Jingfeng Cai, Ronghui Hou*, Yinghong Ma

State Key Lab of Integrated Service Networks, Xidian University, Xi'an, China

Mobile data consumption is expected to increase to 30.6 Exabytes per month [1] in the near future, due to the rapid proliferation of smart mobile devices. To meet high user quality of service (QoS) requirements and enhance the network capacity, small cell is considered as a promising technology by improving spectrum reuse [2]. The cost of deploying the small cells with wired backhaul is a significant part of the total capital expenditure and operational expenditure for operators. An alternative way is to deploy the small cells with wireless backhaul, which is flexible and cost-efficient.However, it is a key challenge to forward a huge volume of traffic data from the core networks through the wireless backhaul link with limited capacity. Distributed caching at the small cell base stations is an effective way to the offload backhaul traffic [3-8].The small cell base stations (SBSs) cache the most popular contents in advance. In case the small cell base station caches the requested file, the request can be served locally without consuming backhaul resources [9].

It is obvious that larger cache capacity would reduce the consumption of backhaul resources. However, SBS normally has a limited cache capacity due to cost concern [4]. Therefore, it is important to analyze whether a given cache capacity can satisfy the user requirement with high probability. On the other hand,the wireless access link and backhaul link may share the same spectrum resources, how to appropriately divide into two parts is also important to improve system performance.

Lots of works study the small cell networks with wireless backhaul. In [10], an auction-based resource trading scheme between a network service provider and multiple content providers is proposed to reduce the downloading latency of the mobile users. The works in [11], [12], and [13] study the access point selection problem in small cell networks with limited backhaul capacity. [11] and [12]show that the access point selection should not only consider the limited wireless backhaul capacity, but also consider the limited access resources. However, the small cell base stations have no caching capability in [11] and[12]. [13] considers the the limited backhaul resources and limited cache capacity, but does not consider the impact of limited access resources on selection scheme.

Many works study the optimal caching policy, that is, whichles should be cached at a certain SBS. The works in [15] - [20] find the optimal caching solution given the user request. If the user requests are not known in advance, the works in [13], [22] and [25] let each SBS cache the most popular contents.

A very related work [9] develops an analytical model to derive the outage probability and average content delivery rate as a function of signal-to-interference ratio (SINR), storage size, and file popularity. The performance of system can be calculated. The results can be used to design a network. However, the outage probability in [9] means the probability that a user’s data rate is less than a threshold or the requestedle does not cache in the associated SBS. [9] does not consider the limited capacity of radio resource and the method it proposed can not be used to congure the resource for a system. In our work, we try to calculate the probability that an SBS’s radio resource is exhausted and obtain the best conguration of system resource.

To our best knowledge, we are the first to study the optimal resources configuration on the system performance for content distribution in dense small cell networks. We formulate our problem as an multi-dimensional markov chain model, which facilitates us to calculate the blocking probability that it is a function of cache capacity, wireless backhaul bandwidth, and wireless access bandwidth. We thus identify the optimal conguration scheme to minimize blocking probability.

The rest of this paper is organized as follows. In Section II and III, we present the system model and develop our analytical model based on multi-dimensional Markov chains.Extensive simulations of resource configuration are conducted to validate our analysis in Section IV. Finally, we conclude this paper in Section V.

Fig. 1. System model.

II. SYSTEM MODEL AND PROBLEM STATEMENT

We assume that each SBS in the OFDMA small cell network schedules a UE with Round-Robin algorithm [23], and therefore,the same amount of spectrum resources is allocated for each user request. For easy representation, we quantify the total spectrum resources intoRunits and one unit is allocated for each user request [12]. In this paper, we consider that the total spectrum resources are shared by wireless access and wireless backhaul. Denoted byRathe units of wireless access andRbthe units of wireless backhaul,and we haveR=Ra+Rb. Similarly, we consider that each request possesses one unit of backhaul resource in case that the content should be downloaded from the remote server. We assume that the channel between SBS and user is independent, and the transmission rate of each user may be different due to the instantaneous channel conditions. And the average channel possessing time for each request follows an exponential distribution with parameterwhereµmdenotes the serving rate of SBSm.

We consider the dense small cell deployment scenario, in which a user can access multiple base stations. For example, ingure 1, that there are two small base stations SBS 1 and SBS 2, which connect to the core network through a wireless backhaul. There are eight user equipments (UEs). UE 1 and UE 2 fall in the coverage range of both SBS 1 and SBS 2. They can associate with either of them. Assume that UE 1 prefer to associating with SBS 1 than SBS 2 due to better channel statement.In case that SBS 1 has no enough access resources or backhaul resources, UE 1 would try to associate with SBS 2.

The set of SBSs in the cellular network is denoted as M ={1,...,M}. We further denoteas the access capacity andas the backhaul capacity of SBSm. Meanwhile, SBSmequips with a cache, which has a capacity ofCm. An SBS downloads the popularles during off-peak hours via backhaul to periodically update its cache according to the control signal from the system administrator, which maintains the popularity information of allles [3].Therefore, some users can be directly served if the requestedle is cached in the SBS.

Fig. 2. Arrival rate of user request of 2 SBSs.

It is assumed that the content popularity follows the Zipf distribution [9]. For a known content library, according to Zipf distribution,the request probability of thei-th most popularle/content is

whereγandKare the parameters for Zipf distribution.Kis the total number of contents.γis the shape parameter, which defines the correlation level of the content popularity.

Since the capacity of the cache is limited,an SBS can not cache all the contents. If the requested content can be found in the cache, a cache hit occurs [9]. The probability of cache hit means the probability that a user’s request can be served by an SBS directly, which only consumes access resource but not backhaul resource. It is assumed that eachle takes one unit of cache capacity [24]. Therefore, the probability that a request can be directly satis-ed by SBSmcan be represented by

We divide the whole area into subareas due to the coverage of SBSs and each subarea is related to a candidate SBS set C⊆M. De-ne {C} the collection of candidate SBS set.For instance, ingure 2, there are three subareas which are related to candidate SBS set{1},{2} and {1,2}, respectively. For clarity,the following discussion assumes the network contains two SBSs, and our analysis can be easily extended to consider multiple SBSs. In this paper, we consider that the user request rate is thought as a user session per second.The arrival rates of user requests are divided into several categories [12]. The request arrival rate is different in different sub-areas.Our problem can be stated as: Given the small cell deployment scenario, the total amount of spectrum resources, and the statistical user request demand, identify the optimal spectrum resources allocation for wireless access andwireless backhaul to minimize the blocking probability with the limited caching capacity.

III. THE PROPOSED SPECTRUM RESOURCES ALLOCATION SCHEME

In order to design a optimal spectrum resource allocation scheme, werstnd a way to calculate the blocking probability for a given resources conguration solution. In this paper,we apply multi-dimension Markov chain to model the system, which facilitates us to obtain the blocking probability. With the blocking probability calculation scheme, we cannd the optimal wireless access and wireless backhaul resources conguration to minimize the blocking probability.

We assume that the system can be time slotted with a very smallδ＞ 0. Denote bythe system state. The system state is identied by the spectrum resources consumption, whereSm= (ia,i) indicates thatiaunits of access resource andiunits of backhaul resource are being possessed by the UEs at SBSm.

It is assumed that the time slotδis small enough that the probability of two or more user requests arrive or leave at a time slotδiso(δ), which can be ignored. Therefore, the probability that statetransits to statefork≥ 2 andk≥lis zero as well as the probability that fromAnd the probability that statetransits to statefork≥ 2 andk≥lis zero as well as the probability that fromIn a word, the transition probability is negligible if there are more than one request in a time slotδ.

Now we present the calculation of transition probability in our multi-dimensional Markov chain by assuming two SBSs. Assuming that the request arrival rate follows Poisson distribution. Denoted by(sessions/s) (resp.the request arrival rate for users whose candidate SBS set only has SBS 1 (resp. SBS 2), as shown ingure 2. Similarly,is the request arrival rate for users whose candidate SBS set is {SBS 1, SBS 2}. And the subscripts inare ordered according to the propagation loss from the candidate SBSs, which means the sessions of typewith less propagation loss from SBS 1 than SBS 2 (vice versa forIn other words, the sessions of typemeans the users prefer to associate with SBS 1 rather than SBS 2.

In order to calculate the transition probabilities, we dene the following events that may happen in the system within the time slotδ:

• A. a user request arrives at an SBS and consumes both access and backhaul resource.

• B. a user request arrives at an SBS but only consumes access resource.

• C. no user request arrives at an SBS.

• D. a user that consumes both access and backhau resource leaves.

• E. a user that only consumes access resource leaves.

• F. no user leaves an SBS.

We identify (K,I) that event K happens at SBS I. Taking SBS 1 at stateas an example, the probability that an event happens at SBS 1 is

The system state that transits fromhappens when both the conditions are satised: (I)a user request consuming backhaul resource arrives at SBS 1 and no user leaves SBS 1; (II)no user request arrives at or leaves SBS 2. We then have

观察组对护理满意评分为(95.68±2.77)分,参考组对护理满意评分为(90.89±3.06)分,两组比较差异显著(T=7.340,P=0.000)。

Meanwhile,the system state that transits fromoccurs when (I) a user request which consumes only access resource arrives at SBS 1 and no user leaves SBS 1, and also (II) no user request arrives at or leaves SBS 2.

The conditions for transition fromto(I) a user that consumes both access resource and backhaul resource leaves SBS 1 and no user request arrives at SBS 1; (II) no user request arrives at or leaves SBS 2. Then, the probability of state transition is

The conditions for transition fromare: (I) a user that only consumes access resource leaves SBS 1 and no user request arrives at SBS 1;(II) no user request arrives at or leaves SBS 2.Therefore, the probability of state transition is

Based on the transition probabilities, we can calculate the steady state probabilities by Kolmogorov forward equation. A user request would be rejected when its access resource is completely possessed, or when its backhaul resource is completely possessed and the request needs to consume the backhaul resource. We calculate the blocking probability that an SBS would reject a user request. Denote byPblock,mthe blocking probability of SBSm. We consider a system that discussed above, and the blocking probability of SBS 1 is calculated as

whereS−mis the state of system except SBSm. For instance, in the above case,S−1isS2in a system of 2 SBSs. Denotethe state set of system except SBSmandP{S1,S−1}a steady state probability of the system. According to the SBS blocking probability, we can calculate the system blocking probability, as(13).

Without loss of generality, we calculate the system blocking probability with M SBS.Firstly, we rewrite the blocking probability of SBSmas (14).Furthermore, we can have the system probability as following.

whereλCis the sum rate (e.gandof request arrival in subareas whose candidate SBS set is C.

With the objective of minimizing the system blocking probability, the optimal spectrum resources allocation can be obtained as the solution to the following formulation (14).(14a) means that SBSmcaches the topCmunits ofles/contents. (14b) implies that wireless access and wireless backhaul of SBSmshare the totalFmunits of spectrum resources,as shown ingure 3.

Without caching, we can easily give an optimal spectrum resources allocation for wireless access and wireless backhaul. A user request consumes an unit of wireless backhaul resource as well as an unit of wireless access resource without cache. Therefore, the optimal resource conguration is to allocate the same amount resources for wireless access and wireless backhaul, as shown in figure 3(a).Denote bythe optimal amount of wireless access resources and the optimal amount of wireless backhaul at SBSm, and we have

Algorithm 1The Optimal Resource Allocation

Phase I - Initialize.

• user request arrival rate.

• SBS resource allocation set

• The cache hit probability of SBS,Phase II - Resource Allocation.Iteration k :

•foreach SBS mdo

- Calculate blocking probabilityPblock,m(k) by (14);

-ifthe newPblock,mis smallerthen

- *--- Update resource allocation of SBSm.

-else

-end if

• end for

• Calculate blocking probabilityPblock(k) by (15).

Until stop condition.

In case that SBSmhas caching capacity, it is obviously that we can allocate more wireless resources for access resources, as shown in figure 3(b). Therefore, we define a step size,α. At iterationk, we moveαspectrum resource of SBSmfromtoThat is,Given the spectrum allocation, we calculate the blocking probability of SBSm,Pblock,m(k). Once the new allocation scheme can reduce the blocking probability of SBSm, we update the resource allocation scheme by the new resource allocation scheme. The algorithm would be stopped at the iteration that none of SBSs' resource allocation scheme is updated. In other word,at iterationk, if we havePblock,m(k) ＞Pblock,m(k-1) for each SBSm, the optimal resource allocation is obtained. To determine the optimal resource conguration scheme, it needs to calculate the blocking probability of resource allocation for each SBSm, yielding a complexity of(Rm) per SBS. As a result, the iteration complexity of proposed algorithm is

Fig. 3. Illustration of spectrum resource allocation at SBS m.

Fig. 4. Allocation of spectrum resource for backhaul.

IV. SIMULATION OF RESOURCE CONFIGURATION

In this section, we conduct simulation experiments to identify the impact of spectrum resources allocation on system performance.The arrival rate of user request follows Poisson process, and the duration time for downloading a content follows an exponential distribution. A user request would be rejected if its associated SBS does not have enough resource to serve it. However, if the rejected user request is in the overlapping area of multiple SBSs, the user would try to access other SBSs. In case that no SBS can serve the request, the user request is blocked. The blocking probability is calculated as the ratio of the number of blocked users to the total number of users. Meanwhile, we calculate the theoretical blocking probability based on our analytic model, and compare the analytic results with the simulation results. As benchmark, we consider a method that each SBS allocates the same amount of access resources and backhaul resources [12].

The network scenario consists of a scenario of 8 small base stations densely deployed in an area, following specications for Scenario 2a in [26]. SBSs are randomly placed within a circle of 50m radius with a minimum distance of 20m between any two SBSs.

When the total spectrum resources is 12,14, 16 units at each SBS,gure 4 presents the optimal allocation solution for backhaul and access to minimize the blocking probability.It is obvious that we should allocate the same backhaul and spectrum resource when the cache capacity is zero under the assumption that each request consumes a unit of wireless access and a unit of wireless backhaul. With the increase of cache capacity, more backhaul resource would be saved, and thus, we should allocate more spectrum resource to reduce the blocking probability. Figure 5 shows the corresponding blocking probability, and we observe that the blocking probability is reduced as the cache capacity is increased.

To compare the impact of SBS density on system, we change the arrival rate of the overlapping area. The larger arrival rate of the overlapping area implies that the density of SBSs is larger. In the second scenario, we set the average arrival rates of user requests that can only be served by one SBS is 0.25,and the average arrival rate of user requests is 0.1 in the overlapping areas. In the third scenario, we set the average arrival rates of user requests that can only be served by one SBS is 0.35, and the average arrival rate of user requests is 0 in the overlapping areas. The other parameter settings are the same as those in therst scenario as show ingure 5. Figs. 6 and 7 show the corresponding simulation results,respectively. Figs. 6 and 7 show that our theoretically analytical system performance results are close to the simulation evaluated results in the second scenario and the third scenario.Figs. 8 - 10 show the impact of overlapping area on blocking probability under the different spectrum resources allocation solution.We observe that the system with larger overlapping areas has the smaller blocking probability. When the overlapping area is larger,more users would access multiple SBSs. This means that the resources of different SBSs can be shared by more users, and therefore, the blocking probability would be reduced. Our simulation results show that the dense SBSs deployment would improve network capacity.Our simulation results suggest that the network topology has the significant impact on the network performance, and the resource configuration should take the network topology into account. By comparing our resource configuration algorithm with the benchmark method, it can be observed that our resource allocation algorithm outperforms in terms of blocking probability, by which a user request would be rejected by a small probability.

Fig. 5. The blocking probability of system(Scenario 1).

Fig. 6. The blocking probability of system(Scenario 2).

We also consider the scenario that users can access three SBSs at most. The average arrival rates of user requests that can only be served by one SBS is 0.08, and the average arrival rate of user requests is 0.035 in the overlapping areas of two SBSs. Figure 12 presents the optimal spectrum resources allocation solution for different cache capacity values, and figure 13 shows the corresponding blocking probabilities. Generally, our simulation results show that caching-based content distribution can effectively improve network performance,and the network topology and the spectrum resources allocation have a signicant impact on network performance.

Fig. 7. The blocking probability of system(Scenario 3).

Fig. 8. Comparison of blocking probability with different overlapping areas (12 units of spectrum resource).

Fig. 9. Comparison of blocking probability with different overlapping areas (14 units of spectrum resource).

Fig. 10. Comparison of blocking probability with different overlapping areas (16 units of spectrum resource).

V. CONCLUSION

We study the spectrum resources allocation for caching-based content distribution in dense small cell networks. In this paper, we consider that wireless access and wireless backhaul share the same spectrum resources, and it need to design a scheme of resource allocation to appropriately divide the total spectrum resources into two parts to improve network performance. We describe a method to evaluate the blocking probability of system, which facilitates us to identify the optimal spectrum resources allocation. Comparing with a benchmark method, it is observed that our algorithm of wireless resource can guarantee the quality of experience (QoE) in terms of blocking probability. Our simulation results show that the network topology, cache capacity and the spectrum resources allocation have signicant impact on system performance. Moreover, our simulation results show that the dense SBSs deployment is a promising way to improve network performance.

Fig. 11. Allocation of spectrum resource that users can access three SBSs at most.

Fig. 12. The blocking probability of system that users can access three SBSs.

This work was supported in part by the National Natural Science Foundation of China(Grants Nos. 61571351, and 61401326), the important national science & technology specific projects 2015ZX03002006-003, Natural Science Basic Research Plan in Shaanxi Province of China (Program Nos. 2016JM6028 and 2016JQ6054).

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