Joint Access Selection and Resource Allocation in Cache-Enabled ...

Joint Access Selection and Resource Allocation in Cache-enabled HCNs with D2D Communications Zhiyuan Tan∗ , Xi Li∗ , F. Richard Yu† , Lei Chen∗ , Hong Ji∗ , and Victor C.M. Leung‡ ∗ Key

Lab. of Universal Wireless Comm., Ministry of Education, Beijing Univ. of Posts and Telecom., P.R. China † Depart. of Systems and Computer Eng., Carleton Univ., Ottawa, ON, Canada ‡ Depart. of Electrical and Computer Eng., The Univ. of British Columbia, Vancouver, BC, Canada

Abstract—With the explosive increase of wireless data traffic, caching is regarded as a promising technology to combine with heterogeneous cellular networks (HCNs), which can offload cellular traffic and improve the system performance effectively. In this paper, we investigate the communication scenario about cacheenabled HCNs with device-to-device (D2D) communications. Both small cell base stations (SBSs) and D2D user equipments (DUEs) have the caching hardware that can store popular contents to serve users locally. With the caching technology introduced, heavy traffic load in the HCNs could be relieved and the request latency could be decreased, which results in better user experience. Meanwhile, due to the constraints of the limited resource, access selection of users and resource allocation are two significant problems that need to be carefully studied. Thus, we propose a novel scheme to study the access selection and resource allocation jointly. First, we formulate the access selection, spectrum allocation as a joint optimization problem to maximize the system capacity, where bandwidth resource is allocated flexibly and the quality of service (QoS) of users is satisfied. Since the original problem is a mixed combinatorial problem, which is a non-convex optimization, an efficient solution is proposed to transfer the original problem to a convex problem so as to reduce computational complexity. In the simulation, we compare our scheme with other three schemes. Simulation results are presented to validate the effectiveness of our proposed scheme. Index Terms—Caching, D2D communication, small cell, access selection, resource allocation

I. I NTRODUCTION With the rapid development of mobile communications, wireless traffic has experienced a tremendous growth [1]. Especially, increasing smartphone usage is resulting in an exponential growth in mobile multimedia traffic, which has brought an unprecedented challenge in the demand for radio resources [2]–[5]. In the conventional heterogeneous cellular networks (HCNs), pico and femtocell base station deployment can promote the network capacity and improve spectrum efficiency and energy efficiency [6]–[8], but the limited capacity of the backhaul link becomes the major bottleneck to hinder the development of HCNs. Device-to-device (D2D) communications underlaying cellular networks, as a method to offload traffic from the cellular base station, have attracted great interests from academia and industry [9]–[14]. Instead of accessing base stations (BSs), mobile users can directly communicate with each other via

D2D links. Due to the proximity of pair users in D2D links, low transmission delay and high data rate can be obtained. Another technology is caching, which can cache popular contents at the mobile network edge nodes to effectivly serve users locally [15]–[17]. Thus, backhaul resource can be saved, request delay can be decreased, and system gain can be obtained significantly [18]. In caching enabled wireless networks, small cell base station (SBS)-enabled caching and D2D-enabled caching have been perceived as two significant ways for centent delivery [19]. Femto-caching is studied in [20], where a distributed scheme is provided to select the proper contents to cache in the corresponding locations. The authors of [21] investigate how to maximize the content sharing in D2D communications to offload cellular traffic. By caching popular content selectively and collaboratively caching, the system capacity can be improved significantly. In [22], a small cell video caching system is proposed and game theory is adopted to achieve pricing and resource allocation. Although some excellent works have been done on HCNs, D2D communications, and caching, few attentions have been payed to the resource allocation issue in cache-enabled HCNs with D2D communications. Moreover, with caching introduced, users have more access selections for the interested contents. And it is very necessary to design an optimal access scheme for users. As we all know, the advantages of small cells and D2D communications could reduce the communication distance among users and offload the cellular traffic. And there is no doubt that cache-enabled nodes including SBSs and D2D user equipments (DUEs) can improve the system capacity and save the backhaul resource obviously. As a result, it is meaningful to consider caching in HCNs with D2D communications. And it is very necessary to jointly consider user access selection and resource allocation problem in cacheenabled HCNs with D2D communications. So in this scenario, with the flexible access selection and the limited resource, how to achieve the optimal access selection and resource allocation becomes a key problem. In this paper, the communication scenario with caching is investigated in HCNs with D2D communications. Then a corresponding scheme jointly optimizing access selection and resource allocation is proposed to maximize the system performance. The contributions of this paper are summarized as follows:

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Fig. 1. A cache-enabled heterogeneous cellular network with D2D communications.

We consider a novel communication scenario that enables caching in HCNs with D2D communications. Specifically, the SBS and DUE have the caching capabilities, and the popular contents can be cached to serve the local users. ∙ Different from existing works, in this paper, we focus on how to choose the optimal transmitter (i.e., D2D transmitter, SBS or MBS) based on the cached contents and requirements of users. Moreover, we propose a joint access selection and resource allocation scheme where the selection of users is optimized and bandwidth resource is allocated to satisfy users’ QoS requirements. ∙ We formulate the system utility function by setting different price coefficients. Due to the non-convexity of original problem, we transfer the original problem to a convex problem by relaxing the corresponding variables and reformulation. Then a feasible solution is provided to solve the proposed problem. Simulation results are presented to show the superiority of our scheme. The rest of this paper is organized as follows. In Section II, we describe the system model and problem formulation. Then the problem solution is presented in Section III. In Section IV, we discuss the simulation results. Finally, conclusions are drawn in Section V. ∙

II. S YSTEM M ODEL AND P ROBLEM F ORMULATION In this section, we present the system model for cacheenabled heterogeneous cellular networks with D2D communications. Then the problem formulation with resource allocation constraints is presented. A. System Model Fig. 1 shows a HCN with D2D communications. Different from conventional HCNs, content caching technology is intro-

duced in SBSs and user equipments (UEs), namely, the nodes including SBS and UEs have the caching capabilities. While the SBS has a large caching capacity to cache the popular content, UE has a relatively smaller one. Thus, when a user wants to obtain its interested content, there are three kind of transmitters to provide service for users, which are macro base station (MBS), SBS, and UEs. When the caching of UE or SBS has the requested content locally, a local communication can be established, such as D2D communications like the link between UE1 and UE2, or a direct communication link between UE3 and SBS1. Otherwise, UEs can retrieve the content from core network via MBS, like UE4. Thus, a complete communication system is established. In this paper, we consider the scenario of a single cell in a HCN, where there are some SBSs and some UEs within the scope of coverage of each SBS. The set of users with demand is denoted by 𝑈𝑟 = {1, ..., 𝑀 }. Let 𝑈𝑡 = {1, ..., 𝑁 } be the set of users with the desired contents, which are regarded as D2D transmitters. Similarly, 𝑈𝑠 = {1, ..., 𝐴} denotes the set of SBSs. User 𝑖 ∈ 𝑈𝑟 can communicate with SBS (which can be indexed by 𝑗, 1 ≤ 𝑗 ≤ 𝐴 ) for interested content delivery, or other users (indexed by 𝑘, 1 ≤ 𝑘 ≤ 𝑁 ) with D2D communications. If a local communication is failed (maybe the content is not found in the caching or requests from different users to the same user make collisions), then the user can access to the MBS (which can be indexed by 𝑗 = 0) for the content. We consider two cellular communication modes taking place in the downlink (DL) transmissions, while D2D communications are used for uplink (UL) transmissions. It is because that contents are typically delivered by BSs to users. Meanwhile, D2D communications in the UL can avoid the interference to other users, and the interference suffered by BS is easy to mitigate [23]. Thus, partial frequency division multiplexing is adopted for bandwidth resource allocation among MBS and SBSs. The total downlink bandwidth is allocated to MBS and SBSs in proportion and the bandwidth resource is shared among SBSs. Due to the smaller transmit power of SBS, the intra-interference among SBSs can be ignored. In addition, the mutual interference between BSs and UEs can be avoided with orthogonal spectrum scheme. B. Problem Formulation In this section, we discuss the problem and make some conditional assumptions. Then the resource allocation constraints are discussed. Then, the utility function is formulated to maximize the system benefits. 1) Conditional Assumption: Due to the fact that the requested contents often can be cached in many nodes, many nodes (DUEs or SBSs) can serve requesters. However, in order to avoid request conflicts, we consider that a requester can only be served by a transmitter and a DUE transmitter can only serve one user. So whether to communicate with SBS/MBS or to establish D2D communications is a vital problem. In addition, please note that how to achieve optimal content caching and caching update scheme

is not involved in this paper. And we assume that the global information about content caching is known in the MBS and a centralized scheduling can be efficiently completed with the assist of software defined network [24]–[27]. Therefore, we focus on how to choose access node and allocate resource to nodes to achieve the maximization of total utility under the condition of knowing the global information. 2) Constraints: Let 𝑥𝑖𝑗 ∈ {0, 1} be the binary variable, where 𝑥𝑖𝑗 equals to one when user 𝑖 is associated with SBS 𝑗 and 𝑥𝑖𝑗 equals to zero otherwise. Similarly, 𝑥𝑖0 ∈ {0, 1} and 𝑥𝑖𝑘 ∈ {0, 1} denote the association between user 𝑖 and MBS or DUE, respectively. Constraint 1 and 2 are access selection constraints. It is considered that every requester can only be served by a transmitter, which is shown as ∑ ∑ 𝑥𝑖𝑗 + 𝑥𝑖𝑘 ≤ 1, ∀𝑖 ∈ 𝑈𝑟 . (1) 𝐶1 : 𝑥𝑖0 + 𝑗∈ 𝑈𝑠

𝑘∈ 𝑈𝑡

Similarly, for D2D communications, only one requester can be linked with one transmitter, which can be formulated as ∑ 𝐶2 : 𝑥𝑖𝑘 ≤ 1, ∀𝑘 ∈ 𝑈𝑡 . (2) 𝑖∈ 𝑈𝑟

Then let 𝑦𝑖𝑗 ∈ [0, 1] denote the fraction indicator of base station bandwidth 𝐵𝑗 , and the downlink bandwidth allocation constraint is formulated as ∑ ∑ 𝐶3 : 𝑥𝑖𝑗 𝑦𝑖𝑗 𝐵𝑗 ≤ 𝐵𝑑𝑙 . (3) 𝑖∈ 𝑈𝑟 𝑗∈ 𝑈𝑠

and D2D pairs bandwidth allocation constraint is formulated as ∑ ∑ 𝐶4 : 𝑥𝑖𝑘 𝑦𝑖𝑘 𝐵𝑘 ≤ 𝐵𝑢𝑙 . (4) 𝑖∈ 𝑈𝑟 𝑘∈ 𝑈𝑡

Then we define an indicating variable 𝑧𝑖𝑗 to describe the content caching results. Here, 𝑧𝑖𝑗 = 1 denotes that node 𝑗 has the desired content of user 𝑖 ,otherwise, 𝑧𝑖𝑗 = 0. As mentioned above, this information has been known as whole information to restrict the resource allocation. Meanwhile, user’s minimum transmission rate should be satisfied, which shown as ∑ 𝑥𝑖𝑗 𝑦𝑖𝑗 𝑧𝑖𝑗 𝐵𝑗 𝑟𝑖𝑗 𝐶5 :𝑥𝑖0 𝑦𝑖0 𝑧𝑖0 𝐵0 𝑟0 + +

∑

𝑗∈ 𝑈𝑠

𝑥𝑖𝑘 𝑦𝑖𝑘 𝑧𝑖𝑘 𝐵𝑘 𝑟𝑖𝑘 ≥ 𝑅𝑖 , ∀𝑖 ∈ 𝑈𝑟 ,

(5)

𝑘∈ 𝑈𝑡

where 𝑅𝑖 is the minimum data transmission rate to satisfy QoS requirement of user 𝑖. 𝑟𝑖𝑗 and 𝑟𝑖𝑘 is the transmission rate between user 𝑖 and node 𝑗 or user 𝑘 per unit bandwidth using the Shannon equation, respectively. 3) Utility Function: Firstly, we denote 𝛼𝑖 as the gain coefficient of received data rate user 𝑖. And let 𝑐0 , 𝑐1 and 𝑐2 denote the use price coefficient of the MBS, SBS and D2D communications for using system bandwidth. After comprehensively considering resources consumption which includes consumed radio bandwidth and backhaul bandwidth and caching resource, we can approximately see that three loss coefficients satisfy

𝑐0 > 𝑐1 > 𝑐2 . In comparison with MBS using radio bandwidth and backhaul bandwidth, SBS and D2D using radio bandwidth and caching resource, can save a lot of backhaul bandwidth. Backhaul resource is very scarce at present but caching resource is enough. In a simply, let 𝑄𝑖 denote the cost of user 𝑖 for using system bandwidth resource. Since the communication mode of user is not sure, the cost of the user 𝑖 can be expressed as 𝑄𝑖 = 𝑐0 𝑥𝑖0 𝐵0 + 𝑐1 𝑥𝑖𝑗 𝐵𝑗 + 𝑐2 𝑥𝑖𝑘 𝐵𝑘 .

(6)

Similarly, the gain of user is formulated as ∑ 𝐺𝑖 = 𝛼𝑖 {𝑥𝑖0 𝑦𝑖0 𝑧𝑖0 𝐵0 𝑟0 + 𝑥𝑖𝑗 𝑦𝑖𝑗 𝑧𝑖𝑗 𝐵𝑗 𝑟𝑖𝑗 + 𝑗∈ 𝑈𝑠

∑

𝑥𝑖𝑘 𝑦𝑖𝑘 𝑧𝑖𝑘 𝐵𝑘 𝑟𝑖𝑘 },

(7)

𝑘∈ 𝑈𝑡

where 𝑦𝑖0 is the user resource allocation indicator. In order to guarantee the fairness during the resource allocation process, we can change the utility of the user 𝑖 as follows by adopting the method in [28], [29], ∑ 𝐺′𝑖 = 𝛼𝑖 {𝑥𝑖0 log(𝑦𝑖0 𝑧𝑖0 𝐵0 𝑟0 ) + 𝑥𝑖𝑗 log(𝑦𝑖𝑗 𝑧𝑖𝑗 𝐵𝑗 𝑟𝑖𝑗 )+ 𝑗∈ 𝑈𝑠

∑

𝑥𝑖𝑘 log(𝑦𝑖𝑘 𝑧𝑖𝑘 𝐵𝑘 𝑟𝑖𝑘 )}.

𝑘∈ 𝑈𝑡

(8) The utility function of the system 𝑈𝑖 is the value that equals to system gain subtracting system cost, which is formulated as 𝑈𝑖 = 𝐺′𝑖 − 𝑄𝑖 . (9) So, the optimization problem of this scheme in the scenario is shown ∑ max 𝑈𝑖 𝑥𝑖𝑗 ,𝑥𝑖0 ,𝑥𝑖𝑘 ,𝑦𝑖𝑗

𝑖∈𝑈𝑟

s.t. 𝐶1 − 𝐶5, 𝐶6 : 𝑥𝑖𝑗 ∈ {0, 1}, 𝐶7 : 𝑥𝑖0 ∈ {0, 1},

(10)

𝐶8 : 𝑥𝑖𝑘 ∈ {0, 1}. which is a mixed binary inter programming problem with continuous and binary variables. III. P ROBLEM R EFORMULATION AND S OLUTION A. Problem Analysis With the system model described above, we can analyze the characteristic of problem (10). 𝑥𝑖∗ (* means 𝑗, 𝑘 ) is binary variable so that the feasible set of problem (10) is non-convex. The objective function is not convex due to the product relationship between 𝑥𝑖∗ and 𝑦𝑖∗ . And 𝑦𝑖∗ is the continuous variables, the joint consideration of 𝑥𝑖∗ 𝑦𝑖∗ increases the complexity of the solution. We all know that a mixed discrete and non-convex optimization problem is expected to be very challenging to find its global optimum. Thus, we have to simplify problem (10).

B. Problem Reformulation

C. Problem Solution

First, following the approach in [28], we relax 0-1 variables such that 𝑥𝑖𝑗 ∈ [0, 1] 𝑥𝑖0 ∈ [0, 1] 𝑥𝑖𝑘 ∈ [0, 1]. This can be regarded as the time sharing factor that represents the ratio of time when user 𝑖 associate with user 𝑘 , SBS 𝑗 or MBS. However, the problem is still non-convex after the relaxing the variables. To make the problem tractable and solvable, a second step is necessary. Next, a proposition of problem (10) is presented. 𝑤 Proposition: if we define 𝑤𝑖𝑗 = 𝑥𝑖𝑗 𝑦𝑖𝑗 , ∀𝑖 and 𝑥𝑖𝑗 log 𝑥𝑖𝑗𝑖𝑗 = 0 for 𝑥𝑖𝑗 = 0, there exists an equivalent formulation of problem (10) as shown in (11). {𝑤 𝑖𝑗 if 𝑥𝑖𝑗 > 0, 𝑦𝑖𝑗 = 𝑥𝑖𝑗 (11) 0 if 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒.

As we know, if problem is feasible, it is jointly convex with respect to all optimization variables 𝑥𝑖∗ and 𝑤𝑖∗ . Based on this and optimal problem (19), the convexity of the problem will be proved. Since the constraints 𝐶1, 𝐶2, 𝐶3′ − 𝐶8′ are linear, they are convex. The utility function is composed of two parts, which are 𝐺′𝑖 and 𝑄𝑖 . Due to the principle that the linear sum of the convex functions is still convex [30], we just need to prove the convexity 𝐺′𝑖 of and 𝑄𝑖 . Obviously, the convexity of 𝑄𝑖 is tenable because of the linear relationship. Then the convexity of 𝐺′𝑖 is proved as [31], which is presented as follows. Firstly, the continuity of function 𝑓 (𝑡, 𝑥) = 𝑥 log(𝑡/𝑥), 𝑡 ≥ 0, 𝑥 ≥ 0 is proved at the point of 𝑥 = 0. Let 𝑠 = 𝑡/𝑥, then 𝑓 (𝑡, 0) = lim 𝑥 log 𝑥𝑡 = lim 𝑠𝑡 log 𝑠 = 𝑡 lim log𝑠 𝑠 = 0. So function 𝑠→∞ 𝑠→∞ 𝑥→0 𝑓 (𝑡, 𝑥) = 𝑥 log(𝑡/𝑥), 𝑡 ≥ 0, 𝑥 ≥ 0 is the well-known perspective operation of logarithmic function, and the perspective function of a convex function is also a convex function based on [10]. Since the 𝑥𝑖∗ log 𝑤𝑖∗ /𝑥𝑖∗ (∗ = 0, 𝑗, 𝑘) is the perspective function of log 𝑤𝑖∗ , and the function log 𝑤𝑖∗ is convex about 𝑤𝑖∗ , so 𝑥𝑖∗ log 𝑤𝑖∗ /𝑥𝑖∗ is convex. Thus, we conclude that 𝐺′𝑖 is a convex function. Finally, the utility function is a linear sum of convex problems. Combined with the fact that the constraints are convex, the convexity of the optimization problem is proved. Since problem in (19) is a convex problem, a lot of methods can be used for solving convex problem, such as interior point method or dual decomposition [30]. Then Lagrangian multiplier method is chosen to solve the convex problem. Due to the limited length of paper, the method is not described in detail here.

Then the origin problem is transferred by substitution of variable 𝑤𝑖𝑗 = 𝑥𝑖𝑗 𝑦𝑖𝑗 into problem (10) except 𝑥𝑖𝑗 = 0. Due to the loss of definition when 𝑥𝑖𝑗 = 0, it is not one-to-one mapping. However, the 𝑥𝑖𝑗 = 0 must hold because of the optimality. Obviously, no resource is allocated to user if the user has no association with the others. Based on formula (11), then formula (8) is transformed as follows: ∑ 𝑤𝑖0 𝑤𝑖𝑗 𝑧𝑖0 𝐵0 𝑟0 ) + 𝑥𝑖𝑗 log( 𝑧𝑖𝑗 𝐵𝑗 𝑟𝑖𝑗 ) 𝐺𝑖 =𝑥𝑖0 log( 𝑥𝑖0 𝑥𝑖𝑗 𝑗∈𝑈𝑠 ∑ 𝑤𝑖𝑘 + 𝑥𝑖𝑘 log( 𝑧𝑖𝑘 𝐵𝑘 𝑟𝑖𝑘 ). 𝑥𝑖𝑘 𝑘∈𝑈𝑡 (12) Constraints 𝐶3 − 𝐶8 can be rewritten as 𝐶3′ − 𝐶8′ . ∑ ∑ 𝐶3′ : 𝑤𝑖𝑗 𝐵𝑗 ≤ 𝐵𝑑𝑙 , (13) 𝑖∈ 𝑈𝑟 𝑗∈ 𝑈𝑠

′

𝐶4 :

∑ ∑

𝑤𝑖𝑘 𝐵𝑘 ≤ 𝐵𝑢𝑙 ,

𝑖∈ 𝑈𝑟 𝑘∈ 𝑈𝑡

𝐶5′ :𝑤𝑖0 𝑧𝑖0 𝐵0 𝑟0 + +

∑

𝑤𝑖𝑗 𝑧𝑖𝑗 𝐵𝑗 𝑟𝑖𝑗

𝑗∈𝑈𝑠

∑

(14)

𝑤𝑖𝑘 𝑧𝑖𝑘 𝐵𝑘 𝑟𝑖𝑘 ≥ 𝑅𝑖 , ∀𝑖 ∈ 𝑈𝑟 ,

(15)

𝑘∈𝑈𝑡

𝐶6′ : 𝑥𝑖𝑗 ∈ [0, 1],

(16)

𝐶7′ : 𝑥𝑖0 ∈ [0, 1],

(17)

𝐶8′ : 𝑥𝑖𝑘 ∈ [0, 1].

(18)

Finally, the optimization problem is formulated as ∑ max 𝑈𝑖 (𝑥𝑖𝑗 ,𝑦𝑖𝑗 )

𝑖∈𝑈𝑟

s.t. 𝐶1, 𝐶2, 𝐶3′ , 𝐶4′ , 𝐶5′ , 𝐶6′ , 𝐶7′ , 𝐶8′ .

(19)

IV. S IMULATION R ESULTS AND D ISCUSSIONS In this section, the performance in our proposed scheme is shown using computer simulations. The performance is mainly considered from two aspects: the number of users and the minimal required data rate per user. Meanwhile, the performance of our proposed scheme is compared with the followed schemes: (a) Scheme 1 only with SBS caching but without D2D, which is similar to that in [32]; (b) Scheme 2 only with SBS and D2D but without caching, which is similar to that in [23] ; (c) Scheme 3 without D2D or caching, which is referred as [33]. And the metrics of performance are measured through the system utility and system cost. In the simulation, we consider a single cell with a MBS located at the center of the cell and five SBSs following a random distribution. The area is covered with a radius of 500𝑚 where devices are uniformly randomly distributed. The transmit power of MBS, SBS and D2D user are 46𝑑𝐵𝑚, 20𝑑𝐵𝑚, and 14𝑑𝐵𝑚, respectively [29]. And the D2D communication maximum distance is 50𝑚 and the available bandwidth of downlink and uplink are 3𝑀 𝐻𝑧 and 1.5𝑀 𝐻𝑧. Then we take that the value of 𝑐0 , 𝑐1 and 𝑐2 are 45𝑢𝑛𝑖𝑡𝑠/𝑀 𝐻𝑧 , 25𝑢𝑛𝑖𝑡𝑠/𝑀 𝐻𝑧 and 15𝑢𝑛𝑖𝑡𝑠/𝑀 𝐻𝑧. And gain coefficient 𝛼𝑖 is 5 × 107 𝑢𝑛𝑖𝑡𝑠/𝑏𝑝𝑠 for simplicity. The downlink bandwidth

7

7

7

x 10

7 Proposed scheme Scheme1 Scheme2 Scheme3

6

5 System Utility [units]

System Utility [units]

Proposed scheme Scheme1 Scheme2 Scheme3

6

5

4

3

4

3

2

2

1

1

0

x 10

0

5

10

15 20 25 Number of requesters

30

35

40

Fig. 2. System utility versus the number of requesters.

0 100

150

200 250 300 350 400 Minimal Requied Transmission Rate [kbps]

450

500

Fig. 4. System utility versus the minimal required transmission rate (the number of receivers is 40).

7

18

x 10

Proposed scheme Scheme1 Scheme2 Scheme3

16

System Cost [units]

14 12 10 8 6 4 2 0

0

5

10

15 20 25 Number of requesters

30

35

40

Fig. 3. System cost versus the number of requesters.

resource is allocated to MBS and SBSs. The D2D communications can leverage all uplink bandwidth resource. Fig. 2 shows the impact of the number of requesters on system utility in the three different schemes. It is assumed that the number of D2D transmitters is 20. And the minimal transmission rate of each user is 100𝐾𝑏𝑝𝑠. From Fig. 2, we can see that the system utility increases as the number of the requesters increases. And our proposed scheme is superior to other three schemes. It can be easily understood that our scheme can achieve the better local communication containing D2D communications and SBSs due to caching. Meanwhile, resource can be reasonably allocated and fully utilized to improve system gain. In the other three schemes, more users associate with cellular network causing to more spectrum and backhaul consumption. The system gain significantly decreases. Among the three comparison schemes, the system performance ordered in descend is scheme 1, scheme 2 and scheme 3. Scheme 3 means each user can only associate

the heterogeneous cellular network which causes the worst performance. As we can seen from Fig. 3, the relation between system cost and the number of requesters is described. We can see the system cost increases with the increasing of the number of requesters. However, the curve of our proposed scheme is obviously lower than the other three curves. And the growth trend is slower compared with the other curves. And the more is requesters, the higher is the cost. The results prove the proposed scheme is cost-effective and achieve better local communication on the another hand. Then system cost of scheme 1 is lower than scheme 2. The cost of scheme 3 is the highest. Another performance measure is revealed in Fig. 4. The effect of minimal transmission rate on system performance is evaluated. The curve of system utility decreases as the value of minimal transmission rate increases and the value of system utility of proposed scheme is superior than the other three schemes. This is because more bandwidth is allocated to satisfy increasing minimal transmission rate, which makes the number of locally served users decrease and the system performance worse. Furthermore, we can see that a network with larger transmission rate requirement tends to be more fair among users compared to that with smaller requirement, thus decreasing the total utility. V. C ONCLUSIONS AND F UTURE W ORK In this paper, we investigated the cache-enabled HCNs with D2D communications. From the perspective of content caching, we focused on how to select the transmission node with the desired content and the resource allocation problem. Furthermore, we proposed a joint access selection and resource allocation scheme to maximize the network capacity. In this scheme, access selection and resource allocation were jointly formulated as an optimization problem, where users can attain

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