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Radio Access Networks (CRAN) are promising technologies with the potential to be game changing for the fifth generation (5G) wireless networks. In particular ...
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A Framework for Joint Wireless Network Virtualization and Cloud Radio Access Networks for Next Generation Wireless Networks ∗

M. Kalil∗ , A. Al-Dweik†‡ , M. Abu Sharkh§ , A. Shami† , and A. Refaey†¶ IBM Analytics, IBM, Toronto, Ontario, Canada. † Western University, London, Ontario, Canada. ‡ Khalifa University, Abu Dhabi, UAE. § Ferris State University, grand Rapids, MI. ¶ Manhattan College, Bronx, NY. Emails: {mkalil3, aaldweik, mabusha, ashami2, ahusse7}@uwo.ca

Abstract—Wireless Network Virtualization (WNV) and Cloud Radio Access Networks (CRAN) are promising technologies with the potential to be game changing for the fifth generation (5G) wireless networks. In particular, these technologies may have significant impact on the capital expenditure, quality of service (QoS) provisioning, as well as spectral efficiency in 5G networks. These two technologies are mostly considered separately in previous works. This article, however, investigates both the gains and requirements of integrating WNV with CRAN. In this work, we propose WNV schemes for CRAN where the objective is to maximize the overall system throughput and minimize delay. The proposed schemes are designed to maintain a high level of isolation between mobile network operators (MNOs), which allows the deployment of different scheduling polices by different MNOs, and managing intercell interference, which may lead to significant throughput gain. Overall, the results presented in this article reveal that a joint CRAN-WNV architecture can be highly efficient when MNOs have unbalanced loads because MNOs with high loads can seamlessly access the underutilized resources of underloaded MNOs. The throughput gain in unbalanced loads can be as much as 50% using optimal sharing schemes when compared to static sharing, and about 18% when compared to WNV without CRAN. The resource allocation problem in the joint CRAN-WNV is formulated, and both optimal and low complexity suboptimal solutions are derived. The obtained results show that integrating the two technologies in a joint architecture can significantly improve the network performance. However, reducing the complexity by adopting efficient sharing techniques may have tangible impact on the throughput when compared to optimal sharing. Keywords—Wireless resource virtualization, CRAN, ICI management, resource allocation.

I.

INTRODUCTION

In recent years, mobile data traffic has experienced substantial growth due to a combination of the increased availability of new devices along with the individual user data demand surge caused by the plethora of data hungry applications. In 2016, the global mobile data traffic grew by 63% with almost half a billion mobile devices and connections newly added compared to 2015 [1]. Moreover, mobile data traffic growth rates are expected to be monotonically increasing until 2021, where it is anticipated to increase by sevenfold. As a result, mobile This work is sponsored by the ICT Fund, grant no. 11/15/TRAICTFund/KU

network operators (MNOs) are in need for cost-cutting scalable solutions that can offer enhanced utilization and coverage of their wireless networks to cope with the mobile data market growth. A possible solution to these challenges is revamping the network technology stack as part of the introduction of fifth generation (5G) networks. With such demand increase, the planned improvement introduced with 5G in terms of capacity, speed and efficiency will be vastly absorbed. Examples for key enabling technologies implemented or in contention with 5G include densification of existing cellular networks using extrasmall cells, provision of peer-to-peer (P2P) communications, multi-tier heterogeneous networks, full duplex communication, massive multiple-input multiple-output (massive MIMO), millimeter-wave technologies, cognitive radio, beam division multiple access (BDMA), cloud-based radio access networks (CRAN) and wireless networks virtualization (WNV) [2]. The latter two technologies are, at least in principle, game changing. Starting with WNV, the effectiveness of the concept of virtualization is already a reality in terms of infrastructure as a service (IaaS). In less than 5 years, cloud computing IaaS offerings have moved from a fledgling idea to the dominant technology that 90% of large corporations use to operate their infrastructure. The success of the cloud model stems from its three defining features where virtualization is the first and foremost, second is the dynamic scalability, and finally, the economic flexibility of providers offering pay-as-you go portfolios. The massive penetration and client satisfaction inspired the introduction of virtualization proposals of other critical resources. Software defined networks (SDN) and network function virtualization (NFV) are now materializing as the mode of operation for networks intertwined within cloud data centers. However, in the wireless service operators’ realm, things are less straightforward. Explicitly, virtualizing wireless resources carries a set of challenges that are yet to be addressed by wireless networks designers even as the introduction of 5G is approaching. Some of these challenges originate from the lack of consensus between MNOs sharing the virtualized resources either due to business reasons or due to the difference in implementation vision. Some are technical challenges that are yet to find a satisfactory solution that would facilitate immediate deployment. The challenges arise with the definition of wireless resource

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virtualization; (what is to be virtualized and shared?) and go on to span fairness of usage and end with implementation nuts and bolts such as computational challenges within a base station. The main attraction of WNV to the C-level executives at MNOs is the direct savings on capital expenditure (CAPEX). WNV enables MNOs to share various resources such as network infrastructure, backhaul, licensed spectrum, core and radio access network, as well as electrical power, yielding better efficiency in terms of energy consumption and resource utilization. Slashing the carbon footprint is a priority for MNOs both to satisfy imposed governmental and environmental requirements and to bring expenses under control. This is no minor issue as energy consumption by communication components was about 50 gigawatt in 2012 [3]. In addition, theoretically, the spectrum utilization should benefit from direct positive impacts. Spectrum utilization improvement is becoming a red hot priority for MNOs. This is because despite the increasing demand for wireless spectrum, stark underutilization of spectrum is a reality that shows in spectrum utilization measurements [4]. A Nokia experiment [5] reports that only 20% of the radio access networks maximum capacity is utilized most of the time while 80% is idle except for peak time. Implementing WNV has the potential to enhance resource utilization, which can be seen in the following two scenarios. First, with WNV, an MNO with underutilized resources can seamlessly handover resources to overloaded MNOs. Even in the scenario where all MNOs are overloaded, pooling more wireless resources and then sharing them among a large number of users would increase the multiplexing gain. Take the case of Rayleigh fading channels, the aggregated capacity of a cell can increase by ln(K), where K is the number of users in the cell. In total, WNV has the potential to save billions in operating expenditure (OPEX) and CAPEX [6–8]. Savings on CAPEX and OPEX in terms of maintenance and skilled personnel are self evident. CRAN is another technology that is to be incorporated in wireless networks separately [2]. CRAN architecture is based on decoupling the baseband processing unit (BPU) and a radio access unit (RAU) in every base-station (BS) as shown in Fig. 1. Therefore, a cell site in CRANs consists only of a low cost RAU, denoted as remote radio head (RRH) while all BPUs are pooled in a cloud at remote data centers and are shared by all BSs. CRAN can achieve the same performance utilizing a number of BPUs lower than that needed by RAN [3]. This design can achieve power consumption reduction of about 71% [9]. Unlike the traditional RAN, CRAN architecture facilitates exchanging of traffic and channel information over the entire network, and hence, can be used to effectively apply networkwide WNV to optimize the allocation of system resources across multiple cell sites and MNOs. One of the main issues affecting the poor efficiency of current wireless networks is the high variance of traffic loads. To provide high quality of service (QoS), the network should be designed to accommodate peak traffic loads in order to achieve low blocking probability. This, in turn, results in resource over-provisioning and low network efficiency. Presently,

a straightforward resolution does not exist under the rigid structure of current wireless networks. Scalable and flexible resource allocation techniques must be considered to handle a broad variety of traffic loads at different times. Therefore, the design of high capacity networks with efficient utilization of the infrastructure in such scenarios is mostly unattainable. In fact, the maximum exploitation of WNV concept is achieved when the sharing MNOs have different load profiles. More specifically, this is ideal when there is a mixed bandwidth demand profiles. In such cases, MNOs with high demands can seamlessly access the excess resources of other MNOs, which would maximize utilization of the shared resource pool since it is constructed in a way similar to how a cloud data center is. This opens dynamic scalability venues for MNOs with different sizes. WNV is not only effective when various loads are at the same location. It can be effective at mitigating coverage and QoS issues in cases where demand is high for everyone. Consider cases where this high demand is faced by certain geographic areas at a certain time. An example would be a sport stadium or a social event. A CRAN-WNV would be primarily effective here as wireless resources should be dynamically assigned across MNOs as well as across cells. Cloud resources can easily be re-deployed to focus on the high demand area and hence, impacting coverage and QoS. Despite the apparent advantages of employing WNV techniques, current network architectures such as long term evolution (LTE) supports coordination only between adjacent base stations (BSs), denoted as evolved Node B (eNB), in a peer-topeer fashion over X2 interface, which makes WNV deployment and resource allocation across the entire network prohibitively complex [10]. Therefore, WNV for traditional LTE networks can only be applied, in its current form, on a small scale over a few adjacent eNBs. We hypothesize that CRAN, once it is integrated with WNV architecture, can be very effective in mitigating both the dynamic traffic requirement challenge and the lack of information exchange between cells. However, a comprehensive scheme that facilitates that integration is not yet available. The aim of this paper is to put forth a solution that virtualizes the wireless resources of cloud-based RANs such that they can be shared between multiple MNOs as shown in Fig. 2. The allocation of wireless resources is determined by the sharing contract between MNOs, the traffic load at each RRH, and the interference between different RRHs. The rest of the paper is organized as follows: Related research work is presented in Section II followed by the contributions of this work. The proposed system and sharing models are presented in Section III. the optimal solution is formulated in Section IV. Low complexity solutions are presented in Section V. Experimental results and analysis are depicted in Section VI, and Section VII concludes the paper. II.

R ELATED WORK AND CONTRIBUTIONS

In the recent literature, it can be clearly noticed that there is a growing interest in virtualizing wireless resources in a single base station [8]. For example, a WNV scheme for eNB is investigated in [7]. The scheme allows MNOs to implement

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3

Fronthaul Backhaul Core Networks Site3

MNO1 Network MNO2 Network

MNO1

BPU Pool

MNO2

Site1 Site2 Site3 Total Bandwidth of MNO1

Total Bandwidth of MNO2

Site2

Aggrega5on Network 1



Evolved Packet Core 1

Site1

Site3 BPU Pool

Aggrega5on Network 2

Site2 Evolved Packet Core 2

Site1

Fig. 1: CRAN LTE network Architecture.

Fronthaul Backhaul Core Networks

RRH3

MNO1 & MNO2 RRH1 RRH2



Virtual BPU Pool RRH2 RRH1

Total Bandwidth of MNO2



Evolved Packet Core1

WRV Hypervisor Aggrega5on Network 2

RRH3 Total Bandwidth of MNO1

Aggrega5on Network 1

Wireless Resource Alloca5on Decisions

Evolved Packet Core2

Fig. 2: Virtualized CRAN shared between two MNOs.

different scheduling policies. However, the scheme does not consider network-wide virtualization nor coordination between interfering cell zones to prevent inter-cell interference (ICI). In addition, the scheme suffers from high complexity because it requires solving two optimization problems to maintain isolation between MNOs. In the first optimization process, the resources of each MNO are allocated to their users. The allocation results of problem one are then fed to the second problem as constraints such that the throughput each user obtains is equal or greater than the throughput achieved when sharing is not considered. An LTE air interface virtualization scheme is proposed in [11], where a hypervisor is added on top of the physical resources. The hypervisor is responsible for virtualizing the eNB into a number of virtual eNBs that can be used by different MNOs. It is shown that more capacity can be achieved by

sharing spectrum resources between different MNOs. However, the scheme does not provide optimal solutions nor manage ICI. Furthermore, the instantaneous channel quality of users is not considered in the scheduling decisions, which limits multiuser diversity gain. More practical scenarios that consider load balancing are studied in [12], where the hypervisor manages the sharing process of multiple eNBs among multiple MNOs. Nevertheless, only fixed resource allocation across BSs is considered. The load is balanced between multiple BSs by moving users from high-traffic cells to low-traffic cells. However, transferring users across cells increases handover overhead, and may degrade the system capacity since users may be transferred to BSs further away, which would reduce the quality of the wireless link. An efficient low-complexity scheme that is able to virtualize

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the wireless resource blocks (RBs) at an eNB and share them between users of multiple MNOs is proposed in [13]. The scheme aims at maximizing the throughput of MNOs users while maintaining access proportional fairness among users as well as MNOs. However, the proposed scheme does not consider network-wide virtualization. A utility-based resource provisioning scheme for WNV with massive MIMO is investigated in [14]. A single BS equipped with a large number of antennas serves users of different service providers. The problem is formulated as a combinatorial optimization problem of high computational complexity. Consequently, a lowcomplexity solution for the combinatorial problem is derived by linear programming relaxation. Cross-layer resource optimization in CRAN has received increasing attention in the last years, most of which investigates the network utility maximization including spectrum utilization, energy efficiency and proportional fairness [3]. With CRAN architecture, a larger number of RRH can be considered in coordinated multipoint CoMP transmission, which improves the transmission performance at the expense of signaling overhead. The tradeoff between system capacity and signaling overhead has been studied in [15]. User clustering for downlink CRAN is studied in [16]. Cooperative clusters for every user is formed such that the network capacity is maximized under limited-capacity backhaul. The impact of single and N-nearest RRH association strategies on CRAN ergodic capacity is investigated in [17], where it is shown that the ergodic capacity gain is not linearly proportional to the RRH density. Therefore, each user should not associate with more than 4 RRHs to balance the performance gain and implementation cost. A resource sharing scheme for a CRAN with capacity constrained fronthaul links is proposed in [18], where a network operator lends radio resources to several service providers as well as controls user admission and association. A thresholdbased policy is introduced to maintain isolation among different service providers, which controls the interference among RRHs. An auction mechanism is designed in [19] to schedule the radio and fiber links resources available in CRAN while maximizing social welfare. The auctioneer owns the CRAN infrastructure, where bidders are mobile operators. Consequently, the auctioneer sells radio resources at BSs and fiber links at fronthaul network. However, the authors assumed that the spectrum resources at RHH are predefined and they do not scale. Minimizing network power consumption of CRAN is investigated in [20], where the power consumption of the transport network and RRHs is considered. The authors assume that transport links and RRHs can support sleep mode. The problem is formulated as a joint RRH selection and power minimization beamforming problem. The network power consumption is reduced by minimizing the number of active RRHs and reducing their transmit power subject to QoS constraints. Through simulations, the authors show that the network power consumption can be notably reduced. Energy efficiency optimization for heterogeneous CRANs is investigated in [21], where RB assignment and power

allocation are optimized subject to particular QoS, intertier interference and maximum transmit power conditions. Using Lagrange dual decomposition method, a closed-form expression is derived for the optimization problem. A crosslayer resource allocation scheme for CRAN that minimizes power consumption in BPU pool, fiber links, and the RRHs is reported in [22]. The proposed scheme minimizes the power by optimizing RRH selection, joint beamforming, and elastic service scaling according to users’ QoS requirement such as the system expected delay being less than a certain threshold. In this work, we consider a network architecture where CRAN and WNV are jointly applied to maximize the network spectrum utilization. The main contributions of this paper are: • An optimal scheme that enables spectrum sharing between multiple MNOs and RRHs is proposed and formulated. The scheme eliminates ICI and considers fair distribution of spectrum resources between RRHs based on their traffic loads. The scheme allows different MNOs to apply different customized resource scheduling policies, and offers efficient resource utilization across the network. Moreover, the scheme maintains high level of isolation between MNOs such that every MNO is guaranteed to be satisfied or access its share of the resources. • A suboptimal scheme that solves the optimization problem with lower complexity is derived. The suboptimal scheme is obtained by dividing the wireless resource allocation problem into sub-problems. The objective of each sub-problem is to allocate one RB to a set of noninterfering RRHs. The allocation per single RB is formulated as a maximum weighted independent set problem, which is solved using binary integer programming (BIP) solvers. • To further reduce the complexity, a low-complexity heuristic algorithm that solves the BIP problem is proposed. The algorithm is greedy and finds the set of non-interfering RRHs for each RB iteratively. The time complexity of the heuristic algorithm is considerably lower than the BIP scheme while its throughput and delay performance are comparable. It is worth mentioning that this work focuses on virtualizing and sharing the spectrum resource between different MNOs, virtualizing other resources such as BPUs and fronthaul network resources can be found in [9]. III. S YSTEM AND S HARING M ODELS Consider the downlink of a cloud-based RAN architecture shared between M MNOs, where N RRHs are distributed to cover a certain geographical area as seen in Fig. 3. The hypervisor, which resides in the cloud, is responsible for sharing the available spectrum bandwidth between MNOs’ users and sites. The total number of users in the system is K, and users are labeled by a unique index k ∈ [1, 2, · · · , K]. As LTE is the most prominent wireless communication standard to be deployed as CRAN [9], LTE physical layer model is assumed in this work. Therefore, orthogonal frequency-division multiple

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5

Virtual BPU Pool User of MNO1 User of MNO2

MNO1 & MNO2

Hypervisor

Fronthaul network

Site1 Site2 Total Bandwidth of MNO1

Physical Network

Total Bandwidth of MNO2

MNO1 & MNO2 Site1 Site2 Total Bandwidth of MNO1

Total Bandwidth of MNO2 MNO-1 Virtual Network

MNO1 & MNO2 Site1 Site2 Total Bandwidth of MNO1

MNO-2 Virtual Network

Total Bandwidth of MNO2

Fig. 3: Virtualized CRAN shared between two MNOs.

access (OFDMA) is used for the downlink transmission. Using LTE terminology, the overall bandwidth of the network is divided into R frequency slots, denoted as RBs, each of which consists of 12 subscribers and occupies 180 kHz bandwidth. To facilitate readability, Table I summarizes the notations frequently used throughout the paper. Each RRH is assumed to be capable of transmitting over any RB. The RRHs are connected to a virtualized pool of BPUs in remote data centers via transport networks such as optical transport networks. The Virtualized pool of BPUs is shared by different MNOs. Wireless channel state and traffic rate information are available at the BPU pool, which enables efficient scaling of the computation capacity [22]. Since BPUs for all RRHs are co-located in one BPU pool, information on RRHs can be easily shared across the data center. Therefore, it is assumed that the wireless link quality for each user and RRHs traffic loads are known at the hypervisor, which is responsible for resource allocation decisions. Generally speaking, each UE can be served by more than one RRH. However, in order to reduce the computational complexity of the proposed algorithms, we assume that each UE is connected to one RRH. Without loss of generality, each UE is assumed to connect to the nearest RRH.

A. ICI Coordination ICI Coordination Schemes for CRAN LTE mobile network are classified into two main groups [9]. The first group eliminates ICI using frequency reuse schemes by allocating different frequencies to interfering zones. Such schemes are relatively simple, as they do not require synchronization between cells. The second group utilizes interference paths constructively, such as CoMP and Joint Transmission (JT) [23]. Although it is proven that using CoMP can improve the system throughput, it requires dynamic coordination of transmission across multiple cells, which requires tighter synchronization and coordination. In this work, ICI is eliminated by dynamically allocating distinct RB sets to interfering cells. Furthermore, RRHs can serve their users independently, which reduces the complexity of the scheduling problem. It is worth mentioning that such assumption is valid in Heterogeneous CRAN, where interference between low power nodes is minimum [21]. In addition, the assumption that Macrocell users are allocated different RBs in CRAN is commonly used in the literature [24], [25], and [26]. Thus, the signal-to-noise ratio (SNR) of the link between

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TABLE I: Summary of the most significant notation. Symbol K, k R, r N, n M, m Pr,n Rm Rm Rm,n Rm,n ¯ m,n R Rn Kn Km,n γr,k ur,k Hr,n,k Cn Φm,n Φth m Sm,n Lm,n sn zsn ,r jsn ,r vn IS

Meaning total number of UEs, UE index total number of RBs, RB index total number of RRHs, RRH index total number of MNOs, MNO index transmit power from RRH n over RB r set of RBs assigned to MNO m number of RBs assigned to MNO m set of RBs assigned to MNO m at RRH n number of RBs assigned to MNO m at RRH n time average number of RBs assigned to MNO m at RRH n set of all RBs assigned to RRH n set of all UEs that connect to RRH n set of UEs that subscribe to MNO m at RRH n SINR of UE k over RB r maximum number of bits transmitted to UE k over RB r channel gain of the link between UE k and RRH n over RB r set of RRH that interfere with RRH n service status of MNO m at RRH n service status threshold of MNO m number of RBs allocated to MNO m at RRH n in case of static sharing load of MNO m at RRH n index of the least satisfied MNO at RRH n utility of the user who maximizes the objective function and belongs to sn index of the user who maximizes the objective function and belongs to sn weight of sn maximum weighted independent set of RRHs

UE k and RRH n over RB r can be expressed as γr,k =

Pr,n Hr,n,k σk 2

(1)

where Hr,n,k is the channel gain of the wireless link between RRH n and UE k over RB r, Pr,n is the transmit power of RRH n over RB r, and σk2 is the additive white Gaussian noise (AWGN) variance. Although it is proven that power allocation schemes such as the water-filling algorithm can improve the transmission efficiency, integrating such techniques in mobile systems is challenging because they require tight tracking of the rapid channel variations [27]. Moreover, it is shown that when the transmission power is high, equal power allocation is as efficient as the optimal power allocation [28]. In this work, we assume equal power allocation similar to the 3GPP-LTE standard [29, 30] such that Pu,n = Pv,n = Pn , ∀{u, v} ∈ Rn , where Rn is the set of RBs assigned to RRH n. In fact, equal power allocation is a common assumption in resource allocation problems [31–33]. LTE supports various modulation and coding schemes (MCSs) [34]. The selection of a particular MCS is determined by SNR and the required block error rate (BLER). A simple MCS selection scheme is performed using a lookup table which maps the received SNR to a MCS for a certain BLER [34]. The maximum number of bits that can be transmitted to UE k over RB r can be calculated as ur,k = bξ(γr,k )Tsym c

(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 bxc refers to the floor function. B. Resource Blocks Sharing Model RBs are assumed to be shared between MNOs based on a contract signed between them. RBs are either shared statically, where each MNO accesses only its share of the resources, or dynamically, where MNOs can access the entire set of RBs. It is worth mentioning that, the static sharing model is used in the simulation as a benchmark to evaluate the performance of the proposed dynamic sharing solutions. As wireless resource virtualization is still in its infancy stage, no well-defined sharing models exist yet [8]. Therefore, a general sharing model is assumed based on the following conditions: 1) In the case of static sharing of RBs, MNOs are assumed to distribute their resources among cells such that the frequency reuse factor is maximized while maintaining a proportional fairness criterion such that X max Sm,n (3a) n

subject to Sm,n +

X

Sm,c ≤ Rm , ∀n

(3b)

c∈Cn

Sm,1 : · · · : Sm,N = (1 ± α)(Lm,1 : · · · : Lm,N ), ∀m (3c)

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where Sm,n is the number of RBs allocated to MNO m at RRH n, Lm,n is the load of MNO m at RRH n, α is a small constant that relaxes the fairness constraints in (3c) to ensure feasible solutions for the optimization problem, R Pm is the number of RBs granted to MNO m such that Rm = R, and Cn is the set of RRHs that m

interfere with RRH n. Constraint (3b) ensures that the number of RBs that are assigned to MNO m at RRH n and its neighboring RRHs is less than MNO m share of the resources Sm,n . The Constraints in (3c) ensure that RBs are fairly allocated to RRHs based on their load. The load can be considered as the number of users or a number of packets queued in buffers for the users. As the fluctuation rate of the load in RRHs is slow compared with the transmission time interval (TTI), which is 1ms in LTE systems for the finest scheduling granularity, the optimization problem in (3) can be solved at a coarser granularity than TTI. Other sharing models can be applied here, however, maximizing the frequency reuse factor while considering a fairness criterion is an intuitive target that MNOs are looking to achieve. 2) In the case of dynamic sharing of the RBs, the service status of MNO m at RRH n should be higher than a certain threshold or, if it is not the case, MNO m should access at least Sm,n RBs. This condition ensures isolation between MNOs such that all MNOs are either satisfied, or can access at least the same number of RBs that they would access in the case of static sharing. The service status of an MNO can be related to aspects such as queue length of users’ buffers, spectral efficiency, or energy efficiency. IV. P ROBLEM F ORMULATION In this work, each MNO aims at maximizing its sum weighted data rates, which is a very common optimization problem in wireless systems [31, 35–37]. The weights are selected by MNOs according to their scheduling policies. To simplify the notations, assume that user k is connected to RRH n and every RRH serves at least one user of each MNO. The scheduling problem can be formulated as   N R M X X X X  w ˆk ur,k βr,k  (4a) max m=1 n=1

k∈Km,n r=1

subscribed to MNO m and connect to RRH n, Rm,n is the number of RBs accessed by MNO m at RRH n, Rk is the set of RBs assigned to UE k, Φm,n and Φth m are the service status and service status threshold of MNO m at RRH n, and βr,k is a binary number indicator defined as  1, if RB r is assigned to UE k βr,k = 0, otherwise. Constraint (4b) represents the exclusive constraint which ensures that (i) each RB is assigned to one UE (at most) at each RRH, and (ii) orthogonal sets of RBs are allocated to RRHs that may interfere with each other. It is assumed that the interference is avoided if interfering RRHs are granted orthogonal sets of RBs. Constraint (4c) ensures that the transport block size for every UE is less than its unserved data size, where Rk is the RB set that is assigned to user k. Constraint (4d) specifies whether the service status of MNO m at RRH n is higher than a certain threshold or, if that is not the case, MNO m should access at least Sm,n RBs. This constraint ensures isolation between MNOs such that MNOs are either satisfied, or can access at least the same number of RBs in case of static sharing. It is noteworthy that constraint (4d) can be split into two constraints by introducing a binary variable ym,n and a sufficiently large upper bound Bm so that Φm,n > Φth m − Bm ym,n

(5a)

Rm,n ≥ Sm,n − Bm (1 − ym,n ).

(5b)

When ym,n = 0, constraint (5a) holds, whereas constraint (5b) becomes Rm,n ≥ Sm,n − Bm , which is always satisfied if Bm is large enough. Note that the constraint Rm,n ≥ Sm,n may still be satisfied. When ym,n = 1, only constraint (5b) holds. Consequently, one constraint holds, and the other one may be satisfied. The formulation in (4) allows MNOs to apply different scheduling policies by weighting their UEs differently. In addition, it guarantees that MNOs use their share of RBs at the overloaded RRH. However, if an MNO is underloaded at a specific RRH, its share of RBs can be granted to other MNOs that are overloaded. Various scheduling policies are proposed for LTE networks [38], including channel-aware policies, such as maximum throughput (MT), proportional fair (PF), and generalized PF (GPF); channel-aware and QoS-aware policies, such as modified largest weighted delay First (M-LWDF) and LOG rule; and energy-aware policies [39].

subject to X X

βr,k +

c∈Cn k∈Kc

X

βr,k ≤ 1, ∀n, r

(4b)

k∈Kn

X

Tr,k ≤ qk , ∀k

(4c)

r∈Rk

(Φm,n > Φth m ) or (Rm,n ≥ Sm,n ) must hold, ∀(m, n) (4d) S where w ˆk is the normalized weight for UE k, Kn = Km,n m

is the set of UEs connected to RRH n, Km,n is the set of UEs

A. Complexity of the Optimal Solution The optimal solution can be formulated as a binary integer programming (BIP) optimization problem, which is computationally infeasible once the problem exceeds trivial sizes. The problem’s complexity increases exponentially with the number of users, MNOs, and RBs. In order to give a glimpse of the BIP problem complexity, the complexity of the subproblem of allocating RBs to RRHs is demonstrated. Let’s take a simple case where 3 RRHs are shared by 2 MNOs and interference is possible. Let’s assume a network of 60 RBs. As

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mentioned earlier, orthogonal sets of RBs should be assigned to RRHs. If each RRH receives 20 RBs, the number of combinations of 20 RBs chosen from 60 RBs for one MNO 60! is 20!(60−20)! = 4.1918 × 1015 . Even if we choose the finest scheduling granularity (one subframe equaling 1ms for LTE), then the problem should yield a solution in less than 1ms. This is practically infeasible. This necessitates developing an algorithm of lower complexity and feasible running time. This issue, like the case in many networking problems, exposes the architecture to vulnerability. In other words, the whole architecture can be perform as well low complexity scheduler.

The LSM at RRH n is defined as ( arg max (Sm,n − Rm,n ), ∀m ∈ Ln , if Ln 6= ∅ m sn = arg max (Sm,n − Rm,n ), ∀m = 1, 2, · · · , M, otherwise. m (7) where Ln is the set of MNOs that have Φm,n < Φth . As the m objective is to maximize weighted sum utility, the assigned RB to the RRH is granted to the user who can maximize the sumutility. The utility and the index of the user who subscribes to MNO sn and maximizes the sum utility can be found, respectively, as zn,r = max w ˆk uk,r

(8)

jn,r = arg max w ˆk uk,r

(9)

k∈Ksn ,n

B. Special Case: Backlogged Traffic Model As discussed in Section IV-A, the complexity of the scheduling problem in (4) is considerably high, which prevents comparing the optimal solution under dynamic traffic models with other schemes. However, the complexity of the optimal solution can be significantly reduced under the backlogged traffic model assumption, where users always have data to transmit. Backlogged traffic model assumption relaxes the constraints (4c) because the data in users’ buffers are assumed to be larger than the transmitted data. Therefore, if RB r is assigned to MNO m at RRH n, the RB should be assigned to the user at RRH n who maximizes the weighted sum data rates and belongs to MNO m. Although the backlogged traffic model might not occur all the time in the network, it reduces the prohibitive complexity of the optimal solution. Hence, the backlogged traffic model is assumed for optimal solution comparisons in Section VI. The scheduling problem for backlogged traffic model can be formulated as max

M X N X R X

umax r,m,n βr,m,n

(6a)

m=1 n=1 r=1

subject to X

βr,m,c + βr,m,n ≤ 1, ∀r, n, m

(6b)

k∈Ksn ,n

The optimization problem per RB can be treated as the maximum weighted independent set (MWIS) of a graph path. Each RRH represents a vertex; an edge (line) is drawn between two vertices if they interfere with each other. A graph can be described by the pair G = (V, E), where the set V is the vertices of G, and the set E is the edges of G. The MWIS is the subset of vertices that has maximum weighted sum such that no two vertices are connected with an edge. For each RB, the MWIS can be formulated as a BIP problem. For example consider 10 cells and 2 MNOs. Assume the total number of users is 200, where each cell has 10 users subscribed to each MNO, and the total number of RBs is 100. In the optimal solution, the number of decision variables is 10 × 200 × 100 = 20,000. For the suboptimal scheme, the number of users that maximizes the sum-utility and subscribed to the LSM is 10. Therefore, the number of decision variables for each BIP problem is 10. As the number of RBs is 100, the suboptimal solution solves 100 BIP problems each of which has 10 decision variables. Fig. 4 shows an example of a graph and its MWIS. For each RB, the MWIS IS can be found by solving the following optimization problem

c∈Cn

(Φm,n > Φth m ) or (Rm,n ≥ Sm,n ) must hold, ∀(m, n) (6c) P max where ur,m,n = max w ˆk ur,k and βr,m,c is a binary k∈Km,n

number indicator defined as  1, if RB r is assigned to MNO m at RRH n βr,m,n = 0, otherwise. V. L OW- COMPLEXITY SOLUTIONS The optimal method basically spans all possible RBs allocations to users for all RRHs searching for the maximum utility. As shown earlier, this can be tricky. A possible suboptimal technique to mitigate complexity is to allocate RBs sequentially. The basic concept is that, at each iteration, the technique aims to satisfy the MNO with the lowest satisfaction rate (LSM) allocating the RB to a user belonging to that MNO which, in turn, maximizes the sum-utility.

IS = max

N X

vn βn

(10a)

n=1

subject to X

βc ≤ 1, ∀n

(10b)

c∈Cn

where βn is a binary variable, equal to one if n ∈ IS and zero otherwise, and vn is the weight of vertex (RRH) n. In order to bias the scheduler towards allocating RBs in favour of highly loaded RRHs, the weights are chosen such that  zn,r (Sm,n − Rm,n ), if Φsn ,n < Φth sn vn = (11) zn,r , otherwise. Table II shows the pseudo code of an iterative lowcomplexity algorithm that solves (10) by using a BIP solver. At each iteration, one RB is assigned to the MWIS of RRHs that maximizes the sum-weighted utility. Line 4 finds the LSM (sn ) at every RRH, the index (jsn ,r ) and the utility value (zsn ,r )

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Maximum Weighted Independent Set

TABLE III: Heuristic algorithm w5 = 1

w1 = 5

RRH-5 RRH-1

w4 = 5

w2 = 4

RRH-4 RRH-2

w3 = 2

1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15:

Rn,m = 0, ∀n, m for r = 1 : R do for n = 1 : N do vn,r = 0 find sn , zsn ,r , jsn ,r , vsn according to (7-9), (11) end for Sind = {1, 2, · · · , N } while Sind 6= φ do n∗ = arg max vn,r n IS ← n∗ ∗ Sind = Sind \ c ∈ {Cn ∪ n∗ } end while assign RB r to UE jn,r , ∀n ∈ IS Rsn ,n = Rsn ,n + 1, ∀n ∈ IS end for

RRH-3

Fig. 4: 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}.

TABLE II: Per RB optimal allocation algorithm 1: 2: 3: 4: 5: 6: 7: 8: 9:

Rn,m = 0, ∀n, m for r = 1 : R do for n = 1 : N do find sn , zsn ,r , jsn ,r , vsn according to (7-9), (11) end for solve the BIP problem in (10) assign RB r to UE jn,r , ∀n ∈ IS Rsn ,n = Rsn ,n + 1, ∀n ∈ IS end for

of the user who subscribes to MNO sn and maximizes the sum utility, and the weight (vsn ) of the RRH sn . In line 6, the algorithm solves the MWIS optimization problem (10) and finds the subset IS . The RB is assigned to users in line 7. The number of RBs assigned increases for each RRH that belongs to IS in line 8. Although the algorithm solves the BIP problem R times each TTI, the complexity of the algorithm is relatively low as compared to (4) because the size of the BIP optimization problem is significantly smaller than the problem in (4). In particular, the BIP has N decision variables. However, for a large number of RRHs, it might be computationally expensive to solve the BIP problem shown in (10) R times every TTI. Therefore, a low-complexity heuristic algorithm that solves the BIP is presented in Table III. The heuristic algorithm is greedy in the sense that it assigns an RB to the RRH that has the maximum weight vn , then excludes its interfering RRHs

from the allocation process. The first 6 lines in the heuristic algorithm are similar to those in Table II, where the LSMs and their users who maximize the sum utility are found. The RRH index that has the maximum weighted utility n∗ is found in line 9 and is added to the subset IS in line 10. The RRH n∗ and its interfering RRHs indices are deleted from the potential set of RRHs Sind . Consequently, interfering RRHs are not assigned the same RBs, thereby eliminating interference. An RB is assigned to jn,r , ∀n ∈ IS in line 13, and Rsn ,n is updated in lines 14. A. The complexity of the heuristic algorithm For every TTI, the heuristic algorithm runs R major iterations (lines 3-21). Each major iteration finds the LSM and a candidate user jn,r for each RRH. Finding the LSM at RRH requires M operations, whereas finding the user (jn,r ) requires Ksn ,n operations. The number of UEs is usually much larger than the number of MNOs, which makes finding jn,r the dominating operation. Assigning each RB to the subset IS requires at most N operations, assuming that no RRHs interfere with each other. Therefore, the worst-case complexity is O(R ×(N +Kmax )), where Kmax is the maximum number of users that connect to an RRH and subscribe to one MNO. Although the suboptimal schemes solve a BIP problem for each RB, it has lower complexity than the optimal solution because the size of its search space is significantly smaller than that of the optimal solution. However, as the number of RRHs increase, it will gradually struggle to solve the R BIP problems in feasible times. Therefore, the demand arises for a heuristic algorithm to solve each BIP independently in trivial time. We present a greedy algorithm to perform that step. In this algorithm, RB is assigned to the RRH with the highest weight. All Interfering RRHs are excluded. VI.

S IMULATION S CENARIOS AND E XPLORATORY R ESULTS In this work, we consider a layout that comprises of 22 hexagonal cells. The number of users for each MNO at each

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A. Scenario 1: Backlogged Traffic Model In this case, throughput of the limited-size layout is evaluated and compared using various schemes. The MT scheduling policy and the backlogged traffic model are adopted for both MNOs. The backlogged traffic model implies that each MNO is fully loaded and operates at full capacity. Therefore, the sharing gain is minimal and it is only due to the multiplexing gain of the wireless resources. To demonstrate the benefit of sharing resources between MNOs, users of MNO2 are forced to hibernate for a random period of time with an average value of Tsleep . Fig. 5 compares the average throughput per UE for a different average number of UEs per cell per MNO. As it can be noted from the figure, the general trend for all schemes is that as the average number of UEs increases the average number of RBs assigned to each UE decreases, which lowers the average throughput per UE. As expected, the performance of non-optimal WNV schemes is upper bounded by the optimal scheme and lower bounded by the static sharing scheme. Moreover, the proposed suboptimal and heuristic schemes outperform the SCWNV scheme and they are only 9% worse than the optimal. The throughput advantage of the proposed suboptimal and heuristic approaches is due to the fact that users can access the entire set of the RBs. On the contrary, SCWNV limits users to access only the RBs that are assigned to their RRHs. On the other hand, the performance of SCWNV scheme outperforms the performance of the static sharing scheme as it virtualizes the resources of both MNOs at each RRH. Static

240 Optimal Suboptimal Heuristic SCWNV [9] Static sharing

220

Average throughput per UE (Kbps)

¯ cell is assumed to be a uniform random variable with mean K. UEs are assumed to be uniformly distributed across each cell and have an average SINR between 5 and 10 dB. The RBs are assumed to be independent and frequency-flat with Rayleigh fading. Each RB is assumed to be fixed during one subframe in the time domain and over one RB in the frequency domain, but changes independently over different subframes, different RBs, and different users which corresponds to a quasi-static channel. For benchmarking purposes, the proposed schemes are compared to the static sharing and the heuristic single-cell WNV (SCWNV) scheme presented in [7]. In the static sharing, each MNO at each RRH receives its share of RBs and allocates them to its users according to the MNO scheduling policy. In the SCWNV scheme, the spectrum resources assigned to all MNOs at a single RRH are virtualized and shared between all UEs connected to the RRH. In the following two subsections, numerical results are presented for two different scenarios. The first scenario considers the optimal solution, and thus only 6 RRHs are considered and the backlogged traffic model is adopted. In the second scenario, the entire layout of the 22 cells is considered and a dynamic traffic model is assumed. Therefore, the optimal solution is excluded due to its high complexity while the proposed suboptimal and heuristic schemes are considered and compared to the static sharing and SCWNV scheme presented in [7].

200

MNO1

180 160 140 120 100

MNO2

80 60 40 20

25

30

35

40

45

50

Average number of UEs per cell per MNO

Fig. 5: Average throughput per UE for Tsleep = 40%.

sharing offers the lowest throughput because the UEs of each MNO only access RBs that are dedicated to the MNO, and they cannot utilize the unused RBs of others MNOs. Although MNO1 and MNO2 own the same number of RBs, the average throughput per user is lower for MNO2’s users because they were forced to hibernate Tsleep of the time. The average throughput per user for the proposed suboptimal and heuristic schemes are slightly lower than that achieved by the optimal scheme. The SCWNV scheme slightly outperforms the static sharing scheme. However, the gain achieved by the WNV schemes for MNO2’s UEs is less than that for MNO1’s UEs for the following reason. WNV offers two types of gains: 1) multi-MNO multiplexing gains as a result of increasing the number of users per cell, and 2) gain results form sharing RBs of underloaded MNOs with overload MNOs. As MNO1 is fully loaded, WNV only offers multi-MNO multiplexing gains to MNO2’s users. On the other hand, MNO2 is assumed to be underloaded and MNO1’s users benefit from both gains. Fig. 6 shows the average aggregate throughput per cell. As number of UEs increases, the average aggregate throughput increases as a result of the multi-MNO multiplexing gain. Since MNO2 users are forced to hibernate 40 % of the time, MNO1 has higher average throughput than MNO2. The average user throughput for different values of Tsleep for users of MNO1 and MNO2 are shown in Figs. 7 and 8, respectively. It is worth noting that Tsleep indicates the load of MNO2. As value of Tsleep becomes longer, the load on MNO2 becomes lighter. In case of static sharing, MNO1 and MNO2 are fully isolated from each other. Therefore, lightening the load on MNO2 has no impact on MNO1, and the average throughput of MNO1 users is constant for any Tsleep value. On the contrary, for WNV schemes the average throughput of MNO1’s users builds up as the MNO2 load drops. As Tsleep increases, the users of MNO2 access less RBs, and therefore

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#10

4

320

Average throughput per UE (Kbps)

2.8

Average throughput per cell (Kbps)

2.6 2.4 2.2

Optimal Suboptimal Heuristic SCWNV [9] Static sharing

MNO1

2 1.8 1.6 1.4

MNO2

1.2 1

300 280 260 240 220 200 180

0.8 20

25

30

35

40

45

50

Average number of UEs per cell per MNO

Fig. 6: Average throughput per cell for Tsleep = 40%.

Optimal Suboptimal Heuristic SCWNV [9] Static sharing

0

0.1

0.2

0.3

0.4

0.5

Probability of MNO2 users are put to sleep mode

Fig. 8: Average throughput per UE for different vales of Tsleep : MNO2 users.

Average throughput per UE (Kbps)

380 Optimal BIP Heuristic SCWNV [9] Static sharing

360 340 320 300 280 260 240

0

0.1

0.2

0.3

0.4

0.5

Probability of MNO2 users are put to sleep mode

Fig. 7: Average throughput per UE for different vales of Tsleep : MNO1 users.

their average throughput decreases or the benefit of MNO1’s users. B. Scenario 2: Dynamic Traffic Model In this scenario, performance is measured through a critical metric which is the average throughput and head-of-line (HoL) packet delay. A simulation environment consistent with the first scenario was employed (MNOs count, and RBs). However, a more realistic system model was chosen as we consider

the entire layout (22 RRHs) and allow MNOs to employ varying scheduling policies. Namely, MNO1 uses the MLWDF scheduling policy, whereas MNO2 applies the MT scheduling policy. In this experiment, UEs are considered active only when they have data to be transmitted. MNO1’s UEs have a Poisson traffic distribution with a packet arrival rate λ, and fixed-size packet of 1 KB. In contrast, MNO2’s UEs - to make sure the system is under sufficient load- are assumed to use a greedy distribution which always requires transmitting data. We start by investigating the performance of the proposed, SCWNV, compared to static sharing schemes when we gradually change the traffic load by changing the packet arrival rate λ, to users’ buffers. The similarity in profiles between MNOs (number of RBs, scheduling policy, number of UEs, and average SINR) dictates the resulting average performance by both MNOs as shown. The average aggregate throughput per cell for users of MNO1 and MNO2 is shown in Figs. 9 and 10, respectively, for different traffic loads of MNO1. As the value of λ increases, the average data arrivals decreases and the load of MNO1 becomes lighter. In the static sharing scenario, MNO2 cannot access RBs that are assigned to MNO1. Therefore, average aggregate throughput of MNO2 is not affected by the variation in the traffic load of MNO1. However, WNV schemes allow MNO2 to access the entire RB pool. Consequently, reducing the MNO1’s load will directly yield more available resources to MNO2. Hence, the throughput of MNO2 grows as the load of MNO1 becomes lighter for all WNV schemes. The suboptimal scheme slightly outperforms the proposed heuristic scheme at the expense of higher computational complexity. It is noted the proposed schemes all perform visibly better than the SCWNV and

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400 Suboptimal Heuristic SCWNV [9] Static sharing

300 250 200

140

150

50 0 20

Suboptimal Heuristic SCWNV [9] Static sharing

120

100

40

60

80

100

120

140

160

180

200

Average packet arrival rate (ms)

Fig. 9: Average aggregate throughput: MNO1 users.

Average HoL packet delay

Average throughput per cell (Kbps)

350

schemes clearly outperform the SCWNV and the static sharing schemes. Fig. 11 shows the average HoL packet delay for different values of λ. The average HoL delay for the suboptimal and the heuristic schemes are similar, but much less than that for the SCWNV scheme and static sharing schemes for small value of λ. For large values of λ, the load on MNO2 is relatively low and the average HoL delay for all schemes converge.

100

80

60

40

20 140 140 Suboptimal Heuristic SCWNV [9] Static sharing

Average HoL packet delay Average HoL packet delay

120 120

0 20

40

60

80

100

120

140

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180

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Average packet delay (ms)

100 100

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

80 80

60 60 40

VII.

40 20 20 0

20 0 20

40 40

60

60

Average packet (ms) 160 80 100 120delay 140 Average packet delay (ms)

80 180

200

Fig. 10: Average aggregate throughput: MNO2 users.

static sharing. This is seen in the difference in the average normalized running time of the schemes: 2.52 × 104 for the suboptimal, 0.712 × 104 for the heuristic, 0.544 × 104 for the heuristic [7], and 1 for static sharing. In terms of complexity, we note that the static sharing scheme sacrifices performance by seeking less complexity. On the contrary, despite being slower than static sharing, heuristic method gets considerably better metric values while executing at acceptable running speed that is faster than the suboptimal and optimal scheme. With higher values of λ which correspond to lower loads, all the algorithms are able to satisfy the demand. As traffic load increases, the distinction starts to materialize between WNV schemes and static sharing scheme for MNO1. The proposed

C ONCLUSION

Wireless Network Virtualization (WNV) is a promising solution to achieve next level gains in capital investment savings, energy efficiency and spectral utilization for 5G environments. In this work, we hypothesized that combining WNV with Cloud Radio Access Network (CRAN) opens up venues for better resource utilization in cases where unbalanced load between mobile network operators (MNOs) is faced. Significant performance gains are also achieved when the whole resource pool is under high demand. In addition, the proposed enhanced architecture has the potential to mitigate dynamic traffic control issues and data sharing between system components in addition to realizing WNV’s potential in terms of capital and operating expenditure savings. Optimal and suboptimal solutions that combine WNV and CRAN while considering wireless resources were proposed. Moreover, a practical solution is introduced in the form of a heuristic technique that works for all problem scales. Experimental results show that the proposed CRAN-WNV architecture outperforms static sharing in terms of both aggregate throughput and delay. This validates the joint architecture design and motivates further work to harvest more utilization gains from CRAN-WRV architectures.

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