power allocation for conventional and

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1182 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 3, MARCH 2014

Power Allocation for Conventional andBuffer-Aided Link Adaptive Relaying Systems with

Energy Harvesting NodesImtiaz Ahmed, Student Member, IEEE, Aissa Ikhlef, Member, IEEE, Robert Schober, Fellow, IEEE,

and Ranjan K. Mallik, Fellow, IEEE

AbstractIn this paper, we consider optimal power allocationfor conventional and bufferaided link adaptive energy harvest-ing (EH) relay systems, where an EH source communicates withthe destination via an EH decodeandforward relay over fadingchannels. In conventional relaying, source and relay transmitsignals in consecutive time slots whereas in bufferaided linkadaptive relaying, the state of the sourcerelay and relaydestination channels as well as the amounts of energy availableat source and relay determine whether the source or the relayis selected for transmission. Our objective is to maximize thesystem throughput over a finite number of transmission time

slots for both relaying protocols. In case of conventional relaying,we propose an offline and several online joint source and relaytransmit power allocation schemes. For offline power allocation,we formulate a convex optimization problem whereas for theonline case, we propose a dynamic programming (DP) approachto compute the optimal online transmit power. To alleviate thecomplexity inherent to DP, we also propose several suboptimalonline power allocation schemes. For bufferaided link adaptiverelaying, we show that the joint offline optimization of thesource and relay transmit powers along with the link selectionresults in a mixed integer nonlinear program which we solveoptimally using the spatial branchandbound method. We alsopropose efficient online power allocation schemes for bufferaided link adaptive relaying. Simulation results show that bufferaided link adaptive relaying provides significant performancegains compared to conventional relaying but requires a highercomplexity for computation of the power allocation solution. Wealso show that bufferaided link adaptive relaying is more robustto changes in the EH rate than conventional relaying.

Index TermsEnergy harvesting, power allocation, conven-tional relaying, buffer-aided link adaptive relaying, convex opti-mization, dynamic programming.

I. INTRODUCTION

IN cooperative communication systems, a source and a num-ber of cooperating relays expend their energy for process-

ing and transmitting data. For some applications, connecting

Manuscript received August 11, 2012; revised May 16 and October 5, 2013;accepted December 9, 2013. The associate editor coordinating the review ofthis paper and approving it for publication was P. Wang.

I. Ahmed and R. Schober are with the Department of Electrical andComputer Engineering, University of British Columbia, Vancouver, BC, V6T1Z4, Canada (e-mail: {imtiazah, rschober}@ece.ubc.ca).

A. Ikhlef is with Toshiba Research Europe Limited, Bristol, 32 QueenSquare, BS1 4ND, UK (e-mail: [email protected]).

R. K. Mallik is with the Department of Electrical Engineering, IndianInstitute of Technology - Delhi, Hauz Khas, New Delhi, 110016, India (e-mail: [email protected]).

This work was supported in part by grants from the Natural Sciencesand Engineering Research Council of Canada (NSERC), the Institute forComputing, Information and Cognitive Systems (ICICS) at UBC, and TELUS.

This paper was presented in part at the IEEE Vehicular TechnologyConference (VTC), Yokohama, Japan, May, 2012.

Digital Object Identifier 10.1109/TWC.2014.012314.121185

the source and the relays to the power grid is cumbersome

or may even not be possible. Pre-charged batteries can be

a viable solution to overcome this problem. In practice, the

limited storage capacity of batteries and high transmit powers

may result in quick drainage of the batteries. As a result, the

batteries need to be replaced/recharged periodically which canbe sometimes impractical. An alternative solution is the de-

ployment of energy harvesting (EH) nodes. EH nodes harvestenergy from their surrounding environment to carry out their

functions. Energy can be harvested using solar, thermoelectric,and motion effects, or through other physical phenomena

[1]. EH nodes can be regarded as a promising option for

deployment as they ensure a long system lifetime without

the need for periodic battery replacements. In EH cooperativesystems, the energy can be independently harvested by the EH

source and/or EH relays during the course of data transmissionat random times and in random amounts. For data transmission

(and for other signal processing tasks), EH nodes expend the

energy from their storage and only the unused energy remains

in the batteries. In particular, at each time slot, the source and

the relays are constrained to use at most the energy available

in their storage. These constraints necessitate the design of

new transmission strategies for the source and the relays toensure optimum performance in an EH environment.

Recently, transmission strategies for and performance anal-

yses of EH nodes in wireless communication systems have

been provided in [2][8]. In [2], a single sourcedestination

noncooperative link with an EH source was considered and

an optimal offline along with an optimal and several suboptimal online transmission policies were provided for allo-

cating transmit power to the source according to the random

variations of the channel and the energy storage conditions. In

[3], a similar system model was considered, where dynamic

programming (DP) was employed to allocate the source trans-

mit power for the case when causal channel state information(CSI) was available. In [4], explicit throughputoptimal and

delayoptimal policies were developed for a single link point

topoint communication system. Several higher layer issues

such as transmission time minimization and transmission

packet scheduling in EH systems were investigated in [6][8]. The use of EH relays in cooperative communication was

introduced in [5], where a comprehensive performance analy-sis was performed for relay selection in a cooperative network

employing EH relays. A deterministic EH model (assuming a

priori knowledge of the energy arrival times and the amount

of harvested energy) for the Gaussian relay channel was

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AHMED et al.: POWER ALLOCATION FOR CONVENTIONAL AND BUFFER-AIDED LINK ADAPTIVE RELAYING SYSTEMS WITH ENERGY . . . 1183

considered in [9], [10], where delay and nodelay constrained

traffics were studied. In [11], cooperative communication with

EH nodes using an energy sharing strategy was studied. The

concept of energy transfer in EH relay systems was consid-

ered in [12], where an offline power allocation scheme was

proposed. The deployment of EH sensors in sensor networkshas been extensively discussed in the literature [1], [4], [13],

[14].

In this paper, we consider a simple single link cooperative

system where the source communicates with the destination

via a decodeandforward (DF) relay and both the source and

the relay are EH nodes. We assume that each node stores the

harvested energy in a battery having finite capacity and the

relay operates in the halfduplex mode. In most of the existing

literature on half duplex relaying [5], [9], [15], [16], it is

assumed that relays receive a packet in one time slot from the

source and forward it in the next time slot to the destination.

We refer to this approach as conventional relaying through-

out this paper. Recently, it has been shown in [17][19] thatequipping relays with buffers can improve the performance

of cooperative communication systems. In fact, using buffersat the relays allows temporary storage of packets at the relay

when the relaydestination channel quality is poor until the

quality of the channel has sufficiently improved. In [18], a

bufferaided adaptive link selection protocol was proposedfor the case where both source and relay have a constant

energy supply. This protocol gives the relay the freedomto decide in which time slot to receive and in which time

slot to transmit. We note that both conventional and buffer

aided relaying are important and deserve consideration since

their applicability depends on the system requirements. For

example, conventional relaying is suitable for delay sensitive

systems because it entails the minimum possible delay. On

the other hand, bufferaided relaying is suitable for delay nonsensitive systems, where a certain amount of delay is tolerable,

but a high average throughput is needed.

In this paper, we consider both conventional and buffer

aided link adaptive relaying protocols. For both protocols,we propose offline and online (realtime) power allocation

schemes that maximize the endtoend system throughput

over a finite number of transmission slots. The offline schemes

are of interest when the amount of harvested energy and

the channel signaltonoise ratio (SNR) for all transmission

slots are known a priori. However, in practice, the amount of

harvested energy and the channel SNR are random in nature

and cannot be predicted in advance. Therefore, in this case,

online power allocation schemes have to be employed takinginto account the available knowledge of the channel SNRs and

harvested energies. Nevertheless, considering offline schemes

is still important since they provide performance upper bounds

for the practical online schemes. For conventional relaying, we

propose an optimal online power allocation scheme which is

based on a stochastic DP approach. To avoid the high complex-

ity inherent to DP, we also propose several suboptimal online

algorithms. In case of bufferaided link adaptive relaying,

we formulate an offline optimization problem that jointly

optimizes the source and the relay transmit powers along withthe link selection variable. Thereby, the link selection variable

indicates whether the source or the relay is selected for

transmission in a given time slot. The optimization problem is

shown to be a nonconvex mixed integer nonlinear program

(MINLP). We propose to use the spatial branchandbound

(sBB) method to solve the offline MINLP problem optimally

[20][22]. We also propose a practical online power allocation

scheme for the bufferaided link adaptive relaying protocol.In general, finding power allocation policies is more chal-

lenging for EH systems than for systems with constant energy

supply because of the randomness of the arrival times and the

randomness of the amounts of harvested energy. On the other

hand, the literature on cooperative wireless sensor networks

with EH, e.g., [1], [4], [13], [14], mainly considers long

term utility, analyzes the error rate performance, or proposesprobabilistic power management and scheduling policies. In

particular, a large, possibly infinite number of transmissiontime slots is assumed to obtain average error rates or the

average throughput. This is in contrast to this paper where

we optimize power allocation and link selection policies over

a finite number of time slots, which leads to more practical

designs for realistic transmission scenarios. It was shown in

[18] that optimizing power allocation and link selection forbufferaided relaying over an infinite number of time slots and

for a constant energy supply always leads to an online solution,

i.e., only knowledge of the current channel state is required

and any additional knowledge about past or future channel

states cannot further improve the solution obtained in [18]. Inother words, for the problem considered in [18] the solution to

the offline optimization problem can be implemented online.

In contrast, since the optimization in this paper is performed

over a finite number of time slots and the amount of energy

available for transmission is random, offline power allocation

and link selection policies outperform online policies, i.e.,

knowledge about past or future channel and energy harvesting

states can further improve performance. Moreover, the bufferaided link adaptive protocol considered in this paper is dif-

ferent from the nodelay constrained protocol in [9]. Firstly,

[9] considers the Gaussian relay channel whereas the source

relay and relaydestination links in this paper are impaired

by timevarying fading. Secondly, [9] only considers offline

power allocation for delay and nodelay constrained relaying

protocols, whereas we consider both offline and online power

allocation schemes for conventional and bufferaided link

adaptive relaying. Thirdly, although the nodelay constrained

relaying protocol in [9] also employs a buffer, unlike the

protocol in this paper, it does not perform adaptive linkselection. In summary, the contributions of this paper are as

follows: We propose optimal offline, optimal online, and sub-

optimal online power allocation schemes for EH nodes

employing the conventional relaying protocol in fading

channels. The optimal offline and online power allocation

schemes are formulated as a convex optimization problem

and a stochastic DP problem, respectively. To reduce the

complexity of the optimal online scheme, several subop-

timal, lowcomplexity online schemes are proposed.

We propose optimal offline and suboptimal online power

allocation schemes for EH nodes employing the bufferaided link adaptive relaying protocol in fading channels.

The optimal offline joint power allocation and link selec-


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Energy Sources: Solar, Wind,

Biomechanical, Piezoelectric etc.

S R D

Battery Battery

, ,

Fig. 1. System model for a single linkSRD system where S andR areEH devices. S and R have batteries with finite storage which can store theenergies harvested from the energy sources. The rectangle boxes in S andRrepresent the batteries and the hashed areas represent the amount of energystored.

tion scheme is formulated as an MINLP problem, which

is solved optimally by the sBB method. Furthermore,

two suboptimal, lowcomplexity online power allocation

schemes are proposed.

Our results reveal that compared to conventional relaying,bufferaided link adaptive relaying is more robust to

changes of the EH rates. Moreover, bufferaided link

adaptive relaying provides significant throughput gainscompared to conventional relaying but requires a high

complexity to compute power allocation solution.

I I . SYSTEMM ODEL

We consider an EH relay system, where the source, S,communicates with the destination,D, via a cooperative relay,R, as shown in Fig. 1. Both S andR are EH devices and areequipped with batteries, which have limited storage capacity

and store the harvested energy for future use. In particular, thebatteries ofS and R can store at most BS,max and BR,maxunits of energy, respectively. The participation ofS andR insignal transmission and processing depends on the amount of

harvested energy stored in their batteries. The harvested energy

can be of any form, e.g. solar, wind, or electromechanical

energy. We assume the transmission is organized in time slots

of duration T. In the following, without loss of generality,we set T = 1, and the system transmits for K time slots.Throughout this paper, we assume that Sis the central node.In particular, Sacquires knowledge about the channel SNRsand the harvested energies, executes the power allocation

algorithms, and conveys the optimal transmit power for Rand the link selection policy (for link adaptive relaying) to

R in each time slot. We assume that Shas perfect knowledgeof the channel SNRs and the energy harvested at R1. Inthe next two subsections, we discuss the signal model, the

system throughput, and the battery dynamics for conventional

and bufferaided link adaptive relaying.

1In practice, the channel SNRs may not be perfectly known to the sourcenode due to different sources of errors in the estimation process, e.g.,background noise, quantization errors, and outdated estimates. Furthermore,feedback errors and delay impair the quality of the estimates of the harvestedenergy at the relay node at the source node. However, studying the effect ofimperfect channel and energy knowledge is beyond the scope of this paperand is an interesting topic for future work.

A. Conventional Relaying

Signal Model: In conventional relaying, during the first time

slot, S transmits and R receives, and during the second timeslot, R transmits and D receives. This sequential processcontinues for K time slots, where K is assumed to be aneven number. The received packet at R in the (2k 1)th timeslot is modelled as

yR,2k1 = hS,2k1x2k1+nR,2k1, k {1, 2, , K/2}, (1)

wherehS,2k1is the fading gain of theSRlink andnR,2k1denotes the noise sample at R. The transmitted packet x2k1contains Gaussiandistributed symbols2. Assuming DF relay-

ing, the detected packet, x2k, is transmitted from R duringtime slot 2k. Thus, the received packet at D is given by

yD,2k = hR,2kx2k+ nD,2k, (2)

where hR,2k and nD,2k denote the fading gain of the RD link and the noise sample at D, respectively. hS,2k1and hR,2k can follow any fading distribution, e.g. Rayleigh,

Rician, Nakagamiq, or Nakagamim fading. nR,2k1 andnD,2k are additive white Gaussian noise (AWGN) sampleshaving zero mean and unit variance. We assume the channels

are quasistatic within each time slot and the channel SNRs

of the SR and the RD links are denoted by S,2k1and R,2k, respectively, where S,2k1 = |hS,2k1|

2 and

R,2k = |hR,2k|2. We assume S,2k1 and R,2k are inde-

pendent and identically distributed (i.i.d.) over the time slots.

Furthermore, S,2k1 and R,2k are mutually independentbut not necessarily identically distributed (i.n.d.). For future

reference, we introduce the average SNRs of the SRand theRD links as S and R, respectively.System Throughput: If x2k1 is transmitted from S with

transmit powerPS,2k1 during time slot 2k 1,

S,2k1 log2(1 + S,2k1PS,2k1) (3)

bits of data can be received errorfree at R . Similarly, ifx2kis transmitted from R with transmit power PR,2k,

R,2k log2(1 + R,2kPR,2k) (4)

bits of data can be received errorfree at D . During the 2kthand the (2k 1)th time slots, S and R, respectively, donot transmit any data, i.e., PS,2k = 0 and PR,2k1 = 0.We assume that R ensures errorfree detection by employingan appropriate error correction coding scheme and hence

x2k = x2k1. Therefore, the endtoend (SD) systemthroughput is given by 12min{S,2k1, R,2k}bits/s/Hz wherethe factor 1

2is due to the halfduplex constraint.

Battery Dynamics: The energies stored in the batteries of

S and R in time slot k are denoted by BS,k and BR,k,respectively. The transmit powers of S and R are limitedby the battery energies, i.e., 0 PS,2k1 BS,2k1 and0 PR,2k BR,2k. We assume throughout this paper thatthe energy consumed by the internal circuitry ofS and R is

2We note that practical modulation and coding schemes can be accommo-dated in the later analysis by multiplying all transmit powers by a constant > 1, which represents performance gap between the practical scheme andoptimal one.


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negligible compared to the transmit power [3]3. The energy

harvester at S harvests HS,m BS,max units of energyfor transmission purpose during the mth time slot, wherem {1, 2, , K}. Similarly, the energy harvester at Rcollects HR,m BR,max units of energy during the mthtime slot. It is worth noting that energies are harvested duringevery time slot m at S and R. Let HS,E E{HS,m} andHR,E E{HR,m} denote the average energy harvestingrate of S and R over the time slots, respectively. Here,E{} denotes statistical expectation. Because of the spatialseparation of S and R, we assume HS,m and HR,m areindependent of each other and i.i.d. over the time slots. Similarto [3], we assume the stored energies at SandR increase anddecrease linearly provided the maximum storage capacities,BS,max and BR,max, are not exceeded, i.e.,

BS,m+1=min{(BS,m PS,m+ HS,m), BS,max}, m (5)

BR,m+1=min{(BR,m PR,m+ HR,m), BR,max}, m. (6)

Furthermore, BS,1 = HS,0 0 and BR,1 = HR,0 0,respectively, denote the available energies at S and R before

transmission starts.

B. Buffer-Aided Adaptive Link Selection

Signal Model: For bufferaided link adaptive relaying, relayR is equipped with a buffer in which it can temporarily storethe packets received fromS. In this case,Sdecides whetherSorR should transmit in a given time slot, k {1, 2, , K},based on the CSI of the SR and the RD links [18].Therefore, unlike conventional relaying, in any time slot k,S orR can transmit packets. Let dk {0, 1} denote a binarylink selection variable, where dk = 0 (dk = 1) if the SR(RD) link is selected for transmission. When dk = 0, the

received packet at R is given by

yR,k= hS,kxk+ nR,k. (7)

On the other hand, when dk = 1, the received packet at D isgiven by

yD,k = hR,kxk+ nD,k. (8)

System Throughput: When dk = 0, S is selected fortransmission and S,k bits of data can be transmitted errorfree via the SR link. Hence, R receives S,k data bits fromSand appends them to the queue in its buffer. Therefore, thenumber of bits in the buffer atR at the end of thekth time slotis denoted as

Qkand given by

Qk = Qk1+ S,k. However,

whendk = 1, R transmits and the number of bits transmittedvia the RD link is given by min{R,k, Qk1}, i.e., themaximal number of bits that can be sent by R is limitedby the number of bits in the buffer and the instantaneous

capacity of theRD link [18]. The number of bits remainingin the buffer at the end of the kth time slot is given byQk = Qk1 min{R,k, Qk1}. We assume that S has

3If the energy consumed by the internal circuitry is not negligible, ourproblem formulations in Sections III and IV have to be changed accordingly.Problem formulations for EH systems accounting for the energy consumed bythe internal circuitry can be found in e.g. [23], [24]. Alternatively, the energyconsumed by the internal circuitry may be supplied by a precharged batteryand only the transmitted energy is generated via EH.

always data to transmit and the buffer at R has very large(possibly infinite) capacity to store them. Therefore, a total

ofKk=1

min{dkR,k, Qk1} bits are transmitted from S to D

during the entire transmission time.

Battery Dynamics:The battery dynamics for the link adaptive

transmission protocol are identical to those for conventional

relaying.

III. POWERA LLOCATION AND L IN K S ELECTION FOR

BUFFER-A IDED R ELAYING

In this section, we propose offline and online joint link se-

lection and power allocation schemes for EH systems employ-

ing bufferaided relaying. Bufferaided relaying is preferable

over conventional relaying for applications which can tolerate

delays but require high throughput.

A. Offline Power Allocation

Our goal is to maximize the total number of transmitted

bits (from S to D) delivered by a deadline of K timeslots for the link adaptive transmission protocol. The offline

(prior) information about the full CSI and the energy arrivals

at S and R in each time slot are assumed to be knownin advance. The resulting maximization problem is subject

to a causality constraint on the harvested energy and the

(maximum) storage constraint for the batteries at both S andR. The offline optimization problem for the link adaptivetransmission protocol can be formulated as follows:

maxT 0, {dk|k}

Kk=1

dklog2(1 + R,kPR,k) (9)

s.t.

qk=1

((1 dk)PS,k+ S,k)

q1k=0

HS,k, q (10)

qk=1

(dkPR,k+ R,k)

q1k=0

HR,k, q (11)

vk=0

HS,kv

k=1

((1 dk)PS,k+ S,k) BS,max, v

(12)v

k=1

HR,kv

k=1

(dkPR,k+ R,k) BR,max, v (13)

q

k=1(1 dk)log2(1 + S,kPS,k)

qk=1

dklog2(1 + R,kPR,k) , q (14)

dk(1 dk) = 0, k, (15)

where T {PS,2k1, PR,2k, S,2k1, R,2k|k {1, 2, , K/2}}. Also, q, k, and v standfor q {1, 2, , K}, k {1, 2, , K}, andv {1, 2, , K 1}, respectively. The slack variablesS,2k1 and R,2k ensure that constraints (12)(14) can bemet for all realizations of S,k, R,k, HS,k, and HR,k. Inparticular, these slack variables represent the power (possibly)


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wasted in each transmission interval4. Constraints (10) and

(11) stem from the causality requirement on the energy

harvested at S and R, respectively. Moreover, (12) and (13)ensure that the harvested energy does not exceed the limited

storage capacity of the batteries at S and R, respectively.Constraint (14) ensures that R cannot transmit more bitsthan it has in its buffer. Moreover, (15) ensures that dk canonly be 0 or 1, i.e., either S or R transmits in a given timeslot, k {1, 2, , K}. We note that, in this optimizationproblem, although we are maximizing the throughput of the

RD link, using constraint (14) incorporates the effect of thethroughput of the SR link. As S,k and R,k are increasingfunctions of PS,k and PR,k, respectively, the optimizationproblem in (9)(15) can be restated as follows:

maxT0, {dk|k}

Kk=1

dkR,k (16)

s.t.

qk=1

(1 dk)(2S,k 1)

S,k+ S,k

q1k=0

HS,k, q

(17)

qk=1

dk(2R,k 1)

R,k+ R,k

q1k=0

HR,k, q (18)

vk=0

HS,kv

k=1

(1dk)(2

S,k1)

S,k+S,k

BS,max, v (19)

vk=1

HR,kv

k=1

dk(2R,k 1)

R,k+R,k

BR,max, v (20)

qk=1

(1dk)S,k

qk=1

dkR,k, q (21)

dk(1 dk) = 0, k, (22)

where T = {S,k, R,k, S,k, R,k|k {1, 2, , K}}.The problem in (16)(22) is a nonconvex MINLP due to

the binary variables dk and the nonconvex and nonlinearconstraints (17)(22). In the following, we propose two op-

timal methods to solve the bufferaided link adaptive offline

optimization problem.

1) Exhaustive Search: For given dk, k {1, 2, , K},the optimization problem in (16)(22) is convex. Therefore,

we can optimize S,k and R,k for given dk {0, 1}very efficiently. In this method, we optimize S,k and R,kfor all possible combinations of dk, k {1, 2, , K},and select from all the solutions that combination of dk,

k {1, 2, , K}, which maximizes the cost function. Thisexhaustive search method provides the global optimal solution

but with an exponential complexity. For instance, for K timeslots we have2K2 possible combinations ofdk and hence tooptimizeS,k and R,k, we need to solve 2K2 optimizationproblems. Therefore, in practice, this approach cannot be

adopted in general, especially for large K. However, theexhaustive search scheme can be effective for small K.

4For example, ifHS,k and HR,k are large values (HS,k and HR,k arerandom variables and cannot be controlled in the optimization problem) andBS,max and BR,max are small, then ifS,2k1 and R,2k were omitted,constraints (12) and (13) would not be satisfied and problem (9)(15) wouldbecome infeasible. Therefore, slack variables S,2k1 and R,2k ensure thatproblem (9)(15) is always feasible.

2) Spatial Branch-and-Bound (sBB):As mentioned before,

our problem is a nonconvex MINLP. One of the recent

advances in (globally) solving MINLP problems is the sBB

method [20], [21]. The sBB method sequentially solves

subproblems of problem (16)(22). These subproblems are

obtained by partitioning the original solution space. For eachsubproblem, the sBB method relies on the generation of rig-

orous lower and upper bounds of the problem over any givenvariable subdomain. The feasible lower bounds are chosen

to be the local minimizers of the (sub)problems whereas the

upper bounds are obtained from convex relaxations. Interest-

ingly, MINLP problems can be solved by using the widely

available open source solver Couenne [21], [22]. Couenne

provides the global optimal solution for both convex and nonconvex MINLP problems. It implements linearization, bound

reduction, and branching methods within a branch and boundframework. The convergence of the sBB method in a finite

number of iterations is guaranteed [22]. However, the worst

case computational complexity of sBB is exponential in the

size of the optimization variables [21].

B. Online Power Allocation

In practice, only causal information about channels and

harvested energies is available for power allocation. Therefore,

the offline power allocation scheme is not readily applicableas, at a given time slot, the future CSI and the upcom-

ing harvested energy are not known in advance. To thisend, we could formulate an optimal online scheme using

stochastic DP. Unfortunately, this approach leads to a very

high computational complexity because of the adaptive link

selection in every time slot and may not be implementable

in practice. Therefore, we propose two efficient suboptimal

online schemes which have low complexity.

1) Suboptimal Harvesting Rate (HR) Assisted Online Power

Allocation: We propose an efficient online power allocation

scheme referred to as HR Assisted. To this end, we formulatean optimization problem which is based on the average data

rate, the average energy causality constraints at SandR, andthe average buffering constraint for K as follows:

max{PS,k0, PR,k0, dk|k}

1

K

Kk=1


s.t. 1

K

K

k=1

(1 dk)PS,k 1

K

K1

k=0

HS,k (24)

1

K

Kk=1

dkPR,k 1

K

K1k=0

HR,k (25)

1

K

Kk=1

(1 dk)log2(1 + S,kPS,k)

= 1

K

Kk=1


1

Kdk(1 dk) = 0, k (27)


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The Lagrangian of (23)(27) is given by

L= 1

K

Kk=1

dklog2(1 + R,kPR,k) 1

K

Kk=1

kdk(1 dk)

S

K

K

k=1

(1 dk)PS,k HS,k1

RK

Kk=1

dkPR,kHR,k1

K

Kk=1

dklog2(1+ R,kPR,k)

(1 dk)log2(1 + S,kPS,k)

, (28)

whereS,R,, andk are Lagrange multipliers. Differenti-ating (28) with respect toPS,k,PR,k, and dkand equating eachof the differentiated expressions to zero leads to the following

optimum values ofPS,k, PR,k, and dk:

PS,k =

S 1

S,k, ifS,k >

S

AND dk = 0,

0, otherwise, (29)

PR,k=

1R

1R,k , if R,k> R AND dk = 1,

0, otherwise, (30)

dk =

1, if (CR> CS) OR

R,k> R AND S,k < S

,

0, if (CR< CS) OR

R,k< R AND S,k > S

,

(31)

where CR = lnR,kR

+ RR,k 1, CS = ln

S,kS

+

SS,k

, = /(1 ), S =Sln(2)/(1 ), and R =

R

ln(2)/(1). We observe that the optimal PS,k

,PR,k

, and

dk depend on the instantaneous channel SNRs and Lagrangemultipliers. The Lagrange multipliers can be solved efficiently,

as shown in the next part of this section, without requiring any

noncausal knowledge. Therefore, the optimalPS,k,PR,k, anddk are readily applicable in a realtime (online) environmentwith low implementation complexity.

Finding the Lagrange Multipliers:Combining (29)(31) and

(24)(26) yields the following conditions for K :

R0

S

S

1

S,k

fS,k(S,k)dS,k

fR,k(R,k)dR,k

+

R

L1

S

1

S,k

fS,k(S,k)dS,k

fR,k(R,k)dR,k

=HS,E, (32)S

0

R

1

R

1

R,k

fR,k(R,k)dR,k

fS,k(S,k)dS,k

+

S

L2

1

R

1

R,k

fR,k(R,k)dR,k

fS,k(S,k)dS,k

=HR,E, (33)

R0

S

log2

S,k

S

fS,k(S,k)dS,k

fR,k(R,k)dR,k

+

R

L1

log2

S,k

S

fS,k(S,k)dS,k

fR,k(R,k)dR,k

=

S

0

R

log2

R,kR

fR,k(R,k)dR,k

fS,k(S,k)dS,k

+

S

L2

log2

R,kR

fR,k(R,k)dR,k

fS,k(S,k)dS,k, (34)

where L1 = S

W

e

R,kRR,k

1 RR,k

1

and L2 =

R

W

e

SS,k

1 SS,k

. Here, W() is the Lambert W

function [25]. For Rayleigh fading, fS,k(S,2k1) =

(1/S)eS,2k1/S

and fR,k(R,2k) = (1/R)eR,2k/R

.We need to solve (32)(34) to find the optimal S, R, and. The solution can be obtained by using the builtin rootfinding function in Mathematica. We note that the optimal

S,R, and are computed offline before transmission starts.When transmission begins, PS,k, P

R,k, and d

k are calculated

based on offline parameters,S, andR and online variablesS,k and R,k.

The solution of problem (23)(27) provides an upper bound

for the practical case where the storage capacity of the batter-

ies is limited. Moreover, the problem may yieldPR,k= 0evenif the buffer is empty atR. To avoid this undesirable behavior,we propose a practical but suboptimal online algorithm which

is summarized in Algorithm 1. At first, we calculate BS,k andBR,k using (5) and (6), respectively. We then calculatePS,k,PR,k, and d

k from (29)(31) and (24)(26). To ensure that

PS,k and PR,k do not exceed the storage limits, we perform

steps 6 to 8 and 11 to 13, respectively. Steps 9 and 17 keep

track of the arrival of data bits into and the departure of databits out of the buffer, respectively. Steps 14 to 16 are adopted

to ensure that R transmits only if there is data in the buffer.2) Suboptimal Naive Online Power Allocation: In the

suboptimal naive power allocation scheme for link adaptive

relaying, at each time slot,k,SandR consider the amount ofenergy stored in their batteries as their transmit powers. Based

on the transmit powers, S and R compute their capacities.

Note that the buffer status should be taken into account in thecomputation of the capacity of R. The SR (RD) link isselected if the capacity ofS is greater (smaller) than that ofR.

C. Complexity

The overhead of bufferaided link adaptive relaying in-

cludes both the computational complexity and the required

feedback of the corresponding power allocation schemes. The

worstcase computational complexity of the sBB algorithmused to solve the offline power allocation scheme for link

adaptive relaying is exponential in K [21], whereas the


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computational complexity of the exhaustive search algorithm

is always exponential in K. Moreover, the worstcase com-plexity of the sBB algorithm is not likely to occur as is

evident from the execution time results shown in Section V.

Determining the exact and/or average complexity of the sBB

algorithm is quite involved and beyond the scope of this paper.The complexities of the proposed suboptimal online schemes

for link adaptive relaying are linear in K.Furthermore, for bufferaided link adaptive relaying, S

needs to know the instantaneous values ofS,k, R,k, HS,k,andHR,kalong with the averagesS,R,HS,E, andHR,Eforexecution of the online power allocation algorithms. Moreover,S also has to track the status of the relay buffer. Aftercalculating the optimal power and link selection policies, Shas to convey PR,k as well as information regrading whichlink is selected to R .

Algorithm 1 HR Assisted Online Scheme For BufferAided

Link Adaptive Relaying

1: Initialize the buffer status, Q0 = 0 bits;

2: fork = 1 to K do3: CalculateBS,k andBR,k using (5) and (6), respectively.4: CalculatePS,k, P

R,k, andd

k using (29)(31) and (24)

(26).

5: ifdk = 0 then6: ifPS,k > BS,k then7: PS,k = BS,k;8: end if

9: Qk = Qk1+ log2(1 + S,kPS,k);

10: else

11: ifPR,k > BR,k then12: PR,k = BR,k;13: end if

14: iflog2(1 + R,kPR,k)> Qk then

15: PR,k = 2Qk1R,k

;

16: end if

17: Qk = Qk1 log2(1 + R,kPR,k);

18: end if19: end for

20: Obtain throughput =Kk=1

dklog2(1 + R,kPR,k).

IV. POWERA LLOCATION FORC ONVENTIONALR ELAYING

In this section, we propose an offline and several online

power allocation schemes for the considered EH system withconventional relaying. We note that conventional relaying is

preferable over bufferaided relaying if small endtoenddelays are required.

A. Optimal Offline Power Allocation

Like for bufferaided relaying, for conventional relaying,

our objective is to maximize the total number of transmitted

bits (from S to D) delivered by a deadline ofK time slotsover a fading channel. We assume offline (prior) knowledgeof the full CSI and the energy arrivals at S and R in eachtime slot. The offline optimization problem for maximization

of the throughput of the considered system for K time slotscan be formulated as follows:

maxT 0

K/2k=1

min{S,2k1, R,2k} (35)

s.t. Constraints (10) (13) with d2k1 = 0 and

d2k = 1, k, (36)

S,2k1PS,2k1 = R,2kPR,2k, k, (37)

where k stands for k {1, 2, , K/2}. Like for bufferaided relaying, constraints (36) ensure the energy causality and

limited energy conditions for conventional relaying. Constraint(37) ensures that the amount of information transmitted from

S to R is identical to that transmitted from R to D so asto avoid data loss at R. Constraint (37) is required since weassume individual power constraints for S and R. This is areasonable assumption sinceSandRhave independent powersupplies.

Using (37) in (35) and (36), the considered offline optimiza-

tion problem can be rewritten as

maxT0

K/2k=1

S,2k1 (38)

s.t.

lk=1

S,2k1PS,2k1

R,2k+ R,2k

2l1k=0

HR,k, l(39)

2mk=0

HR,kmk=1

S,2k1PS,2k1

R,2k+ R,2k

BR,max, m (40)

Constraints (11) and (13) with d2k1 = 0 and

d2k = 1, k, (41)

where T T \ {PR,2k|k}, and l and m stand for l {1, 2, , K/2} and m {1, 2, , K/2 1}, respectively.Problem (38)(41) forms a convex optimization problem and

the optimum solution can be obtained either in closed formby using the Karush-Kuhn-Tucker (KKT) conditions5 or by

using any standard technique for solving convex optimization

problems [26], [27]. Let PS,2k1 denote the optimum solutionof the considered optimization problem. Then, the optimumPR,2k can be obtained as

PR,2k =S,2k1PS,2k1

R,2k. (42)

B. Optimal Online Power Allocation by DP

Unlike bufferaided link adaptive relaying, the link se-

lection policy is pre-defined for conventional relaying, i.e.,d2k1 = 0 and d2k = 1, k {1, 2, , K}. Thisfeature of conventional relaying reduces the complexity of

stochastic DP compared to link adaptive relaying. There-

fore, for conventional relaying, we consider a stochas-

tic DP approach for optimum online power allocation

5The solution of problem (38)(41) can be represented in terms of Lagrangemultipliers by using dual decomposition. Due to space limitation, we omit thesolution here.


8/14


[3], [28]. Let c2k1,2k (S,2k1, R,2k, (HS,2(k1) +HS,2k3), (HR,2k1 + HR,2(k1)), BS,2k1, BR,2k) denotethe state for time slots 2k 1 and 2k. We notethat HS,k = 0 for k < 0. Our aim is to max-imize the total throughput over K time slots. We as-sume the initial state c1,2 = (S,1, R,2, HS,0, (HR,0 +HR,1), BS,1, BR,2) is always known. We define a policy

p = {(PS,2k1(c2k1,2k), PR,2k(c2k1,2k)), c2k1,2k, k =1, 2, , K/2} as feasible if the energy harvesting con-straints 0 PS,2k1(c2k1,2k) BS,2k1 and 0 PR,2k(c2k1,2k) BR,2k are satisfied for all k. Hence, theobjective function to be maximized can be reformulated as [3]

R(p) =

K/2k=1

E{min{S,2k1, R,2k}|c1,2, p}, (43)

where we used the definitions S,2k1

log2(1 + S,2k1PS,2k1(c2k1,2k)) and R,2k

log2(1 + R,2kPR,2k (c2k1,2k)). The expectation iswith respect to the SNRs of the channels and the harvested

energies. In particular, for a given c1,2

, the maximumthroughput can be obtained as

R = maxpP

R(p), (44)

where Pdenotes the space of all feasible policies.The maximum throughput during time slots 2k 1

and 2k is denoted by J2k1,2k(BS,2k1, BR,2k). For agiven c1,2, the maximum throughput, J1,2(BS,1, BR,2),can be recursively obtained from JK1,K(BS,K1, BR,K),JK3,K2(BS,K3, BR,K2), , J3,4(BS,3, BR,4) [3]. Forthe last two time slots K 1 and K, we have

JK1,K(BS,K1, BR,K) =

max0PS,K1BS,K10PR,KBR,K

S,K1PS,K1=R,KPR,K

12

min {S,K1, R,K} (45)

and for time slots 2k 1 and 2k, we obtain

J2k1,2k(BS,2k1, BR,2k) =

max0PS,2k1BS,2k10PR,2kBR,2k

S,2k1PS,2k1=R,2kPR,2k

1

2min {S,2k1, R,2k}

+ J2k+1,2k+2(BS,2k1 PS,2k1, BR,2k PR,2k), (46)

where J2k+1,2k+2(BS,2k+1, BR,2k+2) =

ES,2k+1,R,2k+2,HS,2k1,HR,2k{J2k+1,2k+2(min{BS,2k+1

+HS,2k1, BS,max}, min{BR,2k+2+HR,2k, BR,max})}.

(47)

Here, BS,2k+1 BS,2k1 PS,2k1, BR,2k+2 BR,2k

PR,2k, S,2k+1 (R,2k+2) represents the SNR of the SR(RD) link in the (2k+ 1)th ((2k+ 2)th) slot given the SNRS,2k1 (R,2k) in the (2k 1)th (2kth) slot, and HS,2k1(HR,2k) denotes the harvested energy at S(R) in the(2k1)th(2kth) slot given the harvested energy HS,2k2 (HR,2k1) inthe(2k 2)th ((2k 1)th) slot. It can be shown that the costfunctions in (45) and (46) are concave in PS,2k1 andPR,2k.Thus, (45) and (46) are convex optimization problems and can

be solved very efficiently [26]. Further simplification of (45)

yields

JK1,K(BS,K1, BR,K) =1

2log2(1 + S,K1K1) , (48)

where K1 = min {BS,K1, R,KBR,K/S,K1}. There-

fore, PS,K1 = min{BS,K1,R,KBR,KS,K1

}, andPR,K followsfrom (42). Similarly, (46) can be simplified as

J2k1,2k(BS,2k1, BR,2k) =

max0PS,2k1min{BS,2k1,R,2kBR,2k/S,2k1}

1

2S,2k1

+J2k+1,2k+2(BS,2k1PS,2k1, BR,2kS,2k1PS,2k1

R,2k).(49)

Using (48) and (49), PS,2k1and PR,2k,k {1, 2, , K/2},

can be obtained for different possible values of S,k, R,k,BS,k, and BR,k and can be stored in a look-up table. This isdone before transmission starts. When transmission starts, for

given realizations ofS,2k1, R,2k, BS,2k1, and BR,2k intime slots 2k 1 and 2k, the values ofPS,2k1 and P

R,2k

corresponding to these realizations are taken from the look-uptable.

C. Suboptimal Online Power Allocation

In the proposed DPbased optimal online power allocation

scheme, for a certain transmission time slot, we consider theaverage effect of all succeeding time slots, c.f. (47). Due to

the recursive nature of DP, the computational complexity of

this approach increases alarmingly with increasingK. For thisreason, in the following, we propose three different suboptimal

online power allocation schemes, which perform close to the

optimal DP approach but have reduced complexity.1) Suboptimal Simplified DP Power Allocation (DPI2

and DPI1 Schemes): In this scheme, we use the averageeffect of only 2 (or 4) following time slots to allocate the

transmit power in each time slot. In particular, we assume for

the current time slot that all energies have to be spent over

the following 2 (or 4) time slots. Moreover, in the last two

time slots, either S orR uses up all of its stored energy. Thisscheme reduces the computational complexity at the expense

of a performance degradation. We refer to the suboptimal DPschemes taking into account 4 and 2 time slots as DPI2and DPI1, respectively.

2) Suboptimal HR Assisted Power Allocation (HR As-

sisted Scheme): As for link adaptive relaying, we also

propose an efficient HR Assisted online power allocation

scheme for conventional relaying. To this end, we first formu-late an optimization problem which is based on the averagedata rate and the average energy causality constraints at SandR for K . Then, we revise the optimal solutions takinginto account the energy storage constraints in (5) and (6). The

optimization problem for K can be formulated as

max{PS,2k10, PR,2k0,|k}

1

K

K/2k=1

min{log2(1+ S,2k1PS,2k1),

log2(1 + R,2kPR,2k)} (50)

s.t. Constraints (24) and (25) withd2k1 = 0 and

d2k = 1, k, (51)


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S,2k1PS,2k1 = R,2kPR,2k. (52)

Incorporating (52) into (50) and (51) yields

max{PS,2k10|k}

1

K

K/2k=1

log2(1 + S,2k1PS,2k1) (53)

s.t. 1

K

K/2

k=1

PS,2k1 1

K

K1

k=0

HS,k (54)

1

K

K/2k=1

S,2k1R,2k

PS,2k1 1

K

K1k=0

HR,k. (55)

Problem (53)(55) is a convex optimization problem and using

the optimization techniques described in Section III-B.1, the

optimalPS,2k1 and PR,2k can be obtained as

PS,2k1=min

1

ln(2)(S+ RS,2k1

R,2k)

1

S,2k1

+, BS,2k1

(56)

PR,2k = min

S,2k1PS,2k1R,2k , B

R,2k

, (57)

whereSand Rare Lagrange multipliers associated with (54)and (55), respectively. The optimal S and R are computedoffline using the same method as described in Section III-B.1

for link adaptive relaying before transmission starts. When

transmission begins, PS,2k1 and PR,2k are calculated using

(56) and (57) with offline parameters S and R and onlinevariablesS,2k1, R,2k, BS,2k1, and BR,2k. For the (K1)th and theKth time slots, we ensure that eitherSorR usesup all of the stored energy.

3) Suboptimal Naive Power Allocation (Naive Scheme):

In this suboptimal naive approach, for each time slot, only

the stored energies at hand determine the transmit power, i.e.,this approach does not take into account the effect of the

following time slots, and the transmitting node (S or R) usesup all of its available energy in each transmission interval. To

be specific, for a particular time slot k {1, 2, , K/2},PS,2k1 = min{BS,2k1,

R,2kBR,2kS,2k1

}, and PR,2k followsdirectly from (42).

D. Complexity

In this subsection, we discuss the overheads entailed by the

power allocation schemes proposed for conventional relaying

in terms of computational complexity and the required feed-

back. In the offline and the optimal online power allocationschemes, we solve convex optimization problems where the

number of constraints is a function of K. The requiredcomputational complexity to solve a convex optimization

problem depends on the method used (e.g. bisection method,interiorpointmethod, etc.) and is polynomial in the size of

the problem [26]. Therefore, the worstcase computational

complexity of the offline power allocation scheme for con-

ventional relaying is polynomial in the number of time slots

K [26]. We observe from (46) and (47) that the complexityof the optimal online power allocation scheme by stochasticDP increases exponentially with K. The complexities ofthe simplified versions of DP, i.e., DPI2 and DPI1, are

0 5 10 15 20 25 300

5

10

15

20

25

30

Average SNR (in dB)

Totalnumbero

ftransmittedbits

Optimal Offline

Optimal Online

DPI2

DPI1

Naive

HR Assisted

Fig. 2. Conventional relaying: Total number of transmitted bits vs. averagechannel SNR for K = 10.

linear in K. Moreover, the complexities of the naive and HRassisted suboptimal online schemes are linear in K as well.The complexities of the proposed offline and online power

allocation schemes are further investigated in terms of the

required average execution time in Section V.

The required feedback information also contributes to theoverhead of the proposed power allocation schemes. Like link

adaptive relaying, Sneeds to know the instantaneous valuesof S,2k1, R,2k, HS,k, and HR,k along with the averagesS, R, HS,E, and HR,E for execution of the online powerallocation algorithms. Furthermore, S has to convey PR,k toR.

V. SIMULATION R ESULTS

In this section, we evaluate the performance of the proposed

offline and online power allocation schemes for the conven-

tional and link adaptive relaying protocols. We assume that

the (overall) average harvesting rate is HS,E=HR,E=HE(except in Fig. 9), and HS,k and HR,k independently takevalues from the set {0, HE, 2HE}, where all elements of theset are equiprobable. For Figs. 26, 10, and 11, we assume

HE = 0.5. We adopt BS,max = BR,max = Bmax, whereBmax= 4 for Figs. 2, 3, 7, Bmax= 10 for Figs. 46, 9, 11,andBmax= 100for Fig. 8. We assume i.i.d. Rayleigh fadingchannels withS= R= for Figs. 25, 9, and 11 and i.n.d.Rayleigh fading channels for Figs. 68, and 10. We simulate104 randomly generated realizations of the SRand theRDchannels and the harvested energies atS and R to obtain theaverage throughput.

A. Performance of Different Power Allocation Schemes for

Conventional Relaying

In this subsection, we show the performance of the pro-

posed power allocation schemes for conventional relaying. In

particular, the impact of the average channel SNR and thenumber of time slots on the total number of transmitted bits

is studied.


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0 20 40 60 80 100 1200

50

100

150

200

250

300

350

Number of Time Slots

Totalnumberoftransmittedbits

Optimal Offline

DPI2

DPI1

Naive

HR Assisted

Fig. 3. Conventional relaying: Total number of transmitted bits vs. numberof time slots K for = 25dB.

Fig. 2 shows the total number of transmitted bits for the

power allocation schemes proposed for conventional relayingvs. the average channel SNR, , forK= 10. We observe thatfor all considered schemes, the total throughput increases as

increases. We also notice that the offline scheme performsbetter than the online power allocation schemes for all .This is due to the fact that in the optimal offline scheme we

assume that both causal and noncausal information regarding

the CSI and the harvested energy are available whereas the

online schemes are based only on causal information regarding

the CSI and the harvested energy. Moreover, as expected, the

optimal online scheme outperforms all considered suboptimal

online schemes and performs close to the optimal offline

scheme. The suboptimal online schemes DPI2

and DPI1perform close to each other for all . We note that both DPI2

and DPI1 outperform the HR assisted and the naive schemes.In Fig. 3, we show the total number of transmitted bits

for the power allocation schemes proposed for conventionalrelaying vs. the number of time slots K for = 25 dB.We observe that the optimal offline method achieves the best

performance. Among the different suboptimal online schemes,

DPI2 performs best. The HR assisted scheme provides asimilar performance as DPI2 for largeK. This is mainly dueto the fact that the HR assisted scheme is based on the average

harvesting rate which is more justified for largeK. Moreover,we observe that the difference between the performances of

DPI2 and DPI1 increases with increasing K. This showsthat the consideration of the two next time slots instead ofonly the next time slot for calculation of the optimal transmitpowers becomes more important for larger K.

B. Performance of Different Power Allocation Schemes for

Link Adaptive Relaying

In this subsection, we show the impact of the average

channel SNR and the number of time slots on the total numberof transmitted bits for the different power allocation schemes

proposed for link adaptive relaying.Fig. 4 shows the total number of transmitted bits for link

adaptive relaying vs. the average channel SNR for K= 8

5 10 15 20 25 300

50

100

150

200

250

Average SNR (in dB)

Totalnumbero

ftransmittedbits

Exhaustive Search

sBB

HR Assisted Online

Naive Online

K=8

K=50

Fig. 4. Link adaptive relaying: Total number of transmitted bits vs. averagechannel SNR for K = 8 and K = 50.

and K= 50. Here, we consider the exhaustive search offlinealgorithm for K = 8, and the HR assisted online, the naiveonline, and the sBB offline power allocation schemes for

both values ofK. Recall that the optimal offline exhaustivesearch scheme is only effective for small Kas the complexityincreases exponentially with K. For K = 8, we observethat the exhaustive search and the sBB schemes have exactly

the same performance for all considered . This observationconfirms that sBB scheme finds the global optimum solution

of nonconvex MINLP problems [20], [21]. The performancegap between the offline and the HR assisted online schemes is

small at lowand large at highfor K= 8. Furthermore, theperformance gap increases with for K= 50. ForK= 8, thenaive online power allocation scheme has a small performance

advantage over the HR assisted online algorithm for high ,whereas forK= 50, the HR assisted online algorithm showsbetter performance for all considered .

C. Comparison Between Conventional and Link Adaptive Re-

laying

In this subsection, we compare the power allocation

schemes proposed for conventional and link adaptive relaying.

For offline power allocation, we compare the optimal schemes

and for online power allocation, we compare the suboptimal

schemes for conventional relaying with the HR assisted online

scheme for link adaptive relaying. The optimal DP approach(for conventional relaying) is not included in the comparison

because of its high complexity.1) Total Number of Transmitted Bits vs.K: Fig. 5 shows

the total number of transmitted bits vs. the number of time

slots, Kfor the offline and online power allocation schemesfor conventional and link adaptive relaying. We assume sym-

metric SR and RD channels, i.e., S = R = . Weobserve that link adaptive relaying significantly outperforms

conventional relaying for offline power allocation. The perfor-

mance gap increases with increasing K. This is mainly due tothe fact that, for largeK, we have more flexibility in selectingdk, i.e., in selecting the SR or RD link for transmission to


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20 40 60 80 100 120 1400

100

200

300

400

500

600

700

Number of time slots

Totalnumberoftra

nsmittedbits

Optimal Offline (Link Adaptive)

HR Assisted Online (Link Adaptive)

Optimal Offline (Conventional)

DPI2Online (Conventional)

HR Assisted Online (Conventional)

Offline (Nodelay constrained in [9])

Fig. 5. Comparison of conventional and link adaptive relaying: Total numberof transmitted bits vs. number of time slots K for S = R = = 30dB.

increase the system throughput. In particular, for the offline

case, the link adaptive relaying scheme can transmit 16 and 55additional bits compared to conventional relaying forK= 20and K = 100, respectively. For small K, the HR assistedonline scheme for link adaptive relaying does not show a

better performance than the online schemes for conventional

relaying. However, for relatively large K, e.g. K = 140,the HR assisted online scheme for link adaptive relaying

outperforms the DPI2 and HR assisted online schemes forconventional relaying by 26 and 34 bits, respectively. We

note that the gain of link adaptive relaying over conventionalrelaying is the result of both power allocation and adaptive link

selection since the power allocation affects the link selection

and vice versa. Moreover, in Fig. 5, we have also included

the performance of the nodelay constrained protocol in [9].

We observe that, because we assume a direct SD link isnot available, the performances of conventional relaying and

the nodelay constrained protocol in [9] are identical for all

considered values ofK. This result was already shown in [9,Fig. 4] for nonfading channels and we arrive at the same

result for fading channels.

In Fig. 6, we turn our attention to asymmetric links where

we consider two scenarios for the average channel SNRs.

Scenarios 1 and 2 are valid for S= 20 dBand S= 10 dB,respectively, where R = 30 dB in both cases. We comparethe performance of the HR assisted online scheme for link

adaptive relaying with that of the DPI2 and HR assistedschemes for conventional relaying. In contrast to Fig. 5, in

Fig. 6, we observe that the HR assisted online scheme for

link adaptive relaying outperforms the DPI2 (HR assisted)schemes even for small numbers of time slots, e.g. K= 25.Moreover, Fig. 6 clearly shows that the performance gains

of the HR assisted online scheme for link adaptive relaying

over the DPI2(HR assisted) scheme for conventional relayingare significantly larger for asymmetric links compared to

symmetric links. The larger gains are caused by the flexibility

20 40 60 80 100 120 1400

50

100

150

200

250

300

350

400

450



HR Assisted Online (LinkAdaptive)

DPI2Online (Conventional)


Scenario 1

Scenario 2

Fig. 6. Comparison of online algorithms for conventional and link adaptiverelaying: Total number of transmitted bits vs. number of time slotsK forS = 20dB (Scenario 1) and S = 10dB (Scenario 2) with R = 30dB.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 120

40

60

80

100

120

140

160

180

200

Average harvesting rate





DPI2(Conventional)


Fig. 7. Comparison of conventional and link adaptive relaying: Total numberof transmitted bits vs. HE for K = 60, S = 10dB, and R = 30dB.

introduced by the buffer at the relay. In the link adaptivescheme, the stronger link can be used less frequently since

relatively large amounts of information can be transferred

every time the link is used. Hence, the weaker link can be

used more frequently to compensate for its poor link quality.

In contrast, in conventional relaying, both links are used for the

same amount of time regardless of their respective qualities.2) Number of Transmitted Bits vs.HE: Fig. 7 depicts the

total number of transmitted bits for conventional and link

adaptive relaying vs. the average harvesting rate, HE, forS = 10 dB, R = 30 dB, and K = 60. We observethat the throughput increases with increasing HE for allconsidered power allocation schemes. We note that the slope

of the throughput curves is large for small HE and decreaseswith increasing HE. This behavior is partially (apart fromthe behavior of the log() function) due to the fact that theperformance of all schemes is limited by the finite storagecapability of the batteries. For large HE, additional energycannot be stored in the batteries and therefore the extra amount


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0.5 1 1.5 2 2.5 3 3.5 42000

2500

3000

3500

4000

4500

5000

Average harvesting rate


Link Adaptive

Conventional

Fig. 8. Comparison of the HR assisted online schemes for conventional andlink adaptive relaying: Total number of transmitted bits vs. average harvestingrate for K = 1000, S = 30 dB, and R = 15dB.

t1 t2 t3 t4 t5 t6 t7 t8 t9160

180

200

220

240

260

280

300

Transmission times


Conventional

Link Adaptive

HR Assisted Online

Optimal Offline

Fig. 9. Total number of transmitted bits for offline and online powerallocation schemes for conventional and link adaptive relaying when HR,Echanges over the time of transmission for HS,E = 2, K = 50, andS = R = 30dB.

is wasted. We observe that the optimal offline and the HR

assisted suboptimal online schemes for link adaptive relaying

outperform the corresponding schemes for conventional relay-

ing for all HE.

In Fig. 8, we show the total number of transmitted bitsvs. the average harvesting rate HS,E = HR,E = HE forK= 1000. Here, we study the performance of the HR assistedschemes for conventional and bufferaided relaying for largeK. We observe that, like for small K, bufferaided linkadaptive relaying also significantly outperforms conventional

relaying for large K.

In Fig. 9, we show the performances of different power

allocation schemes for both conventional and bufferaided link

adaptive relaying assuming that HR,Echanges over the timeof transmission. In particular, we fix HS,E = 2 and linearlychangeHR,E, from one transmission time interval to the nextfrom a high value (HR,E= 2 int1) to a low value (HR,E=

2 3 4 5 6 7 8 9 10100

150

200

250

Bmax





DPI2(Conventional)


Fig. 10. Comparison of conventional and link adaptive relaying: Total numberof transmitted bits vs. Bmax forK = 100, S = 10dB, and R = 30dB.

0.25 in t5) and then back to a high value (HR,E= 2 in t9).Each transmission interval, t1, t2, , t9, lasts for K = 50time slots. At the beginning of each transmission interval, ti,the proposed optimization schemes are executed and the total

throughput during theK= 50 time slots is shown in Fig. 9.The change ofHR,Eover time may model the impact that thechange from cloudy weather (t5) to sunny weather (t1and t9)has on a solar energy system. We observe that the throughput

increases (decreases) with increasing (decreasing) HR,E forboth the offline and online power allocation schemes. Most

importantly, the change in throughput is large for conventional

relaying and small for link adaptive relaying. In fact, for link

adaptive relaying, if the relay does not have enough energy to

transmit data, the SR link can be selected for transmissionfor several consecutive time slots and the received data at Ris stored in the buffer and is forwarded to the destination ata later time. On the other hand, for conventional relaying,

in each time slot, the source can only transmit the amount of

data that the relay is able to forward to the destination. For this

reason, the link adaptive protocol is able to cope better with

sudden changes in the EH profile. Note that this behaviour is

observed for both the offline and the online schemes.

3) Total Number of Transmitted Bits vs.Bmax: In Fig. 10,we show the total number of transmitted bits for conven-tional and link adaptive relaying vs. Bmax for S = 10dB, R = 30 dB, and K = 100. We observe that for

all considered power allocation schemes, the throughput firstincreases with increasingBmax but starting at a certain valueof Bmax, the throughput remains unchanged. This can beexplained by the fact that for HE= 0.5small values ofBmaxlimit the performance since the extra amount of harvested

energy cannot be stored in the batteries. However, the constant

throughput of all the schemes for large Bmax indicates that,for the given parameters, increasing the storage capacities of

the batteries beyond a certain value does not improve the

performance of the system. Therefore, Fig. 10 provides an

indication for the required storage capacities of the batteriesat S and R for different power allocation schemes to achievea desired performance.


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20 40 60 80 100 120 140

104

103

102

101

100

101

102

103

104


Executiontime(inseconds)




DPI2(Conventional)


Fig. 11. Comparison of execution times of conventional and link adaptiverelaying: Execution time (in seconds) vs. number of time slots K for = 30dB.

4) Execution Time vs.K: In Fig. 11, we show the averageexecution time (in seconds) vs. the number of time slots, K,for all offline and online power allocation schemes for con-

ventional and link adaptive relaying. We ran all the algorithmson the same computer system. In particular, all simulations

were performed under MATLAB with the Intel(R) Core(TM)

i7-2670QM (@2.20GHz 2.20GHz) processor. Therefore, it is

reasonable to compare the complexity of the algorithms based

on their execution times. We observe that for both the offline

and online schemes for both conventional and link adaptive

relaying the execution time increases with K. Moreover, therequired execution time for the sBB algorithm is higher than

that for the offline scheme for conventional relaying for all

K. The complexity of forming the look-up tables for theDPI2 scheme is not included in this analysis. Fig. 11 pro-vides valuable information about the complexityperformance

tradeoff of the different proposed algorithms. For example,

in case of conventional relaying, the HR assisted scheme

is less complex than the DPI2 scheme with only a smallperformance degradation for sufficiently high average channel

SNR and large K, see Fig. 3. Therefore, it is preferable toapply the HR assisted scheme compared to the DPI2 scheme.Moreover, although the worst case complexity of the sBBalgorithm is exponential in K, from Fig. 11 we observe thatits average complexity is comparable to that of the offline

power allocation scheme for conventional relaying. Thus, forlink adaptive relaying, we can conclude that the sBB algorithm

is preferable over the exhaustive search method (which is not

shown in Fig. 11 due to its very high execution time).

VI . CONCLUSIONS

In this paper, we have considered the problem of transmit

power allocation for single relay networks, where the source

and the relay harvest the energy needed for transmission

from the surrounding environment. Two different transmission

strategies, namely conventional relaying and bufferaided linkadaptive relaying, have been considered. We have proposed

several optimal and suboptimal offline and online power

allocation schemes maximizing the system throughput of

the considered EH systems over a finite number of time

slots. Simulation results showed that the proposed suboptimal

online schemes have a good complexityperformance trade

off. Moreover, we showed that, for both offline and online

optimization, adopting the link adaptive protocol significantlyimproves the throughput compared to conventional relaying,

especially for asymmetric link qualities, and bufferaided linkadaptive relaying is more robust to the changes in the EH

profile than conventional relaying.

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Imtiaz Ahmed(S09) received his B.Sc. and M.Sc.degrees in electrical and electronic engineering(EEE) from Bangladesh University of Engineer-ing and Technology (BUET), Dhaka, Bangladesh,in 2006 and 2008, respectively. Currently, he isworking towards his Ph.D. degree in electrical andcomputer engineering (ECE) at The University of

British Columbia (UBC), Vancouver, Canada. Hisresearch interests include non-Gaussian noise andinterference in wireless systems, energy harvestingbroadband communication systems, and energy har-

vesting sensor networks. His paper was awarded 2nd prize in the IEEE Region10 undergraduate student paper contest in 2006.

Aissa Ikhlef (M09) was born in Constantine, Al-geria. He received the B.S. degree in electricalengineering from the University of Constantine,Constantine, Algeria, in 2001 and the M.Sc. andPh.D. degrees in electrical engineering from theUniversity of Rennes 1, Rennes, France, in 2004and 2008, respectively.

From 2004 to 2008, he was with Suplec, France,pursuing his Ph.D. degree. From 2007 to 2008, hewas a lecturer at the University of Rennes 1. From

2008 to 2010, he was a Postdoctoral Fellow withthe Communication and Remote Sensing Laboratory, Catholic University ofLouvain, Louvain La Neuve, Belgium. He was a visiting Postdoctoral Fellowat the University of British Columbia, Vancouver, BC, Canada, from Augustto November 2009. From 2010 to 2013, he was with the data communicationsgroup, University of British Columbia, Vancouver, Canada, as a PostdoctoralFellow. Since June 2013, he has been with Toshiba Research Europe Limited,Bristol, UK, as a Research Engineer. His current research interests includewireless communications and networking with emphasis on distributed beam-forming and diversity techniques in cooperative communications.

Robert Schober (S98-M01-SM08-F10) wasborn in Neuendettelsau, Germany, in 1971. He re-ceived the Diplom (Univ.) and the Ph.D. degreesin electrical engineering from the University ofErlangen-Nuermberg in 1997 and 2000, respectively.From May 2001 to April 2002, he was a Postdoc-toral Fellow at the University of Toronto, Canada,sponsored by the German Academic Exchange Ser-vice (DAAD). Since May 2002, he has been with theUniversity of British Columbia (UBC), Vancouver,

Canada, where he is now a Full Professor. Since Jan-uary 2012, he has been the Alexander von Humboldt Professor and Chair forDigital Communication at Friedrich Alexander University (FAU), Erlangen,Germany. His research interests fall into the broad areas of communicationtheory, wireless communications, and statistical signal processing.

Dr. Schober has received several awards for his work including the 2002Heinz Maier-Leibnitz Award of the German Science Foundation (DFG), the2004 Innovations Award of the Vodafone Foundation for Research in MobileCommunications, the 2006 UBC Killam Research Prize, the 2007 WilhelmFriedrich Bessel Research Award of the Alexander von Humboldt Foundation,the 2008 Charles McDowell Award for Excellence in Research from UBC, a2011 Alexander von Humboldt Professorship, and a 2012 NSERC E.W.R.Steacie Fellowship. In addition, he received best paper awards from theGerman Information Technology Society (ITG), the European Associationfor Signal, Speech and Image Processing (EURASIP), IEEE WCNC 2012,IEEE Globecom 2011, IEEE ICUWB 2006, the International Zurich Seminaron Broadband Communications, and European Wireless 2000. Dr. Schober

is a Fellow of the Canadian Academy of Engineering and a Fellow of theEngineering Institute of Canada. He is currently the Editor-in-Chief of theIEEE TRANSACTIONS ONC OMMUNICATIONS.

Ranjan K. Mallik (S88-M93-SM02-F12) re-ceived the B.Tech. degree from the Indian Insti-tute of Technology, Kanpur, in 1987 and the M.S.and Ph.D. degrees from the University of SouthernCalifornia, Los Angeles, in 1988 and 1992, respec-tively, all in electrical engineering. From August1992 to November 1994, he was a scientist at theDefence Electronics Research Laboratory, Hyder-abad, India, working on missile and EW projects.From November 1994 to January 1996, he was afaculty member of the Department of Electronics

and Electrical Communication Engineering, Indian Institute of Technology,Kharagpur. From January 1996 to December 1998, he was with the faculty

of the Department of Electronics and Communication Engineering, IndianInstitute of Technology, Guwahati. Since December 1998, he has been withthe faculty of the Department of Electrical Engineering, Indian Institute ofTechnology, Delhi, where he is currently a Professor. His research interests arein diversity combining and channel modeling for wireless communications,space-time systems, cooperative communications, multiple-access systems,difference equations, and linear algebra.

Dr. Mallik is a member of Eta Kappa Nu. He is also a member of the IEEECommunications, Information Theory, and Vehicular Technology Societies,the American Mathematical Society, and the International Linear AlgebraSociety, a fellow of IEEE, the Indian National Academy of Engineering, theIndian National Science Academy, The National Academy of Sciences, India,Allahabad, the Indian Academy of Sciences, Bangalore, The World Academyof Sciences - for the advancement of science in developing countries (TWAS),The Institution of Engineering and Technology, UK, and The Institutionof Electronics and Telecommunication Engineers, India, a life member ofthe Indian Society for Technical Education, and an associate member of

The Institution of Engineers (India). He is an Area Editor for the IEEETRANSACTIONS ONW IRELESSCOMMUNICATIONS. He is a recipient of theHari Om Ashram Prerit Dr. Vikram Sarabhai Research Award in the fieldof Electronics, Telematics, Informatics, and Automation, and of the ShantiSwarup Bhatnagar Prize in Engineering Sciences.

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