumpower constraint. One is the conventional water-filling(CWF); another is the proposed geometric water-filling(GWF). The main principle of WF approaches is that de-termining the optimum water level that maximizes theoverall network throughput. Nevertheless, CWF andGWF algorithms are developed to solve this constrainedoptimization problem using different optimization ap-proaches.

2.1. Conventional Water-Filling (CWF)

CWF is an approach of a wide WF algorithm um-brella that solves a power allocation problem with asum power constraint under non-negative individualpowers. Because of the non-linear equation and theinequality equation as shown in the problem (2), theresulting proposed system is non-linear. In CWF algo-rithm, Karush-Kuhn-Tucker (KKT) conditions are uti-lized to find the solution of the proposed problem. KKTconditions can be considered, on the other hand, as agroup of the optimality conditions. Below is the derived

M.Baljon et al : RESOURCE ALLOCATION FOR WIRELESS NETWORKS WITH ENERGY HARVESTING CONSTRAINTS OVER FADING CHANNELS 11

solution after applying the KKT conditions,8>><

>>:

pi =

⇣µ� 1

hi

⌘+, 8i,

PKi=1pi = P,

µ � 0,

(3)

where (z)+ = max{0, z}. µ is the water level cho-sen to satisfy the power sum constraint with equalityPK

i=1 pi = P . Eqn. (3) is referred as a solution of theCWF problem (2).

2.2. Geometric Water-Filling (GWF)

The GWF approach can be seen as a functional blockthat solves the same CWF RRM problem in Eqn.(2).GWF approach simplifies the CWF algorithm by elimi-nating the complexity of solving the non-linear systemusing KKT conditions into a geometric approach thatprovides explicit solutions and helpful insights to theproblem and the solution. In conventional water-fillingalgorithm, the optimum water level will have to bedetermined first, and then, the power allocation task issolved. In GWF, on the other hand, the highest channelunder water (i0), is aimed to be obtained instead, whichis an integer number. The water volume above the ithchannel (P2(i)) can be determined based on the heightof the ith fading channel (di =

1hi

⌧i

) and the channelwidth (⌧i) as shown below,

P2(i) =

"

P �K�1X

k=l

(di � dk)⌧k

#

, for i = l, . . . ,K. (4)

The main purpose of determining P2(i) is to find themaximal channel index (i0) that makes P2(i) positive.Hence, i0 can be obtained using the following formula

i0 = max{i|P2(i) > 0, 1 i K} (5)Consequently, the allocated power of the ith channel(i = 1, 2, . . . ,K) is determined as follows:

(pi =

hpi

0⌧i

0+ (di0 � di)

i⌧i, l < i i0

pi = 0, i0 < i K,(6)

where the power level of the i0 channel is obtained asfollows:

pi0 =⌧i0Pi0

k=l ⌧kP2(i

0) (7)

On the other hand, GWF algorithm occupies lesscomputational resource compared to CWF. The worst-case computational complexity of GWF approach is(8K + 3) fundamental arithmetical whereas CWF ap-proach has O(K2

) fundamental arithmetic [14]. Moredetailed of GWF algorithm can be found in [14].

3. Single-hop EH Communication SystemsAuthors in [10] presented the RGWF algorithm thatsolves the optimum power allocation problem for apoint-to-point data transmission with EH transmitterover a fading channel, as shown in Fig. 1, based on GWFapproach. Shannon capacity is adopted to achieve themaximum link capacity by determining the rate versuspower relationship of the channel, given by:

R[pi] = log[1 + hipi] (8)

where hi and pi are the channel fading gain and thetransmission power at the ith slot, respectively. The totaltransmitted bits for a given link in the ith time slot withduration ⌧i, is given by:

D(i, ⌧) =X

i

⌧i ·R(pi) (9)

3.1. Problem and Algorithm

In [10], throughput maximization problem for a single-hop system with EH constraints over fading channelsis investigated. The non-negative transmission powersof EH node is defined as pi with non-negative trans-mission durations ⌧i, for (i = 1, 2, . . . ,K), respectively.Moreover,

Pij=1 E

EHj�1 is cumulative harvested energy

on the transmitter. When the input power is subjectto energy causality constraint, it means that the energyharvested can only be used in the current time or in thefuture, but not in the past. In addition, total consumedenergy cannot be more than the total available energy,and an energy causality constraint can be stated asfollows

iX

j=1

⌧j · pj iX

j=1

EEHj�1, 8i. (10)

In other words, by replacing the sum power con-straint in Eqn.(2) into the EH causality constraint, thetarget problem can be defined as a water-filling problemwith EH constraints. As a results, other approaches wereutilized to solve this problem, and they are namelycalled directional water-filling (DWF) [8] and recur-sive geometric water-filling (RGWF) [10], which areextensions of CWF and GWF approaches, respectively.Hence, the throughput maximization problem can beformulated as follows,

max{pi

}K

i=1

PKi=1 ⌧i · log(1 + hipi)

subject to:Pi

j=1 ⌧j · pj Pi

j=1 EEHj�1, 8i,

0 pi, 0 ⌧i, 8i,(11)

Consequently, the objective function of this problemwill be based on the total amount of data that energyharvesting transmitter can forward to the destinationover a given number of transmission time slot K .

3.2. Recursive Geometric Water-Filling (RGWF)

Problem (11) has been solved based on GWF scheme,which eliminates the complexity of employing the KKTmultipliers. The RGWF algorithm, on the other hand,is an recursive version of the geometric water-fillingalgorithm that is used to allocate optimum transmissionpower and maximize the throughput of a single-hoptransmission with EH constraint, while taking into ac-count that channel condition and harvested energy varyin time. In RGWF, GWF can be represented as a func-tional block that is recursively applied to sequentiallysolve the power allocation problem for energy harvest-ing transmission over fading channels. Exact optimalallocated power can be determined to provide insightsinto the given profile and the solution.

In the following, a description of the RGWF algo-rithm is presented.


1) Assuming K is an integer that represents thetotal number of slots in a given transmissiontime (T), the assigned arrival harvested energycan be represented as {1,K, {EEH

i }Ki=1}.2) RGWF sequentially processes for the (K) slots

starting from the second time slot.3) Assuming (L) is the index of current processing

slot, the power levels are updates for slot (L)and its previous (L�n) slots. Hence, a process-ing window is established.

4) GWF algorithm is applied to this window toobtain optimal power allocation for the slotsthat are assigned to this window by solving (4)- (7). The common water level is then found,consequently.

5) Comparing the water level of the current pro-cess window with the previous slot, and then, ifthe non-decreasing water level condition beingsatisfied, the allocated powers for the corre-sponding (L) slots are obtained. Consequently,a new processing window will be created bymoving to the next time slot. Otherwise, thecurrent processing window will be extendedwith one slot in the left side and the same abovesteps are applied.

In this way, the completed optimum power alloca-tion {pi}Ki=1 for the ith time slot (i = 1, . . . ,K) aredetermined within finite loops. That is to say, RGWFcan be written as a formal expression:

{pi}Ki=1 = RGWF (1,K, {⌧i}Ki=1, {hi}Ki=1, {EEHi }Ki=1).

(12)In the following, we use this mapping as a first step

to solve the two-hop communication system with EHconstraints.

4. Two-hop EH Communication Systems4.1. System Model

In this section, we adopt the system model in [15],which consists of a two-hop communication systemwith an EH-S and a half-duplex NEH-R over a fadingchannel, as shown in Fig. 1. The direct transmissionbetween source and destination is negligible becauseof deep fading. For convenience, we consider that thegiven total transmission time period is from [0, T] in-cluding K epochs. Each epoch is represented as eitherarriving new harvest energy or changing in the chan-nel fading gain or both of them. The time differencebetween epochs’ instants (ti�1)th and (ti)th is calledthe ith epoch, which is defined as ⌧i = ti � ti�1,for i = 1, 2, ...,K . Moreover, Ei is the correspondingamount of harvested energy and 1

hi

is the fading levelin the ith interval, for i = 1, 2, ...,K . Without lossof generality, we assume t0 = 0 and tK = T . Theterms epoch and interval are used interchangeably inthis paper. We assume the channel between the source-relay link (hs

i ) experiences fading whereas (hri ) is the

AWGN channel on the relay-destination link for the ithinterval, (i = 1, 2, . . . ,K). In addition, the available

energy is utilized only for transmission purposes. Thus,Shannon capacity is adopted to achieve the maximumlink capacity by determining the rate versus powerrelationship of the channel.

Fig. 1: System model, K=7 epochs in [0,T] with (a) EH source, i.e.,random energy arrivals (Ein), has time-variant channel, and (b)non-EH relay, i.e., relay is powered by battery, experiences AWGNchannel.

In this paper, we propose resource allocationschemes for a two-hop wireless communication with EHconstraints over fading channels for delay limited anddelay tolerant networks. In the following subsection, wediscuss the advantage of RGWF-EH profile in maximiz-ing the network throughput and the transmission policyfor both delay networks’ types.

4.2. RGWF-EH Profile

RGWF algorithm has been shown to provide optimalpower allocation for a single-hop over a fading channel[10]; as it is illustrated in Fig.(2-a), where the plain areasrepresent the fading gain and the shadowed areas rep-resent the allocated power for the epochs. According toFig.(2-a), it is easy to notice that more power is allocatedto the epoch with less fading whereas less power is al-located to high fading epoch, which leads to maximumthroughput. Now, by only plotting the allocated power,we obtain RGWF-EH profile as shown in Fig.(2-b). Thisprofile can be used as a guideline for designing anefficient scheduling scheme that maximizes the networkthroughput for a two-hop communication system. Onthe other hand, a harvested energy arrival profile at thesource node and a bit arrival profile at the destinationare strongly related to each other. Since the source cantransmit no data until energy being physically available,the EH profile at the source controls the number of thetransmitted bits to the relay. Moreover, the bit arrivalprofile at the relay will be shaped based on the num-ber of bits that have already been transmitted by thesource. In addition, according to the energy causalityconstraints, the total power assigned upto the ith epochcannot be greater than the total harvested energy uptothe same epoch. Consequently, EH profile forms thedomain of the harvested energy usage, and all thefeasible transmission polices will be narrowed to thisdomain.


Fig. 2: (a) Optimum power allocation for a single-hop with EHconstraint over a fading channel using RGWF. (b) RGWF-EHprofile.

4.3. Transmission policy

Earlier work [ [8], Lemma 2] illustrates that the trans-mission rate/power of a node is constant between twosequential arrivals of energy. We also keep this policy inour analysis. Although obtaining an optimal transmis-sion policy for a single-hop transmission plays the corerole of designing a two-hop communication system,the objective function for the two-hop transmission isdissimilar. Particularly, the objective function in single-hop transmission is to maximize the throughput in(T), whereas two-hop system has the same overviewexcept the transmission has to be through a relay node.It means that the transmission scheduled time has tobe divided between source-relay and relay-destinationsessions. Therefore, to obtain optimal transmission pol-icy for two-hop transmission, source and relay powerallocation as well as transmission scheduling need tobe well planned in order to maximize the networkthroughput.

In addition, the transmission policy for the EH two-hop communication system is investigated based onboth DT and DL cases. In a delay tolerant network, thesource node keeps transmitting as long as it has a goodchannel condition and sufficient energy to transmit. Therelay node, on the other hand, will start forwarding thereceived bits once the source pauses its transmissiondue to deteriorated channel condition. In contrast, anexample of non-delay tolerant networks is real-timeapplications that impose strict restrictions on packetdelays in such that relay has to forward received packetsas soon as they arrive. Whereas data buffer at NEH-R isneglected in a delay limited network, we assume thatthe data buffer in a delay tolerance network has infinitecapacity at the relay node as well as EH-S has data allthe time.

In the following sections, we will show how wecan take advantage of the obtained RGWF-EH profileto maximize network throughput. The ordinary RGWFalgorithm is only valid for a single-hop power allocationproblem. In order to extend RGWF to two-hop trans-mission, a modified version of RGWF is proposed. Forthroughput maximization problem with a source havingRGWF-EH profile, the transmission policy of a two-hopcommunication has the following properties:

1. The transmission rate/power of a node is con-

stant within the ith interval, for i = 1, 2, ...,K

ps(t) =

(psi t 2 Ls

i

0 t 2 Lri

pr(t) =

(pri t 2 Lr

i

0 t 2 Lsi

where Lsi (Lr

i ) is the set of the source (relay)transmission sets in the given time [0, T ].

2. Emptying both source energy and the relay databuffer at the end of the given transmission time(T ) where lsi and lri are the scheduled time forsource and relay, respectively.PK

i=1 lri · log(1 + hr

i pri ) =

PKi=1 l

si · log(1 + hs

ipsi ), (13)

KX

j=1

lsj · psj =KX

j=1

EEHj�1, (14)

Based on the above discussed properties, we con-clude that a joint source and relay power allocationalong with their scheduled time has to be optimized insuch that a source transmits first and then it is followedby the relay at its allocated scheduling time. On theother hand, the total number of transmitted bits thatare delivered from the source to the destination mustsatisfy (13) by a deadline of K time slots.

5. Throughput Maximization Problem for the DL case

In this section, we aim to maximize network throughputof a two-hop system with EH constraints for the DLnetwork under offline and online knowledge of energystate information (ESI) and channel state information(CSI). EH-S and NEH-R are sharing the same epoch forthe ith interval (i = 1, 2, ...,K) in such that lsi + lri = ⌧iconstraint has to be satisfied whereas the total transmit-ted bits by both nodes have to be equal for each ithinterval (i = 1, 2, ...,K). The non-negative transmissionpowers of EH-S and NEH-R are defined as psi and priwith non-negative transmission durations lsi and lri , fori= 1, 2, ..., K, respectively. The throughput maximizationproblem can be formulated as follows:

max

PKi=1 l

ri · log(1 + hr

i pri )

subject to:PK

i=1 lri · pri ER, 8i,Pi

j=1 lsj · psj

Pij=1 E

EHj�1, 8i,

lri · log(1 + hri p

ri ) lsi · log(1 + hs

ipsi ), 8i,

lsi + lri = ⌧i, 8i,0 psi , 0 lsi , 0 lri , 8i,

(15)where

Pij=1 E

EHj�1 and ER are cumulative harvested en-

ergy on the source and the total available energy on therelay, respectively. Consequently, the objective functionof this problem will be based on the total amount of datathat NEH-R can transmit to the destination for the giventotal number of epochs K . The first and the secondconditions are due to the energy causality constraintsat the source and the relay, respectively, whereas thefourth constraint represents the half-duplex at the relay.Since small end-to-end delay is required, Eqn.(13) canbe further relaxed into the above third constraint, whichshows the equality of transmitted bits by both nodes at


each time instant. Hence, the problem can be rewrittenas following:

max

PKi=1 l

ri · log(1 + pri )

subject to:PK

i=1 lri · pri ER, 8i,Pi

j=1(⌧j � lrj ) · psj Pi

j=1 EEHj�1, 8i,

lri · log(1 + pri ) (⌧i � lri ) · log(1 + hsr,ipsi ), 8i,0 psi , 0 lri , 8i,

(16)

It is noticeable that the above property reduced theproblem (16) into a convex optimization problem and itcan be optimally solved using any conventional convexoptimization techniques [16]. In the following, optimaland suboptimal methods that solve the throughputmaximization problem for a DL network will be dis-cussed.

5.1. Optimal Resource Allocation

One of the most recent advanced methods that providethe global optimal solutions for both convex and non-convex optimization problems is the Interior-Point OP-Timizer (IPOPT) algorithm [17]. Interior-point methodprovides optimal solution for Non-Linear Programming(NLP) problems with enormous inequality constraints.The global convergence of the IPOPT method, whichinvolves the primal-dual interior point algorithm, isproposed by Fletcher and Leyffer [18] utilizing a filterline search method. Specifically, the search directionis found by applying Newton’s method into modifiedKarush-Kuhn-Tucker (KKT) equations. On the otherhand, the filter term is refereed as a set of values thatguarantee the objective and constraint functions neverreturn. A trial point is acceptable only if it achievesconsiderable progress towards the optimization goal aswell as it is not a member of the filter.

5.2. Sub-optimal Resource Allocation

In the optimal transmission policy for the proposedproblem without delay tolerant, there is a single source-relay stage pair in each epoch. Particularly, source andrelay stages for the ith RGWF interval (i = 1, 2, ...,K)

are defined as Lsi = [ti�1, ti�1 + t0i), L

ri = [ti�1 + t0i, ti)

respectively, where the time instants, ti�1, ti, and t0i,are the beginning, the ending of the ith epoch, andthe time when transmission is switched to the relay,respectively. The transmit powers of the ith RGWFinterval (i = 1, 2, ...,K) for the EH-S and NEH-R arepsi = PEH

i , pri = PRM respectively, where PEH

i is theallocated power that is obtained based on applyingRGWF algorithm considering only the source-relay link,and PR

M is the relay power, which is given and fixed.Consequently, by applying Eqn.(17), the initial sched-uled time is obtained for the ith interval (i = 1, 2, ...,K)

t0i =⌧i · log(1 + PR

M )

log(1 + PRM ) + log(1 + hsr,iPEH

i )

. (17)

Remark 1. In the case of ordinary RGWF, where a single-hop is only involved in the transmission, the poweris allocated on the whole ith interval, which includesource and relay transmission period. In this systemmodel, the relay shares the interval with the source andtherefore, RGWF algorithm has to be modified in order

to guarantee that power allocation algorithm is exactlyapplied on the length of source stage. Otherwise, theallocated power on the relay stage, which is a resultof applying RGWF on the whole epoch (⌧i), will beconsidered as wasted power. To overcome the poten-tial problem of assigning source power on the relaytransmission period, the source transmit power is re-allocated for the ith epoch (i = 1, 2, ...,K) as follows:

P ⇤i = PEH

i · ⌧it0i. (18)

The optimum time scheduling will be re-determinedbased on the optimum source transmit power (P ⇤

i ),and subsequently, on the initial scheduled time t0i.Hence, the optimum scheduled time for the ith epoch(i = 1, 2, ...,K), is determined as follows:

t⇤i =

⌧i · log(1 + PRM )

log(1 + PRM ) + log(1 + hsr,iP s

i ), (19)

We can see that solution given in (15) is unique andsatisfies the two-hop transmission policies that are dis-cussed in the beginning of this section. The proposedscheme is refereed as Relay In Partial Epoch (RIPE)algorithm based on RGWF.

5.3. Pre-Defined Data Rates (PDDR) Based

In this subsection, we propose suboptimal performanceconsidering the same problem set-up with only causalknowledge of CSI and ESI. We adapt the pre-definedmulti-rate wireless technology in order to support thetwo-hop DL network with EH constraints. The rateadaptation techniques comprise of scheduling algo-rithms based on instantaneous information of sourceSNR (�s

i ). We assume the fixed relay SNR (�r) is the

only parameter that has to be known in advance. Sincerelay node is powered by a fixed energy source, relaySNR is assumed to be higher than any instantaneousSNR of source node. Hence, resource allocation is ob-tained based on (�s

i ) only, where it is computed asfollows:

�si = hs

i ·2EEH

i�1

⌧i. (20)

The algorithm is proposed as follows. The maximumnumber of bits that the link can afford (Bmax) is deter-mined as follows:

Bmax(n) =⌧i2

· log(1 + (�r)). (21)

Then, (L) pre-defined multi-rate is computed by di-viding (Bmax(n)) into ( 1

L ) scale factors for (n=1, . . . ,L) where (Bmax(1)) is the highest possible transmittedbits and (Bmax(L)) is the lowest possible transmittedbits that source can transmits in its scheduled time. Onthe other hands, the corresponding relay scheduled timethat relay needs to re-transmits (Bmax(n)) is determinedas follows:

trmax(n) =Bmax(n)

rate(�r)

, (22)

Finally, the source scheduled time for ith epoch (tsi ) =

Bmax(n)

rate(�s

i

) is computed. If tsi (⌧i � trmax(n)), then,Bmax(n) is the maximum number of bits that can betransmitted for epoch (i). Otherwise, (n) increases by


one until tsi (⌧i � trmax(n)) condition is satisfied.The above steps are applied for the ith interval (i =

1, 2, ...,K). The following pseudo-code summarizes ouralgorithm.

Algorithm 1 Pseudocode for PDDR

1: Input: �r ;2: Calculate Bmax(n) and trmax(n) using (21) and (22),

respectively.3: Let integer (L > 1), divide Bmax(n) and its corre-

sponding trmax(n) into (L) pre-defined thresholds.4: for i = 1 to K do

5: Calculate tsi =B

max(n)

rate(�s

i

) .6: while tsi > (⌧ � trmax(n)) do

7: n n+ 1

8: end while

9: output: Bmax(n) is the maximum number of trans-mitted bits for epoch (i).

10: end for

11: Output: {Bmax(i,n)}Ki=1.

6. Throughput Maximization Problem for the DTCase

In this section, we consider maximization the num-ber of bits delivered of the two-hop system with EHconstraints by a deadline T for DT network. A delaytolerance network is desirable when the network has noconstraint on the end-to-end delay. Unlikely to the delaylimited network, epoch is never being shared betweennodes, however, it is either being allocated to the EH-Sor NEH-R for the ith interval (i = 1, 2, ...,K) in suchthat the total transmitted bits by both nodes have to beidentical by the end of the K time slots. The throughputmaximization problem for the delay tolerance networkcan be formulated as follows:max

PKi=1 �i · ⌧i · log(1 + hr

i pri )

subject to:PK

i=1 �i · ⌧i · pri ER, 8i,Pij=1(1� �i) · ⌧i · psj

Pij=1 E

EHs,j�1, 8i,PK

i=1 �i · ⌧i · log(1 + hri p

ri )

PK

i=1(1� �i) · ⌧i · log(1 + hsip

si ), 8i,

�i · (1� �i) = 0, 8i,psi � 0, pri � 0, ⌧i � 0, �i 2 {0, 1}8i,

wherePi

j=1 EEHs,j�1 and ER are cumulative harvested

energy on the source and the total available energy onthe relay, respectively. According to the third constraint,which shows the data causality, the amount of datawas transmitted by EH-S is higher than or equal tothe number of transmitted data by the relay at anyinstant of time. Consequently, the objective functionof this problem will be based on the total amount ofdata that NEH-R can transmit to the destination for thegiven total number of epochs K . The above problemis convex Mixed Integer Non-Linear Program (MINLP)since the integer variable �i is either (1) or (0); i.e.,�i 2 {0, 1} and many advanced algorithms recentlyhave been proposed to solve this type of the problemoptimally. In this paper, we propose several schemesthat solve this problem under offline and online setting.

6.1. Optimal Resource Allocation

Beside to IPOPT algorithm is the most recent advancemethod that provides the global optimal solution forNLP optimization problems, Advanced Process Opti-mizer (APOPT) algorithm is approved to solve manylarge-scale optimization problems, such as NLP, MILPand MINLP problems. APOPT is an open source soft-ware solver that provides global optimal solutions forconvex MINLP problems [19].

On the other hand, problem in (23) can be simplysolved using exhaustive search algorithm by giving �i,for the ith interval (i = 1, 2, ...,K). Hence, the onlyvariables that need to be optimized are (psi , p

ri ) for all

possible combinations of �i, for the ith interval (i =

1, 2, ...,K), and only a �i’s combination that maximizesthe overall throughput will be chosen. Because of thecomplexity of exhaustive search algorithm especiallyfor large number of time slots, the exhaustive searchapproach will not be applied in this paper.

6.2. Sub-Optimal Resource Allocation

To solve the problem (23) heuristically, the whole epochwill be either allocated to the source node or the relaynode based on (�s

i ) for the ith interval (i = 1, 2, ...,K).First, RGWF approach will be applied into the source-relay link for the ith RGWF interval (i = 1, 2, ...,K).Hence, the transmit powers of the ith RGWF interval(i = 1, 2, ...,K) for the EH-S and NEH-R are psi = PEH

i ,pri = PR

M respectively. The threshold average capacity(✓c) for (K !1) can be formulated as

✓c =

PKi=1 �

si

K=

PKi=1 h

sip

EHi

K(23)

That is all, the whole interval is assigned to thesource set (Ls

i ) if (�si � ✓c) or it is allocated to the

relay set (Lri ), otherwise. Moreover, the first interval is

allocated to the source set whereas the last epoch to therelay. Eventually, RGWF algorithm is utilized again andit will be only applied on the intervals that are assignedto the source node (⌧ si ). To avoid a vital problem thatresults in pri 6= 0 even when the relay node does nothave data to send, our proposed algorithm solves thatpotential problem as it is shown in (2). The “for” loop(line 15 to 23) ensures that the bit arrival profile atthe relay will be shaped based on the number of bitsthat have been transmitted by the source and the relaynode only transmits if it has stored data in the buffer.The proposed algorithm is referred as Relay In Demandusing Average Capacity (RID-AC). Algorithm 2 showsthe pseudo-code for this scheme.

6.3. Relay In Demand using Average Fading (RID-AF)Based

It is well-known that only causal information of channelstatus and harvested energy is available for real scenarioof resource allocation in wireless communication. This isto say, we proposed an efficient low-complixity schemethat solves (23) with knowledge of CSI only. Similarto the sub-optimal performance of offline transmissionpolicy using average capacity as a threshold, the wholeepoch will be either allocated to source node or relay


Algorithm 2 Pseudocode for RID-AC

1: Input: {⌧i}K�1i , {hi}K�1

i , {EEHi }K�1

i ;2: Let Ls

i = � and Lri = � (empty sets).

3: utilize (12) to compute {pEHi }K�1

i .4: utilize (20) to compute {�s

i }K�1i .

5: utilize (23) to obtain (✓c).6: Ls

i ⌧1 Lri ⌧K

7: for i = 2 to K � 1 do

8: if �si > ✓c then

9: Lsi ⌧i

elseLri ⌧i

10: end if

11: end for

12: Input: {⌧ si }i2Ls

i

, {hsi}i2Ls

i

, {EEHi }K�1

i ;13: utilize (12) agian to compute new {pEH

i }K�1i .

14: Initialize relay buffer, B0 = 0:15: for i = 1 to K do

16: if ⌧i 2 Lsi then

17: Bi = Bi�1 + ⌧ si · log(1 + hsip

si )

else18: if log(1 + hr

i pri ) > Bi then

19: pri =

sBi�1hr

i

20: end if

21: Bi = Bi�1 � [⌧ ri · log(1 + hri p

ri )]

22: end if

23: end for

24: Output: {Bmax(i,n)}Ki=1.

node. However, since the only CSI is avaliabe, theepoch allocation is determined based on the channelfading gain (hs

i ) only as a threshold. Specifically, theepoch is allocated to source or relay for the ith interval(i = 1, 2, ...,K) as(

Lsi ⌧i if i = 1, or 1

hs

i

✓aLri ⌧i if i = K, or 1

hs

i

> ✓a,

where the threshold based on the average fading (✓a) =

·P

K

i=11h

i

K , and () is a scalar factor. We consider thatthe epoch (⌧i) is dedicated to the source in two cases:first at the beginning of transmission, second whenthe channel fading gain is higher than the threshold.In the second case, the ith epoch is dedicated to therelay transmission. Although the proposed solution isheuristic, it has been shown in the numerical resultsthat the proposed algorithms in a delay-tolerant net-work are achieved higher throughput compared to theproposed algorithms in a delay-limited network as wellas Algorithm 2 in [15] with the price of no-boundeddelay. The proposed algorithm is referred as Relay InDemand using Average Fading (RID-AF). The followingflow chart demonstrates the RID-AF algorithm, as it isillustrated in Fig.3.

7. Simulation ResultsIn this section, we provide simulation results to evaluatethe performance of the proposed offline and onlineresource allocation algorithms for both delay-tolerantand delay-limited networks. We set our parameter val-

Fig. 3: Flow chart of RID-AF algorithm.

ues as the same as [13]. We consider a band-limitedfading channel in the source-relay link and additivewhite Gaussian noise channel in the relay-destinationlink, with bandwidth (BW )= 1MHz and noise powerspectral density N0 = 10

�19W/Hz. The path loss andthe transmission block length are assumed to be 100dBand 100ms, respectively. Consequently, the rate powerfunction is determined as r = log(1+

h·P10�3 ). We assume

i.i.d. Rayleigh fading channels, where the gain h followsRayleigh distribution with mean (m = 5) whereas h =

1 for AWGN channels. Energy Harvesting rate PEHi , on

the other hand, follows Poisson distribution with arrivalrate (� = 1), which is multiplied in the unit of theaverage EH rate on the source (EEH

o = [1, 2, . . . , 10]).The simulation was done using Matlab and it was runfor 10000 random EH realizations.

7.1. Performance of RGWF algorithm for a point-to-point communication

Fig.4 shows the average throughput versus the sourceaverage EH rate with infinite energy capacity overRayleigh fading channel. We compare the RGWFscheme performance with a conventional non-EHsource, where the same total amount of energy is avail-able to allocate at the start of the process; and thebaseline performance, where the source node starts itstransmission as soon as the harvested energy arrivesover Rayleigh fading channel. It is shown that with theincreasing rate of the harvested energy, the throughputloss of the RGWF over the non-EH network is more sig-nificant due to the fact that higher amount of harvestedenergy has to follow causality constraint, and therefore,loss flexibility of allocation. On the other hand, theproposed RGWF outperforms baseline scheme in theentire range of energy arrival rate.

7.2. Resource Allocation Schemes for Delay LimitedTwo-hop Communication

In this subsection, we show the performance of the pro-posed resource allocation schemes for a delay limitedrelaying in a two-hop wireless network with EH source


Fig. 4: Simulation results of the throughput versus the source EHrate for a single-hop over Rayleigh channel with m = 5.

over Rayleigh fading channel whereas the non-EH relaylink experiences AWGN environment. We compare thethroughput performance of the proposed algorithms tothe baseline algorithms where fixed power allocationand time scheduling are applied to both nodes. Forexample, each epoch is divided into two-equal timeslots and they are assigned to the source and the relayrespectively. All proposed algorithms are also comparedwith the upper bound of the short-term throughput fora conventional non-EH nodes.

Fig.5 shows the impact of high channel SNR and lowchannel SNR versus the throughput when the channellink faces Rayleigh fading. The figure shows the averagethroughput for the resource allocation schemes thatproposed for a delay-limited network versus (EEH

o ) for(K ! 1) and with a constant relay peak transmitpower PR

M = 10mW . It is noticeable that the averagethroughput increases as EEH

o increases for all consid-ered schemes. As expected, we can also observe that theperformance of the offline proposed resource allocationscheme is superior to the online schemes for all (EEH

o ).The reason behind is because of the fact that the non-causal information of CSI and harvested energy is avail-able before starting the transmission in offline schemewhereas only causal information of CSI and harvestedenergy is available for online case.

On the other hand, Fig.5 can be analyzed fromtwo perspectives. The first perspective shows the largethroughput gap between our proposed RGWF basedalgorithm; RIPE, and the baseline policy from one handand it reaches to its upper bound from another hand. Inaddition, when the network is delay limited, it is clearthat the proposed RIPE algorithms with data rates basedare alternated exactly between the upper bound andbaseline performance, which indicates that the through-put performance is degraded in price of less complexityand less feedback overhead. In addition, the proposedonline RIPE scheme with 10-rates performs better thanthe proposed online RIPE scheme with 5-rates whensource link faces Rayleigh channel duo to the fact thatmore data rates are available as options especially whenthe SNRs are varying among the epochs. Moreover, weobserve that the difference between the performances

Fig. 5: Simulation results of the throughput versus the sourceEH rate for non-delay tolerant two-hop network under Rayleighfading with m = 5.

of RIPE-10 and RIPE-5 rates increases with increasingEEH

o .

7.3. Resource Allocation Schemes for Delay TolerantTwo-hop Communication

In this subsection, we show the performance of pro-posed resource allocation schemes for a delay tolerantrelaying in a two-hop wireless network with EH sourceover Rayleigh fading channel whereas the non-EH relaylink has AWGN channel. We compare the through-put performance of the proposed offline and onlinealgorithms to the baseline scheme where fixed powerallocation and slot allocation are applied to both nodes.For example, assuming the total number of epochs areeven, the odd epochs are assigned to the source andeven epochs are assigned to the relay. All the proposedalgorithms are also compared with the upper bound ofthe short-term throughput for a conventional non-EHtwo-hop network over Rayleigh fading channel.

Fig.6 shows the average throughput for the resourceallocation schemes proposed for a delay tolerant net-work versus average EH rate on the source (EEH

o ) for(K ! 1) and with a constant relay peak transmitpower PR

M = 10mW over Rayleigh fading channel. Itis quite clear that the throughput performance of theRID-AC algorithm has surpassed the performance ofthe RID-AF algorithm with average fading. Moreover,we can notice that the average throughput of the offlineproposed RID-AC scheme increases sharply as (EEH

o )increases, whereas the average throughput of the on-line proposed RID-AF scheme increases exponentiallyas (EEH

o ) increases. Fig.7, on the other hands, showsthe average throughput versus with different sourceaverage EH rate. It can be observed that the averagethroughput has direct relationship with the scale factor,and the network gains the maximum throughput when = 2.

8. Conclusion

This paper considers a single-hop and a two-hop com-munication systems with energy harvesting constraintson the source in a fading channel environment and we


Fig. 6: Simulation results of the throughput versus the source EHrate for delay tolerant two-hop network over Rayleigh channelwith m = 5.

Fig. 7: Average throughput versus with (PEHo =[ 5, 8, 10] mW)

under Rayleigh fading with m = 5.

extended the simple and the elegant RGWF approachthat solves the power allocation problem numericallyinto a simulation representation. The importance of thisrepresentation is that providing more insights to theproblems and the solutions in such that various wire-less systems can be analysed. We show the advantageof adapting the RGWF algorithm for the throughputmaximization problem under Rayleigh fading channel.For a two-hop communication system, we proposedtwo schemes that maximize the network performancefrom throughput perspective for both delay tolerantand non-delay tolerant networks. Transmission schedul-ing time has been derived for the source and the re-lay based on RGWF-EH profile to obtain an efficienttransmission policy. Numerical results illustrated thatoptimizing both transmission scheduling and power al-location result in gaining higher throughput. Moreover,simulations show that the proposed approach is simple,efficient and provide significant guidelines on networkdeployment and resource management in a green radionetwork with EH sources.

Acknowledgement

The authors sincerely acknowledge the support fromNatural Sciences and Engineering Research Council

(NSERC) of Canada under Grant numbers RGPIN-2014-03777, and the support from Al-Majmaah University inSaudi Arabia to this research.

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Mohammed Baljon received the B.Eng.degree in Electrical and Computer En-gineering from King Abdulaziz University,Jeddah, Saudi Arabia, in 2007. He also ob-tained the M.Eng. degree in Internetwork-ing Engineering from Dalhousie University,Halifax, NS, Canada, in 2012. He is cur-rently working toward the Ph.D. degree atthe Department of Electrical and ComputerEngineering, Ryerson University, Toronto,Canada. Currently, his research interests

include energy harvesting networks, relay systems, wireless com-munications and green communications.

Lian Zhao (S’99-M’03-SM’06) received herPhD degree from the Department of Electri-cal and Computer Engineering (ELCE) fromUniversity of Waterloo, Canada, in 2002.She joined the Electrical and Computer En-gineering Department, Ryerson University,Toronto, Canada, as an Assistant Profes-sor in 2003 and a Professor in 2014. Herresearch interests are in the areas of wire-less communications, radio resource man-agement, power control, cognitive radio and

cooperative communications, and smart grid. She has been an Ed-itor for IEEE Transaction on Vehicular Technology since 2013 andawarded TOP 15 Editor in 2015. She has served as the symposiumco-chair for IEEE Global Communications Conference (GLOBE-COM) 2013 Communication Theory Symposium; Web-conferenceco-chair for IEEE Toronto International Conference Science andTechnology for Humanity (TIC-STH) 2009; She has been a memberof NSERC (Natural Sciences and Engineering Research Council)Evaluation Group for Electrical and Computer Engineering since2015. Associate Chair for Graduate Studies at ELCE departmentfrom 2013 to 2015. She received Canada Foundation for Innovation(CFI) New Opportunity Research Award in 2005; Ryerson FacultyMerit Award in 2005 and 2007; Faculty Research Excellence Awardfrom ELCE Department of Ryerson University in 2010, 2012, and2014; and the Best Student Paper Award (with her student) fromChinacom in 2011, the Best Paper Award (with her student) from2013 International Conference on Wireless Communications andSignal Processing (WCSP), and 2016 Best Land Transportationpaper award from IEEE Vehicular Technology Society. She is alicensed Professional Engineer in Ontario, a senior IEEE memberand a member of the IEEE Communication/Vehicular Society.

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