Energy Efficient D2D-Assisted Offloading with Wireless Power Transfer

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1 nergy ffiient DD-Assiste Offloaing with Wireless Power Transfer oong Shang, Liqiang Zhao, Kwang-Cheng Chen,XiaoliChu State Key Laboratory of Integrate Servies Networks, Xiian University, Xi an, Shaanxi, China, 77 mail: Department of letrial ngineering, University of South Floria, Tampa, USA, mail: Department of letroni an letrial ngineering, University of Sheffiel, UK, mail: Abstrat Traffi offloaing via evie-to-evie DD ommuniations has been propose to improve the network apaity an alleviate the inreasing traffi buren on ellular base stations Ss. However, the suess of DD ommuniations largely relies on the DD transmitters DD-Txs willingness of sharing ontents ue to the energy onsumption for transmission. In this paper, we moel an analyze wireless powere DD-assiste offloaing WPDO in unerlying ellular networks, where the DD-Tx is allowe to reeive power from the nearest S as well as other interfering Ss, an then DD-Tx broaasts the popular ontents to nearby users. The average reeive power at DD-Tx an the suess probability of DD-Tx transmission are erive. Furthermore, base on the propose moel, we maximize the network energy effiieny while guaranteeing users require ata rates. Our results onfirm that the maximum energy effiieny of the WPDO network an be ahieve by jointly optimizing the fration of time for wireless power transfer an the offloaing range of DD-Tx. Inex Terms DD ommuniations, energy effiieny, traffi offloaing, unerlay, ellular networks, wireless power transfer. I. INTRODUCTION With the upsurge growth of ata traffi an the explosively inreasing number of mobile evies, traffi offloaing via evie-to-evie DD ommuniations has attrate great attention to improve the network apaity an alleviate the traffi buren of ellular networks by exploiting the physial proximity of ommuniating evies [], []. In DD ommuniations, one of the most traffi emaning soial networking appliations is ontent sharing among multiple evies, suh as vieo streaming [3]. However, the power/energy onsumption to transmit share ontents reates onerns for DD transmitters DD-Txs. In [], an inentive framework for DD base offloaing was propose, where the operator motivate DD-Txs to broaast popular ontents to nearby users in orer to maximize the operator s profit. In [4], the soially enable DD ommuniation was stuie, where the soial interations among users, who knew eah other in real life or in soial networks, were onsiere. In the meanwhile, eiate wireless power transfer WPT through eletromagneti M raiation emerges as an attrative tehnology [5], as it an eliminate the hassle of onneting ables an at as a ost-effetive tehnique to enable oneman energy supplies an uninterrupte operations [6]. The existing literatures stuie raio frequeny RF energy harvesting-base DD ommuniations [7] as well as user equipment relay ommuniations [8], where mobile evies were powere by the ambient RF signals for information transmission. In fat, it was shown in [9] that energy harveste from ambient RF signals an only power small sensors opportunistially with sporai ativities, while offering stable an fully ontrollable power nees to rely on the pointing beam, an thus eiate WPT [6]. On the other han, riven by both eonomial an environmental onerns, network esigners pay more attention to the energy effiient green ommuniations in orer to urb the inreasing power onsumption of wireless networks []. With this in min, we aim at maximizing the network energy effiieny when the DD ommuniations are atuate by the eiate WPT. In this paper, we propose an energy effiient wireless powere DD-assiste offloaing WPDO network, where the DD-Tx is allowe to reeive power from its nearest S by pointing beam as well as other interfering Ss, an then DD-Tx broaasts the popular ontents to users loate in DD-Tx s offloaing region. In the offloaing region, DD users require ata rates an be guarantee. We summarize the ontributions of this paper as follows: Using stohasti geometry, we analytially haraterize the average reeive power at DD-Tx an erive the pratial transmit power of S by onsiering user s require ata rate. In aition, the ensity of ellular users with the impat of DD-assiste offloaing is quantifie. We analytially obtain the suess probability of DD- Tx transmission, an note the existene of optimal time alloation fator the fration of time alloate for WPT that ereases with the DD user s require ata rate. We propose to jointly optimize the time alloation fator an the offloaing range of DD-Tx, suh that the energy effiieny of WPDO network an be maximize. The remainer of this paper is organize as follows. In Setion II, system moel is presente. Setion III formulates the average reeive power at DD-Tx an the pratial transmit power of S. Setion IV analyzes the suess probability of DD-Tx transmission. The energy effiient WPDO network is propose in Setion V. Numerial results are shown in Setion VI. Finally, onlusions are rawn in Setion VII /7/$3. 7 I

2 meter m II. SYSTM MODL ase Station Cellular User DD-Tx DD User Offloaing Region DD link meter m Fig : Wireless powere DD-assiste offloaing WPDO in the ellular ownlink networks, where DD-Txs an be powere by Ss with pointing beam as well as other interfering Ss an broaast popular ontents to the users in the offloaing region with raius of R D. In the offloaing region, DD users require ata rates an be guarantee. A. Network Topology We onsier the ellular ownlink integrate with DD ommuniations, where DD-Txs an broaast popular ontents to the users in proximity as in Fig.. Ss are moele as a homogeneous Poisson Point Proess PPP on the entire plane R with the ensity of λ an are enote as the set of Φ = {b j,j =,,,...}. ah S has the maximum allowable transmit power represente as P m an is equippe with N t antennas. In aition, we assume that eah S an power one DD-Tx in its ell area by maximal-ratio transmission MRT beamforming, an thus the ensity of DD-Txs λ D equals to Ss i.e., λ D = λ. The ell area of j th S b j is V j = x R x b j x b n,b n Φ b j, where a b represents the istane between a an b. Users, whih onsist of ellular users onneting with Ss an DD users using DD links, enote by Φ U are sattere on R base on another inepenent PPP with the ensity of λ u. ah user is assume to be equippe with antenna an has a rehargeable battery with large storage.. User s Assoiation We onsier that both ellular users an DD users have a ommon require ata rate R u Mbps as their pratial traffi eman for the meia servie, where R u an be interprete as the average ata rate in the entire network. ah ellular user onnets to the losest S. In aition, eah DD-Tx has the offloaing region Ω D with the raius of R D. In the offloaing region, DD users require ata rates shoul be guarantee. We efine the probability P on that the esire ontent of a typial user u is the same with the broaast information of an arbitrary DD-Tx, also alle ontent popularity. We suppose that the value of P on an be statistially obtaine by the operator. If a user s esire ontent is same with DD- Tx s broaast information, the user is transferre into DD ommuniation by the operator, an suh vertial hanover proess is transparently performe for the user. C. Channel Moel The banwith of ellular ownlink is MHz, while the banwith for DD ommuniations is D MHz, an D = ρ where ρ represents the frequeny reuse fator [7]. We assume that eah S is apable of performing aaptive power ontrol aoring to zero-elay hannel state information CSI. Therefore, aoring to Shannon s theorem, the transmit power P of S b j for ellular user u ith ellular user in j th ell is alloate to ensure the require ata rate R u, as follows []: R u = Nj log +SINR u SINR u P h bju H α b j u α = Iu C + ID u +, σ where Nj enotes the total number of ellular users serve by the S b j, h bju C Nt is the small-sale faing hannel vetor, H α is the path loss for a referene istane, α is the path loss exponent fator, Iu C iniates the interferene from ellular Ss at u, ID u enotes the interferene from DD- Txs an σ is the aitive noise. More speifially, we have Iu C = P b n Φ b j h b nu gh b nu H bn α u α, g bnu Iu D = P j h ju H α j u α, 3 j Φ D where h bnu is the small-sale faing interfering C Nt gh bnu hannel vetor, an is the MRT beamforming vetor g bnu of S b n, where g bnu is the small-sale faing C Nt hannel vetor from S b n to its assoiate user u. Aoringto[],h bnu gh bnu is a zero-mean omplex Gaussian g bnu gbnu variable, suh that h bnu gh b nu/ exp. D. Wireless Power Transfer A harvest-then-transmit protool at DD-Tx is onsiere [3]. Let T enote the uration of a ommuniation blok, where the sub-bloks of uration θt an θ T are alloate for WPT an information transmission, respetively, where θ θ is the time alloation fator. During θt, DD-Tx aptures power from the nearest S with pointing beam an other Ss. The instantaneous reeive power P R j at DD-Tx j in j th ell is expresse as P R j = P Sbj + P IS = P hbj m H β j max {b j j,v} β + P m h g H b n n H β b n j g bn b n n Φ b j max {b n j,v} β, 4 With a slight abuse of notation we will use h xy to enote the smallsale faing hannel vetor from x to y, where the hannels are assume to experiene Rayleigh faing suh that h xy Gamma N t,.

3 where P Sbj enotes the reeive power of pointing beam, an P IS is the reeive power from other Ss. During θt, we assume that Ss transmit at P m in orer to supply the reliable power at DD-Txs. β is the path loss exponent fator for WPT, an v is a onstant value. It is worth noting that the arrier frequenies of WPT an information transmission an be ifferent. This may iniate that the path loss inexes of these two types of signals i.e., α an β shoul be larifie separately, an thus H β is the path loss for a referene istane. To simplify the notations in the analytial result, here we onsier that DD-Txs with large battery apaity } transmit at the average reeive power P = φ {P R [4], where j φ = η θ θ an η is the RF-to-DC onversion effiieny [5]. In DD-Tx s information transmission, the signal-to-interfereneplus-noise SINR ratio at the DD user u onnete with j is given by SINR u P h H ju = α j u α I C + I D, 5 + σ u u where I C u = P b n Φ h b nu gh b nu H α b n u α, g bnu 6 I D u = P h H nu α n u α, 7 n Φ D j where h ju exp is the hannel power gain, I C u enotes the interferene from ellular networks an I D u iniates the interferene from DD ommuniations. In orer to reflet the powering effiieny an the reliability of DD-Tx information transmission, we efine that the suess transmission of DD-Tx ours when the ata rate at the ege of the offloaing region Ω D exees the preetermine user s require ata rate R u uring a ommuniation blok T. The suess probability of DD-Tx transmission is given by { θ T Psu D =Pr D T log + P h H α ju αr D 8 I C + I D R + σ u u u. In the next setion, we haraterize the average reeive power P an the S pratial transmit power P from system-level perspetive. III. SYSTM-LVL PRFORMANC VALUATION A. Average reeive power at DD-Tx Proposition. In the WPDO network, given the S ensity λ, the number of antennas N t an the transmit power P m, the average reeive power at DD-Tx is given in 9 at the top of the next page. Proof: } The average instantaneous reeive power {P R in 4 an be expresse as j } } {P R j = {P Sbj + {P IS }. In aition, } we have {P Sbj = {P hbj m j Hβ max {b j j,v } β} [ v a = P m N t H β v β f bj j xx ] + x β f bj j xx v b = P mn t H β v β e πλ v + P mn t H β Γ β πλ β,πλ v, where f bj { j x =πλ xe πλx x>, a is obtaine hbj } by using j = N t an the Campbell s Theorem of PPP. In b, Γ, is the inomplete Gamma funtion. esies, {P IS } is obtaine as follows: {P IS } = P m h g H b n n b n j H g bn b n β n Φ b j {max {b n j,v } β} a = P m H β Φ max {b n j,v } β b n Φ b j = P m H β πλ rmax {r, v } β r [ v ] = P m H β πλ v β rr + r β r v = P m H β πλ v β +, β where a follows from h g H bnn b n j g bnn exp. Combining an into, we have the esire result in 9.. S pratial transmit power To haraterize the pratial transmit power of S, we give the following Lemma whih speifies the ensity of ellular users i.e., users that are unable to offloa λ u in the DDassiste offloaing networks. Lemma. In the WPDO network, given the S ensity λ, the offloaing raius R D an the ontent popularity P on,the ensity of ellular users λ u is given by λ u = e PonπλRD λ u. 5 Proof: A typial user u an offloa onto DD ommuniation only if the two requirements are satisfie. First, the istane between u an DD-Tx is within the DD ommuniation range of raius R D. Seon, the esire ontent of u is the same as the broaast information of DD-Tx. We suppose that DD-Txs are istribute with a PPP, an thus

4 P = φp mn t H β v β e πλ v + φp mn t H β πλ β N P j Ru = θ Psu D =exp ψ θ, R u σ H α Γ α + α N t πλ α Γ β,πλ v + φp m H β πλ v β + λ P α π α sin π α, 9 β [ P m πλ α Γ α + + P α v + ] + σ, 3 α ψ θ, R u α πλ ζ ψ θ, R u,r D, P, 4 the Probability Density Funtion PDF of the istane r between u an its nearest DD-Tx is f r r =πλ D re πλdr,r >. 6 Then we have the probability P OL that the istane r is less than R D, i.e., the probability that u is loate in at least one of the offloaing regions of DD-Txs, as follows: P OL = RD f r rr = e πλdrd. 7 Reall that the ontent popularity P on efine in Setion II-, an suppose that there are m DD-Txs in a irular region with the raius of R D entere for u. λ u is given by λ u = P OL λ u + m [ P on m ] λ u, 8 where we regar the ellular users as the PPP with the ensity of λ u for mathematial tratability. Aoring to Poisson istribution of DD-Txs, the Probability Mass Funtion PMF of m is given by [πλ D R D ] m P N DD Tx = m = e πλdrd. m! Therefore, we have m [ P on m ] = P on m P N DD Tx = m m= = e PonπλDRD e πλdrd. 9 Note that in the WPDO network, the ensity of DD-Txs λ D equals to Ss i.e., λ D = λ. Substituting an 7 into 8 gives us the esire result in Lemma. We are now in the position of esribing the proeure for omputing the pratial transmit power of S b j for a typial ellular user u. Proposition. In the WPDO network, given the S ensity λ, the number of antennas N t an the user s require ata rate R u, the pratial transmit power of S b j is given in 3 at the top of the page, where Nj Lemma, P is given in 9. = λ u λ an λ u is given in Proof: Given a typial ellular user u whih requests ata rate R u uring the ommuniation blok T, the pratial transmit power at its serving S b j uring the sub-blok θ T is given by a transformation of as RuN j I P θ { = bj u α Iu C N + ID u + σ}, t where I [x] enotes taking expetation{ of variable x on the interferene I, an we have utilize / hbju } = N t, whih haraterizes the average performane in hannel. We onsier the worst-ase senario, where the interferers transmit at the maximum allowable power, an thus we have Iu C h,φ P m H α bn u α b n Φ b j a = P mh α πλ x α πλ P m H α x = y S α y S α, where a is obtaine by using Campbell s Theorem, an we have utilize h b nu gh bnu =. ys = g bnu bj u is the istane between u an its nearest S. In aition, we have Iu D = h,φd v a = πλ D P H α = P H α πλ D v α j Φ D v α xx + + α P h ju H α max { j u } α,v x α xx v, 3 where a follows from h ju exp. Combining 3 an into { an } noting that λ D = λ, we obtain the approximate I P as follows: N I P j Ru πλ θ H α α y S αnt [ P m α y S α + P v + ] 4 + σ. α Consiering that the PDF of y S is f y S } y = πλ ye πλy y>, we obtain I {P as follows: } I {P = I P fy S yy. 5 y alulating 5, we get the esire result in 3.

5 IV. SUCCSS PROAILITY OF DD-TX Reall that the suess transmission of DD-Tx ours when the ata rate at the ege of the offloaing region exees the require ata rate R u uring ommuniation blok T, whih is efine in 8. Therefore, we have Psu D =Pr { SINR u γth θ } RD, 6 where the SINR threshol γ th θ is θ γ th θ = D. 7 Proposition 3. In the WPDO network, given the time alloation fator θ an the user s require ata rate R u, the suess probability of DD-Tx transmission P{ su D is} given in 4 at the top of the previous page, where P is given in 3 an P is given in 9, an ψ θ, R u = Ru θ D α P H α R D ζ α ψ θ, R u P R D ψ θ, R u,r D, P = 8 α [ F, α ; α ; ψ θ, R ] u P α. R D Proof: aseon6,wehave P h Psu D ju =Pr α αr D I C + I D γ + σ u u th θ { =Pr h ψ θ, R ju T I C u + I D u + σ } a = e ψθ,ruσ L I C u {ψ θ, R u }L I D u {ψ θ, R u }, 9 where ψ θ, R u is given in 8, a follows from h ju exp, L I C { } an L I D { } enotes the Laplae transform of I C an I D, respetively. u u u u In aition, we have { L I C {s} = exp s P u b n Φ / } gbnu h bnu gh b nu α =exp { { λ s P Ru H α b n u π α } α π /α sin }, 3 where we{ suppose } that eah interfering S transmit with the power P base on 3. Further, L I D is u given by L I D {s} = u exp P h s H nu α n u α n Φ D j exp { πλ ζ } s, R D, P, 3 where we approximate that the interfering DD-Txs are loate outsie a irular region with raius R D entere of the u, an ζ is similar to 8 by onsiering s = ψ θ, R u. Combining 3 an 3 into 9, we have 4. Suess Probability Optimal Require Data Rate: R u =.Mbps, Analysis Require Data Rate: R u =.5Mbps, Analysis Require Data Rate: R u =.3Mbps, Analysis Simulation * ereases with Ru R u ereases Time Alloation Fator, Fig : The suess probability of DD-Tx transmission P D su given in 4 with respet to time alloation fator θ uner various require ata rates R u.asr u gets large, the optimal value of θ ereases, suggesting that a large fration of time shoul be alloate for information transmission to optimize the suess probability of DD-Tx. V. NRGY FFICINT WPDO NTWORK In this setion, we propose an energy effiient WPDO network to ahieve the maximum energy effiieny. The optimization problem is given as follows: max : η = R u + Psu D θ, R D Nj R u θ,r D θ+p m P s.t. C: Psu D θ, R D ε C: P θ P m C3: P θ P, 3 where the first term of the numerator in 3 enotes the throughput of ellular link uring T, the seon term of the numerator is the throughput of DD links uring T. Psu D θ, R D is the suess probability given in 4. Nj = λu λ u λ is the average number of DD users in a ell, where λ u is given in 5. The enominator is the sum of the power for S{ information } transmission an WPT, respetively, where P θ is given in 3. The onstraint C guarantees that the minimum suess probability, where ε is a onstant value. The onstraints C an C3 insure that the transmit powers of S an DD-Tx oul not exee their orresponing maximum allowable transmit power P m an P, respetively. VI. NUMRICAL XAMPLS The network operates at =MHz, ρ =, λ = 5 Ss/m, λ u =4 4 users/m, P m =4m, P = m, N t =64, v = v =5m, α =3, β =.5, σ = W, η =, P on =., R u =.3Mbps, ε =.4, unless otherwise state. In Fig., we observe that the suess probability of DD-Tx transmission an be maximize by ajusting the time alloation fator θ, an we onut Monte Carlo MC simulations to valiate the analytial results erive in this paper. Further,

6 nergy ffiieny, Mbps/W Ahievable nergy ffiieny A Optimal *, R D * Time Alloation Fator, Offloaing Raius, R D meter Fig 3: Network energy effiieny η base on 3 as the funtion of the time alloation fator θ an the offloaing raius R D. The network ahievable energy effiieny A is obtaine by jointly optimizing θ an R D. when R u gets large, it is esirable to ivert more time fration in a ommuniation blok to the information transmission at DD-Tx, while a larger fration of time nees to be portione for the WPT when R u is small. In Fig.3, the network energy effiieny η base on 3 is plotte regaring to the time alloation fator θ an the offloaing raius R D. The ahievable energy effiieny A an the optimal strategy θ,r D an be obtaine. Speifially, when R D gets large, although more traffi an be offloa onto DD links, the { suess } probability ereases an the transmit power of S P for ellular link inreases, whih results in the reution of network energy effiieny. In Fig.4, we observe that the A inreases with the number of S antennas N t. This suggests that the performane of the network is greatly improve by using the massive antenna arrays at eah S. In aition, A inreases with the ontent popularity P on, sine more traffi an be offloa onto DD links, whih is a ost-effetive way an improves the network throughput. However, A ereases with the users ensity λ u, sine more power woul be onsume to guarantee the ellular user s require ata rate R u, an thus A ereases. VII. CONCLUSIONS In this paper, we moel an analyze the DD-assiste offloaing network with wireless power transfer. The average reeive power at DD-Tx, the ellular users ensity, the S pratial transmit power an the suess probability of DD- Tx transmission are erive. ase on the propose moel, we evelop an energy effiient WPDO network by jointly optimizing the time alloation fator an the offloaing raius of DD-Tx. The results provie signifiant insights into the esign an appliation of the wireless power transfer enable DD-assiste offloaing network. ACKNOWLDGMNT This work was supporte in part by National Natural Siene Founation of China 6377, Intergovernmental International Cooperation on Siene an Tehnology Innovation 6YF3, an the Projet 838. Ahievable nergy ffiieny, Mbps/W Content Popularity:P on =.3, Users Density: Content Popularity:P on =., Users Density: Content Popularity:P on =., Users Density: A inreases with ontent popularity P on u =4*-4 users/m u =4*-4 users/m u =6*-4 users/m A ereases with users ensity u Antenna Array, N t Fig 4: The ahievable energy effiieny A with respet to antenna array N t uner various ontent popularity P on an users ensity λ u. RFRNCS []. Shang, L. Zhao, an K. C. Chen, Operator s onomy of Devie-to- Devie Offloaing in Unerlaying Cellular Networks, I Communiations Letters, vol. PP, no. 99, pp., 6. [] T. Zhang, H. Wang, X. Chu, an J. 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