A Novel Content Caching and Delivery Scheme for Millimeter Wave Device-to-Device Communications
Theshani Nuradha, Tharaka Samarasinghe, Kasun T. Hemachandra
aa r X i v : . [ ee ss . SP ] N ov A Novel Content Caching and Delivery Scheme forMillimeter Wave Device-to-Device Communications
Theshani Nuradha ∗ , Tharaka Samarasinghe ∗† , Kasun T. Hemachandra ∗∗ Department of Electronic and Telecommunication Engineering, University of Moratuwa, Moratuwa, Sri Lanka † Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, AustraliaEmail: [email protected], [email protected], [email protected]
Abstract —A novel content caching strategy is proposed fora cache enabled device-to-device (D2D) network where theuser devices are allowed to communicate using millimeter wave(mmWave) D2D links ( > Index Terms —content caching, device-to-device communica-tions, millimeter wave, ultra-dense networks
I. I
NTRODUCTION
Small cells and device-to-device (D2D) communications areenvisioned to be promising technologies for enhancing thequality of service (QoS), throughput and energy efficiency ofnext generation wireless networks [1], [2]. Due to scarcityin existing cellular spectrum, millimeter wave (mmWave)frequencies have been considered as an enabling technologyfor high speed D2D communications. In D2D aided cellularnetworks, the successful establishment of D2D connectionsdepends on the availability of popular files in proximitydevices. Therefore, content placement in user devices is ofparamount importance for D2D based traffic offloading. Thispaper presents a novel content caching strategy for a cacheenabled D2D network, where the user devices are allowed tocommunicate using mmWave D2D links as well as conven-tional sub 6 GHz cellular links.Cache placement schemes based on cache hit probabilitymaximization [3], and cache aided throughput maximization[4], can be found in the literature for conventional cellularnetworks. In these works, optimal caching probabilities areobtained such that the achieved content diversity leads to betternetwork performance. When it comes to mmWave networks,a D2D aware caching policy that splits the most popularcontent into two content groups, and randomly distributesthe content groups among the users is proposed in [5]. Thepartitioning of the most popular content is performed based onfairness considerations, such that the two content groups haveequal self cache hit probability in a user device. The contentplacement does not consider the characteristics of mmWave
This work is supported by the Senate Research Council, University ofMoratuwa, Sri Lanka, under grant SRC/LT/2018/2. propagation and the effects of blockage when placing content.A cache hit probability maximization based optimal cacheplacement in a mmWave ad-hoc network is studied in [6].The paper omits the effect of interference from other D2Dlinks, which can be crucial factor on network performance.In this paper, we consider a cloud radio access network(C-RAN) operating in the sub 6 GHz band, and supportsD2D communications using mmWave spectrum. A contentplacement scheme is proposed for user device caching, consid-ering the propagation characteristics of mmWave links and theinterference from other D2D links, which makes it differentto [5] and [6]. In addition, it also considers the popularity andapplication specific QoS constraints of different files, whichmakes it more applicable to next generation wireless networks,where QoS measures such as latency are considered to be keyperformance indicators. Thus, we maximize a different metric,referred to as the successful content reception probability,which is the probability of reception without violating the filespecific QoS constraints. The main contributions of the paperare as follows: • A content placement scheme is proposed for user devicesby solving an optimization problem, that maximizes thesuccessful content delivery probability within the line ofsight (LoS) region of a D2D transmitter. Optimal cachingprobabilities of a multitude of heterogeneous files, thathave their own rate constraints for successful reception,are obtained. • The cache placement scheme is coupled with a userassociation scheme to further improve the offloading gainwithout violating QoS constraints. • The performance of the network in terms of successfuldelivery of content and offloading gain is evaluated bothanalytically and through simulations, to clearly highlightthe gains of the proposed content placement and the userassociation schemes with respective to energy efficiencyas well.The overall scheme improves the successful traffic offloadinggain of the network compared to conventional cache-hit max-imizing content placement and delivery strategies. Significantenergy efficiency improvements can also be achieved in ultra-dense networks.The paper organization is as follows. Section II presents thesystem model and the problem formulation. The solution tothe optimization problem which leads to the content placementtrategy, and the user association scheme are presented inSection III. The performance of the proposed schemes areevaluated theoretically and numerically in Section IV andSection V, respectively. Section VI concludes the paper.II. S
YSTEM M ODEL A ND P ROBLEM F ORMULATION
A. Topological Model
We consider a C-RAN, where the remote radio heads(RRHs) are spatially distributed according to a homogeneousPoisson point process (HPPP) Φ R with intensity λ R . TheRRHs are wirelessly connected to the edge cloud (fronthaullinks) and the edge clouds are connected to the core network(backhaul links). The spatial distribution of the mobile user(MU) devices is modelled using an independent HPPP Φ u with intensity λ u . Content to a MU may either be deliveredfrom a RRH through a cellular link that operates in the sub 6GHz band (transmit power P c , wavelength W c , bandwidth B c )or from another MU through a mmWave D2D link (transmitpower P d , wavelength W d , bandwidth B d ). Content deliverythrough a D2D link will only be possible if the requested fileis in the cache of another proximity MU. Each MU is capableof caching M d files of equal size.RRHs are equipped with omni-directional transmitting an-tennas while the MUs are equipped with omni-directionalantennas for cellular communications and directional anten-nas for mmWave communications. Similar to [5], sectorizedantenna pattern is adopted at the transmitters to approximatethe antenna pattern for the mmWave links. It is assumed thatthe antennas of the transmitter and the receiver are perfectlyaligned for desired links while the interfering transmitterantenna bore-sight is uniformly distributed over [0 , π ] . Thismeans the probability distribution of the i.i.d. random antennagain G ′ associated an interfering mmWave link is given by Pr (cid:8) G ′ = G m (cid:9) = (cid:0) ∆ θ π (cid:1) , Pr (cid:8) G ′ = G s (cid:9) = (cid:0) π − ∆ θ π (cid:1) , and Pr { G ′ = G m G s } = θ (2 π − ∆ θ )(2 π ) , where G m and G s denotethe main and side lobe gains, respectively, and ∆ θ denotes theangle of deviation from the antenna bore-sight.We refer to the MUs that request content as active MUs. Ata given time, the probability of an MU being active is ρ . Theremaining MUs, which we refer to as inactive MUs, can serveas potential D2D transmitters. It is assumed that all RRHs areactive at a given time. Without loss of generality, we considera typical MU located at the origin for our analysis. B. Channel Model
For the cellular links that operate below 6 GHz, the simplepath loss model with a path loss exponent α c is used to modelthe location dependent path loss. For mmWave links, the aver-age LoS ball model is used [7], [8]. According to this model, alink is considered as a LoS link if the link is shorter than D L .Otherwise, it is considered a non-line of sight (NLoS) link.The average size and the density of the blockages determine D L [9]. For mmWave links, blockage effects induce differentpath loss exponents α L and α N for LoS and NLoS links,respectively, with α L < α N . We assume fast Rayleigh fadingwhere the fading power is exponentially distributed with unit mean [5]. The received signal-to-interference-plus-noise-ratio( SINR ) when receiving file i from the D2D transmitter locatedat x ∈ Φ d is given by SINR d,i,x = G m h x r − α d x ˆ N + P y ∈ Φ d \{ x } h y G ′ r − α d y , (1)where Φ d , h x and r x denote the point process of the activeD2D transmitters, fading power and the distance betweenthe MU and the D2D transmitter at x , respectively, α d ∈{ α L , α N } , ˆ N = π N o F N B d P d W d , N o is the noise power spectraldensity and F N is the noise figure of the receiver. Similarly, anexpression for the received SINR when receiving file i througha cellular link from the RRH x ∈ Φ R , which we denote by SINR c,i,x , can be obtained by replacing subscript d in (1) withsubscript c and by replacing both antenna gains G m and G ′ by G T G R , where G T and G R are the antenna gains of thetransmitting RRH and the receiving MU, respectively. C. Content Placement
We assume that MUs request content from a finite contentlibrary of N files of equal size, and the file requests follow aZipf distribution of popularity exponent ǫ . Thus, the probabil-ity of requesting the i -th most popular file is given by β i = i − ǫ P Nj =1 j − ǫ . The rate and the delay constraints of the files may vary with thefile type and the associated application. The rate constraint forthe i -th most popular file is denoted by R i , and this constraintnecessitates an SINR greater than T i = 2 RiB − , for a linkhaving a bandwidth of B ∈ { B d , B c } .Due to the limited storage capacity of the MUs, the propa-gation characteristics of mmWaves, and the rate requirementsof different files, caching content at MUs should be done inan efficient manner. In this paper, we focus on designing acontent placement scheme that offloads the traffic to the D2Ddevices without violating the rate (QoS) constraints, whichare considered to be crucial in next generation networks.Moreover, considering the effects of blockage, it is preferredto have LoS D2D links. Thus, we focus on the successfulLoS reception probability ( SLP ) for the i -th most popular file,which we define as SLP i = Pr { SINR d,i, ˆ x ≥ T i ∩ r ˆ x ≤ D L } , (2)where ˆ x denotes the location of the closest D2D transmitterwho has the i -th file in its cache. The SLP depicts theprobability of receiving content from the nearest LoS D2Dtransmitter without violating the rate threshold.Let the probability of the i -th file being stored in thecache of an MU be q i . We define q , an N -dimensionalcaching probability vector q = [ q , .., q N ] , which denotes theprobabilities of an MU caching the N files in the contentlibrary. We focus on finding q that maximizes the averagesuccessful LoS reception probability ( ASLP ), defined as
ASLP( q ) = N X i =1 β i SLP i , here the SLP i values are averaged over the request probabili-ties, while not violating the MU storage constraints statistically(on average). Note that our objective function captures bothpopularity and the QoS requirements of different content,and also the effects of wireless propagation. The optimizationproblem can be formulated asmaximize q ASLP( q ) = N X i =1 β i SLP i subject to ≤ q i ≤ , i = 1 , . . . , N, N X i =1 q i ≤ M d . (3)III. S YSTEM D ESIGN
A. Successful LoS Reception Probability
An expression for
SLP i can be obtained using fundamentalsof stochastic geometry [10]. That is, from (2), SLP i = Pr n h ˆ x > T i r α L ˆ x (cid:16) ˆ I + ˆ N (cid:17) | r ˆ x ≤ D L o Pr { r ˆ x ≤ D L } = Z D L L ˆ I ( T i x α L ) e − ˆ NT i x αL f r ˆ x ( x ) dx, where ˆ I = P y ∈ Φ d \{ ˆ x } h y G ′ r − α d y and L ˆ I ( S ) is the Laplacetransform of the interference from mmWave D2D links. TheLaplace transform of the D2D interference is given by L ˆ I ( S ) = E Y y ∈ Φ d \{ ˆ x } E G ′ ,h y " e − G ′ hyr − αdy SG m (a) = exp − ρλ u p d Z π Z ∞ − E G ′ ,h y " e − G ′ hyz − αdSG m zdzdφ ! (b) = exp " − πρλ u p d E G ′ "Z D L (cid:18) − G m G ′ z − α L S (cid:19) zdz + Z ∞ D L (cid:18) − G m G ′ z − α N S (cid:19) zdz (cid:21)(cid:21) , where (a) follows from the probability generating functional(PGFL) of the PPP, p d is the probability of receiving therequested content via a D2D link, which has to be separatelycalculated, as shown later Section IV, and the expectation in (b)can be evaluated by using the PDF of G ′ given in Section II,which would result in a product of three exponential functions.It is not hard to see that the resulting expression, which hasmultiple integrals, makes it prohibitively hard for us to useit in a meaningful manner in the optimization problem. Wehave an N -dimensional non-convex constrained optimizationproblem, and even obtaining the optimum solution numericallyis not trivial. Hence, we make few approximations to obtain amathematically tractable expression for SLP i , i.e. , we obtaina convex approximation of the objective function such thatwe can solve the optimization problem in closed form. Wenote that these approximations are made only to design thecontent placement policy, and all assumptions are relaxed inthe remainder of the paper, which includes the performance evaluation and the numerical evaluations in Sections IV andV, respectively.Firstly, we neglect small-scale fading with regards tommWave propagation since it causes only minor changesin received power when the transmitter is within the LoSregion [11], [12]. Secondly, we consider the worst case ofD2D interference where all the user requests are catered byD2D transmitters, and approximate the random interferenceusing the average worst case interference. To overcome thesingularity when computing the D2D interference averagedonly over the large-scale fading, we use the bounded path lossmodel g ( r ) = min (1 , r − α d ) to model the path loss from theinterferers, similar to [13]. With these approximations, andby using Campbell’s theorem, the average interference can bewritten as ¯ I = E X y ∈ Φ d \{ x } G ′ min (cid:0) , r − α d y (cid:1) = λ u ρ π ( G m ∆ θ + G s (2 π − ∆ θ )) × (cid:18) α L − D − α L L α L − D − α N L α N − (cid:19) . From (2), and by considering the maximum search discoverydistance to initiate a D2D communication link to be D R , wehave SLP i = Pr n r ˆ x ≤ min (cid:16) ˆ D i , D L , D R (cid:17)o , where ˆ D i = (cid:20) G m T i ¯ I + T i ˆ N (cid:21) α L . On the assumption that the transmitters having the i -th contentstored in their cache form a PPP of intensity λ u (1 − ρ ) q i , andby using the distribution of the distance to the nearest MU ina PPP, we have SLP i = 1 − exp (cid:0) − πλ u (1 − ρ ) q i D i,c (cid:1) , (4)where D i,c = min n ˆ D i , D L , D R o . B. Optimum Content Placement
Once the approximations are applied, it is straightforwardto see that the optimization problem becomes convex. TheLagrangian can be written as L ( q , µ ) = − N X i =1 β i exp (cid:0) − πλ u (1 − ρ ) q i D i,c (cid:1) + µ N X i =1 q i − M d ! , where µ is the non-negative Lagrangian multiplier. By apply-ing Karush-Kuhn-Tucker (KKT) conditions, we have q i ( µ ) = − ln (cid:2) µ/ (cid:0) β i πλ u (1 − ρ ) D i,c (cid:1)(cid:3)(cid:2) λ u (1 − ρ ) D i,c (cid:3) , nd according to the first inequality constraint, the optimum q i should satisfy q ⋆i = min { max { q i ( µ ⋆ ) , } , } , and accordingto the second constraint, which is met with equality, givesus P Ni =1 min { max { q i ( µ ⋆ ) , } , } = M d . This can be usedto find µ ⋆ through a simple root finding algorithm such asbisection search [3], [4]. C. User Association
In a hybrid (multi-tier) wireless network, it is importantto associate users with the appropriate tiers to achieve trafficoffloading while maintaining QoS constraints. In our systemmodel, an MU may receive content via a LoS D2D link, aNLoS D2D link or a cellular link. Therefore, it is importantto recognize the appropriate method of content delivery. From(4), one can see that an MU can successfully receive the i -th file from a D2D transmitter in the LoS region if thedistance to the D2D transmitter is less than D i,c . However,we have assumed the worst case D2D interference whenobtaining D i,c . This means, it may be possible to increasethis threshold further without violating the rate constraints,which will facilitate more offloading. Since q is now defined,the probability of receiving the requested content from aD2D transmitter within the LoS region can be calculatedas γ = P Ni =1 β i (1 − q ⋆i ) (cid:0) − exp (cid:0) − πλ u (1 − ρ ) q ⋆i D L (cid:1)(cid:1) , where we have used the fact that the D2D mode initiateswhen the required content is not found in self-cache. We canuse γ to scale the worst-case average interference to havea tighter approximation of the interference from the activeD2D transmitters. Hence, assuming that the interference isdominated by the D2D transmitters in the LoS region, wecan obtain an updated distance threshold value that satisfiesthe QoS requirement as ˆ D i,L = (cid:20) G m T i γ ¯ I + T i ˆ N (cid:21) /α L . By replacing subscript L with N , we can obtain a similardistance threshold ˆ D i,N for a transmitter in the NLoS region.The proposed user association scheme can be summarizedas follows. For the i -th file, the MU first checks its own cache.If not found, it checks with D2D transmitters who are closerthan D i,u = min n ˆ D i,L , max n ˆ D i,N , D L o , D R o , for a D2D connection. If both actions fail, the MU connectsto the nearest RRH through a cellular link. The process issummarized in Algorithm 1.The rationale behind the distance thresholds can be ex-plained as follows. When ˆ D i,L < D L , it is straightforwardthat the threshold is ˆ D i,L , as any transmitter outside this (bothLoS and NLoS) will not satisfy the rate constraints. When ˆ D i,L > D L , we particularly focus on transmitters between D L and ˆ D i,L , who are NLoS according to the channel model.Whether these NLoS transmitters can transmit successfullyor not will depend on the value of ˆ D i,N . To this end, if ˆ D i,N < D L , none of the NLoS transmitters will be ableto transmit successfully. Thus, we set the threshold as D L . Algorithm 1
User Association Scheme f i ← Requested file A L ← circular region with the radius min n ˆ D i,L , D R o A N ← circular region with the radius min n ˆ D i,N , D R o if f i in the device self cache then Get file from self cache else if ˆ D i,L ≤ D L AND f i in A L then Get file from the closest LoS D2D transmitter else if ˆ D i,N > D L AND f i in A N then Get File from the closest NLoS D2D transmitter else if f i in Edge cloud then Get file from the edge cloud (fronthaul link) else
Get file from the core network (backhaul link) end if end if
However, when D L ≤ ˆ D i,N ≤ ˆ D i,L , all NLoS transmittersbetween D L and ˆ D i,N will satisfy the rate constraints, thuswe pick ˆ D i,N as the threshold. Hence, overall, the distancethreshold is given by max n ˆ D i,N , D L o . The user associationpolicy tries to make use of candidate NLoS transmitters aswell, to further facilitate offloading. Note that we will have ˆ D i,L > ˆ D i,N for all meaningful link lengths as α N > α L .IV. P ERFORMANCE A NALYSIS
Having placed content, and have decided on the userassociation policy, a performance analysis of the networkpresented in Section II will be carried out in this section. Notethat the assumptions made in Section III are relaxed in thisanalysis since the assumptions were made only to obtain amathematically tractable objective function.An offloading event occurs when a content request is servedby self cache or via a D2D link. To this end, the probabilityof finding the required content in the device cache itself isgiven by p s = P Ni =1 β i q ⋆i . The probability of receiving therequested content via a D2D link is given by p d = N X i =1 β i (1 − q ⋆i ) (cid:0) − exp (cid:0) − πλ u (1 − ρ ) q ⋆i D i,u (cid:1)(cid:1) . (5)Thus, p d + p s gives us the offloading probability.We define the successful reception probability ( SP ) as theprobability of an MU receiving content without violatingthe rate constraints. The SP through a D2D link is givenby P Ni =1 β i (1 − q ⋆i ) Pr { SINR d,i, ˆ x ≥ T i ∩ r ˆ x ≤ D i,u } , andsimilarly, the SP through the cellular network is given by P Ni =1 β i (1 − q ⋆i ) e − πλ u (1 − ρ ) q ⋆i D i,u Pr { SINR c,i,x ≥ T i } . Thesum of these two probabilities and p s gives us SP .An expression for Pr { SINR c,i,x ≥ T i } can be obtainedusing the fundamentals of stochastic geometry, by following aimilar approach to the one shown in Section III. Consideringthe closest RRH to be located at x ∈ Φ R , Pr { SINR c,i,x ≥ T i } = Pr n h x > T i r α c x (cid:16) ˆ I c + ˆ N c (cid:17)o = Z ∞ L ˆ I c ( T i z α c ) e − ˆ N c T i z αc f r x ( z ) dz, where ˆ I c = P y ∈ Φ R \{ x } h y r − α c y , ˆ N c = π N o F N B c G T G R P c W c , and f r x is the PDF of the distance to the nearest RRH, given by f r x ( z ) = 2 πλ R z e − πλ R z , for z ≥ . Furthermore, we have L ˆ I c ( S ) = E Y y ∈ Φ R \{ x } E h y h e − h y r − αcy S i = exp (cid:18) − πλ R Z ∞ x (cid:18) −
11 + v − α c S (cid:19) vdv (cid:19) . An expression for Pr { SINR d,i, ˆ x ≥ T i ∩ r ˆ x ≤ D i,u } can beobtained along similar lines, and by appropriately changingthe distance limits in the integration. To this end, we get Pr { SINR d,i, ˆ x ≥ T i ∩ r ˆ x ≤ D i,u } = Z D L ˆ I ( T i z α L ) e − ˆ NT i z αL /G m f r ˆ x ( z ) dz + Z D D L L ˆ I ( T i z α N ) e − ˆ NT i z αN /G m f r ˆ x ( x ) dz where f r ˆ x is the PDF of the distance to the nearest MU in aPPP of intensity λ u (1 − ρ ) q ⋆i , D n D L , ˆ D i,L , D R o and D n D L , min (cid:16) ˆ D i,N , D R (cid:17)o . Moreover, L ˆ I ( S )= exp (cid:18) − πρλ u p d E G ′ (cid:20)Z ∞ (cid:18) − G m G ′ Sy − α ( y ) (cid:19) ydy (cid:21)(cid:19) , where α ( y ) = (cid:2) − (1 − α L ) { y ≤ D L } (cid:3)(cid:2) − (1 − α N ) { y>D L } (cid:3) , the expectation can be straightforwardly evaluated using thePDF of G ′ given in Section III, and p d is given by (5).V. N UMERICAL R ESULTS AND D ISCUSSIONS
In this section, the performance of the proposed scheme isevaluated using simulations. The simulation parameters are setto align with previous works [3], [5], [9], [12] and presented inTable I. We consider R i = R ∀ i ∈ { , . . . , N } for simplicity.We compare the performance of the proposed system (S-1)with the system proposed in [3] (S-2), where the content isplaced to maximize the cache hit probability and the contentdelivery is based on D2D links within a radius of D R , whichis the maximum discovery distance of an MU.Fig. 1 compares the SP performance of the overall systems,and S-1 outperforms S-2 in all considered scenarios. When D L decreases (blockage density increases), the SP reducesin both systems. However, we can observe the performancegap between S-1 and S-2 increasing. Since S-1 has prioritizedthe LoS region for both content placement and delivery, itis more robust to changes in D L . On the other hand, S-2,that has focused on D R (which is generally larger than D L ),may encounter frequent unsuccessful D2D transmissions when TABLE IS
IMULATION P ARAMETERS
RRH density λ R / km User requesting probability ρ f c = 1 GHz) α c f c = 28 GHz) α L , α N P c
100 mWPower consumption for backhaul P b P d G m G s -9dBNoise power density N o -178 dB/HzNoise figure F N
10 dBContent Library size N M e M d B c
20 MHzBandwidth in mmWave link B d D R
150 m
200 400 600 800 1000 1200 14000.20.30.40.50.60.70.8
Fig. 1. The behavior of the overall SP of the system with λ u for different[ D L ,R, ǫ ] combinations. the blockage density increases. When both rate constraintsand D L reduce, the SP of S-2 decreases with λ u . This isdue to the increased interference from D2D links and theQoS requirements not being satisfied with S-2. However, sinceS-1 considers the effect of interference in both the contentplacement and delivery (user association), the SP increaseswith λ u , making S-1 a promising approach for future ultra-dense networks. When ǫ is reduced while keeping the otherparameters fixed, the overall success of both the systemsreduce. The reduction in ǫ leads to the content requestsspreading out over a large range of files, which in fact reducesthe probability of successfully receiving a file over a D2D link.Since both systems have averaged the objective functions overall possible files, a similar trend is observed for all values of ǫ . Fig. 2 compares the offloading probability ( OP d ) of the twosystems. S-2 having a higher offloading probability is ratherobvious since considering D R leads to a larger offloadingregion with S-2. However, the figure also conveys that aconsiderable portion of the offloaded traffic in S-2 will not besuccessfully delivered, and hence, the successful offloadingprobability ( SOP d ) of S-2 is lower than S-1. When D L
00 400 600 800 1000 1200 14000.20.30.40.50.60.70.80.9
Fig. 2. Offloading and the successful offloading probabilities of the D2Dnetwork for 1 Gbps data rate, where ǫ = 1 . .
200 400 600 800 1000 1200 14000.511.522.533.544.55 10 Fig. 3. The Energy Efficiency of the D2D link with λ u for different [ D L ,R, ǫ ] combinations. reduces, the unsuccessful offloading of S-2 increases, but inS-1, the gap between the two offloading probabilities remainslow as it is more robust to changes in D L , as described withrespect to Fig. 1.Energy efficiency (EE) can be computed by the ratio be-tween the average throughput from successful transmissionsand the average power consumption, per user request. Someinsights on the EE of the two systems can be inferred fromFig. 2. When λ u increases, the probability of initiating a D2Dlink increases in both schemes. This leads to the averagethroughput from successful transmissions increasing, and theaverage power consumption decreasing. However, the averagethroughput from successful transmissions of S-1 increases ata higher rate with λ u compared to S-2. On the other hand,the average power consumption of S-2 decreases at a higherrate with λ u compared to S-1 due to the higher offloading.Therefore, the overall EE of the two systems are almostsimilar. However, one can identify that the EE of D2D linksis significantly higher for S-1, compared to S-2, which isillustrated in Fig. 3. This is due to the unsuccessful D2D trans- missions in S-2 resulting in device energy wastage. When λ u is varied from 200 to 1400 /km , for D L = 75 m and ǫ = 1 . ,on average, a 1.3 fold improvement in terms of EE is observedwith S-1 compared to S-2. This improves significantly when D L is further reduced. For example, on average, a 3.5 foldimprovement can be observed at D L = 50 m. This depicts thesuperior performance of S-1 in ultra-dense networks with highblockage. VI. C ONCLUSIONS
The performance of a cache enabled D2D network, whereD2D communications occur exclusively in the mmWave band,has been studied using a stochastic geometric framework. Asa result, a novel content caching scheme in user devices tomaximize the successful content delivery probability of LoSD2D links has been introduced. The performance gains of theproposed content placement and delivery schemes have beenhighlighted through simulations. The numerical results haveshown that the proposed scheme achieves higher successfulcontent offloading, improved energy efficiency while satisfyingQoS requirements of the users, and superior performance inultra-dense networks with high blockage.R
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