Yanli Xu

The College of Information Engineering, Shanghai Maritime University, Shanghai 201306 China.

I. INTRODUCTION

Recently, applications such as social video,security monitoring, multi-anchor interaction and content sharing spring up accompanied by massive content trafcs. It prompts content traffic to occupy a more and more important position in the mobile data traffic (about accounts for almost percent of the mobile data traffic currently with an -fold increase over the next years [1]). To ease the burden of core network, a popular approach is the application of proximal transmission to content delivery in which user equipment (UE) can obtain required contents from neighboring nodes which cache them in advance; see [2-4] for a small subset. To support proximal content delivery,caching is a precondition which has taken two main directions in the literature. Therst one focuses on caching at helpers such Wi-Fi access point (AP), small cell base station(BS) or deployed caches; see [5-8] for a small subset. This caching way usually brings out bottlenecks for content delivery due to the requirement of high-rate backhaul links [9]and finance cost due to infrastructure construction. The second direction, which is also more relevant to our work, focuses on caching at UEs and deliver content to neighbors via device-to-device (D2D) technique. We discuss these works in more detail next.

Smart D2D caching can bring resource ef-ciency such as improving spectral reuse [10],thereby, some works such as [11] study how to best cache content in a D2D network under certain channel conditions. With considering stochastic characters of channel and user dis-tribution, performance of randomized caching in D2D networks is studied in [12] to maximize the density of successful delivery. UE selection determining which UEs are selected to cache contents for proximal content sharing is studied in [13-15]. Optimal content caching at UEs is regarded as a ZipF distribution in[16], which has similar trend as the content demand distribution. Caching decision problems minimizing the average caching failure rate are formulated and solved in [17]. Incentive mechanism to make selfish nodes cache contents is investigated in [18]. The impact of UE mobility on UE caching and performance is considered in [19, 20]. Taking social relationship among UEs, social ties are utilized for improving the caching and delivery efciency in [21].In addition, different from prior peerto-peer (p2p) networks, D2D content delivery can be well controlled by BSs as an alternative to BS delivery. Thereby, the cooperation between caching BSs or/and caching UEs is studied in [22-24]. For example, femtocaching and D2D caching strategies at femto and UE are proposed separately in [25] by considering femeto-D2D cooperation.

Most of recent existing works on D2D-aided content delivery in cellular networks are targeted to realize the functionality of UE caching to improve network performance such as delivery efficiency and energy efficiency.For many kinds of mobile traffic delivery such as video transmission, quality-of-service(QoS) provisioning is essential to guarantee user experience. How to cache to satisfy QoS requirement for D2D delivery with the constraint of caching capacity at UEs and without pre-known neighbor demands has not been well addressed. In this paper, impacts of QoS requirement and UE caching capacity on caching are analyzed, which enable UEs caching useful contents for neighbors without exchanging information of user demands. Based on these analyses, caching strategy is proposed to prepare enough potential D2D links for the delivery of different contents based on hybrid quality requirements. The left parts of the paper are organized as follows. In Section II, the system model is set up for both network model and content delivery model. In Section III, theoretical analyses are performed for content caching at UEs in cellular networks and related results are presented. Factors affecting content caching such as QoS requirement of content requests and caching capacity are studied and a caching management scheme is proposed. Simulation results and related discussions are presented in Section IV. Finally,Section V concludes this paper.

II. SYSTEM MODEL

2.1 Network Model

We consider an infinite planer cellular network where UEs are randomly located. UEs transmit data with two alternative transmission modes, i.e., cellular mode in which transmission traverses BS and D2D mode in which proximal UEs communicate with each other directly without the relay of BS. For the sake of avoiding mutual interference and reducing implementation complexity, communication links under different transmission modes use orthogonal resources for interference mitigation. D2D communication links employ spatial reuse for higher resource efciency thanks to proximal transmission. UEs and simultaneous transmitters are assumed to be distributed according to Poisson point processes (PPPs)with densitiesρuandρs, respectively, which is a popular model for characterizing locations of nodes in wireless environment and widely used for the analysis of D2D communications[26-28].

Without loss of generality, we study the content delivery performance at a snapshot for easy elaboration. Impacts from time on caching policy are also considered. Corresponding to two transmission modes indicated above, a UE can obtain its requested content via either cellular content delivery (from small cell BSs or macro cell BSs) or D2D content delivery(from a neighbor of the UE). To constrain the D2D delivery for better content distribution performance, we give a following assumption on cooperation regions and content sharing.

Assumption 1. When UE requests content,BSs only schedule UEs which cache the content and locate in the cooperation region of this UE to help it obtain the requested content via D2D communications (D2D delivery mode is selected). The cooperation region of UE is the circle centered at this UE with a cooperation distanced0. If there is no D2D UE in the cooperation region providing a QoS-guaranteed content delivery, BS will schedule a cellular delivery for the content request (cellular delivery mode is selected). That is, the mode selection is determined by transmission range,whether UE caching the requested content or not and QoS constraint of content request.

For a linki→j, the transmission over it is regarded to be successful when the signal-interference-ratio (SIR) at the receiver is larger than a threshold. We assume that the thermal noise is negligible and this assumption may be easily relaxed (e.g., see [29,30]) but at the cost of complicating the derived expressions without providing additional insight. For a communication linki→j, the received SIR at can be expressed by

whereEidenotes the transmission power of UEi,dijis the distance from the transmitterito the receiverj,Ijis the interference at the receiverjfrom the set Ω of simultaneous transmitters andHijcharacterizes the fast fading power fromitoj.

Then the successful transmission probability of linki→jwith link distancedijis

whereγthis the decoding threshold at the receiver.

2.2 Content request and delivery

Requests for contents are modeled by Poisson arrival processes. The sum of requests for all contents also follows a Poisson arrival process according to the queuing theory [31] and the arrival rate is

whereλlis the arrival rate of requests for a contentslandLis coexisting contents in the system.

Each UE has a storage capacity called a cache. To support the D2D content delivery,UEs need to pre-cache some contents. Unlike wireline communications, multiple UEs may receive signal from a transmitter due to wireless broadcast characteristic. Here we make the most of this characteristic by scheduling more UEs to receive transmitted contents to prepare for D2D delivery. About the content delivery, we give the following assumption.

Assumption 2.When a UE requests a content, a selected node (BS or D2D UE) delivers the requested content to the UE. Other available UEs (e.g. UE having no data to send or receive) will also listen to the delivered content and cache received contents according to an employed caching strategy.

Considering that the cache capacity of UEs is limited, UE employs a temporary-storage method for received contents in which UE puts a received content for a period of time in case that some neighbors need these contents. We assume that each UE independently aborts its cached content after a certain amount of time which is exponentially distributed with mean 1/θlfor contentlwhereθlis the discarding rate. The smallerθlis, UE can response the request forlwith longer time. Meanwhile,θlshould not be too small to avoid the cache overowing at UEs. The appropriate selection ofθlis studied in Section III based on constraints of QoS requirements of content and cache capacity of UEs. Usually, for more popular contents which has larger requested rate,it will be cached with longer time. For a cache of UE withLcontents, the total aborting rate of contents is

III. CACHING STRATEGIES FOR D2D CONTENT DELIVERY

A UE retrieving a required content from its neighbors is premised by pre-caching at UEs in D2D-supported content delivery strategies.Each UE caches contents according to a certain caching policy which will be discussed later. The caching policy enables D2D delivery to satisfy a content request by guaranteeing enough neighboring UEs caching the required content while satisfy caching capacity constraint by discarding some contents.

3.1 Impact of QoS requirement of content request

To secure the QoS of content delivery based on the caching policy to be proposed, we use a determinate guarantee for a design guideline as follows. For content request oflwith QoS constraintQl, the average successful delivery probabilityξlfor a random link should be larger than the constraint, i.e.,ξl≥Ql. Of course, other performance metrics can be used for evaluating the QoS such as delivery rate,time delay and so on. Here successful delivery probability is analyzed as an instance. The methodology can be used for other QoS metrics.

For content delivery in cellular networks,there are usually two choices, i.e., pull and push. For the pull option, a UE requests its required content and then its neighbor UEs or BS makes a response to this request via sending the content to this UE. For the push option, instead of request and response, a UE which has cached content may send them at regular intervals. Other UEs in the range of this UE listen to broadcast contents and cache them based on a pre-dened caching strategy.Thus, more UEs may benet from once transmission. However, frequent transmission leads to excessive energy consumption. To obtain benets of both options, here a hybrid strategy is proposed for content delivery and caching.In this strategy, a UE requiring contentrstly sends its request. Then the nearest neighbor caching this content is scheduled by BS to send this content to this UE. Here we do not assume that the geographically nearest neighbor always has cached the requested content to make the model more practical. If the nearest neighbor has cached the requested content when a UE sends its request, the performance of content delivery will be better than that derived in this paper. The transmission power is set toη0d0αto cover the cooperation region with radiusd0and targeted receiving powerη0. UEs outside this region can also cache this content if they can decode it. Finally, all available UEs (scheduled by BS) will listen to the delivery signals. With this strategy, theγjin (1) for a receiverjcan be calculated by

where ?tis interfering set constructed by simultaneous transmitters reusing resources.

According to (2), the successful delivery probability for the linki→jcan be calculated as follows.

where LI′jis the Laplace transform of

and Γ(·) is the Gamma function. From (6),we see that the average successful transmission is affected by path loss (determined by link distance) and simultaneous transmitters(determined by scheduling).

For a UE obtaining a content under D2D mode, BS schedules the nearest neighbor caching this content to transmit the content to this UE. Assuming that each UE cacheslwith probabilityPl, UEs cachinglalso follow PPPs according to the thinning theory[32].Then the distribution of the distance between UE and its nearest neighbor cachingl,fl(r),can be expressed by[33]

whereρlis the density of UEs cachingl.

Thereby, the expected probability that it is responded by neighbor UE can be written as follows by averaging the location of transmitters.

Substituting the Probability Distribution Function (PDF) in (7) into (8) as follows:

To guarantee a served probabilityQl, we needξl≥Ql. Thus, the caching policy should make the density of UEs cachinglsatisfy the following lemma.

Lemma 1.To guarantee a served probability of requests for contentl,Ql, the minimum density of UEs cachingl,ρlo, is the solution of (10).

which can be easily obtained by numerical calculation.

Proof:Taking the derivative ofξlin (9)with respective toρl, we have

Thus,ξlmonotonically increases withρland there is a minimumρlto letξl≥Ql. Lettingξl=Qlyields the conclusion.

To support the D2D content delivery with QoS requirements, UEs need to cache some contents according to the caching policy to ensure there are enough UEs caching the requested content. From Lemma 1, the criterion of caching policy affected by QoS is that the density of UEs cachinglis larger thanwhich can be easily obtained by numerical calculation. Here we use G to show the relationship betweenand some affecting parameters such asQl,ρsandd0, i.e.,for easy elaboration. We give the following example for a clearer show of this criterion.

An example: For a UE which requires contentl, it sends the request to neighbors within the cooperation region with area sizeσ. Then the minimum number of cached UEs in the region isPractically, redundant UEs are used for guaranteing the delivery performance,thereby, the caching policy targets to provide

To guarantee a minimum densityfor content request ofl, we next discuss the caching policy used by each UE. The premise of cachinglfor a UE is thatlis successfully received by this UE. A UE may successfully receive several different contents simultaneously at different resource blocks (RBs). For a UEjin the system, the probability that it cacheslis denoted byWhenjlistens to the content delivery oflfrom a transmitter with distancer, the successful delivery probability is exp (?πκρsr2) as indicated in (6). Let the caching probability atjbe

Then for a UE in the system, the probability thatlis in its cache isWe note that the probability that contentlin the cache of UE is independent to its location.Concerning with the caching policy at each UE, we have Lemma 2.

Lemma 2.For a UEj, the minimum probability that it intends to cachelcan be written as

Proof:Forl, the probability that a UE in the system caching it can also be expressed by

Constrained by QoS content request,ρlshould be larger thanρlo. Thus,Plneeds to satisfy

Substituting (15) into (12) yields the conclusion.

From Lemma 2, we observe that this caching policy implicitly separates UEs which cache the same content spatially, which can better utilize distributed caching for D2D content delivery.

After one round of content delivery, some of UEs around the transmitter may cache this content. Then the number of caching UEs increases with time. However, excessive UEs cachinglwill not further improve delivery performance since the densityρlof caching UEs is enough for guaranteeing content requests oflas indicated above. In addition, the caching capacity of UEs is limited. Thereby,after several loops, UE will not cachinglwhich will be noticed by cellular BSs. After receiving the notice, UE will not receivel.

3.2 Impact of Caching Capacity

Abundant caching at UEs guarantees the delivery QoS for content requests as analyzed in the last Abundant caching at UEs guarantees the delivery QoS for content requests as analyzed in the last sub-section. However,redundant caching may lead to the overow of UE cache due to limited capacity. Therefore,the constraint of caching capacity should be considered for the content caching at UEs. To avoid overflow, some contents received by a UE are pre-dropped while some are cached. To satisfy QoS requirements of different content requests with limited cache capacity, which contents are cached and how long of the caching time for a content staying in a cache will be discussed in this section.

As analyzed in the above sub-section, the probability that a UE cachingl(i.e., UE successfully receivesland caches it) isPl. When each UE caches contents for the minimum guaranteed UE density, the expectation of contents cached by this UE, i.e., the expectation of content arrival rate at the cache of UE can be calculated by

Considering the limited capacity of UE cache, contentlis discarded with rateθl. To study the discarding rate for different cached contents at UE, werstly analyze the overow probability at UE. For a cache with sizeM,the probability that there ismpackets in the cache is

whereνandθare total arrival and leaving rates of all packets at a UE, respectively.

proof:

Thus, we have

Solve the geometric progression of left part in (20), (21) can be obtained as follows.

Thus,p0can be written as

Including (22) into (19) yields (17).

Lettingm=M, we can obtain the probability (it is called block probability here) that cache is full as follows based on (17).

Thus,pMdecreases withθ, that is to say,there is a lower boundθ0ofθto make overflow probability smaller than?0. For the discarding rate to avoid frequent overow, we have the following lemma.

Lemma 3.Constrained by cache capacity of UEs, the caching strategy should discard contents with rateθ0, which is the solution of(25).

Proof:To guarantee the overow probability below a threshold, we needpM≤?0. SincepMdecreases withθ, the minimum tolerantθ,θ0, is the solution ofpM=?0. IncludingpMin (23) into this equality yieldsthe conclusion.

From Lemma 3, we see that UE can avoid cache overflow by adjustingθsmartly. For example, if there areLcontents in its cache,then the sum discarding rateshould be larger thanθ0.

3.3 Caching scheme

Based on above analyses, the caching policy for different contents used by D2D UEs should satisfy the following theorem.

Theorem 1.To support D2D content delivery with guaranteed QoS, the caching policy at UEs for received contents acts as follows: UE caches contentlwith probabilitywhereris the distance between the UE and the transmitter. UE discardslwith rateθl.θlsatisfieswhen there areLcontents in the cache andθ0is the solution of (25).

Based on Theorem 1, we propose a small cell-assisted content caching scheme at UEs to prepare UE caching for D2D content delivery with the consideration of content QoS and UE caching capacity. In this scheme, when a UEjsuccessfully receives contentl, itrstly calculates the caching probability based on (13).Then the UE generates a random numberτ0and compares it with the calculated probability. The UE determines to cache this content ifPl

j≥τ0. Simultaneously, UE sets a countdown clock to determine when to discard this content according to its caching capacity by calculatingθl. For example, the storage time oflis set to 1/θl.jdiscardslwhen 1/θlseconds elapses. Furthermore, UE will report that it discards the content to its serving small cell BS. For example,θlis firstly initialized by a constantδ. Then, the total discarding rate of all contents in its cache is updated byθ=θ+θl. UEcomparesθandθ0calculated by (25). Ifθ＜θ0, UE increasesθlbyand then updatesθuntilθ≥θ0is a pre-dened maximum discarding rate to avoid UEs frequently to cache some content and discard it for a while. Finally, UE reports the new cached contents number (e.g.,l) to the small cell BS it belonging to.

For small cell BSs, it stores sketch content caching information of UEs in its coverage,which is reported by each UE. For example,when a small cell BS receives a reported message from UEjwhich cachesl, it updates the number of UEs cachingland the correspond-ing density. When the density of UEs caching a content is larger than an essential density such asρlo, the BS will broadcast an acknowledge message to its serving UEs. Then these UEs will not receivelagain. That is,lis an unexpected content forj. Otherwise,lis an expected content. The implementation of content caching scheme is listed in table I.

IV. SIMULATION RESULTS

In this section, some simulation results will be presented to evaluate the performance of caching strategies for D2D content delivery in cellular networks. The default value of simulation parameters are shown in Table 2.

Firstly, we compare successful transmission probability for a D2D link against the link distancedijunder different settings of simultaneous transmitter density and path loss factor in figure 1. Results show that the analyzed results matchthat of simulation, which verify the analyses of content delivery performance. Thisgure also indicates thatε(dij)decreases with the increase of interference or link distance. Thereby, the scheduled number of simultaneous transmitters and cooperation region affect the content delivery performance which should be considered for the design of content caching as indicated in this paper.For example, the minimum density of UEs caching contentlis a function ofρsandd0,i.e.,The successful transmission probability increases withαsince interference is reduced whenαincreases due to worse path loss of interference links.

Table I. Content caching scheme.

Table II. Simulation parameters.

The expectation of successful delivery probability,ξl, for a content request oflunder different delivery cases is shown in figure 2. Since the nearest neighbor cachinglis scheduled for the content delivery to the request UE, successful delivery probability is affected by the neighbor location. Hence, expectation of successful delivery probability is presented. From thisgure, we observe thatξlincreases withd0andρldue to more cooperative UEs for its content request. However,the increase ofξlbecomes be bounded whend0grows larger due to marginal contributions of farther UEs. Furthermore,ξlis reduced by the increase ofρswhich leads to severer interference. Thereby, given communicationenvironment and QoS requirement (Ql), caching strategy should be well managed (e.g., enough cached UEs is prepared) to satisfy the QoS requirement. For example, forQl=0.8 as labeled in this figure, there are the minimum cooperation distancesunder different cases to satisfy the QoS requirementSimilarly, given a cooperation range, we can adjustρlto achieve this goal. A clearer show for this caching strategy is shown ingure 3.

Fig. 1. Successful transmission probability for a link with distance dij.

Fig. 2. Expectation of successful delivery probability for a content request against cooperation distance.

Fig. 3. Expectation of successful delivery probability for a content request against density of cached UEs.

As shown in figure 3,varies withρlunder different delivery cases such as cooperation distance, interference and path loss. Given a QoS requirement, we can adjust the number of UEs caching this content to satisfy the content request. For example, forQl=0.9,minimumρlunder different casesandcan be obtained from the analyses of this work. Then, when the density of UEs which are scheduled to cachelis larger than the minimumρl, we can guarantee

With the criterion ofρl, each UE can adjust caching probability for each content as proposed in Section III. Based on the proposed caching strategy which intends to spatially separate UEs caching the same content,gure 4 presents simulation results on the caching results. It is shown that some UEs cachelaccording to the proposed caching strategy with caching probabilityPl. Number of caching UEs increases withPlas expected by comparing two sub-gures. Furthermore, UEs caching the same content are generally separated as expected which is more convenient to satisfy content requests from everywhere of the network via D2D communications while avoid excessive caching redundancy.

Based on proposed caching scheme, the CDF of delivery performance of content requests is shown in figure 5 under different QoS requirements. From this figure, we observe that most of request UEs in the network can obtain QoS-guaranteed contents via D2D communications when UEs cache the content according to the caching policy, which proofs the proposed scheme quite useful. Of course,when there are no enough UEs to support a minimumρl, QoS requirement cannot be satised by D2D content delivery. For this case,cellular delivery via small cell or macro cell should be utilized.

Fig. 4. Spatial distribution of cached UEs under different caching probabilities.

To ensure that the overflow probability of UEs is tolerable during the process of supporting D2D content delivery, contents will be discarded according to a rate proposed by the caching scheme. As shown ingure 6, the proposed caching scheme provides a possible way to limit the overow probability of UE below a targeted probability under different cases.For example,PM＜ 0.05 when?0=0.05.

V. CONCLUSION

Generally, the device-to-device (D2D) technology-assisted content delivery has attracted a lot of attention to offload traffic in content-centric networks. By utilizing caching at abundant distributed user equipments (UEs),content can be more conveniently acquired with less cost for fetching. Thus, smart caching is the primary condition to realize this convenience and efciency.

Fig. 5. The CDF of delivery performance of content requests versus QoS requirements.

Fig. 6. Block probability versus number of cached contents at a UE.

In this paper, we focus on UE caching strategies to indicate how to prepare caching contents with limited cache capacity to guarantee quality-of-service (QoS) requirements of D2D content delivery without pre-known neighbor demands. To achieve this object, some theoretical results are presented, which show the criteria of UE caching to satisfy the QoS require-ment of a content request. The probability of a UE caching content is adjusted based on these analyses. Furthermore, limited caching capacity of UEs is also considered for the caching strategy by constraining the overflow probability of UE cache. Based on these criteria of caching, a caching strategy is proposed. These analyses and strategies provide important insights into directing how to caching at UEs for QoS-guaranteed D2D content delivery.

ACKNOWLEDGEMENT

This work is supported by the National Natural Science Foundation of China under grant 61601283, 61472237 and 61271283.

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