QoS-Aware Power-Efficient Schedulerfor LTE Uplink

Mohamad Kalil,Member, IEEE, Abdallah Shami, Senior Member, IEEE, and

Arafat Al-Dweik, Senior Member, IEEE

Abstract—The continuous increase of mobile data traffic has created a substantial demand for high data rate transmission over mobile

networks. However, mobile devices are provided with small batteries that can be drained quickly by high data rate transmission.

Motivated by the fundamental requirement of extending the battery utilization time per charge of mobile devices, this work presents two

power-efficient schedulers for mixed streaming services in LTE uplink systems. Our objective is to minimize the total transmission

power for all users. The proposed schedulers are subject to rate, delay, contiguous allocation, and maximum transmission power

constraints. We first consider an optimal scheduler that uses binary integer programming (BIP). Then, we propose an iterative

scheduler that performs a low-complexity greedy algorithm which solves the BIP problem. We compare the performance of the pro-

posed schedulers to the state-of-the-art schedulers such as the energy-aware resource allocation (EARA) [1] and the proportional fair

(PF) [2] in terms of rate, delay, average transmission power and complexity. Simulation results show that the proposed schedulers offer

a remarkable transmission power reduction as compared to the PF and the EARA schedulers, and satisfy the QoS requirements.

Index Terms—QoS, LTE, scheduling, uplink, power minimization

Ç

1 INTRODUCTION

THE continuous introduction of mobile applications andservices leads to a significant increase of data usage over

mobile devices. To accommodate the drastic growth ofmobiledata traffic and improve the system capacity, long-term evo-lution (LTE) technology has been developed by the third gen-eration partnership project (3GPP). LTE provides superiorspeed, low latency and better quality of service (QoS) formobile networks. The target peak cell aggregated downlinkthroughput within a 20 MHz spectrum can reach 300 Mbit/sin downlink, and 75 Mbit/s in uplink by applying multiple-input multiple-output (MIMO) configurations [3]. However,the high speed data links offered by LTE systems increase thepower consumption of the user equipments (UEs) [4]. Inuplink mobile communication systems, the power source ofthe UE is limited to a battery. Nevertheless, the improvementof battery technologies ismuch slower than the steadily risingdemand for transmission power by UEs. Consequently, thebattery life per charge is currently one of the main factors thatdominate the reliability ofmobile devices.

To enhance the power efficiency of UEs, LTE uses singlecarrier frequency division multiple access (SC-FDMA) inthe uplink, while orthogonal frequency division multipleaccess (OFDMA) is used for the downlink. SC-FDMA has alower peak-to-average power ratio (PAPR) when comparedto OFDMA. The low PAPR advantage allows the poweramplifier at the transmitter to operate close to the saturation

point which improves its efficiency. However, the lowerPAPR feature of SC-FDMA requires contiguous allocationof the resource blocks (RBs) [3].

A possible solution to extend the battery life per charge isto incorporate power-aware resource allocation techniquesin the uplink system design. Such techniques are able toreduce the transmission power of the UEs, which extendsthe battery life per charge and reduces the overall multi-user interference of the system. Many techniques to mini-mize transmission power have been studied previously forvarious systems such as single-carrier transmission [5],multi-user systems [6], and OFDMA systems [4].

In general, modulation and coding schemes (MCSs) areless power-efficient at higher transmission rates [5], [7].Therefore, transmitting at lower rates and reducing thetransmission power can reduce the energy required totransmit the data. However, lower data rates compromisethe QoS requirements.

In this paper, we propose power-efficient schedulers forLTE uplink systems. The proposed schedulers are able tominimize the total transmission power while maintainingthe LTE uplink physical layer (PHY) constraints and the QoSrequirements. The main contributions of this work are: first,an optimal formulation of the resource allocation problem inthe LTE uplink is presented. The formulation considers themaximum transmission power threshold of the users. Inaddition, the challenge of solution infeasibility is addressedby adding additional weights to the objective function. Sec-ond, the proposed schedulers are designed and evaluatedfor a realistic LTE framework, where each user requestsmany bearers with different QoS requirements. Third, a lowcomplexity iterative resource allocation algorithm is derivedto solve the optimal formulation with comparable powerconsumption and comparable performance. The computa-tional complexity of the proposed schedulers is analyzed.

� M. Kalil and A. Shami are with Western University, London, Ontario,Canada. E-mail: {mkalil3, ashami2}@uwo.ca.

� A. Al-Dweik is with the Department of Electrical and ComputerEngineering, Khalifa University, UAE, and with Western University,London, Ontario, Canada. E-mail: dweik@fulbrightmail.org.

Manuscript received 21 Apr. 2014; revised 6 Sept. 2014; accepted 6 Oct. 2014.Date of publication 16 Oct. 2014; date of current version 29 June 2015.For information on obtaining reprints of this article, please send e-mail to:reprints@ieee.org, and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TMC.2014.2363839

1672 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 8, AUGUST 2015

1536-1233� 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

It is worth noting that part of this work has been pre-sented in [8] where a simplified system model is considered.The system simplification is achieved by assuming continu-ous-rate adaptation (Shannon capacity) and the size of thetransmitted block was limited to integer number of fixedlength data units. Unlike the work reported in [8], this workconsiders a practical system model in which a discrete set ofmodulation and coding schemes are used, and the systemmodel allows transmitting variable length transport blocks(TB). Moreover, the current work presents the block errorrate (BLER) analysis and the system results are compared tothe PF scheduler [2], which is derived according to the pro-posed system model. The work also presents the systemperformance for various system parameters such as thenumber of users and bearers.

The rest of the paper is organized as follows. Section 2presents the related work. Section 3 presents the systemmodel. The system constraints and the objective of the workare presented in Section 4. The optimal and iterative formu-lations of the proposed scheduler are described in Sections5 and 6, respectively. In Section 7 the PF scheduler is dis-cussed. Intra-user scheduling is described in Section 8. Sim-ulation results are presented in Section 9, and Section 10concludes the paper.

2 RELATED WORK

The resource allocation problem for OFDMA systems hasbeen widely investigated in the literature [9], [10]. As eachRB cannot be assigned to more than one user, the resourceallocation is a combinatorial optimization problem [9],which cannot be solved in polynomial time. Many studieshave solved the allocation problem by using the convexrelaxation method [9], [10]. The relaxation replaces thebinary variables by continuous variables in the interval½0; 1�, then Lagrange multipliers are derived to solve theresource allocation. However, due to the contiguity con-straint in SC-FDMA, the resource allocation methods thatare applied to OFDMA are not directly applicable to theLTE uplink [11]. More details about the convex relaxationmethod are discussed in Section 4.

Most recent research efforts on LTE uplink haveaddressed the maximization of the total utility of the system[12], [13], [14], [15]. The utility function may depend onusers’ throughputs, maximum permitted delays, or fairnessbetween users [16]. A sum-rate maximization problem isinvestigated in [12]. The allocation problem is formulated asa set packing problem which is NP-hard. Consequently,low-complexity algorithms based on message-passing para-digm are proposed to solve the allocation problem in poly-nomial time. Another sum-rate maximization schedulerthat considers multiuser scheduling with transmit antennaselection is investigated in [13]. Based on local ratio testapproach, suboptimal polynomial-time algorithms are pro-posed to solve the allocation problem. A schedulingapproach based on a genetic algorithm is presented in [14]to solve the sum-rate maximization problem in LTE uplinksystems. Nevertheless, sum-utility maximization problemsusually lead to transmitting data using the maximum allow-able transmission power, which often lowers the transmitterpower efficiency [17].

A general packet scheduling scheme for LTE uplink isconsidered in [15]. The problem is proven to be MAX SNP-hard. Consequently, two approximation algorithms for thescheduling problem are proposed to reduce complexity.The algorithms are evaluated for a specific scenario thatincorporates the queue length and channel quality informa-tion. Lee et al. [2] investigated the proportional fair (PF)scheduler for the LTE uplink. The scheduling problem isproven to be an NP-hard because of the contiguity con-straint. Heuristic algorithms were proposed and comparedin terms of system throughput and fairness.

Few articles in the literature have considered power-efficient transmission in the LTE uplink. For example,Dechene and Shami [1], [18] considered power-efficientresource allocation subjected to rate and synchronoushybrid automatic repeat request constraint. At everytransmission time interval (TTI), each user transmits afixed data rate. The solution feasibility was guaranteedbecause maximum transmit power is not considered.However, practical LTE uplink systems limit the maxi-mum transmission power to a threshold value, and thedata arrives randomly to the users’ buffers with differentQoS requirements. Another power-efficient schedulerthat considers the buffers’ queue state information ispresented in [19]. The problem was formulated as aconstrained Markov decision process (MDP), offline solu-tions were then derived. However, the maximum trans-mission power threshold is not considered. Besides, thesolution complexity is high due to the large size of thesearch space. Furthermore, the offline solution is applica-ble only to a particular scenario, meaning that differentsolutions must be derived for different scenarios. Forexample, adding a user to the system leads to a differentsolution.

3 SYSTEM MODEL

This study considers an LTE uplink multiuser system in asingle cell, where K UEs communicate with an evolvedNode B (eNB). It is assumed that each user has a maximumof four bearers, or logical channels, associated with differentQoS requirements, an assumption which is justified inSection 3.1. The overall cell bandwidth is divided equallyinto M RBs, each of which contains 12 adjacent subcarriers.The bandwidth of an RB is 180 kHz. To facilitate the read-ability, Table 1 summarizes the notations frequently usedthroughout the paper.

The contiguity constraint which is required by SC-FDMAcan be modeled by constructing a binary matrix R as fol-lows. Each column in R represents a potential contiguousallocation, while each row represents an RB. The columnindex c in the matrixRwith the sizeM � 1 is denoted by rc.Therefore,R can be expressed as

R ¼ ½r1; r2; . . . ; rC �: (1)

where C is the number of columns inR, which can be calcu-lated for a system that hasM RBs as [1]

C ¼ 1

2MðM þ 1Þ: (2)

KALIL ET AL.: QOS-AWARE POWER-EFFICIENT SCHEDULER FOR LTE UPLINK 1673

For example, a system with 3 RBs has an R that is equalto

R ¼1 0 00 1 00 0 1

1 0 11 1 10 1 1

24

35: (3)

To better understand the meaning of allocating one columnofR to a user, consider that the column r1 is allocated to userk. The first element in r1 is one, which indicates that RB num-ber one is allocated to user k. The second and third elementsin r1 are zeros, which indicates that RB numbers two andthree are not allocated to user k. As can be seen in (3),R con-tains only contiguous allocations, for example the column

½1 0 1�T is not contiguous allocation and cannot exist inR.The LTE frame duration is 10 ms and it is composed of 10

LTE subframes. Each subframe has a duration of 1 ms, andrepresents a TTI [3]. When the normal cyclic prefix is used[3], each subframe consists of 14 SC-FDMA symbols, eachwith a duration of 66:67 ms. Following the assumption usedin [1], three symbols in each frame are assigned to uplinkphysical control signaling. The total number of data sym-bols in each RB per subframe is ð14� 3Þ � 12 ¼ 132. Fig. 1shows the LTE subframe structure.

The LTE physical layer supports various modulation andcoding schemes. The MCS and the RBs that are assigned toa user determines the uplink transport block size. Supposethat the column vector rc and the MCS number j areassigned to user k, the TB size that user k can transmit overa TTI is calculated as follows

Tkðj; cÞ ¼ 132� zj � rck k� �

; (4)

where zj is the MCS efficiency for the MCS number j interms of the number of useful bits per symbol, rck k is theHamming weight of rc, which represents the number of RBsthat are allocated to user k, and xb c denotes the largest inte-ger number less than or equal to x.

The selection of MCS is determined such that the BLER islower than the target BLER, which is 10 percent for LTE sys-tems [3]. The BLER for each MCS depends on the effectivereceived signal to noise ratio (SNR). A simple criterion forchoosing appropriate MCSs is based on a set of SNR thresh-olds [3]. Given the effective received SNR for a user, theeNB selects the most spectrally efficient MCS that satisfiesBLER < 10 percent. In practice, the BLER values are deter-mined through a link-level simulator for all MCSs. Fig. 2presents the simulation curves of the adopted MCSs in anLTE uplink over an additive white Gaussian noise (AWGN)channel [20]. Table 2 shows the modulation, code rate, spec-tral efficiency, and SNR thresholds for the MCSs [21]. TheSNR thresholds can be obtained from Fig. 2.

The effective instantaneous received SNR for user k whois assigned column rc at TTI t is given by [1], [22]

gk½t� ¼1

rck kXm2rc

ak;m½t�Pk;m½t�s2

; (5)

where Pk;m½t� is the transmission power of user k over the

RB m during the TTI t, ak;m½l� ¼ hk;m½t��� ��2, hk;m½t� is the chan-

nel frequency response of RB m at TTI t seen by user k, and

s2 is the AWGN variance.To reduce the signaling overhead, LTE specifies that

when a user is assigned more than one RB, one power levelshould be transmitted over the assigned RBs [13]. In otherwords Pk;1 ¼ Pk;2 ¼ � � � ¼ Pk;m: Therefore, the RB index mcan be dropped, and (6) can be written as

TABLE 1Summary of the Most Significant Notation

Symbol Meaning

K Number of UEsM Number of RBsk UE Indexj MCS IndexJ Number of MCSsR Contiguous allocation matrixrc The column number c in the matrix Rc RBs contiguous-chunk indexC Total number of contiguous chunks possibleDn

k Maximum permitted-delay for bearer n of UE kQn

k Maximum queue length corresponding toDnk

�dnk Average delay of bearer n of UE k (ms)qnk Average queue length of bearer n of UE k (bits)q̂nk Maximum allowed average queue length of bearer

n of UE k�nk Arrival rate of bearer n of UE k (ms)

Tk;j;c TB size achieved by the choice k; j; cPth Maximum transmission power thresholdEk TB size satisfies the rate and the delay constraints

of UE k

Fig. 1. The structure of the LTE subframe.

Fig. 2. BLER-SNR curves for all Table 2 MSC, from Index 1 (leftmost) toindex 15 (rightmost) [20].

1674 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 8, AUGUST 2015

gk½t� ¼1

rck k2Xm2rc

ak;m½t�Pk½t�s2

; (6)

where Pk½t� ¼ rck kPk;m½t� is the total transmission power ofuser k at TTI t. Using (6), the required power to achieve aneffective SNR of gk½t� is

Pk½t� ¼ gk½t�Xm2rc

ak;m½t� !�1

rck k2s2: (7)

To recap, when user k transmits Pk over the RB chunkthat is represented by rc, the effective received SNR of theuser is gk, which can be mapped to an appropriate MCSthrough Table 2. Consequently, the TB size of user k can becalculated from (4).

3.1 LTE QoS and Buffer Status Reports (BSRs)

LTE systems are designed to support a wide range of appli-cations and services. In general, the user might run multipleapplications simultaneously, each application requires dif-ferent QoS. For example, a user can play real-time gamewhile downloading a file using a file-transfer protocol. TheeNB establishes multiple radio bearers per user to supportmultiple QoS requirements as shown in Fig. 3. The LTEdefines two main radio bearer categories [3]:

1) Bearers with guaranteed bit rate (GBR) are estab-lished for real-time applications such as voice andvideo, which require certain GBR to satisfy their QoSrequirements.

2) Non-GBR (NGBR) bearers do not guarantee any par-ticular bit rate and are used for non-real-time appli-cations such as buffered video streaming.

The QoS class identifier (QCI) and the allocation andretention priority (ARP) are the bearer QoS parameters. TheQCI is a scalar that specifies Internet Protocol (IP) levelpacket characteristics of the bearers. The ARP of a bearer isused for admission and handover control. When the bearer

is established, the ARP has no effect on packet transmis-sions, which are managed only by their QCI specifications[3]. LTE uplink scheduling takes place in the eNB, whereinformation about buffered data sizes is reported for all UEswho have data to be transmitted using the buffer statusreporting (BSR) mechanism. A BSR has two possible for-mats [3]: short BSR format and long BSR format. The shortformat reports one bearer, while the long format reports upto four bearers. The choice of short or long format is deter-mined by the number of non-empty buffers. If a user hasonly one bearer, the short format is used to conserve chan-nel resources because the short format report requires fewerbits. Although UEs may have more than four non-emptybuffers, the maximum number of reporting bearers is four.In the long format scheme, bearers are grouped into fourgroups before they are reported, and therefore consideringusers with four bearers is practically acceptable. In thispaper, we assume that each user has a maximum of fourbearers, where each bearer is modeled as an infinite first-infirst-out buffer in the radio link control (RLC) sub-layer.

3.2 Uplink Data Transmission Procedure

The sequence of uplink data transmission is shown in Fig. 4.The UE receives uplink traffic from upper layers. Data for

TABLE 2List of MCS Indices [21]

Indexj

Modulation CodingRate

SpectralEfficiency z

Effective SNR(dB) gk

0 — — 0 bits > �6:75361 QPSK 78/1024 0.15237 �6:7536 : �4:96202 QPSK 120/1024 0.2344 �4:9620 : �2:96013 QPSK 193/1024 0.3770 �2:9601 : �1:01354 QPSK 308/1024 0.6016 �1:0135 : þ0:96385 QPSK 449/1024 0.8770 þ0:9638 : þ2:88016 QPSK 602/1024 1.1758 þ2:8801 : þ4:91857 16QAM 378/1024 1.4766 þ4:9185 : þ6:70058 16QAM 490/1024 1.9141 þ6:7005 : þ8:71989 16QAM 616/1024 2.4063 þ8:7198 : þ10:51510 64QAM 466/1024 2.7305 þ10:515 : þ12:45011 64QAM 567/1024 3.3223 þ12:450 : þ14:34812 64QAM 666/1024 3.9023 þ14:348 : þ16:07413 64QAM 772/1024 4.5234 þ16:074 : þ17:87714 64QAM 873/1024 5.1152 þ17:877 : þ19:96815 64QAM 948/1024 5.5547 > þ19:968

Fig. 3. An example of four bearers established for a user.

Fig. 4. Uplink data transmission sequence.

KALIL ET AL.: QOS-AWARE POWER-EFFICIENT SCHEDULER FOR LTE UPLINK 1675

multiple logical channels are queued in the RLC sub-layerbuffers. Information about buffered data sizes is reported tothe eNB over the physical uplink control channel using theBSR procedure. The scheduler in the eNB makes allocationdecisions according to a specific scheduling policy. Basedon the allocation decisions, the eNB sends allocation mapsto the users over the physical downlink control channel.The user’s allocation map specifies the assigned RBs, powercontrol entity and MCS [23]. The power control entity speci-fies the uplink transmission power for each user. The RBschunk and MCS that is assigned to a user determine theuplink transport block size. However, how the TB is sharedbetween users’ buffers is left to the user policy, which is dis-cussed in Section 8.

In the UE media access control (MAC) sub-layer, a MACprotocol data units (PDU) is formed according to thereceived map allocation. The MAC PDU contains data fromone or more RLC PDUs in addition to the MAC header. TheMAC passes the MAC PDU to the physical layer, whichadds the cyclic redundancy check (CRC) bits to the MACPDU and then transmits the entire packet as a TB over thephysical uplink shared channel to the eNB. The PHYresponsibility is to deliver the TB with an error probabilityless than a targeted BLER.

3.3 Delay Analysis

As mentioned in Section 3.1, the BSR does not report explicitinformation about PDU delays, but reports the sizes of thequeued data in the UE buffers. In this section, the PDUdelay is mapped to the size of the queued data. The queueevolution during TTI tþ 1 can be described as

qnk ½tþ 1� ¼ qnk ½t� þ ank ½t� � Tnk ½t�; (8)

where qnk ½t� is the number of pending bits at the beginning ofTTI t, ank ½t� is the number of bits arriving at TTI t with anaverage arrival rate of �n

k , and Tnk ½t� is the number of trans-

mitted bits from bearer n of user k at TTI t.LTE defines a packet delay budget (PDB) for each bearer,

which defines an upper bound for the time that a packetmay be delayed between the UE and the packet data net-work gateway. In LTE, the outage delay outage level shouldbe less than 2 percent [3]

P�dnk > �Dn

k

�< 0:02; (9)

where dnk is the head of the line packet delay, and �Dnk is the

PDB. For high data traffic load, the following approximationis valid [8]

P�dnk > �Dn

k

�� e

�� �Dn

k=�dn

k

�; (10)

where �dnk is the average value of dnk . Therefore, in the case of

high data traffic load, controlling �dnk is approximately equiv-alent to controlling the delay violation probability P ðdnk >�DnkÞ. The justification for the assumption of heavy data traf-

fic is that most delay violations take place when the trafficload is heavy. By substituting (9) into (10), the requiredaverage delay for bearer n of user k is given by

�dnk < ��Dnk

lnð0:02Þ : (11)

This work focuses on the air-interface delay between UEsand eNB. We assume that the air-interface delay Dn

k contrib-utes to d of the PDB as follows

Dnk ¼ d �Dn

k; (12)

where 0 � d � 1. Using Little’s theorem [19], the averagedelay can be computed as

�dnk ¼ �qnk�nk

; (13)

where �qnk is the average queue size. Substituting (13) and(12) into (11), the bearer air-interface delay can be controlledby controlling the average number of bits in the users’queues

qnk < q̂nk (14a)

q̂nk ¼ � Qnk

lnð0:02Þ ; (14b)

where q̂nk is the maximum allowable average queue lengthof bearer n of user k that satisfies the delay requirement,and Qn

k ¼ Dnk � �n

k is the average queue length that corre-sponds to the air-interface delayDn

k .It is worth noting that the size of the data buffers is

assumed to be greater than the PDBs for all bearers. If thesize of a buffer is less than the PDB, the PDB is assumed tobe the maximum buffer size for that bearer.

It is assumed that the eNB knows, or at least can esti-mate, the average arrival rates for all bearers and users. Oneway to estimate the average arrival rates is reported in [24].Suppose that the scheduler successfully maintains the delayrequirements of buffer number n of user k such that qnk � q̂nk ,the average arrival rate �n

k is equal to the long-term averageof the service rate Tn

k .

4 SYSTEM CONSTRAINTS AND OBJECTIVE

The resource allocation in LTE uplink requires the followingconstraints to maintain the physical layer restrictions andthe QoS requirements:

1) Exclusivity constraint: for every TTI, a single RB isallocated to no more than one user.

2) Contiguity constraint: SC-FDMA restricts the RBallocations to be contiguous. Each column in thematrix R represents a contiguous RB allocation. Thecontiguity constraint can be maintained by assigningone column from the matrixR to each user.

3) Power constraint: the LTE standard specifies Pth asthe maximum transmission power threshold that theuser cannot exceed.

4) Rate constraint: minimum bit rate for the GBRbearers must be maintained.

5) Delay constraint: NGBR bearers subject to PDB. Asdiscussed in Section 3.3, the delay constraint can bemaintained by controlling the average queue length.

1676 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 8, AUGUST 2015

The objective of this work is to minimize the sum oftransmission power consumed by the users while maintain-ing their QoS. We are seeking to answer the following ques-tion: how should the available resources, in terms of RBsand transmission power, be assigned to the users so that thetotal transmission power is minimized without violatingthe users’ QoS requirements? Without loss of generality, afinite time horizon of length F TTIs is chosen. We assumethat the current time is t and the observation interval is½t; tþ F �. Denote Wðx½t�; LÞ as a sliding-average window oflength L for variable x

Wðx½t�; LÞ ¼ 1

L

XtþL

l¼t

x½l�; (15)

and denote Pk;j;c½l� as the transmission power required toachieved the target BLER when user k transmits using theMCS number j over the RB allocation number c at TTI l. Theresource allocation problem can be written as

minXtþF

l¼t

XKk¼1

XJj¼1

XCc¼1

Pk;j;c½l�bk;j;c½l� (16a)

subject to

\Kk¼1

rcbk;j;c½l� ¼ ;; 8l; j; c (16b)

Pk;j;c½l� � Pth; 8l; k; j; c (16c)

W�Tnk ½t�; F

� rnk (16d)

W�qnk ½t�; F

�� Dmarg � q̂nk ; (16e)

where bk;j;c½l� is a binary number indicator that is equal to 1if and only if the MCS number j and the column rc areselected for user k at TTI l, J is the total number of MCSs,Dmarg 2 ð0; 1Þ is a margin used to maintain the delay lessthan the maximum in (14), and rnk is GBR of the bearer num-ber n of user k. Note that the exclusivity constraint is main-tained by (16b), where the summation over c restricts theusers to only contiguous RB allocations and maintains thecontiguity constraint. The power, rate, and delay constraintsare maintained by (16c), (16d), (16e), respectively.

The problem shown in (16) is a discrete time stochasticcontrol process. One way to solve this problem is to formu-late it as a constrained MDP. Although general techniquesexist to solve MDPs, they suffer from the curse-of-dimensionality problem [25], where the number of statesgrows vastly with the numbers of both users and bearers.Consequently, formulating and solving constrained MDPsis non-trivial as it deals with an extremely large number oftransition probabilities. Therefore, approximated solutionsare often provided [25]. Moreover, a comprehensive knowl-edge of the users’ channel responses and arrival processesmay be required to solve the MDP. A similar problem inOFDM systems is investigated in [10] by relying on stochas-tic convex optimization. For each TTI, the allocationdepends on the instantaneous channel gains and Lagrangemultipliers. The multipliers are associated with the QoSrequirements and are estimated online using stochastic

approximation tools. However, many approximations areused while turning this problem into a stochastic convexoptimization. First, Shannon’s capacity formula is used(continuous rate adaptation) instead of a practical discreteset of MCSs. Second, the exclusivity constraint is relaxed.The relaxation replaces the binary indicators by contentiousvariables belong to the interval ½0; 1�. In OFDMA eachbinary number refers to a single RB or subcarrier. Having afraction of a subcarrier translates into time sharing betweenusers for the subcarrier which creates a form of time-divi-sion multiple access. However, in SC-FDMA, the allocatedRBs for a particular user should be adjacent, and sharingchunks of RBs over time is not applicable because the con-tiguous allocation is not guaranteed [11]. Third, it isobserved that, optimum values of the multipliers can neverbe found. Therefore stochastic approximation is used to esti-mate the multiplier values.

An alternative approach to solve (16) is to design a non-causal optimal offline scheduler, which gives a guideline todesign and evaluate online suboptimal schedulers. The off-line optimal scheduler requires a prior knowledge of botharrival data units and channel state information forft; tþ 1; . . . ; tþ Fg at TTI t. Therefore, the problem turnsinto a discrete time deterministic control process, which canbe solved, for example, by binary integer programming(BIP). Nevertheless, the search space of this formulation isextremely large and can be calculated as follows. For one

TTI, for user k, there are 12MðM þ 1Þ possible allocations in

the frequency domain as shown in (2). For each possibleallocation, J MCSs exist. Therefore, the total number of

choices possible for user k is J2 MðM þ 1Þ. For the K users,

the search space is J2 MðM þ 1Þ� �K

. Consequently, the

search space for F TTIs is

J

2MðM þ 1Þ

� �KF

: (17)

For example, assume a system with the following parame-ters: M ¼ 6 RBs, J ¼ 15 MCSs, K ¼ 4 and F ¼ 10 TTIs. The

search space size is 8:5590� 1099.In the following sections, a computationally feasible ver-

sion of the scheduling problem is presented.

5 BIP FORMULATION

To simplify the scheduler and to avoid the computationally-excessive optimization in (16), a formulation of the optimi-zation problem for a single time slot (F ¼ 1) is presentedhere. The exclusivity, contiguity, and power constraintsmust be satisfied for each TTI because they are related tothe physical system. However, the rate and delay con-straints are based on averages, which means they are softand it is not necessary to satisfy them every TTI. In otherwords, the rate and/or delay might not meet their QoSrequirements at certain times, but on average over a longtime interval, the QoS requirements are met. Allowing therate and delay constraints to be soft avoids infeasible instan-taneous solutions. Such solutions appear when the instanta-neous required data transmission rate is greater than theinstant channel capacity. However, we assume that, in thelong term, the channel capacity can provide the required

KALIL ET AL.: QOS-AWARE POWER-EFFICIENT SCHEDULER FOR LTE UPLINK 1677

QoS. In cases where the QoS requirements are greater thanthe available channel capacity, scheduling becomes infeasi-ble, and dropping users may be the only feasible solution[10]. An admission control procedure is responsible fordeciding which user should be dropped or admitted in suchcases. This study does not consider admission control pro-cedures, and it is assumed that the average channel capacitycan manage the required QoS.

The following key observation can be extracted from (7).Given that user k has to transmit Tk bits, the transmissionpower of user k can be decreased by a) increasing the effec-tive SNR by assigning RBs that have less fading; and/or b)transmitting the Tk bits over a longer period of time (moresubframes). The second point needs more elaboration. Fig. 5shows a logarithmic relationship between the spectral effi-ciency of the MCSs in Table 2 and their corresponding effec-tive SNRs. From (7), the transmission power decreases as afunction of the effective SNR for a specific RB chunk alloca-tion, which implies that the transmission power is logarith-mically related to the spectral efficiency of the transmission.For example, transmitting four symbols using MCS numberfour is equivalent to transmitting one symbol using MCSnumber nine. Although, the former transmission requiresadditional four time slots, it consumes only 43 percent of thelater transmission power consumption. Therefore, splittingthe data and transmitting lower data rates over more sub-frames eventually lowers the total transmit power. However,the data rates shouldmaintain the users’ QoS requirements.

Modulation and coding schemes are less power-efficient athigher transmission rates [5]. Therefore, we design the sched-uler to judiciously transmit the minimum number of bits thatsoftly satisfies the rate and the delay constraints at each TTI.Then by optimal power allocation, optimal chunk of RBs isassigned to each user. Define Bn

k as the minimum number oftransmit bits that satisfy both the rate and the delay con-straints to bearer n of user k at TTI t. Therefore, the total TBfor user k that satisfies the rate and the delay constraints is

Ek ¼X4n¼1

Bnk:

As the rate and the delay constraints are converted to softconstraints, the minimum-cost solution is a trivial one, i.e.,no power is consumed if no data is transmitted. To addressthis issue, we define an extra weight rk;j;c which is added tothe applied power cost as follows

rk;j;c ¼ logðEkÞ � log�Tk;j;c=E

GBRk

�; Tk;j;c > 0; (18)

where the Tk;j;c are the TB achieved using MCS j over the RB

allocation number c, and EGBRk is the number of bits that sat-

isfies all the GBR bearers of user k

EGBRk ¼

Xn2NGBR

k

Bnk ; (19)

where N GBRk is a set contains the index of the GBR bearers

that belongs to user k.The weights rk;j;c measure how close the Ek are to the

actual transmitted TB Tk;j;c. To better illustrate extraweights, consider the demonstration shown in Fig. 6. Twomain interesting characteristics can be observed. First, users

with higher EGBRk values have higher weights, which gives

them a higher priority through the scheduling. Second, asthe number of bits transmitted increases, weight values

drop rapidly when Tk;j;c < EGBRk , but slightly when Tk;j;c >

EGBRk . The second characteristic implies that satisfying GBR

requirements for all users are more important than that forNGBR requirements.

In this context, for single TTI, (16) is expressed as (timeindex is omitted for simplicity)

minXKk¼1

XJj¼1

XCc¼1

ðrk;j;c þ Pk;j;cÞbk;j;c (20a)

subject to

Tk;j;c � Ek (20b)

ð16bÞ; ð16cÞ: (20c)

Fig. 5. Spectral efficiency versus SNR for the MCS that are shown inTable 2.

Fig. 6. Extra weight demonstration for Ek ¼ 200 bits.

1678 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 8, AUGUST 2015

5.1 Binary Integer Programming

In this work, the bintprog optimization package from MAT-LAB is used to solve the non-convex problem. The generalform of a BIP optimization can be presented as

min cTx (21a)

subject to

Ax � b; Aeqx ¼ beq; (21b)

where the vector c represents the weights rk;j;c plus thetransmission power costs Pk;j;c, and the binary decision vec-tor x minimizes the objective function and represents theterm bk;j;c in (20a). Constraints (20b), (20c) are maintained

by linear inequality and equality constraints, Ax � b;Aeqx ¼ beq, respectively, where A,Aeq are matrices contain-ing the coefficients of the inequality and equality con-straints, and b, beq are vectors that fulfill the inequality andequality constraints, respectively. The exclusivity and conti-guity constraints are defined as follows. Consider user kwith contiguous allocation matrix R as in (3) with a dimen-sion of M � C. Each column in R presents a feasible contig-uous allocation. For each feasible contiguous allocation, Jdifferent MCSs are possible, the matrix which contains allfeasible contiguous allocations for all MCSs is defined as

Ak ¼ ½R;R; . . . ;R|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}J

�: (22)

Each column in (22) is associated with a potential transmitpower cost calculated from Pk;j;c. The power constraint ismaintained by deleting columns with potential transmis-

sion power greater than Pth. Define the matrix Athk which

has all columns in Ak less than or equal to Pth. Define

matrix A which concatenates all matrices Athk for all users

as follows:

A ¼ Ath1 ;A

th2 ; . . .A

thK

�; (23)

where each row in A represents a single RB, to ensure theexclusivity constraint, and the vector b ¼ 1M , where 1M is avector of M ones. The equality constraints maintain aunique selection from all feasible allocations for all datasizes per user, and therefore

XJj¼1

XCk

c¼1

bk;j;c ¼ 1; 8k:

The equality constraints are expressed as follows

Aeq ¼

1TAth1j j � � � 0T

AthKj j

..

. . .. ..

.

0TAth1j j � � � 1T

AthKj j

26664

37775; (24)

where Athk

�� �� is the number of columns in Athk which denotes

the number of potential allocation choices for user k, and

1Tx ;0

Tx are row vectors of length x of ones and zeros, respec-

tively. The vector beq is defined as beq ¼ 1K to guaranteethat only one of the possible allocations is assigned for eachuser.

5.2 Complexity of BIP

Consider the worst case scenario, where all columns inA0

k; 8k are less or equal to Pth. The search space of BIP for-mulation is similar to the search space of (17) for a singleTTI (F ¼ 1)

1

2JMðM þ 1Þ

� �K

: (25)

For example, assume a system with the following param-eters: M ¼ 6 RBs, J ¼ 15 MCSs, and K ¼ 4. The BIP worst

case search space size is 9:8456� 109. Thus, the approach asformulated is still computationally expensive. Therefore,low-complexity algorithms are needed to solved theresource allocation problem.

6 ITERATIVE ALGORITHM

In this section, an iterative algorithm is proposed to solvethe BIP with much less computational complexity. The algo-rithm belongs to the greedy algorithm family. The objectiveis to minimize the summation of the total users’ costs byassigning RBs to the users iteratively. In each iteration, a sin-gle RB is assigned to a user who can achieve maximumreduction in the cost function. Therefore, the algorithmneeds M iterations to assign all the RBs to users. For eachiteration, the algorithm finds the best RB for each user. Thebest RB of user k is defined as the RB that has the highestinstantaneous channel response (ak;m) and satisfies the con-tiguous allocation of user k. Then, the change in the user’scost value before and after assigning the best RB is calcu-lated for each user. As the algorithm is greedy, the user whohas the maximum positive change in the user’s cost functionis granted the allocation. The pseudo-code in Table 3describes the algorithm. The proposed algorithm consists offour main steps as follows:

Lines 1-7. Find the minimum rate (Ek) for each user k thatsatisfies the rate and the delay constraints. In addition, inthis step the following parameters are initialized: the set ofusers index K, the set of non-assigned RBsM, the set of RBsthat assigned to users Mk; 8k 2 K, and the initial cost foreach user Ck ¼ logðEkÞ; 8k 2 K. It is worth noting that theinitial cost of a user is equal to maximum extra weight ofthe user.

Lines 8-14. Find the best feasible RB F k for each user k.Users, who have been assigned one or more RB, are limitedto their neighboring RBs (line: 11). Therefore, two RBs arefeasible at most to any user who has been assigned one ormore RBs. For example, suppose that user k has beenassigned the RB numbers f4;5;6g. Therefore, the feasibleRBs to user k are 3 and 7 if they are not assigned to anyuser. However, users who have not yet been assigned RBscan select any RB of the non-assigned RBs set M (line: 13).In the case that a user has more than one feasible RB, thealgorithm selects the RB that has the maximum instanta-neous channel response.

Lines 15-21. After finding the best feasible RB to eachuser, the users’ cost values of the new potential allocationsets are computed C

k; 8k 2 K. Then, the potential costreduction DCk for each user is computed, where DCk is thedifference between the actual cost value Ck and the poten-tial cost value C

k. If all users do not benefit (reduce their

KALIL ET AL.: QOS-AWARE POWER-EFFICIENT SCHEDULER FOR LTE UPLINK 1679

cost values) from the new potential allocation sets, the algo-rithm stops (lines 19 and 20). The COST ðMk; EkÞ functionfinds the total costs, i.e. rk;j;c þ Pk;j;c, associated with assign-

ing the set of RBs Mk to user k. In case of Mk ¼ ;, the totalcost is COST ð;; EkÞ ¼ logðEkÞ, as illustrated in line 5.

Lines 22-26. Determine the winning user who achievedthe maximum cost-reduction DC

k (lines 22). Then the algo-rithm assigns RB F

k to the winning user (lines 24), andupdates the set of non-assigned RBs (lines 25).

6.1 Complexity of the Iterative Algorithm

For each major iteration (lines 6-17), an RB is allocated, andtherefore, the maximum number of major iterations is M.The first major iteration for each user requires at most Moperations to compute costs. When a user is assigned one ormore RB, this number is reduced to two at most to the lowerand upper RB. Assume that each user performs two opera-tions. For K user there are 2�K operations in each majoriteration. Therefore, the complexity of the proposed itera-tive algorithm is OðMKÞ. In a similar example to that inSection 5.2, the complexity of the worst case is in the orderof 24 operations, which is significantly less than the optimalalgorithm complexity.

7 PROPORTIONAL FAIR SCHEDULER

The PF scheduler has been widely investigated in the litera-ture. The objective of the PF scheduler is maximizing thetotal throughput of the system while maintaining level offairness between users. Lee et al. [2] investigated the PF

scheduler for SC-FDMA systems. The scheduling problemis reported as a NP-hard problem.

To determine the power efficiency of the proposed algo-rithms, PF scheduler is used as the baseline scheme for com-parison. We have modified the PF scheduler of [2] to copewith our system model. The objective function at TTI t canbe expressed as

maxXKk¼1

XJj¼1

XCk

c¼1

vk½t� � Tk;j;c½t�; (26a)

subject to

ð16bÞ; ð16cÞ; (26b)

where vk½t� is a scheduling weight assigned to user k at TTIt. The scheduling weights depend on transmission historyfor users as follows

vk½t� ¼1

WðTk½t� 1�; LPF Þ; (27)

where WðTk½t� 1�; LPF Þ is a sliding-average windowdefined in (15) of length LPF . Users who have low historicalaverage data rates are assigned higher weights than thosewho have high historical average data rates, whichincreases their chances of obtaining more RBs during thescheduling.

The PF scheduling worst-case search space is the same asBIP. However, for the BIP scheduler, the number of avail-able MCSs is often less than that for PF scheduler becausethe BIP scheduler avoids rate transmission higher than Ek.Therefore, the complexity of the BIP is expected to be lowerthan that for the PF.

8 INTRA-USER SCHEDULING

In all the scheduling schemes discussed above, the sched-uler output is the set Tk; 8k ¼ 1; 2; ::K, which indicates theTB size for each user. We assume that UEs share their TBsbetween their bearers as follows:

1) GBR bearers should be satisfied beforeNGBR bearers.2) Within the same radio bearer category (GBR or

NGBR), the allocated resources are distributed pro-portionally to Bn

k . In case of PF scheduler, Bnk are

replaced by the queues length of bearer n.The pseudo-code in Table 4 describes the intra-user

scheduling, where Tnk denotes the portion of Tk allocated to

bearer n of user k.

TABLE 3Iterative Allocation

1:M ¼ f1; 2; . . . ;Mg2: K ¼ f1; 2; . . . ;Kg3: for k 2 K do4: find Ek

5: Ck ¼ logðEkÞ6: Mk ¼ ;7: end for8:while jM 6¼ ;j do9: for k 2 K do10: ifMk 6¼ ; then11: F k ¼ argmax

m2fminðMkÞ�1;maxðMkÞþ1g\Mfak;mg

12: else13: F k ¼ argmax

m2Mfak;mg

14: end if15: M

k ¼ Mk [ F k

16: Ck ¼ COST ðM

k; EkÞ17: DCk ¼ Ck �C

k18: end for19: ifC

k < 0; 8k 2 K then20: exit21: else22: k ¼ argmax

kfDCkg

23: Ck ¼ Ck

24: Mk ¼ Mk [ F k

25: M ¼ M n F k

26: end if27: end while

TABLE 4Intra-User Scheduling for User k

1: EGBRk ¼

Pn2NGBR

kBn

k

2: ENGBRk ¼

Pn =2 NGBR

kBn

k

3: if EGBRk < Tk then

4: Tnk ¼ Bn

k ; 8n 2 NGBRk

5: Tnk ¼ ðTk � EGBR

k Þ � ðBnk=E

NGBRk Þ; 8n =2 N GBR

k6: else7: Tn

k ¼ Tk � ðBnk=E

GBRk Þ; 8n 2 N GBR

k

8: Tnk ¼ 0; 8n =2 N GBR

k9: end if

1680 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 8, AUGUST 2015

9 NUMERICAL RESULTS

The simulation default parameters are shown in Table 5.The channel is modeled as a quasi-static frequency-flat Ray-leigh fading channel. The channel gain is assumed to beconstant over each RB bandwidth, but change indepen-dently over consecutive RBs. Moreover, we assume thatusers experience independent fading. For Rayleigh fadingchannel, the distribution of the instantaneous receivedchannel gain a follows the exponential distribution [26]

p ak;m

� �¼ 1

ake�ak;m

ak ; (28)

where ak is the expected value of ak;m and denotes the aver-age channel gain (ACG).

Table 6 presents bearers profiles. NGBR bearers servenon real-time applications. We assume that the data arrivalsfor non real-time traffic follow a Poisson distribution as ithas been used in related works [7], [19], [24].

GBR bearers serve real time applications which requireminimum guaranteed bit rates. Transmission resources arereserved for GBR bearers in the admission control function.Therefore, an eNB establishes GBR bearers “on demand” forusers [27]. In this work, the virtual token queue (VTQ) isadopted to model the GBR buffers as used in [28], [29]. Eachbearer is modeled as a VTQ, where tokens arrive at a con-stant rate equal to the guaranteed bit rate of the bearer. Inother words, for each TTI a token of size rnk is added to theVTQ corresponding to queue n of user k. The number oftokens is reduced according to the actual amount of datatransmitted for the bearer. The minimum number of bits thatsatisfies a GBR bearer is determined by the number of tokensin the virtual queue. For example, assume the virtual queuehas qnk ½t� tokens, the minimum bit rate that satisfies the bitrate requirements of the bearer n of user k is rnkq

nk ½t� bits.

9.1 Experiment 1: Two Userswith Identical Conditions

In this experiment, we consider a two-user scenario with anidentical traffic load and channel profile. Because the users

experience identical conditions in terms of channel and traf-fic load, it is sufficient to show results for only one user.Each user is assumed to have two bearers, namely B1 andB2.

Fig. 7 compares the transmit power for the three schedu-lers. The BIP consumes slightly less power than the iterativescheduler, and both of them consume approximately 43%less power than the PF scheduler. To better visualize theefficiency of the schedulers, consider the following scenario:users transmit data until the total power consumptionreaches 80 Watt. Note that 80 Watt is equivalent to transmit-ting at the maximum power threshold (200 mW) for 400TTIs. Fig. 8 shows that the BIP and iterative schedulers pro-long the battery life considerably compared with the PFscheduler for the same QoS requirements.

Fig. 9 compares the average queue length of the twobearers for the three schedulers. All the schedulers succeedin maintaining average queue lengths of the NGBR dataless than the threshold. As the intra-scheduling serves theGBR bearers before the NGBR bearers, the queue lengths ofthe GBR bearers are shorter than the queue lengths of theNGBR for all schedulers. The PF scheduler tends to transmitaggressively, i.e., the maximum achievable data rate.

TABLE 5Simulation Default Parameters

Parameter Value Parameter Value

Coherence time 1 ms M 10UE # 2 Iteration # 1e4BW 15 KHz Cells interference Avoidanced 1 Dmarg 0.9Pth 23 dBm LPF 50Channel fading Rayleigh L 8Target BLER 10 percent s2 1

TABLE 6Users’ Data Profile

Index Type �nk (Kbps) Dn

k (ms) Qnk (bits) q̂nk rnk (Kbps)

B1 NGBR 100 20 2,000 511 0B2 GBR - - - 50B3 NGBR 75 20 1,500 383 0B4 GBR - - - - 30

Fig. 7. Experiment 1: Average transmitted power per user per TTI (Watt).

Fig. 8. Experiment 1: Battery life comparison.

KALIL ET AL.: QOS-AWARE POWER-EFFICIENT SCHEDULER FOR LTE UPLINK 1681

Therefore, the average queue lengths of the PF scheduler arelower than those for the other two schedulers. The queuelengths of the BIP scheduler are slightly shorter than thequeue lengths of the iterative scheduler.

Fig. 10 shows the probability density function (PDF) ofthe delay for the NGBR bearer at average channel gainof 10. Note that delay violations occur when the number ofbuffered data bits in the queue is greater than 20 ms. Thequeue length PDF of the BIP and iterative schedulers arealmost identical but are more spread out than the PDF ofthe PF scheduler. However, maximum queue lengths areless than half of the maximum allowed delay (20 ms) forthe BIP and iterative schedulers, and less than one-tenth forthe PF scheduler. Fig. 11 shows the average transmissionrate for all bearers and schedulers. All the rates converge tothe arrival rates and satisfy the rate requirements, whichalso implies that the data queues are stable. The increase intime complexity of the three schedulers are compared inFig. 12. The MATLAB functions tic and toc were used tomeasure the running time. As expected, the running time ofthe iterative scheduler is significantly less than that for BIPand PF. Increasing ACG has no effect on the iterative and

BIP running times. However, it is directly proportional tothe PF time complexity. As ACG increases, more MCSs areconsidered in each RB chunks, which increases the size ofthe search space evolved in each iteration.

9.2 Experiment 2: Two Users with IdenticalConditions but Different ACG

To illustrate the behavior of the PF scheduler, we considertwo users with different ACGs. The ACG of user one isfixed to 10, whereas the ACG for user two varies from 10 to30 (10 to 14.8 dB). The transmission power for user one anduser two are shown in Figs. 13 and 14, respectively. Increas-ing the ACG of user two reduces transmit power consump-tion. However, this increase has no effect on the powerconsumption of user one who experiences a constant aver-age channel fading.

Fig. 15 shows the queue length in bits for all users andbearers. Successfully, the three schedulers maintain aver-age queue lengths of the NGBR bearers less than the max-imum allowed average queue length (�qnk < q̂nk ). As usertwo ACG increases, shorter queue lengths are observed.However, user one queue length remains unchanged. In

Fig. 9. Experiment 1: Average queue length per bearer per user.

Fig. 10. Experiment 1: Probability density function of the delay of theNGBR bearers at ACG¼10.

Fig. 11. Experiment 1: Average transmission rate per bearer per user.

Fig. 12. Experiment 1: Time complexity comparison.

1682 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 8, AUGUST 2015

summary, the proposed schedulers isolate the users fromeach other. Users who experience good channel condi-tions consume less power than users who experience

severe fading conditions. Fig. 16 shows that the transmis-sion rates are equal to the data arrival rates, whichimplies that all the data arrived has been transmitted.

Fig. 13. Experiment 2: Average transmitted power per TTI for user1 (Watt).

Fig. 14. Experiment 2: Average transmitted power per TTI for user2 (Watt).

Fig. 15. Experiment 2: Average queue length for the NGBR bearers inbits.

Fig. 16. Experiment 2: Average transmission rate per bearer per user.

Fig. 17. Experiment 3: Average transmitted power per user per TTI(Watt).

Fig. 18. Experiment 3: Delay per bearer averaged on all users.

KALIL ET AL.: QOS-AWARE POWER-EFFICIENT SCHEDULER FOR LTE UPLINK 1683

9.3 Experiment 3: The IterativeAlgorithm Evaluation

This experiment evaluates the scheduling performance on arelatively large-scale scenario. Due to the fact that the BIPand PF schedulers are computationally heavy, and theirtime complexity increases exponentially with the number ofusers as discussed in Sections 5.2 and 7, simulation experi-ments are performed only for the iterative scheduler. Wecompare the proposed algorithm with the energy-awareresource allocation (EARA) scheduler reported in [1]. Notethat EARA does not consider the maximum transmit powerthreshold nor the dynamic traffic behavior. Similar to theproposed algorithm, we assume that the EARA allocatesEk½t� bits to UE k at TTI t. The simulation setup is similar tothe one given in Table 5, but the number of RBs grows to 40.

Each user has four bearers as described in Table 6. Allusers are assumed to experience ACG of 10. Fig. 17 exhibitsthe average transmit power per user. For both algorithms,the number of users is proportional to the average transmis-sion power as a result of the increased competition forresources. Although the EARA is not practical because itdoes not consider the maximum transmit power threshold,it consumes more power than the proposed algorithm.Fig. 18 shows the delay of the four bearers averaged over allusers. The delay of the EARA is slightly lower than thedelay of the proposed algorithm. As the number of usersincreases, the delay becomes longer and approaches theirthresholds. However, both algorithms succeed to maintainthe delay less than the threshold. The average data rates areshown in Fig. 19. The algorithms manage to transmit aver-age data rates equal to the average data arrival rates.

10 CONCLUSION

In this paper, we developed a framework for power-effi-cient scheduling in LTE uplink systems. Both the QoSrequirements and the channel fading parameters were con-sidered. The scheduling problem was formulated and pre-sented as a multi-stage problem. Then, it was simplifiedinto a single point binary integer programming problem.Subsequently, a low-complexity iterative scheduler was

proposed to solve the binary integer programming problem.The iterative scheduler proved to consume slightly morepower compared to the binary integer programming sched-uling approach, but it has considerably lower computa-tional complexity. Simulation results were used to comparethe proposed schedulers with the proportional fair sched-uler in terms of power efficiency, delay, transmission rate,and complexity. The results show that the proposed schedu-lers maintained the required QoS and reduced the totaltransmit power under different practical scenarios. Thesepower savings were achieved because of the schedulers’attribute of transmitting data at low rates while maintainingthe required QoS.

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Mohamad Kalil received the BSc and MScdegrees in electrical engineering from the JordanUniversity of Science and Technology, Jordan, in2009 and 2011, respectively. He is currentlyworking towards the PhD degree in electrical andcomputer engineering at the University of West-ern Ontario, London, Ontario, Canada. Hisresearch interests include cross-layer design,radio resource management, and wireless net-work virtualization. He is a member of the IEEE.

Abdallah Shami received the BE degree in elec-trical and computer engineering from the Leba-nese University, Beirut, Lebanon, in 1997 and thePhD Degree in electrical engineering from theGraduate School and University Center, City Uni-versity of New York, New York, NY, in September2002. Since July 2004, he has been with WesternUniversity, Canada, where he is currently a pro-fessor in the Department of Electrical and Com-puter Engineering. His current research interestsinclude the area of network-based cloud comput-

ing and wireless/data networking. He is currently an associate editor forIEEE Communications Survey and Tutorials, IET Communications Jour-nal, andWiley Journal of Wireless Communications and Mobile Comput-ing. He has chaired key symposia for IEEE GLOBECOM, IEEE ICC,IEEE ICNC, and ICCIT. He is a senior member of the IEEE and the chairof the IEEE Communications Society Technical Committee on Commu-nications Software.

Arafat Al-Dweik (S’97M’01SM’04) received theMSc and PhD degrees in electrical engineeringfrom Cleveland State University, Cleveland, OH,in 1998 and 2001, respectively. From 2001 to2003, he worked as an assistant professor andchair of the Communications Technology Depart-ment at the Arab American University, Jeneen,Palestine. From 2003 to 2014, he was an assis-tant and then an associate professor at theDepartment of Electrical and Computer Engineer-ing, Khalifa University, UAE. He is currently with

the School of Engineering, University of Guelph. Moreover, he is aresearch fellow at Newcastle University, Newcastle upon Tyne, UnitedKingdom, and an adjunct professor at Western University, London, ON,Canada. He has several years of industrial experience in the USA, recip-ient of the Fulbright Scholarship, and has been awarded several awardsand research grants. He is an associate editor of the IEEE Transactionson Vehicular Technology. His research interests include wireless com-munications, synchronization techniques, OFDM technology, modelingand simulation of communication systems, error control coding, andspread spectrum systems. He is a senior member of the IEEE.

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KALIL ET AL.: QOS-AWARE POWER-EFFICIENT SCHEDULER FOR LTE UPLINK 1685