Femtocaching assisted multisource D2D content delivery in cellular networks
 Xiaoyan Zhao^{1, 2},
 Peiyan Yuan^{2}Email authorView ORCID ID profile,
 Yajun Chen^{1} and
 Pei Chen^{1}
DOI: 10.1186/s1363801709107
© The Author(s) 2017
Received: 7 March 2017
Accepted: 29 June 2017
Published: 14 July 2017
Abstract
The influxes of diversified services and mass data lead to exponential growth of traffic load in mobile cellular networks. Cacheenabled devicetodevice (D2D) communication provides a general framework to alleviate this situation. In contrast to previous singlesource D2D models, this paper investigates a comprehensive content delivery framework based on a threetier heterogeneous network (HetNet), where base station (BS), femtocaching auxiliary equipments (FAEs), and user terminals(UTs) are included. The cooperative D2D communication can be implemented from both FAEs and UTs to handle the ongoing explosive increase in ultradense scenario. Moreover, duplicate storage for requesting data in multiple neighbor nodes makes manytoone D2D communication possible at the user layer. Considering the case that cellular users and D2D links reuse the same resources in the uplink period, the nonoutage probability of the cellular communication is defined to guarantee the main communication quality. Under the constraints subject to cumulative interference, an optimization objective function based on multisource D2D communication is deduced to achieve unprecedented average data rate. Numerical simulations show that our system yields network throughput exponentially while transferring traffic load of the BS reasonably.
Keywords
Devicetodevice communication Content delivery Manytoone Nonoutage probability Heterogeneous network1 Introduction
The latest report of the global system for Global Mobile Communication Systems Association (GSMA) has shown that three quarters of the world’s population will be linked together through mobile terminals by 2020. Wireless data business is therefore expected to increase by a factor of 11 compared to the current, and each user needs to consume at least 1 Gb per day in the next 5 years [1]. This explosive growth is mainly caused by mobile multimedia traffic and other emerging content transmission such as popular videos and social networking services (SNS), which almost rise by a factor of 65 times [2]. The urgent demand for the thousandfold growth of mobile data inevitably leads to a slowdown, or even breakdown of the cellular systems. Thus, cellular networks are undergoing unprecedented paradigm shift in the way by which data is delivered [3].
Note that available researches mainly focus on the singlesource caching model, i.e., they either use femtocaching helper (i.e., SBS) or exploit UTs to carry on D2D communication. Although these two approaches were described separately, the measures were effective and brought about some enlightenment to us, e.g., these two strategies can also be mixed to some extent. Moreover, current wireless technologies such as time/frequency division multiple access and maximum ratio transmission (MRT) [14] support multiple users to transfer data simultaneously. For example, under MRT, each suitable UT and SBS in the cooperation communication radius can beamform to a RU such that the signals from the neighboring nodes and SBSs are coherently combined and ultimately result in diversity gain. That is to say, one RUT can receive contents from both the SBSs and other UTs, which can be called multisource caching model. Here, the socalled multisource caching, drawing a contrast with the single source(e.g., either SBSs or UTs), mainly refers to the collaboration between different types of storage devices(i.e., both SBSs and UTs). The heap offers us a feasible solution to the traffic offload problem from a technical and economical perspective. Accordingly, we propose a threetier communication architecture in heterogeneous network incorporating femtocaching helpers and UTs to offload the backbone network traffic. This joint design offers not only two different caching gains and multiplexing gains but also diversity gains owning to manytoone D2D communication. Manytoone D2D communication means that each RUT may detect several mobile users storing the needed file within its scope of power coverage in the ultradense environment. In other words, three conditions are required for suitable UTs to take place manytoone D2D: (1) they are within the transmission range of RU; (2) they have the file which is needed by RU; (3) there are more than one UTs matching both of criteria 1 and 2. In general, high data rate and low transmission delay can be obtained due to the proximity of paired devices in D2D links, thus introducing proximity gain. Nevertheless, it is unsurprisingly that the multisource caching model proposed in this paper will introduce cumulative interference caused by multipair D2D links in the uplink transmission period. To achieve maximum transmission rate and to obtain high user satisfaction, nonoutage probability of system is deduced to describe the influence of cumulative interference on the performance of cellular systems.

Combining the storage advantages of fixed equipments and mobile terminals in ultradense environment, we model a threetier heterogeneous architecture to distribute data. Furthermore, we introduce the concept of manytoone D2D communication in the user layer.

We present an optimization objection in terms of average transmission rate to discuss the performance characteristics of the heterogeneous network. Under the cumulative interference constrain due to multipair D2D links, nonoutage probability of system is derived and simulated.

We define the concept of user satisfaction to analyze the pareto solutions of the optimization problem. Moreover, we evaluate the impact of various parameters on user satisfaction, such as the request probability and D2D communication radius.
The remainder of the paper is organized as follows: after reviewing the main related works in Section 2, the threetier content delivery mode is elaborated in Section 3. In Section 4, the average transmission rate and nonoutage probability are derived. Numerical results in terms of network throughput and user satisfaction are discussed in Section 5. Finally, conclusive remarks are presented in Section 6.
2 Related work
D2D communication attracts a lot of attentions recently, and the potential research orientations include content delivery/dissemination [6, 7, 10], resource allocation [15–17], social awareness video multicasting [18, 19], and so on. Existing researches for the content delivery can be mainly classified into two perspectives. The first one is to deploy SBS with mass storage device which does not require highspeed backhaul links. For example, in [6, 7], small base station called helper was introduced and placed in fixed position to serve user requests. Chou et al. [8] utilized mobile SBS to study the deployment problem and address the waste of resources in small cells. In [9], a costeffective integration access technology between WiFi and cellular wireless was characterized for femtobased stations to fulfill time/spacevarying traffic. In general, the scheme based on auxiliary devices in small cells, such as helper, femtobased station, and SBS can highly provide a performance boost to the network traffic. However, along with the growth in the number of helpers, each RUT can be covered by multiple helpers, and the hit rate will be increased as well as the interference and the investment cost. In addition, another potential deficiency of the small cellbased infrastructure is that, during peak traffic period, the backhaul linkcapacity requirement to respond data is enormously high [4]. Obviously, if the storage capacity of existing devices (e.g., UTs) is considered, storageinvestment efficiency will be further improved.
The second one is pushed even further by utilizing the storage ability of mobile UTs [7, 10, 13], which prestore popular files in UTs through various storage strategies. The authors of [10] mainly focused on exploiting cognition to the cacheenabled D2D in the multichannel cellular network, in which the number of users in a cell is formulated as mutually independent Poisson point processes (PPPs). Authors in [11] presented a paradigm for wireless video content dissemination based on caching popular files in mobile users with no additional infrastructure cost. Similarly, [12] put forward a systematic scheme in wireless contentcentric networks. The storage capacity of users is adopted to maximize the content delivery capability with a fixed amount of wireless resources. Yang et al. [13] presented a comprehensive framework on D2D communication and advocated to proactively cache contents in partial users with caching ability when the network is offpeak. The studies have shown that prestoring files in the UTs can increase spectral efficiency, thus introducing reuse gain. This scheme allows only one neighboring nodes to communicate with a RUT in the meantime, which can be described as onetoone D2D communication. Nevertheless, the mobile devices like UTs cannot guarantee the effective transmission of popular files because of the unstable topology, limited storage capacity as well as constrainedenergy in a sparse environment. Fortunately, this model can bring caching gains by taking advantage of multiple neighbor nodes to store the same required file. Therefore, we can activate multiple possible D2D links simultaneously in the dense or ultradense network named as manytoone D2D communication.
In particular, the authors in [7] discussed about caching in these two ways. They introduced SBS placed in fixed position to serve user requests, and also adopted UTs’ large hard disks built in to act as mobile helper stations. However, significant varies still exist between the reference [7] and our proposed system:
1. We mainly focus on the combination of the two approaches, in contrast, the reference [7] discussed about these two ways separately as well as other literatures. High data rate and system throughput can be obtained owning to caching gains, multiplexing gains, diversity gains, and proximity gains in our joint design.
2. We introduce the concept of manytoone D2D communication in the user layer and make full use of the user redundancy in the dense environments. On the contrary, users in [7] were divided into smaller cluster based on their locations and at most one D2D transmission was allowed in each cluster at a time. That is to say, the authors in [7] only allowed onetoone D2D communication when they considered UTs for storage.
3. The interference of the proposed system is more complex than the reference [7]. There will inevitably be more interruptions for the cellular communication due to cumulative interference caused by manytoone D2D communication. Thus, it is important to seek the tradeoff at which interference and system throughput can supplement each other.
Therefore, efficient resource allocation and interference management have key impacts on the performance of content delivery in D2D and cellular coexisting system [15–17]. For theoretical derivations, only a single pair of D2D link reuse system resources is considered. Thus, it is always simplified to describe the interference, i.e., only one D2D pair is allowed to active within the power range of a user node or in a cluster. However, it is very critical to estimate the caused interference accurately when we calculate the system performance, such as maximize the data rate [16].
In short, the key study of this paper is to put forward a new strategy based on the study and the analysis of related literatures, which can not only take full advantage of the stability of SBS but also have the further numerical superiority and cost advantage of UTs. In other words, due to the different aspects of both traditional delivery methods, the joint design of these two approaches can be tried in practical project to offload the network traffic effectively and economically.
3 System model
4 Problem formulation and analysis
4.1 Problem formulation
where γ is the signaltointerferenceplusnoise ratio (SINR) of the BS when D2D pairs reuse the given cellular resources. The performance of cellular communications should be guaranteed before D2D pairs are allowed to share the uplink resource [22]. Accordingly, the BS must be firstly satisfied as long as its SINR is no less than the threshold γ _{0}. And likewise, in order to ensure the reliability and stability of the D2D communication in the uplink transmission, the SINR of D2D receiver γ _{ d } needs to exceed a given threshold γ _{ D }.
The Zipf exponent γ _{ r } characterizes the distribution function by controlling the relative popularity of files. Larger γ _{ r } means higher content duplicate requests, i.e., the top few popular files account for the majority of requests.
An important aspect of the joint optimization is the storage allocation because hit ratio and transmission rate can be varied by caching different files in neighbor nodes. Caching multiple copies of a file can increase the chances to get diversity gains and multiplexing gains. For simplicity, we assume that all files have the same size, and one file is a basic storage unit. The library files are available in the BS, and users can directly connect via a cellular communication. Meanwhile, let C _{ f } denotes the storage capacity of each FAE, which is measured by the maximum number of files it can store.
Using the collaboration storage capacity of UTs and FAEs is an important feature of this article. In a general random geometric graph, it is shown that finding the optimal deterministic file assignment is NPhard even when terminals are static and interference is ignored [23]. However, in our three layers caching system, if we assume that each UT can access no more than one, we can find a simple centralized placement method for FAE. Given that there are m static memory units in each FAE, it should store the top m most popular files without repetition, while the storage capacity C _{ f } is equal to the number of storage units in FAE, i.e., C _{ f }=m. Each FAE can store on average up to m files with m≤M.
The exponent of caching distribution γ _{ c } is one of our decision variables which is not necessarily equal to γ _{ r }.
4.2 Transmission rate

1. FAE. Given that there are m storage units in a FAE, each FAE should store the top m most popular files without repetition. Define binary random variable α _{ i }, such that α _{ i } is equal to 1 if 1≤i≤m ; otherwise, it is equal to 0. If the ith file on demand is one of the top m popular files, the transmission rate that FAE can provide, denoted by \(\overline {R_{F}}\), is equal to:$$ \overline{R_{F}} = \alpha_{i}R_{f} e^{\eta_{f}} = \left\{\begin{array}{ll} R_{f} e^{\eta_{f}}, & 1 \leq i \leq m\\ 0, & m \leq i \leq M \end{array}\right. $$(6)
R _{ f } refers to the ideal transmission rate of FAE and η _{ f } indicates the attenuation coefficient of Rayleigh fading. Based on the dedicated bands frequency allocation strategy, the cochannel interference of FAEs can be ignored, and the SINR of its received signal is given by \({\gamma _{f}} = \frac {{{P_{F}}{x_{iF}}d_{iF}^{ \sigma \;}{H_{iF}}^{2}}}{{{{\mathrm {N}}_{0}}}}\). Thus, the ideal transmission rate R _{ f } can be obtained by Shannon theory [25].
$$ {R_{f}} = Clb\left({1 + \frac{{{P_{F}}{x_{iF}}d_{iF}^{ \sigma \;}{H_{iF}}^{2}}}{{{{\mathrm{N}}_{0}}}}} \right) $$(7)where P _{ F } denotes the transmit power of FAE, d _{ iF }, and H _{ i,F } represent the distance and the channel gain between the ith user and the conterminous FAE, respectively. Path loss exponent is denoted as σ, and x _{ iF } is the log normal shadow fading coefficient between the ith D2D and the FAE. N _{0} is white Gauss noise, and C is the available spectrum bandwidth.

2. Neighbor user. Each UT caches files at random and independently following the Zipf distribution with exponent γ _{ c }. The number of neighbor nodes is usually referred to the binomial distribution with parameters N and P, i.e., K=B(N,P), the probability of k neighbor nodes can be expressed as:$${P_{r}(K = k) = \left({~}_{k+1}^{N}\right)p^{k+1}(1p)^{Nk1}} $$(8)where \(p = \frac {\pi r^{2}}{A}\), r is determined by the power level for each transmission, and A is the coverage area of the cell. Thus, the numerical probability of cooperating users for the transmission to the ith file, that is to say, the numerical probability of neighbor nodes who have stored the ith file is:$${}{ \begin{array}{rcl} P(T_{i} = c) & = & \sum_{k=1}^{N}P\{cK=k\}P_{r}(K=k)\\ \\ & = & \sum_{k=c}^{N}\left({~}_{c}^{k}\right)\beta_{i}^{c}(1\beta_{i})^{kc}P_{r}(K=k) \end{array}} $$(9)After a request to the ith file, the average number of D2D links that one hit can be established as:$${E(D) = \sum_{c=1}^{M}cP(T_{i} = C)} $$(10)Taking into account the request probability of the ith popular file, the mean value of any request for files can be summed up as:$${}{\overline{E}(D) = \sum_{i=1}^{M}p_{i}E(D) = \sum_{i=1}^{M}p_{i}\sum_{c=1}^{M}c P(T_{i} = C)} $$(11)
\(n\overline {E}(D)\) can represent the total number of D2D communication activated by n requesting users at the same time, i.e., \(n\overline {E}(D)\) equals to the number of D2D pairs T _{total} mentioned in the later. An important theme to notice is that P _{ r }(K=k) is a function of r. Thus, \(\overline {E}(D)\) and T _{total} are both functions of variable r and γ _{ c }.
Then, the transmission rate provided by the neighbor users, denoted by \(\overline {R_{D}}\), can be formulated as:$$ \overline {\;{R_{D}}} = \overline{E}(D)\;{R_{d}}{e^{ {\eta_{d}}}} = \;{R_{d}}{e^{ {\eta_{d}}}} \sum\limits_{i = 1}^{M} {p_{i}} \sum\limits_{c = 1}^{N} cP\left({{T_{i}} = c} \right) $$(12)R _{ d } refers to the ideal transmission rate of D2D communication. Due to reusing the same frequency resources with the cellular communication, the interference of D2D receiver comes from two aspects: white Gaussian noise and the cellular communication. Therefore, when uplink resources allocation is performed efficiently, the SINR of D2D users can be calculated by \({\gamma _{d}} = \frac {{{P_{D}}{x_{iB}}d_{iB}^{ \sigma }{H_{iB}}^{2}}}{{{P_{C}}{x_{CB}}d_{CB}^{ \sigma }{H_{CB}}^{2} + {{\mathrm {N}}_{0}}}}\), and then R _{ d } can be derived through the Shannon formula [25]:$${{R_{d}} = Clb\left({1 + \frac{{{P_{D}}{x_{iB}}d_{iB}^{ \sigma }{H_{iB}}^{2}}}{{{P_{C}}{x_{CB}}d_{CB}^{ \sigma }{H_{CB}}^{2} + {{\mathrm{N}}_{0}}}}} \right)} $$(13)where P _{ D }, P _{ C } denote the transmit power of D2D users and one cellular user, d _{ iB } and d _{ CB } represent the distance between the ith D2D sender and cellular user to the BS, respectively. H _{ iB } and H _{ CB } denote the channel gain. σ and x _{ iB } are expressed as the path loss exponent and the log normal shadow fading coefficient between the ith D2D sender and BS.

3. BS. The base station will carry out data communication only when the required files are not stored in the neighbor nodes and FAE. Defined P _{ B } as the transmit power of each resource block, the transmission rate can be calculated by:$$ {{\begin{aligned} \overline {{R_{B}}} &= (1  {\alpha_{i}})P\left({{T_{i}} = 0} \right) \cdot {R_{b}}{e^{ {\eta_{b}}}}\\ \hspace{5mm} &= \left\{ {\begin{array}{*{20}{c}} {{R_{b}}{e^{ {\eta_{b}}}} \sum\limits_{k = 1}^{N} {{\left({1  {\beta_{i}}} \right)}^{k}}{P_{r}}\left({K = k} \right),\;\;\;\;\;m < i \le M}\\ {\;\;0, {\mathrm{1}} \le \;i \le m} \end{array}} \right.\; \end{aligned}}} $$(14)In this case, a file has to be transmitted from the BS and the RU can be thought of as an casual cellular user. Because D2D communications occur in the uplink direction, cellular users, as the receiver of the downstream link communication, are not affected by D2D communication. Then, the ideal transmission rate of BS R _{ b } can be described as:$${ {R_{b}} = Clb\left({1 + \frac{{{P_{B}}{x_{iB}}d_{iB}^{ \sigma }{H_{iB}}^{2}}}{{ {{\mathrm{N}}_{0}}}}} \right) } $$(15)
Notice that P(T _{ i }=c) is a function of γ _{ c } and r, consequently, we can be informed that the optimization formula is a function of several variables, such as γ _{ c }, γ _{ r }, and r as well as the number of requesting user n. It can be generated by varying one or more of the parameters in a general form.
4.3 Noise and cochannel interference
In addition to the traditional interference in cellular systems, there are two kinds of interference in the D2D coexisting with cellular system. One is the interference from D2D pairs to the traditional cellular system; the other is the interference from the cellular system to the D2D receiver. For our theoretical derivations, we assume FAEs in the system utilize the dedicated mode which is assigned by the orthogonal resource, interference caused by FAE to BS and users can be negligible, or can be made negligible through an appropriate frequency reuse scheme. Furthermore, we presume that multiple D2D links to the same RUT can be operated on the different resources sharing bandwidth and each cellular wireless resource can be reused up to one at most in the uplink period. The main reason we reuse the frequency resources in the uplink is that BS, as the uplink receiver of cellular communication, has more powerful ability to suppress noise interference than UT (i.e., the receiver in the downlink). This ability is ideally suitable for our proposed system, which may introduce larger cumulative interference caused by multiple D2D links. For simplicity, we neglect intercell interference and consider one macro cell in isolation. Thus, the main purpose of this paper is to analyze the model taking into account cochannel interference, which means that the same resource block is spatially reused.
In order to guarantee D2D communication, the SINR of D2D users should be greater than its threshold when it is reusing with the cellular uplink resources, i.e., γ _{ d }≥γ _{ D }. As shown in 4.2, the SINR of D2D users is a function related to D2D transmit power and the distance from the cellular user to the D2D receiver, and so it is best for D2D communication to reuse the resources of cellular user who is as far as possible from the D2D receiver. Moreover, even the parameters in this function are not associated with those in the optimized objective function, we can derive the minimum transmit power of D2D from this constraint.

Cumulative interference of the base station caused by multiple D2D transmitters can be described by Ψ _{ D } while T _{total} is the number of D2D links:$${ {\psi_{D}} = \sum\limits_{i = 1}^{T_{\text{total}}} \sqrt{{P_{D}}{x_{iB}} d_{iB}}^{\,\,{\sigma}/2_{H_{iB}}}} $$(17)

Uplink signals Ψ _{ C } to the BS transmitted by cellular user can be expressed as:$${ {\psi_{C}} = \sqrt{{P_{C}}{x_{CB}} d_{CB}}^{\,\,\, \sigma/2_{H_{CB}}}} $$(18)
Thus, if more than one D2D links multiplex cellular uplink resources at the same time, the communication performance of the BS will be influenced by the system parameters such as transmit power, distance between D2D transmitter and BS, SINR threshold γ _{0} as well as the number of D2D pairs T _{total}. T _{total} indicates the total number of D2D links when n users generate requests simultaneously and can be seen as a variable relate to r and γ _{ c }.
4.4 User satisfaction
Here, α is the weighted coefficient, \(P_{N\text {out}}^{*}\) and \(R_{\text {total}}^{*}\) are minmax normalization values. Finding the optimal solution analytically in closed form does not seem feasible, numerical solutions are possible with very low effort. Nevertheless, the pareto solutions of the optimization problem can be obtained using the above equation and numerical experiments based on the multi objective optimization model.
5 Numerical results and analysis
In the aforementioned references, parameters such as the popularity profile of data files and D2D communication radius are always assumed to be known perfectly. In practice, such an assumption cannot be dynamically adjusted and reasonably justified in different circumstances.
In the following, we provide some numerical results to investigate the effects of relevant parameters on the system throughput with the simple caching strategies. Unless specified otherwise, all figures set limits according to the following except those considering the effect of the parameters. The BS has a coverage area of R=500 m with a storage capacity of M=100 files. In the described system, FAEs use dedicated channels and only a linear impact on the network throughput. For the sake of simplicity, only four FAEs are installed in fixed position. Each FAE has a coverage area of 200 m, and its capacity is 30% of the total files. All channels are subject to path loss model where σ=3. The noise power of the receiver is 70 dBm, and bandwidth of one channel is set to 1 MHz. We use the Monte Carlo experiment to prove the effectiveness of the proposed algorithm, and the number of Monte Carlo experiments is 10000. In the process of the experiment, we assume that the BS uses a transmission scheme similar to the fourthgeneration longterm evolution (LTE) standard, based on an OFDMTDMA physical layer. The FAEs are operating with dedicated spectrum resource and have multiple antennas, i.e., WiFilike links. We envision that UTs have singleantenna although multiantenna system is inevitable in the future.
The number of D2D links generated by user layer is an important criterion that affects the system throughput and cumulative interference. Thus, the first part of the experiment begins with the influence of each parameter on it.
Furthermore, we note that N value has lower impact on the average number of D2D links compared with γ _{ c }. The reason is that user requests are based on the probability of request in the experimental process. Changing the popularity Zipf distribution exponent γ _{ c } has greater impact on the popularity of the document. If the request is subject to the uniform distribution, N will have a greater impact on the chance of D2D connection with a fixed radius.
From now on, in order to analyze the influence of the system interference, we just present the simulation results of nonoutage probability in which the average number of D2D links is a crucial technical parameter.
6 Conclusions
Content delivery strategy based on active storage in local is an effective way to settle the explosion of mobile data traffic. In this paper, we introduced cooperative transmission scheme by jointly using the storage capacity of UTs and FAEs. Aiming at the scenarios which have multiplepair D2D links in the system, the network transmission rate is optimized on the premise of guaranteeing the main communication performance. Furthermore, the optimal D2D communication distance and storage probability exponent can also be found based on multiobjective optimization problem. The analytical and simulation results show that the proposed scheme can obviously improve the network throughput, can reduce the transmission delay, and can restrain the mutual interference among different links effectively. Meanwhile, the data traffic of the most popular files can be offloaded to D2D communication, which can provide high spectral efficiency and free up BS to provide other business.
In the future, we still have a lot of additional work to do, such as the question of storage optimization as well as the cooperative strategies of content allocation between UTs and FAEs. Furthermore, more complex D2D scenes need to be studied, e.g., multiple D2D users reuse the same CU resource simultaneously.
Declarations
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant No. U1404602, the Young Scholar Program of Henan Province under Grant No.2015GGJS086, the Science and Technology Foundation of Henan Educational Committee under Grant No. 14A510011, the Science and Technology Key Research Program of Henan Province with No. 172102210341, the Dr. Startup Project of Henan Normal University under Grant No.qd14136, and the Young Scholar Program of Henan Normal University with No. 15018.
Authors’ contributions
XZ put forward the idea and wrote the manuscript. PY took part in the discussion and gave the original ideas, he also guided, reviewed, and checked the writing. YC and PC carried out the experiments and analyzed the experimental results. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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