I Introduction
Wireless user penetration is consistently increasing with a continuous emergence of new and sophisticated userdefined applications. This steers wireless technologies to evolve rapidly from one generation to the next generation striving to soothe the yearning for more enhanced spectral efficiency, energy efficiency, quality of experience, operation cost, etc. Even though the existing wireless networks ensured a very promising performance in these contexts, new demands on capacity and other performance have never ceased to emerge [3]. Besides, with the advent of the Internet of everything [1, 8], the incompetence of these legacy technologies became more apparent. Therefore, researchers are continuously in a toiled search for new technologies that can be adopted on top of the existing ones for future generation networks. Among many other impressive ideas, moving away from the traditional centralized infrastructure and towards the usercentric distributed network infrastructure is a promising one [16, 14, 15, 18, 17, 6, 10].
Note that a usercentric network platform significantly reduces energy consumption [6], increases network throughput [10] as well as enhances the utilization of the muchneeded spectrum [16, 14, 15]. On the other hand, edge caching is the concept of storing popular contents close to the end users. Therefore, leveraging edge caching, usercentric network infrastructure efficiently utilizes the network bandwidth and significantly reduces the congestion on the links to the centralized cloud server [16, 14, 15]. Besides, edge caching is considered as a promising scheme to support video applications due to their traffic volume escalation and stringent QoS requirements [4]. To mitigate this bottleneck, one of the prominent advocacy of caching is to alleviate the bandwidth demand in the centralized network segments by storing the popular video contents in the local/nearby nodes. Furthermore, in various missioncritical delaysensitive applications, edge caching can perform much better than the cloud caching approach due to the significant reduction in the delay [2].
In the literature [14, 15, 18, 12, 13, 5], several researchers studied edge caching in terms of different performance metrics. Tan et al. conducted static popularity based throughput maximization analysis in [15]. A novel content delivery delay minimization problem was studied in [18]. Shanmugam et al. [12] also considered both coded and uncoded cases for caching contents at the helper nodes to minimize the content downloading time. Song et al. [13] proposed a dynamic approach for the scenarios of the single player and the multiple players. Recently, Jiang et al. considered a cache placement strategy to minimize network costs in [5].
In comparison to these works, we develop a new caching platform that allows user caching, device to device (D2D) communications and collaborations among cacheenabled end nodes. Furthermore, long shortterm memory (LSTM) based sequential model is proposed for content popularity prediction, where the dynamic nature of the content’s popularity is discerned. In summary, the contributions in this paper are listed as follows:

To capture the shorttemporal user dynamics, LSTM is used for forecasting user preferences ahead of time.

To fully exploit the advantages of edge caching, a collaborative communication framework is proposed, in which different nodes in the same cluster can share contents among each other.

We formulate the optimization problems to minimize the content sharing costs under the constraints of limited and dynamic storage capacities at both the users and the base stations (BSs) for both heterogeneous caching placement and homogeneous caching placement scenarios.

We further analyze the content sharing cost and develop collaborative edge caching algorithms to configure the parameters of caching placement.

Numerical results are illustrated to validate the theoretical findings and the performance gain of the proposed algorithms.
The outline of this paper is as follows. Section II describes the system model and proposed dynamic user preference prediction. Section III introduces the caching model and optimization problems. The algorithms are given in Section IV. Section V presents the performance results, followed by the concluding remarks in Section VI.
Ii System Model and Dynamic User Preference Prediction Modeling
This section presents the proposed usercentric system model, followed by the proposed content access protocols and dynamic user preference prediction model.
Iia UserCentric System Model
In our proposed system model, a set of D2D users  denoted by , where ; are distributed in the coverage area of the BSs. Let denotes the caching size of all the users. Considering a clusterbased system model, we assume that each cluster consists of several BSs^{1}^{1}1In each cluster, different BSs use orthogonal bandwidth so there is no interference within a cluster. Within a cluster, we consider an equal number of BSs with equal caching capacity. Let , where and represent the set of BSs and the cache storage size of each BS, respectively. For simplicity, we assume that each BS serves an equal number of users. We denote a D2D requesting node and the serving BS as the tagged D2D node and the tagged BS^{2}^{2}2Throughout this paper, the name serving BS and tagged BS are used interchangeably., respectively. Furthermore, all the D2D nodes in a single cell  under the coverage region of a BS, are assumed to be in the communication range of each other and all the D2D users are in the communication range with at least one of the BSs.
Note that, in this paper, most popular contents are taken in the content catalog  denoted by , where . Note that this assumption of fixed content is made only during a period. Considering the age of information and content freshness, similar to [16, 14], we assume that new popular content is added periodically while removing the least popular ones. Furthermore, following the widely used notion, we assume that all of the contents have the same size  denoted by . Note that if the content sizes are different, we can always divide the content into segments of equal size and store those segments [7].
IiB Proposed Content Access Protocols
We carefully design our proposed model to satisfy the critical latency of realtime communication by delivering the requested contents from local caches as much as possible. If a tagged user needs to access the desired content, before sending the content request to other nodes, it first checks its own cache storage. It sends the content request to its D2D neighbors that are residing under the same cell and are within its communication range only if it does not store the requested content in its own storage. If the content is available in one of the D2D neighbor nodes, that content can be instantly served from that neighbor to the tagged user. If none of the D2D nodes store the requested content, the request is forwarded to the serving BS. The serving BS delivers content to the tagged user if the content is found in its storage. If the requested content does not exist in the serving BS’s cache, the serving BS forwards the request to the neighboring BSs residing in the same cluster. If the content is not available in any of the above local caches, it can be downloaded from the cloud, which is considered to be the least favorable choice.
Besides, we model the problem formulation in two steps. In the first step, we depict the dynamic content preferences of the users. Note that we intend to model peruser content preference in a dynamic manner. The second step performs the caching placements based on the prediction. The goal is to store the most probable ‘to be requested’ contents in future time slots. Using the actual requests of the users, we finally present the optimization model aiming to minimize total content sharing costs. In the next section, we present the prediction model.
IiC Dynamic User Preference Prediction
Note that if we only take content popularity into account, it dynamically varies over time and locations, let alone user preferences. Driven by this, we first acquaint different terms to facilitate the perception of several aspects used in our dynamic user preference prediction.
IiC1 Content Popularity
It is the probability distribution of the contents, which expresses the number of times a content
is accessed or requested by all of the users. If we consider only a small geographic region such as a small cell, this distribution is usually regarded as local popularity. In most of the legacy networks, Zipf distribution has been widely used to model the content popularity [12]. The probability mass function (pmf) of this Zipf distribution is represented by , wheredenotes the skewness of the content popularity.
IiC2 User Content Preference
The user content preference defines the conditional probability of requesting a content by a user given that the user actually makes a request. It is mathematically expressed as
(1) 
where represents the probability that user requests content at time slot given that it actually makes a request. Note that .
IiC3 Activity Level of User
We now define the probability that a user sends a content request as its activity level. It is denoted as
, where . Please note that the above derivation and more discussion about it are presented in the online technical report [9].IiD Predicting Dynamic User Preferences Using LSTM
This subsection presents a special kind of recurrent neural network (RNN), namely the LSTM, which is developed to avoid the long term dependencies in the RNN. Usually, the structure of LSTM includes three gates, namely forget gate, input gate and output gate
[11]. Given the historical dataset for time slots, we focus on LSTM based prediction model. This prediction model forecasts the probability of making a request and what content a user will demand in that request at time slot , . Please note that the steps and pertinent discussions about our proposed prediction model are provided on the online technical report [9]. For our training purposes, we fed an entire row to the input of the LSTM block, meaning that the input of the LSTM is an entire row of the usercontent matrix obtained from Alg. 1 of [9]. After running Alg. 1, we calculate activity levels , and preference probabilities that are clearly described in the online technical report [9].Furthermore, notice that the preference probability can be modeled for all the future time slots . Based on the requirements, we can set to any reasonable time window. Furthermore, if per slot time scale analysis is required, we can easily model that by considering only the per time slot user’s preference probabilities. Therefore, our proposed modeling is flexible for both of these cases. However, as placing the content for each forecast time slot may not be costefficient due to practical hardware limitations, we consider long term request probability in this paper. Without loss of any generality, assuming a fixed forecast window, the future content preferences of the users are considered as the average of the predicted , . Now, let denote this fixed time window chosen by the network administrator. Then, the average , , is considered as the preference probability of user for evaluating the system performance^{3}^{3}3 represents only the optimization time slots, while represents all time slot.. Let denote this preference probability that is used for the performance evaluation. This quantity can be calculated as
(2) 
Iii Caching Model and Content Sharing Cost
This section discusses the caching policy and introduces our objective functions.
Iiia Caching Models
We consider a probabilistic caching model for caching at the edge nodes  D2D users and BSs. Let us define the probabilities that the BS () and the user () cache the content () by and , respectively. Due to physical storage limitations, we have the constraints of and , , and . Without loss of generality, the tagged user and its associated BS (or its serving BS) are the focus of the study in the following. Let the remaining BSs be denoted by , where . Similarly, let the set of users in the coverage of be defined as , where is the number of users including the tagged user.
IiiA1 Heterogeneous Caching Model
In the heterogeneous caching placement strategy, the caching policy at node is different from that of node . We define the probability of getting a content from the tagged user’s own cache storage , from the D2D neighbors , from the serving BS , from the neighbor BSs and from the cloud respectively as follows:
(3)  
(4)  
(5)  
(6)  
(7)  
(8) 
IiiA2 Homogeneous Caching Model
In the homogeneous caching model, the cacheenabled nodes store the same set of contents. Thus, the probabilities of storing a content into the cacheenabled nodes are equal for all the local nodes in the same tier, i.e. and , where , . For simplicity, we get rid of the superscripts and denote the storing probabilities for the D2D nodes and BSs as and , respectively. Furthermore, we denote by the number of users in the cell. Then, we rewrite (38) as
(9)  
(10)  
(11)  
(12)  
(13)  
(14) 
We now determine the cost of collaborating and sharing the contents among different nodes in the following subsection.
IiiB Content Sharing Cost
We consider two types of costs, namely (a) the storage cost and (b) the communication cost. The communication cost represents the transmission cost per bit per meter. If a content has a size of bits, the transmission cost between two D2D nodes that are meters apart is calculated as , where is the cost per byte transmission in case of D2D transmission. For simplicity, we consider equal storage cost  denoted by , for all nodes. The cost of obtaining the content from node is, therefore, . Here, , and represent the costs of extracting a content from the cloud, the other BS in the same cluster, the serving BS and the other D2D nodes in the same cell, respectively. Furthermore, we assume that the transmission cost is zero if the requested content is in its own storage. But the storage cost is still included in this particular case. The relationships of the costs are presented in Proposition 1, which is presented in the online technical report [9]. In the following, we calculate the average content access cost for the heterogeneous and homogeneous caching models.
IiiB1 Heterogeneous Caching Model Case
In the case of heterogeneous caching placement, we calculate the average content access cost as
(15)  
where and represent the tagged user and serving BS, respectively. Moreover, and are calculated by and .
We then intend to minimize the content sharing cost by the following optimization problem:
(16a)  
(16b)  
(16c)  
(16d) 
In problem , the constraints in (16b) and (16c) indicate that the total contents cached at each node (i.e., the D2D node and the BS) must not exceed their storage capacity. The constraint in (16d) simply states that the caching probabilities must be in the range of .
IiiB2 Homogeneous Caching Model Case
Similarly, the average cost in the homogeneous caching placement case is derived as
(17)  
where represents the tagged user, while is the number of users in the cell. and .
Note that in the legacy homogeneous caching models, we assume equal caching policy for all the nodes in the same tier. Besides, same user preference modeling is considered. Heterogeneous content preferences of the users is used to demonstrate the effectiveness of dynamic user preference prediction. Following the homogeneous notions, the optimization problem is reformulated as
(18a)  
(18b)  
(18c)  
(18d) 
Iv Efficient Problem Solvers
The optimization problems and are nonconvex due to nonlinear combinatorial decision variables. Furthermore, user preferences vary dynamically over different time slots. Considering these dynamic variations, we intend to capture the long term caching placement probabilities at the cacheenabled nodes. The significance of doing this is that the system may need to forecast the requested contents in multiple future time slots. If the binary cases^{4}^{4}4A binary case considers only or . For example, if , the content is not cached at the user node ., are considered, the obtained results are only for a single time slot. Instead, the goal of this work is to optimize the caching placement probabilities for the scenarios in a relatively long term. Let and denote the cache placement indicator functions at the users and the BSs, respectively for time slot . Here, indicates that content is placed into the cache storage of user at time slot ; otherwise. As such, the cache placement probabilities are determined as follows:
(19) 
(20) 
where is the total number of time slots.
Iva Algorithm for Heterogeneous Caching Placement
Due to mixinteger and nonconvex nature, is highly challenging to solve. Besides, the heterogeneity in preference and caching models leads to a large number of system parameters. Therefore, we analyze three scenarios for content placements at the edge nodes in the heterogeneous case. The three subcases are (a) collaborative greedy caching  base station first (nonoverlapping) (b) collaborative greedy caching  user first (nonoverlapping) and (c) collaborative greedy overlapping caching. Owing to space constraints, we only discuss the last one. However, interested readers can find the other two algorithms in our online technical report [9].
Collaborative Greedy Overlapping Caching: In this case, we adopt a greedy caching mechanism. As the cost of getting the requested contents from other nodes is higher than storing the content at the requester node, this algorithm aims to place as many toberequested contents as possible into the requester cache storage. Recall that the prediction model can forecast what contents a user will request ahead of time. Therefore, it makes sense to adjust the caching policy based on the user’s preferences. Using the forecast information, the toberequested contents, by the users, are placed into their cache storage for each time slot. This gives the indicator functions s. Finding the indicator functions then gives the long term cache placement probabilities. For the BS’s cache storage, the remaining contents are placed based on their popularity profiles. Finally, the caching placement probabilities and are calculated using (19) and (20), respectively. The detailed operations for this case are summarized in Alg. 2.
IvB Algorithm for Homogeneous Caching Placement
Now, we study homogeneous caching placement, which is eventually a special case of heterogeneous caching placement. Recall that in the homogeneous caching policy, all similar tier nodes store the same copy of content into their caches. However, as the joint optimization problem
is not a convex problem, it is also difficult to obtain the optimal solution. As such, we now derive an efficient heuristic algorithm that solves
. The detailed procedures are presented in Alg. 5 in the online technical report [9].V Results and Discussion
The simulation parameter setting is given as follows: total number of contents is ; total number of users is ; total number of BSs in a cluster is ; total number of users under a serving BS is ; is in the range of ; is in the range of ; number of historical time slots is , ; number of optimization time slots is , ; = 2000; .
We first generate the initial content request number following Alg. 1 of [9]. After that, the correlated request numbers are generated using , where , and represent initial generated number for time slot , the rest time slots for which the correlated data are being generated and amplitude, respectively. Moreover, we consider is random variable with 0 and 1; , and for our simulation. Note that, as the requested incident number is an integer and nonnegative, we perform the necessary replacement of any negative number with and rounding. We stress out that the proposed LSTM is a powerful solution and can be readily extended for any other kind of corelated data generation process. Given enough data samples, our proposed method is capable of predicting dynamic user preferences efficiently.
Now, using the proposed prediction model in Alg. 1, the contents that will be requested in the next time slot by the users are sequentially predicted. The prediction made by this model for the most popular content of user is illustrated in Fig. (a)a. We also present the temporal dynamics over time for some selected users from all the cells in the following. Thanks to the LSTM solution, the dynamic user preference changes of the users and all the contents, in all time slots, are well captured. We illustrate only a sample of how the popularity of the contents and activity of the users change over time in Fig. (b)b. Using these values, the content preference probabilities of the users are measured. We then use these results for the caching policy designing in the following experiments.
To this end, we compare the performance between the static caching placement [15] and the proposed dynamic predictionbased caching strategy in Fig. (c)c. Particularly, we consider the homogeneous caching model for a static estimation based model of [15] to compare the results of the proposed scheme. In the static case, there is no information about the temporal dynamics of the user preferences and activity levels of it for all time slots . Therefore, the caching placement probabilities remain constant in all time slots. On the other hand, our proposed scheme captures all of the temporal dynamics. Hence, it very well knows what content will be requested by the users and at what time the users will place those requests. Therefore, the proposed algorithm can proactively design the optimal caching placement. It is not difficult to find that the proposed dynamic predictionbased caching strategy outperforms static caching placement [15]. This observation validates the beneficial contribution of the dynamic predictionbased caching strategy. Therefore, we only show comparisons among the proposed caching schemes in the following.
In Figs. LABEL:Cost4differentBSCacheSizeWithCd4 and LABEL:Cost4differentuserCacheSizeWithCb12, we illustrate the cost performance of our proposed schemes for different cache sizes. As the heterogeneous caching strategy allows storing diversified contents at the edge nodes, the performance of it is much higher than that of the legacy homogeneous caching placement schemes. Moreover, the performance of the three proposed algorithms  for the heterogeneous caching strategy, may vary depending on the cache sizes of the edge nodes. However, it is perceived that the proposed greedy overlapping caching placement performs significantly better than all the other cases if the edge nodes have reasonable cache sizes. Consequently, we fairly conclude that the system administrator has the flexibility of choosing the best algorithm based on its initial cache storage sensing of the edge nodes. Therefore, our proposed dynamic caching solution is efficient, flexible, agile and scalable compare to that of similar legacy schemes. Note that more critical discussions are presented in our online technical report [9] due to space constraints.
Vi Conclusion
In a content delivery network, obtaining accurate content popularity prediction is immensely influential yet a difficult task. Following the LSTM model, we have successfully captured the temporal dynamics of the user preferences and their activity levels. With the theoretical analysis and experimental simulation in this paper, we demonstrated that the system performance highly depends on the prediction of the content dynamics and popularity. We furthermore made fair comparisons among different cache placement strategies and concluded that the proposed greedy overlapping caching mechanism outperforms other alike caching schemes.
0.92
References
 [1] (2011) Internet of things: applications and challenges in technology and standardization. Wireless Personal Commun. 58 (1), pp. 49–69. Cited by: §I.
 [2] (2018) Caching and computing at the edge for mobile augmented reality and virtual reality (ar/vr) in 5g. In Ad Hoc Networks, pp. 169–177. Cited by: §I.
 [3] (201108) The global footprint of mobile communications: the ecological and economic perspective. IEEE Commun. Mag. 49 (8), pp. 55–62. External Links: Document, ISSN 01636804 Cited by: §I.
 [4] (201407) Basestation assisted devicetodevice communications for highthroughput wireless video networks. IEEE Trans. Wireless Commun. 13 (7), pp. 3665–3676. External Links: Document, ISSN 15361276 Cited by: §I.
 [5] (2020) Cache replacement strategy with limited service capacity in heterogeneous networks. IEEE Access 8 (), pp. 25509–25520. Cited by: §I.

[6]
(2020)
Ecovehicular edge networks for connected transportation: a decentralized multiagent reinforcement learning approach
. arXiv preprint arXiv:2003.01005. Cited by: §I, §I.  [7] (201702) Contextaware proactive content caching with service differentiation in wireless networks. IEEE Trans. Wireless Commun. 16 (2), pp. 1024–1036. External Links: Document, ISSN 15361276 Cited by: §IIA.
 [8] (2020) 6G: envisioning the key issues and challenges. arXiv preprint arXiv:2004.04024. Cited by: §I.
 [9] (2020) User preference learning aided collaborative edge caching for small cell networks. Technical report. External Links: Link Cited by: §IIC3, §IID, §IIIB, §IVA, §IVB, §V, §V, 3.
 [10] (2020) Dynamic power allocation and virtual cell formation for throughputoptimal vehicular edge networks in highway transportation. arXiv preprint arXiv:2002.10577. Cited by: §I, §I.
 [11] (2014) Long shortterm memory recurrent neural network architectures for large scale acoustic modeling. Cited by: §IID.
 [12] (201312) FemtoCaching: wireless content delivery through distributed caching helpers. IEEE Trans. on Inf. Theory 59 (12), pp. 8402–8413. External Links: Document, ISSN 00189448 Cited by: §I, §IIC1.
 [13] (201710) Learningbased content caching and sharing for wireless networks. IEEE Trans. on Commun. 65 (10), pp. 4309–4324. External Links: Document, ISSN 00906778 Cited by: §I.

[14]
(2019)
Twintimescale artificial intelligence aided mobilityaware edge caching and computing in vehicular networks
. IEEE Trans. Veh. Tech. (), pp. 1–1. External Links: Document, ISSN 00189545 Cited by: §I, §I, §I, §IIA.  [15] (201810) D2D communications in heterogeneous networks with fullduplex relays and edge caching. IEEE Trans. Ind. Informat. 14 (10), pp. 4557–4567. External Links: Document, ISSN 15513203 Cited by: §I, §I, §I, Fig. 2, §V.
 [16] (201811) Mobilityaware edge caching and computing in vehicle networks: a deep reinforcement learning. IEEE Trans. Veh. Tech. 67 (11), pp. 10190–10203. External Links: Document, ISSN 00189545 Cited by: §I, §I, §IIA.
 [17] (2018) Smart grid communication infrastructures: big data, cloud computing, and security. John Wiley & Sons. Cited by: §I.
 [18] (201808) Cooperative edge caching in usercentric clustered mobile networks. IEEE Trans. Mobile Comput. 17 (8), pp. 1791–1805. External Links: Document, ISSN 15361233 Cited by: §I, §I.
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