Virtual Resource Allocation in Software-Defined Information-Centric ...

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2016.2529660, IEEE Transactions on Vehicular Technology

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, XXX 2016

Virtual Resource Allocation in Software-Defined Information-Centric Cellular Networks with Device-to-Device Communications and Imperfect CSI Kan Wang, Hongyan Li, Member, IEEE, F. Richard Yu, Senior Member, IEEE, and Wenchao Wei

Abstract—In this paper, we propose an architecture of software-defined information-centric network virtualization with device-to-device (D2D) communications, which facilitates the dynamic virtual resource allocation and content caching via a software defined networking (SDN) controller with a global view of system. In our proposed framework, substrate physical resources can be virtualized and shared among multiple mobile virtual network operators (MVNOs). Meanwhile, by means of integrating D2D communications into information-centric wireless networks, content caching is enabled not only in the air but also in mobile devices. In addition, taking into consideration the inaccurate channel estimation and measurement, we formulate the virtual resource allocation and caching optimization as a discrete stochastic optimization problem, in which imperfect channel state information (CSI) is incorporated. Because the formulated virtual resource allocation problem is a large-scale combinational optimization problem, we exploit discrete stochastic approximation (DSA) approaches to cope with it. Finally, extensive simulations are conducted to demonstrate the effectiveness of proposed scheme with different system parameters. Simulation results show that MVNOs can benefit from not only the sharing of physical infrastructure but also the caching functionality existing in both the air and mobile devices. Index Terms—Software defined networking (SDN), deviceto-device (D2D) transmissions, wireless network virtualization, caching strategy, imperfect channel state information (CSI), discrete stochastic approximation (DSA). Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. This work is supported by the National Science Foundation (91338115, 61231008, and 61372089), National S&T Major Project (2015ZX03002006), the Fundamental Research Funds for the Central Universities (WRYB142208, JB140117), Program for Changjiang Scholars and Innovative Research Team in University (IRT0852), the 111 Project (B08038), SAST (201454), the Natural Sciences and Engineering Research Council of Canada (NSERC) and China Scholarship Council. Kan Wang and Hongyan Li are with the State Key Laboratory of Integrated Service Networks, School of Telecommunications Engineering, Xidian University, Xi’an, Shaanxi 710071, China (e-mail: [email protected]; [email protected]). Hongyan Li is the corresponding author. F. Richard Yu is with the Depart. of Systems and Computer Eng., Carleton University, Ottawa, ON, Canada (e-mail: [email protected]). Wenchao Wei is with Shanghai Aerospace Electronic Technology Institute, Shanghai, China (e-mail: [email protected]).

I. I NTRODUCTION

W

ITH the explosion in the number of wireless services and applications, wireless network virtualization has been proposed as a promising solution for next generation networks [1], [2]. With network function virtualization (NFV) [3], wireless physical infrastructure can be decoupled from the services and applications that it provides. In this context, a critical entity to accomplish virtualization is the network hypervisor [4], which can virtualize the underlying networks, monitor virtual networks, and allocate virtual resources. Since substrate resources can be abstracted and sliced into multiple virtual networks, different mobile virtual network operators (MVNOs) can dynamically share the physical infrastructure, thus significantly reducing the capital expenses (CapEx) and operation expenses (OpEx) of wireless access networks operated by infrastructure providers (InPs) [5]. In addition, MVNOs running on top of the virtual networks can provide specific services (e.g., VoIP) to subscribers, which facilitates the attraction of more subscribers for mobile network operators (MNOs). From the InPs’ point of view, they can also achieve more benefits by leasing isolated virtual slices to MVNOs [6]. Another promising technology is information-centric networking (ICN), which facilitates the prompt delivery of services to subscribers. Inspired by the fact that users are getting increasingly interested in what the content is rather than where it is from, ICN aims to better cope with the transition from the sender-driven end-to-end networking paradigm to receiver-driven content retrieval paradigm [7]. Compared to traditional networks, ICN-based networks can provide not only scalable and timely content retrieval, but also security and mobility management for users [8]. Characterized by the builtin network caching and receiver-driven content retrieval, air caching in ICN-based networks has attracted great attentions in next generation wireless networks [9], [10]. The integration of ICN and wireless network virtualization can further facilitate the improvement of applications and services demanded by subscribers. In particular, informationcentric network virtualization enables the sharing of both the infrastructure and content, which can produce gains from both the virtualization and built-in network caching. Although some works have focused on wireless network virtualization and ICN, device-to-device (D2D) communications are not investigated explicitly in the information-centric wireless network virtualization architecture [11]. As a promising approach to

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offload traffic from base stations (BSs), D2D communications can enable the sharing of radio connectivity and direct information delivery between two close users [12], [13]. Indeed, by exploiting D2D communications, the information-centric wireless network can benefit from the large number of mobile devices involved. That is because the integration of D2D into information-centric wireless network can enable the content caching not only in the air1 , but also in mobile devices. Moreover, after virtualization, virtual contents can be shared among multiple subscribers from different MVNOs. However, the implementation of information-centric virtualization with D2D communications in current running cellular networks poses challenges. Firstly, it is non-trivial to deploy new mechanisms in existing systems due to the existence of proprietary and diverse protocols and interfaces among network devices [1], [7]. Secondly, devices and protocols in current networks cannot support a dynamic configuration needed for a fast and efficient virtual resource allocation [15]. Software defined networking (SDN), which enables the adoption of new technologies and dynamic reconfiguration in running networks, can be regarded as a promising network platform to realize the information-centric virtualization architecture [16], [17]. Via SDN controller with a global view of the network, operators can manage and optimize resource allocation efficiently in response to time-varying network conditions. In addition, SDN enables a fast control over devices in a vendor-independent way by means of standardized interfaces (e.g., OpenFlow) [18]. In this paper, we study software-defined information-centric cellular network virtualization. The contributions are as follows.

Discrete stochastic approximation (DSA) approaches [20] are employed to cope with the discrete stochastic optimization problem. We first derive an aggressive DSA algorithm for networks with static channels, then apply adaptive step size DSA to time-varying networks. • Extensive simulations are conducted to demonstrate the effectiveness of proposed scheme with different network parameters. Simulation results show that MVNOs can benefit from not only the sharing of physical infrastructure but also the caching functionality in both the air and mobile devices. In addition, DSA schemes can achieve performance comparable to that of the optimal strategy, in which perfect CSI is available. The rest of the paper is organized as follows. Section II shows an architecture of software-defined information-centric cellular network virtualization with D2D communications. Section III formulates the virtual resource allocation as a sumutility maximization problem with imperfect CSI involved. Section IV solves the problem based on DSA approaches. Section V presents and discusses the simulation results. Finally, this work is concluded in Section VI.

We present a virtualized software-defined informationcentric cellular network architecture, which facilitates the dynamic network virtualization and content caching, as well as the D2D communications. Meanwhile, several good features of SDN (e.g., separation of the control and data planes, logically centralized control, global view of the network, ability of programming the network) are exploited in the architecture to facilitate the resource allocation formulation. In particular, by means of content caching in mobile devices (via D2D communications), the virtualized content can be shared by subscribers from different MVNOs. The virtual resource allocation and caching optimization is formulated as a discrete stochastic optimization (DSO) problem [19], in which imperfect channel state information (CSI) is incorporated. Due to the inaccurate channel estimation and measurement, CSI available in the virtual SDN controller is in general imperfect. Besides, the transmission delay inevitably exists when delivering CSI, thus aggravating imperfectness. Therefore, imperfect CSI needs to be carefully handled in the formulated problem.

For the implementation of timely and efficient resource sharing in ICN-based cellular networks, existing devices in the infrastructure must support the dynamic fast configuration. However, current devices and protocols are not designed to react dynamically to changes (e.g., of channel information or subscriber attributes) in environments [15]. Meanwhile, due to the existence of proprietary and diverse protocols and interfaces among network devices, compatibility issues arise when integrating ICN with wireless network virtualization. To be specific, the prevailing ICN-related network architectures consist of DONA, PURSUIT, SAIL, COMET, content centric networking (CCN), etc. [7], while there are multiple diverse projects towards network virtualization in both academia and industry as well, e.g., XBone, UCLP, VNRMS, PlanetLab, GENI [1]. It is intractable for network devices to understand so many diverse protocol standards in both ICN and network virtualization. Fortunately, the SDN paradigm, with its control and data planes separated, is a promising platform to implement information-centric network virtualization in a vendoragnostic manner [16]. The concept of SDN stems from the OpenFlow system at Standford University. SDN has attracted great interests from both academia and industry [21]–[24]. The SDN controller, with a global view of the network, is capable of directly programming the behavior of each device in the network. An example of software-defined information-centric cellular

•

•

1 The

concept “cache in the air” is termed as caching contents in either radio access network (RAN) or mobile core network in [14]. Nevertheless, it specially means the caching function at BSs in this paper.

•

II. S YSTEM M ODEL In this section, we will introduce the virtualized softwaredefined information-centric cellular network architecture, then present an illustration with D2D communications incorporated, followed by the network resource virtualization scheme. A. Software-Defined Information-Centric Cellular Network Virtualization



3


Content publish

Core networks

SDN controller Network application

Content directly from BS (cellular transmission)

Content request

Content directly from user (D2D transmission)

Content from core networks

Legacy cellular transmission

Hypervisor

Information-centric cellular transmission

Virtual network 2 control plane Virtual SDN controller 2

Virtual SDN controller 1

OpenFlow

Network application

BS with Content

Control plane

Data plane

User 1

User 2

Virtual network 2

Virtual network 1

vSDN controller 1 vSDN controller 2 Backhaul

vSDN controller 3

User 3

User 2

User 1

MVNO1

MVNO2

Control plane User with content

User 4 User 2

User 1 User 3

Hypervisor

User 3

Content

User 4 User 1 User 1

User 3

Gatweway

Information-centric D2D communication

User 2

Core networks

Fig. 1: An example of software-defined information-centric cellular network virtualization.

network virtualization is depicted in Fig. 1, where the hypervisor enables the virtualization of both the control and data plane. In this context, the physical substrate network is abstracted and sliced into multiple virtual networks, while the physical computing platform is virtualized into multiple virtual machines. As illustrated in Fig. 1, two virtual networks are abstracted: one is the traditional cellular network without content caching, and the other one is the ICN-based network which enables the content caching in the BS. For the control plane, the SDN controller and network application server are sliced into two individual virtual control planes, each of which is comprised of a virtual SDN controller with mobile applications running on top of it. With the hypervisor, two virtual SDN networks are realized, each of which is managed by its corresponding virtual SDN controller.

B. Software-Defined Information-Centric Cellular Network Virtualization with D2D Communications As mentioned above, the incorporation of D2D communications into information-centric network virtualization is non-trivial, since existing mobile devices in current networks cannot support a dynamic configuration, which is needed for a fast and efficient virtual resource allocation. In traditional cellular networks, only BS or gateway is responsible for pairing the potential D2D users if the content request from one user matches that of another one [11]. In the meantime, new functions and standards (e.g., Proximity Services (ProSe) in 3GPP Release 13 [25]) residing in mobile devices are necessary for the introduction of D2D communications, which poses new challenges [15]. Nevertheless, following the approach in Subsection II-A, we can deploy SDN architecture to tackle this bottleneck to introduce D2D technology.

Fig. 2: An illustration of information-centric network virtualization with D2D communications.

In this architecture, after virtualization, the virtual SDN controller has a global view of its specific virtual network, and can directly program the behaviour of network devices (consisting of mobile devices), in a vendor-agnostic manner [18]. By this means, in the virtual information-centric network with D2D communications, cellular BS or gateway is no longer responsible for pairing D2D users; instead, the virtual SDN controller coordinates the D2D communications in a more efficient approach, to make a decision to perform D2D connection or to use a legacy cellular communication for a specific user. In particular, mobile devices can directly follow the instructions from virtual SDN controllers then provide corresponding functions, instead of participating in control plane protocols. An illustration with D2D communications incorporated is presented in Fig. 2, where legacy cellular transmission, ICNbased cellular transmission and D2D communication co-exist in the same network.

C. Network Resource Virtualization Scheme In the architecture of virtualized software-defined information-centric cellular networks, the SDN network hypervisor is responsible for mapping physical networks (including infrastructure, radio resources, contents and caching memory, etc.) to virtual slices, and abstracting physical SDN controllers to virtual SDN controllers. Via virtualization, not only BS but also mobile devices can be virtualized to virtual nodes for association since D2D transmissions are incorporated. In this context, the BS may be leased by multiple MVNOs at different prices from InP. Meanwhile, potential D2D transmitters with popular contents will be paid by some MVNOs in order to set up D2D communications. In this case, the user considered as transmitter and the one regarded as receiver can belong to the same MVNO or different MVNOs, as shown in Fig. 2,



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where user 3 of MVNO 1 directly transmits content to user 4 of MVNO 2 via D2D communication. In the proposed architecture, time is divided into equal periods, which are further split into three phases: content request, data transmission and caching refreshment, respectively. In the content request phase, each user with content on demand will send a content request to its subscribed MVNO, and then MVNOs forward requests to the SDN network hypervisor. For the hypervisor, it needs to detect the content distribution information across networks, and eventually determine the virtual network abstraction as well as virtual resource allocation. In the data transmission phase, requesting users will receive contents via either cellular or D2D transmission according to instructions from the virtual SDN controller. In the caching refreshment phase, users and the BS will eventually refresh the caching memory based on the decisions made in the content request phase. It should be noted that, the caching refreshment must be conducted at the end of each period, since it is only after the transmission that the delivered contents are fully available to users. III. P ROBLEM F ORMULATION Consider the scenario with one InP but with multiple MVNOs, and assume that the single-hop [7] and one-toone (i.e., unicast) D2D communications [11] work in the infrastructure. Let M and Im be the set of MVNOs and users owned by MVNO m ∈ M, respectively. Assume that there S are totally I users, denoted as I = m Im . For simplicity of notation, we denote (m, i) as the user i ∈ Im . In addition, let J = {1, · · · , J} be the set of users which can be considered as transmitters in potential D2D pairs. Note here that, users in J are actually handled as transmitters which can be shared by multiple MVNOs, while those in Im are in practice regarded as subscribers in MVNOSm. For ease of notation, we further let j = 0 and J0 = J {0} be the BS and all transmitters (consisting of both D2D transmitters and BS) in InP, respectively. For practical implementation, all transmitters in J0 can be virtualized to slices by means of resource isolation (at subchannel or time-slot level, or even hardware level, etc.) [3], [26]. In this paper, we adopt the resource isolation at the subchannel level, i.e., allocating orthogonal subchannels to different transmitters. We further let K = {1, · · · , K} denote the set of all subchannels in the system. At each resource allocation interval, it is assumed that each user (m, i) has a content request ci for MVNO m. Then, MVNO m forwards this request to the hypervisor, which eventually is responsible for association, subchannel allocation as well as decisions on caching contents. Let ami be the j content distribution indicator, namely, ami = 1 indicates that j content ci is readily stored in the memory of transmitter j mi be the association and ami j = 0 otherwise. Moreover, let xj indicator variable, i.e., if transmitter j is allocated to user mi = 0. In addition, let yjk = 1; otherwise, xmi (m, i), xmi j j mi be the allocation indicator variable, i.e., yjk = 1 indicates that subchannel k is allocated to the link between user (m, i) mi and transmitter j and yjk = 0 otherwise. Denoting hmi jk

as the channel gain between user (m, i) and transmitter j on subchannel k, from the Shannon formula, it follows that the achievable rate by user (m, i) on subchannel k when associating with transmitter j can be calculated as ! mi ph 1 jk mi rjk = B log2 1 + , (1) Γ No B where B denotes the bandwidth of each subchannel, No is the noise spectral density, and p is the equal power allocation per subchannel. Note here that Γ denotes the SINR gap to Shannon capacity, which can be described as a function of the desired bit error ratio (BER), the coding gain and noise margin, e.g., in M-QAM (quadrature amplitude modulation) Γ = − ln(5BER) 1.5 [27], [28]. For the caching refreshment on each user (m, i), we introduce binary variable zjmi ∈ {0, 1} as the cache refreshing variable, namely, zjmi = 1 represents that user (m, i) caches content ci sent by transmitter j and 0 otherwise. In addition, let v mi ∈ {0, 1} be the caching refreshment variable on the BS, i.e., v mi = 1 indicates that the BS caches content ci requested by user (m, i) and 0 otherwise. Note that, we do not need to focus on the caching function on transmitters in D2D pairs, since all D2D transmissions are based on the fact that the required contents are already available in transmitters. As a result, v = {v mi }i∈Im ,m∈M only makes sense for BS. As mentioned above, caching functions exist in both BS and users. From the point of view of MVNOs, we denote αmi as the revenue of MVNO m from user (m, i) per unit of received data rate, βij the price for per unit of consumed radio bandwidth when user (m, i) associates with transmitter j, γij the price of per unit of consumed backhaul bandwidth for user (m, i) on transmitter j, and φmi the revenue of MVNO m per unit of estimated backhaul bandwidth reduction by means of caching content on user (m, i), ψmi the price of per unit of space in the memory of user (m, i) for MVNO m, respectively. Denote the size of content ci by sci . Mathematically, the utility for the link between user (m, i) and transmitter j ∈ J (i.e., D2D transmissions) can be formulated as: umi j =

X

mi mi mi yjk (αmi rjk − βij B − (1 − ami j )γij rjk )

k mi +zj (φmi eci

(2) − ψmi sci ),

mi where αmi rjk denotes the revenue of received data rate, βij B mi the cost of consumed radio bandwidth, (1 − ami j )γij rjk the cost of consumed backhaul bandwidth, respectively, provided that subchannel k is allocated to the link between user (m, i) and transmitter j. Meanwhile, φmi eci and ψmi sci denote the revenue on estimated backhaul bandwidth and the cost of caching content in the memory, assuming that user (m, i) caches the received content ci . It should be noted that wireless network virtualization, ICN as well as D2D communications are readily formulated in (2), thus necessitating the introduction of SDN paradigm. In particular, we assume that the backhaul bandwidth reduction via D2D communications is equal to the instantaneous wireless data rate on the associated D2D link. Then the term



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mi (1−ami j )rjk can present the backhaul bandwidth consumption via the D2D communication between user (m, i) and transmitter j on subchannel k, and has the following observations:

•

•

ami j

if = 1 (i.e., transmitter j stores the required conmi tent by user (m, i)), the term (1 − ami j )rjk reduces to zero, which is also consistent with the scenario that in reality D2D transmissions do not consume any backhaul bandwidth. if ami j = 0 (i.e., the required content by user (m, i) is not mi mi available in transmitter j), then (1 − ami j )rjk = rjk . In this case, it is unrealistic to use the D2D communication due to the non-existence of content ci in the memory of j. Henceforth, we must set the unit price γij at a sufficiently mi large value (e.g., larger than rjk by three or four orders of magnitude in the simulation) such that umi j tends to be a significantly small negative. As such, when optimizing the resource allocation, it will automatically avoids the mi irrational cases that yjk > 0 but ami j = 0. However, for mi aj = 0 and j = 0, due to BSs’ capability of backhaul, it is feasible to set γi0 at a reasonable value.

For the potential transmission between user (m, i) and the BS, the related utility function could be formulated as:

umi 0 =

X

mi mi mi y0k (αmi r0k − βi0 B − (1 − ami 0 )γi0 r0k )

k mi +z0 (φmi eci − ψmi sci ) +v mi (1 − ami 0 )(φmi eci −

(3) ψmi sci ),

in which the term v mi (1 − ami 0 )(φmi eci − ψmi sci ) evaluating the net caching revenue in BS is added compared to (2). In this paper, it is assumed the popularity of the c-th most popular content is characterized by a ZipfPpopularity distribution with parameter θ, i.e., qc = cCθ , C = ( c 1/cθ )−1 with θ ≥ 1 [29]. Here, for ease of notation, we denote qci as the requested rate for content ci across networks. Therefore, for MVNO m, the expected reduced backhaul bandwidth consumption during the next period via caching content ci q s can be calculated as eci = cTi pci , where Tp is the duration per period. The resources (transmitter, radio and caching memory) allocated to users for transmissions should be such that the total utility seen by all MVNOs should be maximized. Considering all the constraints and utility functions described above, the sum-utility maximization problem can be mathematically formulated as follows:

max

(x,y,z,v)

s.t. C1 :

X X X

umi j

(4a)

m∈M i∈Im j∈J0

X

xmi j ≤ 1, ∀m, i,

X

xmi j ≤ 1, ∀j ∈ J , (4b)

m,i

j∈J0

mi mi mi C2 : xmi j ≥ yjk , xj ≥ zj , ∀m, i, j, k,

C3 : C4 :

xmi 0

≥v XX

mi

, ∀m, i,

(4c) (4d)

mi yjk ≤ 1, ∀k,

(4e)

mi mi yjk rjk ≥ sci /T, ∀m, i,

(4f)

m,i j∈J0

C5 :

XX

j∈J0

C6 : C7 : C8 :

k

X

zjmi ≤ 1, ∀m, i,

X

mi

j∈J0 zjmi sci

v

X

zjmi ≤ 1, ∀j ∈ J ,

(4g)

m,i

≤ Si , ∀m, i, j, s c i ≤ S0 .

(4h) (4i)

m,i

Here, C1 represents each user could only be connected to one transmitter and there exists only one receiver for each D2D pair. C2 and C3 implicitly impose that the association variable must be larger than or equal to the subchannel allocation variable as well as the caching variable. That is to say, only mi mi when xmi and v mi can take the value one. j = 1 that yjk , zj C4 guarantees that one subchannel can only be allocated to at most one potential link. C5 is the data rate requirement, ensuring that the required content is fully delivered to each user within one period. C7 and C8 are the caching limitations on the memory of users and BS, respectively. IV. V IRTUAL R ESOURCE A LLOCATION A LGORITHM WITH I MPERFECT CSI In this section, we will firstly present the impact of imperfect CSI on virtual resources, then give aggressive DSA and adaptive step size DSA for networks with static and timevarying channels, respectively. A. Imperfect CSI After virtualization, CSI can be forwarded to the virtual SDN controller by wireless RAN via OpenFlow. However, the observed CSI by the virtual SDN controller is typically imperfect due to the following two reasons. First, inevitable measurement errors always make the estimation of CSI inaccurate [11]. Second, the transmission delay in the southbound interface [15] between virtual control plane and wireless RAN actually makes the estimation lag behind the current network conditions. Therefore, it is necessary to optimize the virtual resource allocation under imperfect CSI. The imperfect estimation of hmi jk can be formulated as ˆ mi = hmi + ∆hmi , h jk jk jk

(5)

where ∆hmi jk denotes the estimation error, which can be modelled as a zero mean Gaussian random variable with standard mi variance σjk [30]. For different users, different transmitters



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and different subchannels, ∆hmi jk are in general independent and identically distributed (i.i.d) random variables [31]. Let H be the channel gains across networks, which constitute a matrix with dimensions I × (J + 1) × K. Note from problem (4) that the total utility of all MVNOs can be determined by H and optimization variables x, y, z, v. For simplicity, we denote X = {x, y, z, v} as the collection of all variables. Since y is with dimensions I × (J + 1) × K, x and z are with dimensions I × (J + 1), v with dimension I, there are totally O((J + 1)IK ) possible combinations for virtual resource allocation, of which the set can be denoted as Φ = {X1 , X2 , · · · , XN } with N = O((J + 1)IK ). The total utility of MVNOs canP be expressed as a function mi of H and X, i.e., U (H, X) = m,i,j uj . Our objective ∗ is to find the optimal solution X for the discrete stochastic optimization problem, i.e., X∗ = arg max U (H, X). X∈Φ

(6)

However, channel gain matrix H is not available in virtual SDN controllers due to the estimation error as well as the transmission delay. As in [32]–[34], we can utilize the training sequence approach for channel estimation. By this means, different training preambles can be employed, enabling the unbiased estimation of CSI. Moreover, in traditional orthogonal frequency-division multiple-access (OFDMA) networks, many schemes have been proposed to increase the estimation efficiency, which can be categorized into two classes. One exploits the parametric channel estimation to reduce the error, and one allows for the reduction of feedback information by means of limited-feedback methods (e.g., quantized CSI, channel quality rank indicator feedback). ˆ t, Assume that the estimation of H at time slot t is H from which virtual SDN controllers can calculate the noisy ˆ t , Xt ), where Xt denotes the version of U (H, Xt ) as u(H ˆ t is the subchannel allocation selected at time slot t. If H t t t ˆ , X ), ∀t is a series of unbiased estimation of H , then u(H i.i.d. random variables. We can reformulate the virtual resource allocation as ˆ t , Xt )], X∗ = arg max E[u(H t X ∈Φ

(7)

which is solved at time slot t. One possible method to obtain the optimal expectation of ˆ t , Xt ) is to calculate the empirical averrandom variable u(H age. According to the strong law of large numbers (LLN), the averaged result acquired from a large number of experiments is a good approximation of the expectation, and will tend to be closer as more experiments are conducted. As a result, for a specific Xt with a large number of experiments T , the ˆ t , Xt ) will approach the expectation empirical average of u(H t t ˆ E[u(H , X )], namely,

u ˆ(Xt ) ,

1 T

t X

ˆ s , Xt ) → E[u(H ˆ t , Xt )]. u(H

s=t−T −1

And the optimal virtual resource allocation is

(8)

X∗ = arg max u ˆ(Xt ). t X ∈Φ

(9)

This problem has two unique characteristics. First, the objective function u ˆ(Xt ) is the expectation of the stochastic t t ˆ function u(H , X ). Due to the randomness, the accurate statistical characteristics are difficult to obtain. On the contrary, an estimate of u ˆ(Xt ) is available by means of averaging over a ˆ t , Xt ). When the variance large number of observations of u(H t t ˆ of u(H , X ) is considerably large, it will be tough to acquire the accurate estimate of u ˆ(Xt ) [32]. Second, the solution space is significantly large. To find X∗ , one direct method is to exclusively search over the solution space Φ. Yet, for each t − T − 1 ≤ s ≤ t, N = O((J + 1)IK ) combinations needs to ˆ s , Xt ), and the total number to compute be calculated for u(H t u ˆ(X ) over the interval T is T · N . Therefore, the exclusive method has a complexity of exponential time, which is not a polynomial time algorithm. Also, the exclusive search method depends a large value of period T ; otherwise, the statistical average makes no sense for ˆ t , Xt )]. However, due to the dynamics the calculation of E[u(H of ICN-based cellular networks, channel coherence time is in general smaller than sample size T . That is to say, channel gains in cellular networks cannot remain constant during the time period T [11]. Discrete stochastic approximation (DSA) has been considered as an effective method to overcome these disadvantages due to its low complexity and useful application in communication networks [32]–[35]. In particular, DSA is one kind of iterative optimization algorithms to find the optimal solution, without exhaustively searching over the solution space [32]. In the following, we will first derive aggressive DSA for networks with static channels, then apply adaptive step size DSA to time-varying networks. B. DSA for Static Channels Assume that there are totally N feasible combinations of variable X for problem (4). Let en be a N ×1 vector with 1 at the n-th position and 0 otherwise, and Ψ = {e1 , e2 , · · · , eN }. Consequently, there exists a one-to-one mapping between the virtual resource allocation decision Xt ∈ Φ at time slot t and ψ t ∈ Ψ [33]. At each time slot t, virtual SDN controllers are responsible for updating the occupation probability vector π t = [π t (1), π t (2), · · · , π t (N )]T , where π t (n) ∈ [0, 1] and P t 1≤n≤N π (n) = 1. The DSA-based virtual resource allocation algorithm is summarized in Algorithm 1. As observed in Algorithm 1, the majority of computation complexity for each iteration comes from Step 6 and 7, namely, the calculation of utility function u(Ht , Xt ) (or ˜ t )) for each input Xt (or X ˜ t ). Considering in (2) as u(Ht , X well as (3) that the linear complexity O(I(J + 1)K) is neces˜ t ), the overall complexity sary for both u(Ht , Xt ) and u(Ht , X with respect to Algorithm 1 reaches Tmax O(2I(J + 1)K), where Tmax denotes the maximum number of iterations at which the algorithm converges. Then, what we need to demonstrate is that Tmax is bounded, namely, Algorithm 1 converges in a finite number of iterations.



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Algorithm 1 Aggressive DSA for Virtual Resource Allocation 1:

2: 3:

4:

5: 6:

7:

8: 9: 10: 11: 12: 13:

14: 15: 16: 17: 18: 19: 20: 21:

Network hypervisor virtualizes the available resources (bandwidth, content, and caching function) t←0 Virtual SDN controllers pick one feasible allocation decision Xt from Φ, and make π t (Xt ) = 1 and π t (X) = 0 for all X 6= Xt Initialize the optimal virtual resource allocation decision Xt∗ ← Xt for t = 0, 1, . . . do Given estimation Ht and Xt , virtual SDN controllers execute the virtual resource allocation and obtain u(Ht , Xt ) ˜ t ∈ Φ, another Given another randomly picked X t ˜t realization u(H , X ) is calculated ˜ t ) then if u(Ht , Xt ) < u(Ht , X t+1 t ˜ X ←X else Xt+1 ← Xt end if Virtual SDN controllers update the occupation probability vector 1 π t+1 ← π t + (ψ t+1 − π t ) t t+1 t∗ t+1 t+1 if π (X ) < π (X ) then X(t+1)∗ ← Xt+1 else X(t+1)∗ ← Xt∗ end if Output Xt∗ t←t+1 end for

˜ t )} > P {u(Ht , Xt ) ≥ u(Ht , X ˜ t )}, P {u(Ht , Xt∗ ) ≥ u(Ht , X (12) and the number of iterations (slots) is sufficiently large. Proof: Inequality (11) states that it is more likely to go to the global virtual resource allocation result Xt∗ from Xt rather than from the opposite direction. And (12) represents ˜ t to Xt∗ that it is more likely for the state to move from X rather than to any other state. As shown in [32], [33] that, the sequence {Xt } is a homogeneous irreducible and aperiodic Markov chain within solution space Φ, and more likely move to Xt∗ rather than to other states in Φ. Consequently, what we need to demonstrate is that (11) and (12) hold. Let µx and σx2 be the mean and variance of random variable u(Ht , Xt ), respectively. By means of the cumulative Pempirical t distribution function Ft (u) = (1/t) t′ =1 I{u(Ht′ ,Xt′ ) u(Ht , Xt )} > P {u(Ht , Xt ) > u(Ht , Xt∗ )}. (13) Due to the fact that the difference of two normally distributed variables also follows a normal distribution, (13) can be formulated as P {N (µx∗ −µx , σx2∗ +σx2 ) > 0} > P {N (µx −µx∗ , σx2 +σx2∗ ) > 0}. (14) Since U (Ht , Xt∗ ) > U (Ht , Xt ) holds, it is straightforward that µx∗ − µx > 0. Therefore, (14) follows from the fact that the left-hand side random variable in (14) is with larger mean but the same variance compared to the right-hand side one. Next, (12) can be formulated as ˜ t )} > P {u(Ht , Xt ) > u(Ht , X ˜ t )}, P {u(Ht , Xt∗ ) > u(Ht , X (15) which is equivalent to following inequality: µ ∗ − µx˜ µx − µx˜ px . >p 2 2 σx∗ + σx˜ σx2 + σx2˜

(16)

As in [32] and [33], (16) can be verified through extensive simulations. Consequently, Algorithm 1 is convergent to the global optimum.

C. DSA for Time-Varying Channels P {u(Ht , Xt∗ ) ≥ u(Ht , Xt )} > P {u(Ht , Xt ) ≥ u(Ht , Xt∗ )}, In the static CSI described in the previous section, with (11) the increase of number of iterations, π t must get increasingly 0018-9545 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.



conservative. Therefore, a fixed step size, v t = 1t , is adopted, so that Xt∗ will not move far away from the optimal solution X∗ . Note that, only when ψ t − π t takes a large value that Xt∗ can be substituted by Xt+1 . However, in the environment of time-varying channels, the algorithm with step size v t = 1t tends to be trapped into a local optimal solution with a high probability while getting excessively conservative [11]. Consequently, the choice of the step size will play a significant role in the performance on the algorithm. On the one hand, the faster the channel changes, the larger v t should be. On the other hand, the closer Xt∗ is from X∗ , the smaller v t should be [32]. Nevertheless, the dynamics of time-varying channels are not available in virtual SDN controllers in advance. Intuitively, v t is considered as a probability taken value between 0 and 1. And two representative cases are as follows: when v t = 0, (10) reduces to π t+1 ← π t , which will be trapped into a fixed solution; when v t = 1, (10) reduces to π t+1 ← ψ t , which is equivalent to the exhaustive search. In order to adaptively regulate the optimal step size v t∗ in time-varying channels, least-mean-square (LMS) algorithm can be applied to DSA [32], [33]. Besides the track of Xt∗ , we also need to optimize the optimal step size v t∗ in each step t. For DSA with adaptive step size, π t can be considered as a function with respect to v t and denoted as π v,t . Then, its v,t mean-square derivative with respect to v t is Jv,t = ∂π ∂v t by definition, namely, π v+∆,t − π v,t − Jv,t |2 } = 0. (17) ∆→0 ∆ Meanwhile, taking the partial of both sides of (10) with respect to v t , we can have lim E{|

Jv,t+1 = Jv,t + ǫv,t − v t Jv,t = (1 − v t )Jv,t + ǫv,t , v,t

t+1

(18)

t

where ǫ = ψ −π . The adaptive step size DSA is presented in Algorithm 2, + where η is denoted as the learning rate, and {a}vv− is the − + projection of real number a into interval [v , v ]. Algorithm 2 Adaptive DSA for Virtual Resource Allocation 1: 2: 3: 4: 5: 6: 7:

Initialization, sampling and acceptance as in Algorithm 1 Adaptive filter for updating state occupation probabilities ǫv,t ← ψ t+1 − π t π t+1 ← π t + v t ǫv,t + v t+1 ← {v t + ηǫv,t Jv,t }vv− Jv,t+1 ← (1 − v t )Jv,t + ǫv,t Output Xt∗

V. S IMULATION R ESULTS AND D ISCUSSIONS In this section, we present some simulation results to evaluate the performance of proposed algorithms. The following parameters are studied: 1) the number of users, 2) the access price ratio between MVNOs, and 3) the price ratio between traditional access and D2D communications. Two metrics,

8

(i) total utility of MVNOs and (ii) total reduced backhaul usage, are utilized as performance measurement. In addition, for performance comparison, the following four algorithms are presented: 1) the exhaustive searching algorithm with perfect CSI, 2) the DSA algorithm with imperfect CSI, 3) the exhaustive algorithm based on perfect CSI but without (w.o.) content caching, and 4) the exhaustive algorithm based on perfect CSI but w.o. D2D communications. A. System Parameters We investigate a time-slotted system consisting of one BS and 20 D2D transmitters. The radius of the cell is set to 500m. The clustered-based distribution model [37], where multiple users are located within one cluster with a radius of 50m, is adopted, since D2D communications typically occur within short ranges. In addition, assume that there are totally 5 kinds of contents distributed in the network, and each content can be held by the BS with a probability of 50%. For each D2D transmitter, there is a probability of 20% for it to hold any of these content. Likewise, it is assumed that each user requests for any content at a time with a probability of 20% equally. As such, ami j is eventually available. We further assume a Zipf popularity distribution with θ = 1.5 [29]. In the system, there are 20 subchannels, each of which has a bandwidth of 180KHz. The transmit powers of BS and D2D transmitter are 46dBm and 24dBm, respectively. As in [12], the path loss model 35.3 + 37.6 log(d(m)) is designated. The noise spectral density is -174dBm/Hz. As in [11], SCME channel model is adopted, where the carrier frequency is set as 2.11GHz, user velocity is 6Km/h, and sample duration is 1ms. In addition, block fading with a block size of 100 is assumed for channel fading. For measurement error, the CSI noise is assumed as a zero-mean normal variable with the standard deviation being 5% of the expectation. Additionally, two MVNOs (denoted as MVNO 1 and MVNO 2) can charge their subscribers at different prices to access the network. Meanwhile, subscribers are able to access the network via either cellular or D2D transmissions, which can have different access prices likewise. For simplicity, we only evaluate the effect of unit price βij on the metrics in the simulation, and set αmi = 10, γij = 1, φmi = 10, and ψmi = 1.5, ∀m, i, j, in the following. B. Effects of the Number of Users In this subsection, we compare the proposed scheme with other three algorithms under different numbers of users, ranging from 2 to 20. The adopted DSA is the adaptive step-size one as in Algorithm 2, in which the learning rate η is 0.8, the lower bound of ν is 0, and the upper bound of ν is 0.9. For simplicity and to overcome the effect of price, we set βij = 10 for all i ∈ I and j ∈ J0 . Fig. 3 shows the the total utility obtained by MVNOs with the increase of the number of users in the system. From Fig. 3, it is obvious that multi-user diversity gain can be obtained



9


×107

1011

Total utility of MVNOs (units)


2.8 Perfect CSI DSA w.o. caching w.o. D2D 1010

109

2.7

2.6

2.5 Perfect CSI DSA w.o. caching w.o. D2D

2.4

2.3

2.2 108

2

4

6

8

10

12

14

16

18

0

20

Fig. 3: Total utility of MVNOs under different numbers of users.

0.2

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Access price ratio between MVNO 1 and MVNO 2

Number of users

Fig. 5: Total utility of MVNOs vs. the price ratio between MVNO 1 and MVNO 2.

×107

×107

5 4.5 4 3.5

3 Perfect CSI DSA w.o. caching w.o. D2D

2.5

Total reduced backhaul usage (Mbps)


5.5 2.4

2.35

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2.25 Perfect CSI DSA w.o. caching w.o. D2D

2.2

2.15

2.1 2

4

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8

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0.2

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Access price ratio between MVNO 1 and MVNO 2

Fig. 4: Total reduced backhaul usage under different numbers of users.

Fig. 6: Total reduced backhaul usage vs. the price ratio between MVNO 1 and MVNO 2.

by introducing more users in different locations. Besides, the performance of DSA can approach that of the scheme with perfect CSI (which can be considered as the upper bound) within a 4% difference on average. It should be noted that in the scheme w.o. D2D, the caching functions only exist in BS and not in D2D users; by comparison, the scheme w.o. caching only lacks of caching capabilities in BS but can support multiple D2D pairs, and thus gets more utilities from the point of view of MVNOs. In particular, the scheme w.o. D2D almost remains constant with the increase of the number of users, since introducing more users makes no sense if D2D communications are forbidden. In Fig. 4, we compare the total reduced backhaul usage seen by MVNOs under different numbers of users. It is obvious that the value in the scheme w.o. D2D increases remarkably as the number of users ranges from 2 to 20, which can be explained as that a large proportion of gains in utilities stems from caching popular contents. Similarly, the scheme w.o. D2D gets the least backhaul bandwidth savings compared to other three schemes due to the non-existence of caching functions in D2D users.

C. Effects of Access Prices In this subsection, we compare the proposed scheme with other three schemes at different access prices. The impact of the price ratio between MVNO 1 and MVNO 2 is evaluated at first, followed by the ratio between traditional access and D2D communications, provided that the number of users with content requirement is 10. Fig. 5 and Fig. 6 show the performance of algorithms under different price ratio between MVNO 1 and MVNO 2, provided that the ratio between traditional access and D2D communications is set to 1 for each MVNO. From Fig. 5, it can be observed that the total utility of the schemes decreases as the price ratio increases, but with a decreasing change rate. The total utility of all schemes will converge except for the one w.o. D2D. That is because as the price ratio increases, InP will charge MVNO 1 more money for its subscribers to obtain services, thus decreasing the total utility. Fig. 6 illustrates the effect of the price ratio on the total reduced backhaul usage. From Fig. 6, it can be seen that the scheme w.o. D2D is independent of the price ratio. However, all other



10


Perfect CSI DSA w.o. caching w.o. D2D

2.75

6.5

×109

6



×10 7

2.7

2.65

2.6

2.55

5.5 5 4.5

Perfect CSI DSA w.o. caching w.o. D2D

4 3.5 3

2.5 0.2

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Price ratio between D2D communications and traditional access

2.5 0

100

200

300

400

500

600

700

800

900

1000

Iteration number

Fig. 7: Total utility of MVNOs vs. the price ratio between D2D communications and traditional access.

D. Convergence Performance In this subsection, we investigate the convergence performance of the schemes under static channels. There are 10 users distributed in the network, and the price ratio between MVNOs and between access modes are both set to 1. Fig. 9 shows the total utility of MVNOs. The standard deviation of CSI noise is 5% of the expectation of channel gains. The results corresponding to the aggressive DSA algorithm are averaged over 100 drops. From Fig. 9, it can be observed that the performance of the aggressive DSA algorithm can approach that of the scheme with perfect CSI with the increase of the number of iterations.


×10 7 Perfect CSI DSA w.o. caching w.o. D2D

2.2 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Fig. 9: Total utility of MVNOs under static channels.

2.0

Price ratio between D2D communications and traditional access

Fig. 8: Total reduced backhaul usage vs. the price ratio between D2D communications and traditional access.

three algorithms are sensitive to the variation of the price ratio. Fig. 7 and Fig. 8 illustrate the performance of schemes under different price ratio between traditional access and D2D communications, provided that the ratio between MVNO 1 and MVNO 2 is set to 1 for each access mode. Both in Fig. 7 and Fig. 8, the performance decreases with the increase of the price ratio, due to the fact that both MVNO 1 and MVNO 2 will charge their subscribers more fee to access the network since InP leases its physical resources to MVNOs at a higher price. Meanwhile, the scheme w.o. D2D remains unchanged when the price ratio varies; on the contrary, all other three schemes decrease with a decreasing change rate. In addition, in Fig. 8, the backhaul reduction of the scheme w.o. D2D exceeds that of the one w.o. caching, when the price ratio is greater than 0.6. That is due to the fact that as the D2D access price increases, even with the scheme w.o. caching (but w.o. D2D), more and more users begin to shift to the cellular access, resulting in lower and lower backhaul reduction. When the D2D access price is sufficiently high, the scheme w.o. caching can be lower than that w.o. D2D due to the non-existence of caching function in the BS.

VI. C ONCLUSION AND F UTURE W ORK In this paper, we studied software-defined informationcentric cellular network virtualization with D2D communications. First, we developed a framework that supports both both information-centric wireless virtualization and D2D communications by means of SDN technology. Then, in the proposed framework, we considered the virtual resource allocation optimization to maximize the total utility seen by all MVNOs. Different from the existing works, we formulated the radio resource allocation and caching decision not only in the air but also in mobile devices. In addition, due to the inaccurate channel estimation and measurement, the virtual resource allocation and caching optimization was formulated as a discrete stochastic optimization problem, where imperfect CSI is taken into account. To tackle this large-scale combinational optimization problem, we exploited DSA-based schemes to overcome the impact of channel estimation error, considering both static channels and time-varying channels. Extensive simulation results showed that MVNOs can benefit from both information-centric wireless virtualization and D2D communications, and the proposed schemes can achieve nearoptimal performance and good convergence property. R EFERENCES [1] C. Liang and F. R. Yu, “Wireless network virtualization: A survey, some research issues and challenges,” IEEE Commun. Surveys Tutorials, vol. 17, no. 1, pp. 358–380, Firstquarter 2015.




[2] C. Liang, F. R. Yu, and X. Zhang, “Information-centric network function virtualization over 5g mobile wireless networks,” IEEE Network, vol. 29, no. 3, pp. 68–74, May 2015. [3] R. Kokku, R. Mahindra, H. Zhang, and S. Rangarajan, “NVS: A substrate for virtualizing wireless resources in cellular networks,” ACM/IEEE Trans. Networking, vol. 20, no. 5, pp. 1333–1346, Oct. 2012. [4] A. Khan, A. Zugenmaier, D. Jurca, and W. Kellerer, “Network virtualization: a hypervisor for the Internet?” IEEE Commun. Mag., vol. 50, no. 1, pp. 136–143, Jan. 2012. [5] T. Forde, I. Macaluso, and L. Doyle, “Exclusive sharing & virtualization of the cellular network,” in Proc. IEEE Symp. on New Frontiers in Dynamic Spectrum Access Net. (DySPAN), May 2011, pp. 337–348. [6] C. Liang and F. R. Yu, “Wireless virtualization for next generation mobile cellular networks,” IEEE Wireless Commun., vol. 22, no. 1, pp. 61–69, Feb. 2015. [7] G. Xylomenos, C. Ververidis, V. Siris, N. Fotiou, C. Tsilopoulos, X. Vasilakos, K. Katsaros, and G. Polyzos, “A survey of informationcentric networking research,” IEEE Commun. Surveys Tutorials, vol. 16, no. 2, pp. 1024–1049, Secondquarter 2014. [8] B. Ahlgren, C. Dannewitz, C. Imbrenda, D. Kutscher, and B. Ohlman, “A survey of information-centric networking,” IEEE Commun. Mag., vol. 50, no. 7, pp. 26–36, July 2012. [9] N. Golrezaei, K. Shanmugam, A. Dimakis, A. Molisch, and G. Caire, “Femtocaching: Wireless video content delivery through distributed caching helpers,” in Proc. IEEE INFOCOM, Mar. 2012, pp. 1107–1115. [10] C. Fang, F. R. Yu, T. Huang, J. Liu, and Y. Liu, “A survey of green information-centric networking: Research issues and challenges,” IEEE Comm. Surveys Tutorials, vol. 17, no. 3, pp. 1455–1472, Thirdquarter 2015. [11] Y. Cai, F. R. Yu, and C. Liang, “Resource sharing for software defined D2D communications in virtual wireless networks with imperfect nsi,” in Proc. IEEE Globecom, Dec. 2014, pp. 4448–4453. [12] D. H. Lee, K. W. Choi, W. S. Jeon, and D. G. Jeong, “Two-stage semidistributed resource management for device-to-device communication in cellular networks,” IEEE Trans. Wireless Commun., vol. 13, no. 4, pp. 1908–1920, Apr. 2014. [13] G. Liu, F. R. Yu, H. Ji, V. Leung, and X. Li, “In-band full-duplex relaying: A survey, research issues and challenges,” IEEE Commun. Surveys Tutorials, vol. 17, no. 2, pp. 500–524, Secondquarter 2015. [14] X. Wang, M. Chen, T. Taleb, A. Ksentini, and V. Leung, “Cache in the air: exploiting content caching and delivery techniques for 5g systems,” IEEE Commun. Mag., vol. 52, no. 2, pp. 131–139, Feb. 2014. [15] C. Bernardos, A. De La Oliva, P. Serrano, A. Banchs, L. Contreras, H. Jin, and J. Zuniga, “An architecture for software defined wireless networking,” IEEE Wireless Commun., vol. 21, no. 3, pp. 52–61, Jun. 2014. [16] B. Nunes, M. Mendonca, X.-N. Nguyen, K. Obraczka, and T. Turletti, “A survey of software-defined networking: Past, present, and future of programmable networks,” IEEE Commun. Surveys Tutorials, vol. 16, no. 3, pp. 1617–1634, Thirdquarter 2014. [17] W. H. Chin, Z. Fan, and R. Haines, “Emerging technologies and research challenges for 5G wireless networks,” IEEE Wireless Commun., vol. 21, no. 2, pp. 106–112, Apr. 2014. [18] N. A. Jagadeesan and B. Krishnamachari, “Software-defined networking paradigms in wireless networks: A survey,” ACM Computing Surveys, vol. 47, no. 2, p. 27, Jan. 2014. [19] S. Andradottir, “A global search method for discrete stochastic optimization,” SIAM J. Optimiz., vol. 6, no. 2, pp. 513–530, May 1996. [20] T. H. de Mello, “Variable-sample methods for stocahstic optimization,” ACM Trans. Model. Comput. Simul., vol. 13, no. 2, pp. 108–133, Apr. 2003. [21] Y. Cai, F. R. Yu, C. Liang, B. Sun, and Q. Yan, “Software defined device-to-device (D2D) communications in virtual wireless networks

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with imperfect network state information (NSI),” IEEE Trans. Veh. Tech., 2015, dOI:10.1109/TVT.2015.2483558. Q. Yan, F. R. Yu, Q. Gong, and J. Li, “Software-defined networking (SDN) and distributed denial of service (DDoS) attacks in cloud computing environments: A survey, some research issues, and challenges,” IEEE Commun. Survey and Tutorials, vol. 18, no. 1, pp. 602–622, 2016. Q. Yan and F. R. Yu, “Distributed denial of service attacks in softwaredefined networking with cloud computing,” IEEE Commun. Mag., vol. 53, no. 4, pp. 52–59, Apr. 2015. L. Cui, F. R. Yu, and Q. Yan, “When big data meets software-defined networking (SDN): SDN for big data and big data for SDN,” IEEE Network, vol. 30, no. 1, pp. 58–65, Jan. 2016. “Proximity-based services (ProSe); Stage 2,” 3rd Generation Partnership Project (3GPP), Sophia-Antipolis, France, TS 23.303 V12.3.0, Dec. 2015. M. Hoffmann and M. Staufer, “Network virtualization for future mobile networks: General architecture and applications,” in Proc. IEEE Int. Conf. Commun. (ICC), Jun. 2011, pp. 1–5. K. Son, S. Lee, Y. Yi, and S. Chong, “Refim: A practical interference management in heterogeneous wireless access networks,” IEEE J. Sel. Areas Commun., vol. 29, no. 6, pp. 1260–1272, Jun. 2011. G. Liu, H. Ji, F. R. Yu, Y. Li, and R. Xie, “Energy-efficient resource allocation in full-duplex relaying networks,” in Proc. IEEE Int. Conf. Commun. (ICC), Jun. 2014, pp. 2400–2405. P. Blasco and D. Gunduz, “Learning-based optimization of cache content in a small cell base station,” in Proc. IEEE Int. Conf. Commun. (ICC), Jun. 2014, pp. 1897–1903. M. Awad, V. Mahinthan, M. Mehrjoo, X. Shen, and J. Mark, “A dual-decomposition-based resource allocation for ofdma networks with imperfect csi,” IEEE Trans. Veh. Tech., vol. 59, no. 5, pp. 2394–2403, Jun. 2010. N. Mokari, K. Navaie, and M. Khoshkholgh, “Downlink radio resource allocation in OFDMA spectrum sharing environment with partial channel state information,” IEEE Trans. Wireless Commun., vol. 10, no. 10, pp. 3482–3495, Oct. 2011. I. Berenguer, X. Wang, and V. Krishnamurthy, “Adaptive MIMO antenna selection via discrete stochastic optimization,” IEEE Trans. Signal Process., vol. 53, no. 11, pp. 4315–4329, Nov. 2005. R. Xie, F. R. Yu, and H. Ji, “Dynamic resource allocation for heterogeneous services in cognitive radio networks with imperfect channel sensing,” IEEE Trans. Veh. Technol., vol. 61, no. 2, pp. 770–780, Feb. 2012. V. Krishnamurthy, X. Wang, and G. Yin, “Spreading code optimization and adaptation in CDMA via discrete stochastic approximation,” IEEE Trans. Inform. Theory, vol. 50, no. 9, pp. 1927–1949, Sept. 2004. Q. Guan, F. R. Yu, S. Jiang, and V. Leung, “Capacity-optimized topology control for manets with cooperative communications,” IEEE Trans. Wireless Commun., vol. 10, no. 7, pp. 2162–2170, July 2011. G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics. John Wiley & Sons Inc., Apr. 1986. B. Kaufman and B. Aazhang, “Cellular networks with an overlaid device to device network,” in Proc. Asilomar Conf. Signals, Systems & Computers (ACSSC), Oct. 2008, pp. 1537–1541.




Kan Wang received the B.S. degree in broadcasting and television engineering from Zhejiang University of Media and Communications, Hangzhou, China, in 2009. He is currently working toward the Ph.D. degree in military communications with the State Key Lab of ISN, Xidian University, Xi’an, China. From Oct. 2014 to Oct. 2015, he was also with Carleton University, Ottawa, ON, Canada, as a visiting scholar funded by China Scholarship Council (CSC). His current research interests include 5G cellular networks, resource management, and interference alignment.

12

Wenchao Wei is currently with Shanghai Aerospace Electronic Technology Institute, Shanghai, China. His research interests include satellite data system design, space data processing, and space-based telemetry & telecontrol technology.

Hongyan Li (M’08) received the M.S. degree in control engineering from Xi’an Jiaotong University, Xi’an, China, in 1991 and the Ph.D. degree in signal and information processing from Xidian University, Xi’an, in 2000. She is currently a Professor with the State Key Laboratory of Integrated Service Networks, Xidian University. Her research interests include wireless networking, cognitive networks, integration of heterogeneous network, and mobile ad hoc networks.

F. Richard Yu (S’00-M’04-SM’08) received the PhD degree in electrical engineering from the University of British Columbia (UBC) in 2003. From 2002 to 2006, he was with Ericsson (in Lund, Sweden) and a start-up in California, USA. He joined Carleton University in 2007, where he is currently an Associate Professor. He received the IEEE Outstanding Leadership Award in 2013, Carleton Research Achievement Award in 2012, the Ontario Early Researcher Award (formerly Premiers Research Excellence Award) in 2011, the Excellent Contribution Award at IEEE/IFIP TrustCom 2010, the Leadership Opportunity Fund Award from Canada Foundation of Innovation in 2009 and the Best Paper Awards at IEEE ICC 2014, Globecom 2012, IEEE/IFIP TrustCom 2009 and Int’l Conference on Networking 2005. His research interests include cross-layer/cross-system design, security, green IT and QoS provisioning in wireless-based systems. He serves on the editorial boards of several journals, including Co-Editorin-Chief for Ad Hoc & Sensor Wireless Networks, Lead Series Editor for IEEE Transactions on Vehicular Technology, IEEE Communications Surveys & Tutorials, EURASIP Journal on Wireless Communications Networking, Wiley Journal on Security and Communication Networks, and International Journal of Wireless Communications and Networking. He has served as the Technical Program Committee (TPC) Co-Chair of numerous conferences. Dr. Yu is a registered Professional Engineer in the province of Ontario, Canada.


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