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Wireless Resources Virtualization for Cloud RadioAccess Networks (C-RAN)

M. Kalil∗, Student Member, IEEE, A. Shami∗, Senior Member, IEEE, and A. Al-Dweik∗†, Senior Member, IEEE,∗Western University, London, Ontario, Canada, emails: mkalil3, ashami2, aaldweik@uwo.ca

† Department of Electrical and Computer Engineering, Khalifa University, Abu Dhabi, UAE. email:dweik@kustar.ac.ae

Abstract—The cloud radio access network (C-RAN) concept isa strong candidate for next-generation wireless networks due toits flexibility, scalability, increased asset utilization, and energysavings. While resources are centralized in C-RAN architecture,wireless resource virtualization (WRV) can offer substantial ca-pacity increase and efficiency gain. This paper provides solutionsfor virtualizing C-RANs wireless resources and sharing them be-tween multiple mobile network operators (MNOs). The proposedsolutions dynamically allocate wireless resources to users whosubscribe to MNOs across the network. In addition, the proposedsolutions maintain a high level of isolation between differentMNOs, provide efficient and fair resource utilization, enabledifferent scheduling polices, and manage intercell interference(ICI). An optimal solution is formulated as a combinatorial prob-lem, which is computationally expensive. Consequently, two low-complexity suboptimal solutions with comparable performanceare provided. The optimal and suboptimal solutions are comparedin terms of complexity and performance. The optimal solutionoutperforms the suboptimal by only 6% at the expense of asignificantly higher time complexity.

Keywords—Wireless resource virtualization, C-RAN, ICI man-agement, resource allocation.

I. INTRODUCTION

Mobile network operators (MNOs) are desperate for cost-effective, scalable, and innovative solutions in order to improvenetwork capacity and coverage to handle the ever-growingdemand for mobile data transmission. Traditional solutionsof deploying more base stations (BSs) and acquiring newspectrum licenses are becoming economically unsustainable.Therefore, cellular wireless networks should develop new tech-niques to enhance the utilization of the computing and wirelessresources. Recent spectrum utilization measurements show thatthe bandwidth licensed to MNOs is mostly underutilized [1],[2]. According to a recent study by Nokia [3], only 20% of aradio access network’s full capacity is used at any given timewith 80% idle waiting for peak hour demand.

Typically, the average traffic load in cellular networks isconsidered lower than the peak load. In addition, the peakload time depends on the geographical location, becausedifferent locations might have different peak load times. Forexample, peak loads in residential neighborhoods occur atnight, whereas peak loads in central office districts happenduring business hours. Conventionally, BSs consist of net-work elements running purpose-built software and dedicatedhardware. Therefore, efficient network design becomes very

challenging because the network must employ sophisticatedscalability techniques to handle a wide range of traffic loadsat different times. Resource over-provisioning is costly, whileunder-provisioning compromises service quality. Moreover,adding new services or modifying existing ones is not atrivial process because it creates an impediment to networkscalability, increases the time to market, and obstructs efficientutilization of the infrastructure.

With the growth of cloud-hosted development platformsand services, new promising solutions are on the horizon forMNOs. In 2010, China Mobile introduced the Cloud RadioAccess Network (C-RAN) as a new platform for future mobilenetwork infrastructure [4]. In C-RAN, the baseband processingresources are aggregated and virtualized on a cloud data center,which allows better utilization of computing resources andmore cooperative sharing of radio resources across wirelessnodes. C-RAN technology promises MNOs with significantreductions in capital expenditure (CAPEX) and operatingexpenditure (OPEX), as well as reduced energy consumption.Using C-RAN is expected to reduce power consumption byabout 71% compared to traditional RAN [5].

The main concept behind C-RAN architecture is to decouplethe radio function unit of RANs and the processing unit, asshown in Fig. 1; where a low-cost remote radio head (RRH)replaces the radio function unit. The baseband processingfunctions and resource management are delegated to basebandprocessing units (BPUs), which are pooled on a cloud inremote data centers. In traditional RAN architectures, theprocessing resources of BSs cannot be shared or scaled basedon the traffic load. Since the processing power in C-RAN iscentralized, innovative cloud-based solutions can be applied toimprove the utilization of processing resources. Consequently,C-RAN architecture requires fewer BPUs compared to thetraditional RAN architecture [6], [7].

Centralizing baseband processing and management enablesbetter coordination across RRHs because cell site information,such as traffic loads, user-channel conditions, and user-trafficrequirements, are available across the network. Such informa-tion can be effectively exploited to optimize the allocationof radio resources across cell sites, manage intercell interfer-ence (ICI), and improve coverage and handover procedures.In addition, sharing information can enhance capacity byfacilitating the implementation of new technologies such asICI coordination (ICIC), self-organizing networks (SON), andcoordinated multipoint (CoMP) transmission.

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Similar to C-RAN that centralizes the computing resources,wireless resource virtualization (WRV) is a new paradigmaims at centralizing wireless spectrum resources and sharingthem between MNOs. WRV enables network operators tocreate multiple logical networks on a single physical substrateyielding better efficiency in terms of energy consumption andresource utilization. A new study from ABI Research [8] showsthat over a period of five years, deploying active infrastructure-sharing worldwide can save up to 60 billion USD in OPEXand CAPEX.

As MNOs need to continually enhance the capacity of mo-bile networks, sharing radio resources between multiple MNOsfacilitates carrier resource aggregation and supports higherpeak rates. It also introduces multi-MNO multiplexing gains asa result of increasing the number of users per cell. For instance,in a Rayleigh fading channels, the aggregated capacity of a cellcan increase by ln(K), where K is the number of users in thecell [9]. Furthermore, network sharing facilitates new businessmodels in the wireless market. For example, operators withoutLong Term Evolution (LTE) licenses or network resources willbe able to provide LTE services by renting LTE radio resourcesfrom other MNOs.

Combining C-RAN and WRV will help MNOs to overcomethe challenges inherent to the current mobile networks. Theaim of this paper is to virtualize the wireless resources ofcloud-based RANs such that they can be shared between mul-tiple MNOs. An entity called Hypervisor is added on top of thephysical network as shown in Fig. 1, which is responsible forallocating the available wireless resources to users subscribedto different MNOs. The allocation of wireless resources isdetermined by the sharing contract between MNOs, the trafficload at each RRH, and the interference between differentRRHs. The rest of the paper is organized as follows: SectionII discusses related work in the field and the contributionof this work. Section III presents the system model, andproblem formulation. The optimal solution of the problemis presented in Section IV. Low-complexity schedulers arepresented in Section V. Section VI presents and discussessimulation results, and Section VII concludes the paper.

II. RELATED WORK AND CONTRIBUTIONS

Part of the work discussed in this paper is reported in[10], where the wireless resources of a single cell zoneare virtualized. However, this work addresses effective wire-less resource-scheduling techniques across multiple cell zonesshared between multiple MNOs. In contrast to [10], the presentwork considers a network-wide virtualization and coordinationbetween interfering cell zones to prevent ICI. Moreover, thecurrent work manages the interference between different cellzones by using graph theory. In addition, more solutions andperformance comparisons are provided in this work.

In the recent literature, it can be clearly noticed that there isa growing interest in virtualizing networks’ wireless resources.For example, an LTE air interface virtualization scheme isproposed in [11], where a hypervisor is added on top of thephysical resources. The hypervisor is responsible for virtu-alizing the evolved NodeB (eNB) into a number of virtual

BPU Pool

Optical Network

Hypervisor

MNO-1

Virtual

Network

MNO-2

Virtual

Network

RRH

Virtual RRH

for MNO-1

Virtual RRH

for MNO-2

Fig. 1. Virtualized C-RAN shared between two MNOs.

eNBs that can be used by different MNOs. It is shown thatmore capacity can be achieved by sharing spectrum resourcesbetween different MNOs.

More practical scenarios that consider load balancing arestudied in [12], [13], where the hypervisor manages the sharingprocess of multiple eNBs among multiple MNOs. Neverthe-less, only fixed resource allocation across BSs is considered.The load is balanced between multiple BSs by moving usersfrom high-traffic cells to low-traffic cells. However, transfer-ring users across cells increases handover overhead, and maydegrade the system capacity as users may be transferred to BSsfurther away, which would reduce the quality of the wirelesslink.

Another framework for wireless network virtualization thatseparates service providers from a network operator is reportedin [14]. The service providers (SPs) are responsible for QoSmanagement, while the network operator is responsible forspectrum management. The interaction between SPs and thenetwork operator is modeled as a stochastic game regulatedby the network operator. The role of the SPs is to compete forwireless resources for each subscribed user.

Network virtualization substrate (NVS) [15] is a flow-levelsolution that divides the wireless resources on a single BSsinto different slices. NVS enables customized flow schedulingper slice, where each slice can be seen as a virtual MNOthat supports a set of flows. An admission control procedureis assumed to restrict the number of flows established and

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to guarantee feasible solutions. However, NVS schedules theresources for each BS independently, which may deterioratethe network resource utilization [2]. In addition, NVS failsto maintain a minimum aggregate resource allocation foreach slice across the network. For example, assume that anentity (flow group) reserves 50% of the spectrum resource;irrespective of the demands, then, NVS allocates 50% or fewerresources to the entity at every BS in the network. To addressthis shortcoming, the same authors of [15] presented NetShare[2], a flexible solution to dynamically reschedule network re-sources to flow groups, based on both their aggregate resourcereservations and demands at each BS. With NetShare, flowgroups compute the resource demands for resources generatedby their subscribers at each BS and report them to a centralcontroller. Feedback is sent from the central controller to eachBS in order to reconfigure its NVS scheduler to meet individualusers requirements across the network. However, NetShare isapplied to a traditional RAN architecture, where each BS hasa fixed number of radio resource blocks (RBs) regardless ofits instantaneous traffic load. Thus, when a BS is congestedwith a high number of users, users requirements may not besatisfied.

In multi-cell systems, the same frequency bands can beassigned to users in different cells, which is referred to as thefrequency-reuse (FR) principle, which is used to increase bothcoverage and capacity. However, to minimize ICI, cells that usethe same frequency bands should be separated by a sufficientdistance. Several ICIC techniques have been proposed formulti-cell systems as described in [16] and the referenceslisted therein. The most promising is the fractional FR (FFR),which is adopted by 3GPP LTE [17].

The performance of FFR has been extensively studied fortraditional cellular networks [18], [19], [20]. For C-RANarchitecture, a dynamic FR scheme based on FFR is proposedin [21]. The wireless resources are assigned to cell zones usinga graph-coloring approach. Each color represents a certainsegment of bandwidth. To minimize ICI, different colorsshould be assigned to any interfering zones.

A dynamic interference coordination scheme for downlinkmulti-cell systems is presented in [22]. The allocation problemis divided into two sub-problems, one at the BS level and theother at the central controller. It is assumed that BSs are ableto communicate with each other using an X2 interface. At theBS level, each sector potentially allocates bandwidth chunks toits connected users. Then, each sector sends a request to thecentral controller. The request specifies a list of bandwidthchunks to be restricted at the dominant interfering zones,conflicting requests are resolved by the central controller,which sends a refined list of chunks that should be restrictedto each sector.

Minimizing network power consumption of C-RAN is inves-tigated in [23], where the power consumption of the transportnetwork and RRHs is considered. The authors assume thattransport links and RRHs can support sleep mode. The problemis formulated as a joint RRH selection and power minimiza-tion beamforming problem. The network power consumptionis reduced by minimizing the number of active RRHs andreducing their transmit power subject to QoS constraints.

Through simulations, the authors show that the network powerconsumption can be notably reduced. The performance ofCoMP transmission schemes in a C-RAN architecture for LTE-A Heterogeneous networks is studied in [24]. With C-RANarchitecture, a larger number of RRH can be considered inCoMP transmission, which improves the transmission perfor-mance.

The main objective of this paper is to propose a new modelthat virtualize the wireless resources of cloud-based RANs,then efficiently share them between multiple MNOs’ users.The main contributions of this paper are:• An optimal model is proposed to enable sharing wire-

less resources between multiple MNOs and RRHs. Themodel considers many aspects, including ICI manage-ment, the fair distribution of resources between RRHsbased on their traffic loads, a high level of isolationbetween MNOs, the ability for different MNOs to applydifferent and customizable resource scheduling policies,and efficient resource utilization across the network.

• Low-complexity suboptimal solutions are provided. Thetime complexity of the suboptimal solutions is consid-erably lower than the optimal while their throughputand delay performance are comparable. The suboptimalsolutions are obtained by dividing the wireless resourceallocation problem into sub-problems. The objective ofeach sub-problem is to allocate one RB to a set of non-interfering RRHs. The allocation per single RB is for-mulated as a maximum weighted independent set prob-lem, which is solved using binary integer programming(BIP) solvers. In addition, a low-complexity heuristicalgorithm that solves the BIP problem is proposed. Theperformance of each suboptimal solution is comparedwith the optimal solution as well as with a static sharingsolution.

III. SYSTEM MODEL

Consider the downlink of a cloud-based RAN architectureshared between M MNOs, where N RRHs are distributedto cover a certain geographical area of interest. The RRHsare connected to a pool of BPUs in remote data centers viatransport networks such as optical transport networks. It isassumed that the wireless link quality and expected traffic loadare known for each user at the data center, which is responsiblefor resource allocation decisions. We assume that orthogonalfrequency-division multiple access (OFDMA) is used for thedownlink transmission. The total number of RBs available inthe network is R. Each RRH is assumed to be capable oftransmitting over any RB. The total number of user equipments(UEs) served by the network is K; each UE communicateswith a single RRH.

Without loss of generality, we assume that each UE connectsto the nearest RRH, and is labeled by a unique index k ∈[1, 2, · · · ,K]. A table that maps each UE to a particular MNOand an RRH is assumed to be available for BPUs. To facilitatereadability, Table I summarizes the notations frequently usedthroughout the paper.

The number of bits that can be transmitted over one RBis determined by the signal-to-interference plus noise ratio

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TABLE I. SUMMARY OF THE MOST SIGNIFICANT NOTATION.

Symbol MeaningK, k total number of UEs, UE indexR, r total number of RBs, RB indexN,n total number of RRHs, RRH indexM,m total number of MNOs, MNO indexPr,n transmit power from RRH n over RB rRm set of RBs assigned to MNO mRm number of RBs assigned to MNO mRm,n set of RBs that belongs to MNO m at RRH nRm,n number of RBs that belongs to MNO m at RRH nRn set of RBs that is granted to RRH nKm,n set of UEs that subscribe to MNO m at RRH nKn set of all UEs that connect to RRH nKm,n number of UEs that subscribe to MNO m at RRH nγr,k SINR of RB r seen by UE kHr,k channel gain of RB r seen by UE kCn set of RRH that interfere with RRH nΦm,n the service status of MNO m at RRH nΦthm the service status threshold of MNO mNm set of RRHs connected to UEs subscribed to MNO m

(SINR) at the receiver, which depends on the transmit power,channel fading parameters, interference introduced by otherRRHs, and thermal noise, which can be expressed as

γr,k =Pr,kHr,k∑

c∈CnPr,cHr,c + σ2

(1)

where γr,k is the SINR of the link between UE k who connectsto RRH n over RB r, Pr,n is the transmit power of RRH n overRB r, Hr,k is the channel gain of the wireless link betweenRRH n and UE k over RB r, which includes antenna gainand directivity, path loss, small-scale fading, and shadowing,σ2 is the additive white Gaussian noise (AWGN) variance, andCn is the set of RRHs that interfere with RRH n. Similar to[22], [25], [26], equal power allocation is assumed such thatPu,n = Pv,n,∀u, v ∈ Rn, where Rn is the set of RBs thatare granted to RRH n.

The indices of RRHs that interfere with each other can bedescribed by an N×N binary symmetric matrix C, where theelement cu,v = 1 if RRH u interferes with RRH v; otherwise,cu,v = 0. RRH u is assumed to interfere with RRH v if thedistance between RRH u and RRH v is less than a threshold.

In this work, we consider the LTE physical layer model thatsupports various modulation and coding schemes (MCSs) [27].The maximum number of bits that can be transmitted to UEk over RB r can be calculated as

Qr,k = bξ(γr,k)Tsymc (2)

where ξ(γr,k) is the spectrum efficiency of the selected MCS,Tsym is the total number of symbols in a single RB, and bxcrefers to the floor function.

The selection of a particular MCS is determined by SINRand the required block error rate (BLER). A simple MCSselection scheme is performed using a lookup table whichmaps the received SINR to a MCS for a certain BLER. TableII shows the modulation, code rate, spectral efficiency, and

SINR thresholds for a BLER of 10% as specified by the LTEstandard [27].

TABLE II. LIST OF MCS USED IN LTE AND THEIR SNRTHRESHOLDS [27]

Modulation & Coding Rate ξ (bits/symbol) SINR (dB)— 0 > −6.7536

QPSK, 78/1024 0.15237 −6.7536 : −4.9620QPSK, 120/1024 0.2344 −4.9620 : −2.9601QPSK, 193/1024 0.3770 −2.9601 : −1.0135QPSK, 308/1024 0.6016 −1.0135 : +0.9638

QPSK, 449/1024 0.8770 +0.9638 : +2.8801

QPSK, 602/1024 1.1758 +2.8801 : +4.9185

16QAM, 378/1024 1.4766 +4.9185 : +6.7005

16QAM, 490/1024 1.9141 +6.7005 : +8.7198

16QAM, 616/1024 2.4063 +8.7198 : +10.515

64QAM, 466/1024 2.7305 +10.515 : +12.450

64QAM, 567/1024 3.3223 +12.450 : +14.348

64QAM, 666/1024 3.9023 +14.348 : +16.074

64QAM, 772/1024 4.5234 +16.074 : +17.877

64QAM, 873/1024 5.1152 +17.877 : +19.968

64QAM, 948/1024 5.5547 > +19.968

Radio resources are assumed to be dynamically granted toMNOs based on a contract signed between MNOs; the contractspecifies the resource percentage each MNO obtains in everypossible load scenario. As wireless resource virtualization isstill in its infancy stage, no well-defined sharing models existyet [15]. Therefore, a general sharing model is assumed suchthat

Ψ1 : Ψ2 · · · : ΨM = δ1 : δ2 : · · · : δM (3)

where Ψm is the RB access probability for MNO m across allRRHs, and

∑Mm=1 δm = 1, 0 ≤ δm ≤ 1,∀m.

In the case of static sharing, MNOs are assumed to dis-tribute their resources such that the frequency reuse factor ismaximized while maintaining a proportional fairness criterionsuch that

max∑n∈Nm

Λm,n (4a)

subject toΛm,n +

∑c∈Cn

Λm,c ≤ Rm,∀n (4b)

Λm,1 : · · · : Λm,Nm= (1± α)(Lm,1 : · · · : Lm,Nm

) (4c)

where Λm,n is number of RBs allocated to MNO m at RRH n,Lm,n is the load of MNO m at RRH n, Nm is the set of RRHsthat serves the UEs subscribed to MNO m, and α is a smallconstant that relaxes the fairness constraints in (4c) to ensurefeasible solutions for the optimization problem. The load canbe considered as the number of users or a number of packetsqueued in buffers for the users. As the fluctuation rate of theload in RRHs is slow compared with the transmission timeinterval (TTI), which is 1ms in LTE systems, the optimizationproblem in (4) can be solved at a coarser granularity thanTTI. As a matter of fact, other sharing models can be appliedhere, however, maximizing the frequency reuse factor whileconsidering a fairness criterion is an intuitive target that MNOs

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are looking to achieve.

IV. PROBLEM FORMULATION

In this work, each MNO aims at maximizing its sumweighted data rates, which is a very common optimizationproblem in wireless systems [22], [28], [29], [30]. The weightsare selected by MNOs according to their scheduling policies.Assume that user k is connected to RRH n, the schedulingproblem can be formulated as

max

M∑m=1

∑n∈Nm

∑k∈Km,n

R∑r=1

wkur,k βr,k

(5a)

subject to ∑c∈Cn

[∑k∈Kc

βr,k

]+∑k∈Kn

βr,k ≤ 1,∀n, r (5b)

∑r∈Rk

Tr,k ≤ qk,∀n, k (5c)

(Φm,n > Φthm) or (Ψm,n ≥ Λm,n) must hold, ∀(m,n)(5d)

where ur,k is the data rate achieved by assigning RB r to UEk, wk is the normalized weight for UE k, Kn =

⋃mKm,n is

the set of UEs connected to RRH n, Km,n is the set of UEssubscribed to MNO m and connect to RRH n, Ψm,n is thenumber of RBs accessed by MNO m at RRH n, Rk is the setof RBs assigned to UE k, Φm,n and Φthm are the service statusand service status threshold of MNO m at RRH n, and βr,kis a binary number indicator defined as

βr,k =

1, if RB r is assigned to UE k0, otherwise.

Constraint (5b) represents the exclusive constraint whichensures that (i) each RB is assigned to one UE (at most) at eachRRH, and (ii) orthogonal sets of RBs are allocated to RRHsthat may interfere with each other. It is assumed that the inter-ference is avoided if interfering RRHs are granted orthogonalsets of RBs. Constraint (5c) ensures that the transport blocksize for every UE is less than its unserved data size, whereRk is the RB set that is assigned to user k. Constraint (5d)specifies whether the service status of MNO m at RRH n ishigher than a certain threshold or, if that is not the case, MNOm should access at least Λm,n RBs. This constraint ensuresisolation between MNOs such that MNOs are either satisfied,or can access at least the same number of RBs in case of staticsharing. It is noteworthy that constraint (5d) can be split intotwo constraints by introducing a binary variable ym,n and asufficiently large upper bound Bm so that

Φm,n > Φthm −Bmym,n (6a)

Ψm,n ≥ Λm,n −Bm(1− ym,n). (6b)

When ym,n = 0, constraint (6a) holds, whereas constraint(6b) becomes Ψm,n ≥ Λm,n − Bm, which is always satisfied

if Bm is large enough. Note that the constraint Ψm,n ≥ Λm,nmay still be satisfied. When ym,n = 1, only constraint (6b)holds. Consequently, one constraint holds, and the other onemay be satisfied.

The formulation in (5) allows MNOs to apply differentscheduling policies by weighting their UEs differently. Inaddition, it guarantees that MNOs use their share of RBs atthe overloaded RRH. However, if an MNO is underloaded at aspecific RRH, its share of RBs can be granted to other MNOsthat are overloaded.

A. Radio Resource Scheduling Polices

In wireless networks, radio resource scheduling plays avital role in achieving maximum spectrum utilization, QoSsatisfaction, and fairness between UEs. To achieve such goals,users are weighted according to the UEs service status andthe scheduling policy. The service status of a user can berelated to aspects such as queue length, traffic priority, andpast performance levels achieved. The product of the weightand the data rate achieved using a specific RB interprets theusers priority of using the RB. It is worth mentioning that theusers’ weights may vary with time.

Various scheduling policies are proposed for LTE networks[31], including channel-aware policies, such as MaximumThroughput (MT), Proportional Fair (PF), and GeneralizedPF (GPF); channel-aware and QoS-aware policies, such asModified Largest Weighted Delay First (M-LWDF) and LOGrule; and energy-aware policies [32]. Table III illustrates ex-amples of scheduling policies along with their types, targets,and weight definitions.

B. Complexity of BIP Solution

The scheduling problem given in (5) is a BIP optimizationproblem, which is NP-hard. The complexity of solving suchoptimization problems is considerably high and grows expo-nentially with number of users, MNOs, and RBs. Therefore,obtaining the optimal solution is computationally prohibitiveeven for a single MNO [22], [26].

In order to give a glimpse of the complexity of the BIPproblem, one part of the problem is considered, which involvesassigning RBs to RRHs. Consider a small scenario wheretwo MNOs share three RRHs that interfere with each other.Assume that the total number of RBs in the network is 60. Asthe RRHs interfere with each other, orthogonal sets of RBsshould be assigned to RRHs. If each RRH receives 20 RBs,the number of combinations of 20 RBs chosen from 60 RBsfor one MNO is

60!

20!(60− 20)!= 4.1918× 1015.

For example, if the finest scheduling granularity is chosen,which is one subframe (1ms) for LTE systems, the optimizationproblem should be solved in less than 1ms; which is practicallyinfeasible. Therefore, low-complexity algorithms should beused as alternatives for solving the problem.

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TABLE III. EXAMPLES OF DIFFERENT SCHEDULERS [31]

Scheduler Type Target WeightMT channel-aware, QoS-unaware throughput wk = 1PF channel-aware, QoS-unaware fairness & throughput wk = 1/Tk, where Tk is the past average throughput for UE k.

GPF channel-aware, QoS-unaware fairness & throughput wk = (uk)η1/(Tk)η2 , where η2, η2 are constants tune thescheduler.

M-LWDF channel-aware, QoS-aware queue stability wk = −Dklog(αk)/Dmaxk , where αk is the acceptable delay

violation probability, Dmaxk is delay threshold, and Dk is the head-

of-line packet delay.LOG rule channel-aware, QoS-aware queue stability wk = bklog(ck +akDk), where ak, bk, and ck are constants tune

the scheduler.

V. LOW-COMPLEXITY SOLUTIONS

The optimal solution in (5) is achieved by jointly allocatingRBs to users subscribed to different MNOs across all theavailable RRHs. However, it is computationally expensive totake all RBs in the scheduling problem into consideration,as seen in Section IV-B. A possible approach to reduce thecomplexity is to allocate RBs sequentially. In this section, twoiterative low-complexity solutions are proposed, each of whichallocates a single RB at each iteration. The basic concept isthat, if RB r is assigned to RRH n, it should be assigned toa user who is subscribed to the least satisfied MNO (LSM).As the objective is to maximize weighted sum utility, theassigned RB to the RRH is granted to the user who canmaximize the sum-utility. To allocate RB r, the set of LSM atevery RRH is denoted by 1×N vector sr = [s1,r, · · · , sN,r],where sn,r is the index of the LSM at RRH n. The vectorszr = [z1, · · · , zN,r] and jr = [j1,r, · · · , jN,r] denote theutilities and indices, respectively, of the UEs subscribed to srand who have maximum utility, where

zn,r = maxk∈Ksn,n

uk,r

jn,r = arg maxk∈Ksn,n

uk,r

and uk,r is the utility of UE k.The optimization problem per RB can be seen as the

maximum weighted independent set (MWIS) of a graph path.Each RRH represents a vertex; an edge (line) is drawn betweentwo vertices if they interfere with each other. A graph can bedescribed by the pair G = (V,E), where the set V is thevertices of G, and the set E is the edges of G. The MWIS isthe subset of vertices that has maximum weighted sum suchthat no two vertices are connected with an edge. Fig. 2 showsan example of a graph and its MWIS.

The MWIS IS can be found by solving the followingoptimization problem

IS = max

N∑n=1

vn βn (7a)

subject to ∑c∈Cn

βc ≤ 1,∀n (7b)

where βb is a binary variable, equal to one if n ∈ IS and

w5 = 1

w3 = 2

w4 = 5 w2 = 4

w1 = 5

RRH-1

RRH-3

RRH-2 RRH-4

RRH-5

Maximum Weighted Independent Set

Fig. 2. Example of interference graph G = (V,E) of five weighted vertices(RRHs), where V = 1, 2, 3, 4, 5, and E = (1, 4), (1, 5), (2, 4), (3, 5).The independent sets are = 1 ,2 ,3, 4, 5, 1, 2 ,1, 3, 1, 2, 3,2, 3, 2, 5, 2, 3, 4, 2, 4, 5, 3, 4, 4, 5. The MWIS is 1, 2, 3.

zero otherwise, and vn,r is the weight of vertex (RRH) n. Inorder to bias the scheduler towards allocating RBs in favourof highly loaded RRHs, the weights are chosen such that

vn,r =

zn,r exp(Ωsn,n), if Φsn,n < Φthsn0, otherwise.

where Ωm,n is the number of RBs requited by MNO m atRRH n. Table (IV) shows the pseudo code of an iterative low-complexity algorithm that solves (7) by using a BIP solver.At each iteration, one RB is assigned to the MWIS of RRHsthat maximizes the sum-weighted utility. Lines 5-8 find theLSM (sn) at every RRH. To avoid assigning RBs to MNOsthat have no data to transmit, the service status of the LSMhas to be lower than the threshold Φm,n < Φthm . Lines 9-10find the index and the utility value of the user who subscribesto MNO sn and maximizes the sum utility. In line 12, thealgorithm solves the MWIS optimization problem (7) and findsthe subset IS . The RB is assigned to users in line 14. Thenumber of RBs requited is decremented for each RRH that

7

TABLE IV. PER RB OPTIMAL ALLOCATION ALGORITHM

1: input: Λm,n, Ωm,n,∀m,n2: Rn = R,∀n3: for r = 1 : R do4: for n = 1 : N do5: vn,r = 06: ∆Ωm,n = Λm,n − Ωm,n,∀m7: Ωm,n = Λm,n + ∆Ωm,n,∀m8: sn = arg max

mΩm,n,∀m such that Φm,n < Φthm

9: zn,r = maxk∈Ksn,n

uk,r

10: jn,r = arg maxk∈Ksn,n

uk,r

11: end for12: solve the BIP problem in (7)13: assign RB r to UE jn,r,∀n ∈ IS14: Ωsn,n = Ωsn,n − 1,∀n ∈ IS15: update Ωsn,n & Φsn,n,∀n ∈ IS16: end for

belongs to IS in line 13, whereas Ωsn,n,Φsn,n are updated inline 20. The algorithm runs until all RBs have been assigned.

Although the algorithm solves the BIP problem R timeseach TTI, the complexity of the algorithm is relatively lowas compared to (5) because the size of the BIP is small. Inparticular, the BIP has N decision variables. However, for alarge number of RRHs, it might be computationally expensiveto solve the BIP problem shown in (7) R times for each TTI.Therefore, a low-complexity heuristic algorithm that solvesthe BIP is presented in Table V. The heuristic algorithm isgreedy in the sense that it assigns an RB to the RRH thathas the maximum weight vn,r, then excludes its interferingRRHs from the allocation process. The first 11 lines in theheuristic algorithm are similar to the algorithm shown in TableIV, where the LSMs and their users who maximize the sumutility are specified. The RRH index that has the maximumweighted utility n∗ is found in line 14 and is added to thesubset IS in line 15. The RRH n∗ and its interfering RRHsindices are deleted from the potential set of RRHs Sind.Consequently, interfering RRHs are not assigned assignedthe same RBs, thereby eliminating interference. The RB isassigned to jn,r,∀n ∈ IS in line 18, and Ωsn,n, Ωsn,n,Φsn,nare updated in lines 19-20.

A. The complexity of the heuristic algorithmFor every TTI, the heuristic algorithm runs R major iter-

ations (lines 3-21). Each major iteration finds the LSM anda candidate user (jn,r) for each RRH. Finding the LSM atRRH requires M operations, whereas finding the user (jn,r)requires Ksn,n operations. The number of MNOs is usuallymuch larger than the number of UEs, which makes findingjn,r is the dominating operation. Assigning each RB to thesubset IS requires at most N operations, assuming that noRRHs interfere with each other. Therefore, the worst-casecomplexity is O(R×(N+Kmax)), where Kmax = max

n,mKm,n

is the maximum number of users that connect to an RRH andsubscribe to one MNO.

TABLE V. HEURISTIC ALGORITHM

1: input: Λm,n, Ωm,n,∀m,n2: Rn = R,∀n3: for r = 1 : R do4: for n = 1 : N do5: vn,r = 06: ∆Ωm,n = Λm,n − Ωm,n,∀m7: Ωm,n = Λm,n + ∆Ωm,n,∀m8: sn = arg max

mΩm,n,∀m such that Φm,n < Φthm

9: zn,r = maxk∈Ksn,n

uk,r

10: jn,r = arg maxk∈Ksn,n

uk,r

11: end for12: Sind = 1, 2, · · · , N13: while Sind 6= φ do14: n∗ = arg max

nvn,r

15: IS ← n∗

16: S∗ind = Sind \ c ∈ Cn ∪ n∗17: end while18: assign RB r to UE jn,r,∀n ∈ IS19: Ωsn,n = Ωsn,n − 1,∀n ∈ IS20: update Ωsn,n & Φsn,n,∀n ∈ IS21: end for

VI. SIMULATION MODEL AND NUMERICAL RESULTS

A layout made of a total of 22 hexagonal cells, as shown inFig. 3, is considered. Two scenarios are considered; small-sizeand large-size. In the small-size scenario, only RRHs 1, 3 and4 are considered. Comparisons are shown for the optimal, BIP,heuristic, and static sharing schemes. The large-size scenarioconsiders the 22 RRHs. Because of the high complexity of theoptimal solution for the large-scale scenario, results are shownonly for BIP, heuristic, and static sharing schemes. UEs aredistributed uniformly across RRHs such that the same numberof UEs are connected to each RRH. The channel is modeledas a quasi-static frequency-flat Rayleigh fading channels. Eachchannel is assumed to be fixed during one subframe in timedomain and over one RB in frequency domain, but changesindependently over different subframes, different RBs, anddifferent users.

A. Experiment 1In this experiment, throughput and complexity comparisons

are shown for the small-size scenario. Three RRHs are con-sidered each of which serves the same number of UEs. Thenetwork is shared between two MNOs, each of which owns 18RBs and serves a total number of 9 UEs. The MT schedulingpolicy is assumed for both MNOs. To show the worst-casescenario, a backlogged traffic model is assumed: users alwayshave data to transmit, and the probability that one MNOis underloaded is zero. Therefore, MNOs receive the samenumber of RBs as in the static sharing scenario. The servicestatus thresholds are Φm,n =∞,∀m,n.

Fig. 4 compares the average aggregate throughput of theMNOs for different average SINRs. As MNOs undergo similar

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Fig. 3. Network layout used in the simulation. For the small-size scenraio,only the red RRHs (1, 3, and 4) are used. For the large-size scenario, all RRHsare used.

conditions in terms of the number of UEs, the average SINR,the traffic model, the scheduling policy, and the number ofRBs, their performance is similar. Therefore, showing aggre-gate throughput of both MNOs is a sufficient performanceindicator. As average SINR increases, aggregate throughputincreases for all solutions. The optimal scheme outperforms theother solutions. The BIP and the heuristic solutions are compa-rable, performing only 6% lower than the optimal solution. Theperformance of the static sharing solution is the worst, 20%lower than the optimal solution. In the static sharing scheme,each RRH can only use a certain part of the spectrum, whichlowers the chances of assigning an RB with a high SINR fora large number of UEs. In contrast, in other three schemesRRHs have access to all parts of spectrum.

The normalized running times of the four solutions arecompared in Fig. 5. The optimal solution takes 1.9386× 109

times longer than the static sharing solution. The running timefor the suboptimal solutions (BIP and heuristic) is considerablylower than the optimal solution. The BIP scheme takes about43.7 times more to solve the assignment problem compared tothe heuristic scheme as it requires solving the BIP optimizationproblem. It is worth mentioning that the complexity of theoptimal solution exponentially increases with the number ofUEs, RBs, and RRHs. However, the complexity of the BIPproblem involved in the BIP scheme exponentially increasesonly with the number of RRHs; its complexity increaseslinearly with the number of RBs, and does not depend onthe number of UEs.

B. Experiment 2The whole layout, which consists of 22 RRHs, is considered

in this experiment. The performance of the suboptimal andthe static sharing solutions is compared for the worst-casescenario, which assumes a backlogged traffic model. Complex-ity, average throughput, and throughput for the worst and bestusers are shown for different numbers of UEs per RRH. Both

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Fig. 4. MNOs’ average aggregate throughput of the small-size scenario.

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Fig. 5. Running time for the optimal, BIP, heuristic, and static sharingsolutions.

MNOs apply the MT scheduling policy. The average SINR isset to 10 dB for all users.

Since both MNOs have similar profiles in terms of thenumber of RBs, scheduling policy, number of UEs, and av-erage SINR, an average result for both MNOs is shown. Fig.6 illustrates the average throughput per UE. As the numberof RBs is fixed, the competition for resources grows as thenumber of UEs increases. Consequently, the average numberof RBs assigned to any single user is lower. Therefore, theaverage throughput per UE deceases as the number of UEsincreases in the network for all schemes. In this case, theBIP scheme outperforms the heuristic scheme by only 3%.A performance degradation of 20% is noticed for the staticsharing scheme as compared to the BIP scheme. As theworst-case scenario is shown, using WRV adds an extra 20%

9

throughput in this experiment.The average aggregate throughput across the network is

shown in Fig. 7. As the number of UEs increases, multiplexinggain improves, which increases the aggregate throughput of thenetwork.

The average throughput for the worst and the best usersare exhibited in Figs. 8 and 9, respectively. The worst andthe best users have similar trend: the BIP solution performsslightly outperforms the heuristic scheme, but much better thanthe static sharing solution. The key point is that the proposedsuboptimal schemes maintain a high level of isolation betweenusers, RRHs, and MNOs, even though wireless resources aretotally shared across the network.

The complexity of the schemes is measured and pointedout in Fig. 10, which is closely analogous to the small-size scenario. The static sharing scheme is the least complexsolution, since the RB allocation is independent for each RRH.The heuristic solution is solved considerably slower than staticsharing but faster than the BIP scheme.

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Fig. 6. Average throughput per UE for both MNOs.

C. Experiment 3In contrast to experiments 1 and 2, which investigate net-

work performance for the worst-case sharing scenario, exper-iment 3 studies the WRV gain in a non-saturated network, atleast for one MNO. The simulation variables are similar toexperiment 2 in terms of the average SINR, the number ofRRHs, MNOs, UEs, and RBs. Nevertheless, MNO1 appliesthe M-LWDF scheduling policy, while MNO2 applies theMT scheduling policy. The data traffic for UEs subscribed toMNO1 are modelled by Poisson traffic model with an averagepacket arrival rate λ [22], [30], [33]. Fixed-sized packet of4000 bytes arrives to each user’s buffer. UEs subscribed toMNO2 are assumed to be greedy and always have data totransmit.

Fig. 11 shows the average head-of-line (HoL) packet delayfor different values of λ. As the value of λ increases, the

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Fig. 7. Total aggregate throughput of all UEs.

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sers

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Fig. 8. Average throughput of the worst user.

average data arrivals deceases. Consequently, MNO1 becomesfurther underloaded. The average HoL delay for the BIP andthe heuristic schemes are similar, but much less than thatfor the static sharing scheme. The dynamic sharing schemesmaintain an average delay which is 100 times less than thestatic scheme.

The average aggregate throughput for MNO1 and MNO2is illustrated in Figs. 12 and 13, respectively. As the valueof λ increases, the average aggregate throughput of MNO1decreases because less data arrives to the UEs’ buffers. Inthe static sharing scenario, RBs assigned to MNO1 are notaccessible by MNO2. Therefore, average aggregate throughputof MNO2 is not affected by the variation in the traffic load ofMNO1. For the BIP and the heuristic schemes, the throughputof MNO2 grows as the load of MNO1 becomes lighter.Reducing the load of MNO1 allows MNO2 to access more

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Fig. 9. Average throughput of the best user.

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Fig. 10. Running time of the BIP, hueristic, and static sharing schemes.

RBs that would be granted to MNO1 if it is overloaded.To sum up, using the proposed BIP and heuristic schemes

would improve the performance of the network; lower the HoLdelay for MNOs’ users, and increase the aggregate throughputof MNO2. These improvements result from the cooperationbetween MNOs; in cases such that one MNO is overloaded,the unloaded MNOs help to serve users who subscribe to theoverloaded MNO.

VII. CONCLUSION

In this paper, we presented wireless resource virtualizationschemes for cloud-based radio access networks (C-RANs).The proposed schemes dynamically share wireless resourcesbetween multiple mobile network operators (MNOs). Optimaland suboptimal solutions are provided and compared with eachother as well as with a static sharing scheme, where each MNO

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elay

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Fig. 11. Average head-of-line packet delay of MNO1’s UEs.

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Fig. 12. Average aggregate throughput of MNO1’s UEs.

is assigned a fixed set of radio RBs. The optimal solutionis formulated as a binary integer programming optimizationproblem, which is known to be computationally expensive.Consequently, to reduce the complexity of the optimal formula-tion, two low-complexity suboptimal schemes are derived. Theperformance of the suboptimal solutions is slightly lower thanthe optimal solution at the benefit of a significant lower runningtime. The performance of the proposed schemes are comparedin terms of throughput, delay, and time complexity. Thesimulation results show that the proposed schemes outperformstatic sharing in terms of both aggregate throughput and delay.

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