THE rapid growth of Information and Communications

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1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO., FEBRUARY 4 9 Optimizing Netwok Sustainability and Efficiency in Geen Cellula Netwoks Xiaoxia Zhang, Student Membe, IEEE, Zhongming Zheng, Student Membe, IEEE, Qinghua Shen, Student Membe, IEEE, Jing Liu, Membe, IEEE, Xuemin Sheman Shen, Fellow, IEEE, and Liang-Liang Xie, Senio Membe, IEEE Abstact In this pape, we study the esouce allocation in a device-to-device DD communication undelaying geen cellula netwok, whee the base station BS is poweed by sustainable enegy. Ou objective is to enhance the netwok sustainability and efficiency by intoducing powe contol and coopeative communication. Specifically, we popose optimal powe adaptation schemes to maximize the netwok efficiency unde two pactical powe constaints. We then take the dynamics of the chaging and dischaging pocesses of the enegy buffe into consideation to ensue the netwok sustainability. To this end, the enegy buffe is modeled as a G/D/ queue whee the input enegy has a geneal distibution. Powe allocation schemes ae poposed based on the statistics of the enegy buffe to enhance the netwok efficiency and sustainability. Both theoetical analysis and numeical esults demonstate that ou poposed powe allocation schemes can impove the netwok thoughput dastically while maintaining the netwok sustainability at a cetain level. Index Tems Geen cellula netwoks, DD communications, coopeative communications, netwok sustainability, spectum efficiency, powe allocation. I. INTRODUCTION THE apid gowth of Infomation and Communications Technology ICT industy has boosted the development of wieless communication, which has aised ove 6 billion cellula uses woldwide []. With astonomical escalation of mobile teminals, the cellula industy has unpecedented gowth of data taffic equiement, which leads to enomous enegy consumption. In, moe than 4 million base stations have been deployed to povide sevices fo mobile uses, causing an extemely high enegy consumption of 5MWh pe yea in aveage []. Among the devices of cellula netwoks, the BSs occupy almost 6% of the whole netwok s enegy consumption [3]. Nowadays, the enegy cost of cellula netwoks has become a significant potion of the opeational expenditue with the incease of enegy pice. Fo example, the opeational cost of a BS poweed by electical gid is appoximately 3 US dollas pe yea, and the cost may be ten times moe if the BS is poweed by diesel powe geneatos in the ual aea []. Theefoe, it is essential to Manuscipt eceived June 5, 3; evised Septembe 6 and Novembe 7, 3; accepted Novembe 4, 3. The associate edito coodinating the eview of this pape and appoving it fo publication was Y. Sanada. X. Zhang, Z. Zheng, Q. Shen, X. Sheman Shen, and L.-L. Xie ae with the Depatment of Electical and Compute Engineeing, Univesity of Wateloo, Wateloo, Ontaio, Canada, NL 3G {x79zhang, z5zheng, qshen, sshen, llxie}@uwateloo.ca. J. Liu is with Shanghai Jiao Tong Univesity, Shanghai, China, 4 jingliu lj@sjtu.edu.cn. Digital Object Identifie.9/TWC /4$3. c 4 IEEE conside how to decease the enegy consumption, especially the enegy consumption of BSs, to fulfill the eve gowing uses equiement and educe the opeational cost in cellula netwoks. To povide sustainable and clean powe, eco-fiendly geen enegy, e.g., sola, wind and hydo, is emeging as a popula substitute of taditional enegy. Geen wieless devices, i.e., wieless devices poweed by geen enegy, ae anticipated to be widely deployed to constuct the next-geneation wieless netwoks. In taditional electicity gid based wieless netwoks, the netwok devices ae geneally poweed by limited yet stable esouces, e.g., coal, petoleum and natual gas. One of the most citical eseach issues in this field is to maximize the enegy efficiency, such that the enegy utilization can be impoved. Howeve, unlike taditional enegy, geen enegy chaging capability highly depends on its location, local weathe and time, which is natually sustainable and highly dynamic. Fo example, the havested enegy by sola panels is diffeent in daytime and night within the same day, which also vaies at diffeent locations depending on the intensity of sola adiation. The dynamic chaging capability and availability of geen enegy may cause intemittent powe suppot fo geen wieless devices, which have shifted the fundamental design citeion and the main pefomance metic of geen wieless communication netwoks fom enegy efficiency to enegy sustainability. Theefoe, how to efficiently allocate the havested enegy to ensue the netwok sustainability and fulfill the explosively inceasing use demand has become an essential eseach issue. On one hand, many woks [4] [7] have addessed the enegy sustainability issue of geen wieless communication netwoks. In [4], a stochastic famewok to model the dynamics of geen enegy buffe is designed, and a distibuted admission contol stategy is poposed to guaantee high esouce utilization and to impove enegy sustainability. In [5], [6], netwok planning in geen wieless netwoks is consideed, and the minimum netwok device deployment poblem is fomulated. Heuistic algoithms ae poposed to fulfill uses QoS equiement and guaantee netwok sustainability by using the minimal numbe of netwok devices. In [7], a hybid utilization of wind and sola powe is consideed. Authos find that the combined use of wind and sola powe can povide moe stable and lowe-cost geen enegy fo WLAN mesh nodes in cetain geogaphic locations, i.e., Toonto, Seattle, Phoenix, etc., compaed with using wind o sola powe only. On the othe hand, to fulfill the eve gowing uses e-

2 3 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO., FEBRUARY 4 quiement of high-data-ate communications, vaious pomising technologies, e.g., device-to-device communication and coopeative communication, have been intoduced to cellula netwoks. By utilizing DD communication, cellula devices can tansmit data with each othe diectly without BSs, and the netwok thoughput of wieless cellula netwoks can be significantly impoved [8] []. Howeve, DD communication nomally shaes the same spectum with egula cellula tansmissions, which limits the pefomance of the whole netwok. To futhe enhance the netwok pefomance, coopeative communication is emeging as a pomising technology. With the help of elays, coopeative communication can significantly incease the netwok thoughput by taking advantage of the boadcast natue of wieless channels. Consideing the unique featues of the elay channel, wieless elay netwoks have been studied fom vaious pespectives, including tansmission famewok [], [3], coopeative potocol [4], [5], and elay positioning [6], [7], etc. Among these, esouce allocation, including powe allocation is one of the most efficient methods to maximize the utilization of the existing limited esouces and impove the netwok pefomance [8]. Fo example, [9], [] study the esouce allocation schemes when the souce and the elay occupy othogonal channels. With the assumption that the souce and the elay tansmit in the same channel, [] focuses on the powe allocation schemes to impove the achievable ate with the elay adopting the amplify-and-fowad scheme. [], [3] investigate the powe allocation schemes fo decode-and-fowad elays. In this pape, we aim at impoving the netwok s oveall thoughput by exploiting the benefits of DD and coopeative communication, while maintaining the netwok sustainability in geen cellula netwoks. Specifically, we conside a geen device-to-device communication undelaying cellula netwok whee the BS is poweed by sustainable enegy. Coopeative communication is utilized to impove the tansmission efficiency, and the BS helps to elay the souce s signal to the destination. The coopeative BS adopts the decode-andfowad potocol and tansmits in the same channel with the souce. This type of coopeation can bette exploit the boadcast natue of wieless signals while impoving the utilization of existing allocated spectal esouces. We focus on designing efficient powe allocation schemes and make the following contibutions: Both geen enegy and wieless communication technologies ae consideed to povide an efficient tansmission egime in a device-to-device communication undelaying cellula netwok, whee a BS poweed by sustainable enegy is deployed in the netwok. To impove the netwok thoughput, the BS is equipped with coopeation devices to assist the communication between the souce and the destination. Efficient powe allocation schemes ae poposed to maximize the oveall thoughput unde two pactical types of powe constaints depending on whethe uses ae able to adjust thei tansmission powe. Ou powe allocation schemes can effectively impove the netwok thoughput while ensuing that the enegy havested fom the envionment can sustain the wieless communication without any node outage. An analytical famewok to model the dynamics of the geen enegy chaging and dischaging pocesses is pesented. The enegy buffe can be appoximated as a G/D/ queue whee the enegy chaging pocess has a geneal distibution. The distibution of the buffe stoage is deived, which sheds some light on the geen netwok designs. The emainde of the pape is oganized as follows. Section II intoduces the system model and the elay channel achievable ate. In Section III, we discuss the powe adaptation schemes to maximize the achievable ate of each single-use channel. Depending on whethe the souce node is able to adjust its powe levels, we solve the optimization poblem unde two types of powe constaints: total powe constaint and BS powe constaint. Section IV futhe takes the dynamics of the sustainable enegy into consideation. The enegy buffe is modeled as a G/D/ queue and powe allocation schemes that can ensue the netwok sustainability ae poposed. Section V contains some numeical esults, and Section VI povides concluding emaks and possible futue wok. II. SYSTEM CONFIGURATION A. Netwok Model The stuctue of the DD communication undelaying cellula netwok consideed in this pape is shown in Fig.. The netwok consists of a set of wieless uses and a single BS, whee all the uses ae located within the tansmission ange of the BS. The wieless channels of cellula netwok and DD communication ae othogonal with each othe, thus the intefeence between cellula netwok and DD communication is ignoable. Wieless uses can communicate with each othe by eithe cellula netwok though the BS o by diect data tansmission though device-to-device communication. As the BS occupies almost 6% enegy consumption of the whole netwok, a geen BS, i.e., a BS poweed by enewable enegy, is equipped in the netwok. Since the enewable enegy is by natue intemittent and vaiable, the BS is associated with a echageable battey with lage capacity to buffe the dynamically chaged enegy and to povide a constant powe output. To ensue the netwok connectivity, a back up enegy souce, such as powe gid o battey is also available at the BS to povide tempoay powe supply in some exteme cases when the havested enewable enegy cannot suppot eliable communication. Fo DD communication in the netwok, each wieless use can communicate with all othe uses within the netwok, and has the same time peiod fo tansmission. The geen BS can act as a elay and is capable of coopeation with the souce nodes to tansmit data to the destinations. The coopeative potocols most commonly used ae Amplify-and-Fowad AF and Decode-and-Fowad DF. AF elays simply amplify the eceived signals and fowad them to the destination. To avoid popagating the intefeence and noise fom the souce-elay channel, elay would employ exta esouces such as time slots o fequency bands fo othogonal tansmission. On the othe hand, DF could completely eliminate the noise since the elay decodes the eceived signal befoe fowading it, so the souce and the elay ae able to tansmit at the same time and on the

3 ZHANG et al.: OPTIMIZING NETWORK SUSTAINABILITY AND EFFICIENCY IN GREEN CELLULAR NETWORKS 3 Fig.. netwok. A geen device-to-device communication undelaying cellula same fequency band to impove the spectal efficiency. In this wok, consideing that each use only has a shot peiod fo tansmission, we adopt DF potocol at the BS to bette exploit the boadcast natue of wieless signals. In ode to maintain fainess, each use has the same time peiod T fo data tansmission, which is scheduled by the BS though Time Division Multiple Access TDMA in a synchonized manne. Duing each time peiod, only one souce-destination pai, i.e., one communication channel is pemitted fo tansmission in the netwok. Suppose thee ae m pais in the netwok, epesented by M = {,...,m}. Let i be the cuent active channel, i =,...,m. The souce node, destination node and the BS fo channel i ae denoted as s i and d i and, espectively. As only one souce-destination pai is allowed to tansmit, each tansmission channel in this netwok foms a thee-teminal elay channel. To avoid the confusion, in the est of this pape, the tem BS and elay node will be used intechangeably. With the help of the BS as the elay node, a single-hop and long-distance tansmission can be changed into two-hop and shote-ange tansmissions. The pesence of an intemediate node can significantly enhance the tansmission pefomance by the two-phase communication, i souce node s i tansmits to elay node and ii elay node tansmits to the destination d i along with node s i. B. Achievable Rate The highest infomation theoetic achievable ate of the discete memoyless DF elay channel when channel i is active is given by: R i max min{ix s i ; Y X,IX si,x ; Y di }, px si,x whee x si, y di, y and x ae denoted as the input to the channel, the output of the channel, the obsevation by the elay node and the input symbol chosen by the elay, espectively. The fist tem IX si ; Y X is the lagest ate that the elay node can decode the signal, and the second tem IX si,x ; Y di is to ensue that the destination can decode. The highest achievable ate of the elay channel is obtained with an optimal joint pobability between the codes sent by the souce and the elay. In the DD netwok, assume that all wieless channels ae independent Rayleigh fading channels with path loss. The channel gain coefficients ae denoted by h si, h di and h sid i, epesenting the channel conditions fo the souce-bs, BSdestination and souce-destination channels, espectively. The channel gain coefficients can be obtained though a feedback channel in cellula netwoks. In this pape, we assume that these coefficients can be estimated accuately at the BS. As some eseach woks have addessed the esouce allocation with impefect channel state infomation, e.g. [4], [5], this issue can be investigated in the futue. The eceived signals at the elay node and at the destination node at time t ae given by y t =h six si t+z t, y di t =h sid i x si t+h di x t+z di t, whee z t and z di t ae independent zeo-mean Gaussian noises eceived at the elay node and at the destination node d i both with vaiance σ. Duing each use s tansmission peiod, both the use and the elay send a sequence of length n. The input sequence at the souce node is subject to the following aveage powe constaint: n n t= x s i t s, 3 and the tansmitting powe constaint at the elay node when channel i is active is given by n n t= x t. 4 When channel i is active, the highest achievable ate of the elay channel is given by R i = = max max px si,x β min h si d i β s + min{ix si ; Y X,IX si,x ; Y di } { log + hs i βp s i, + σ log σ h si d i i βp s + } h di P i. Rate 5 is achieved by the joint supeposition encoding pocess among the souce node s i and the elay node, which consists of consecutive blocks of tansmission. Duing each block, two codes ae geneated: one code u containing the subsequent block s message and the othe code x fo the cuent block s message. Duing each tansmission block, the elay node sends x containing the cuent block s message with its maximum tansmission powe P i. The souce node s i, on the othe hand, divides its total tansmission powe P s i into two pats, βp s i i and βp s with diffeent puposes, whee β = β. βp s i i is used fo tansmitting u and βp s is devoted to coopeate with the elay fo tansmitting x to the destination. The code x si sent by s i is the supeposition of u and x. 5

4 3 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO., FEBRUARY 4 III. RATE MAXIMIZATION FOR ASINGLE-USER CHANNEL It can be obseved fom 5 that the achievable ate R i is a function of the tansmission powes P s i and P i when the location of the BS is fixed. Theefoe, each single use s achievable ate can be impoved by optimally adapting the tansmission powes. In this section, we conside two types of tansmission powe constaints and discuss the optimal powe adaptation schemes and the maximum single use s achievable ates sepaately. Both wieless uses and the BS can adopt diffeent powe levels fo data tansmission. Theefoe, we aim to maximize the tansmission efficiency, i.e., to maximize the oveall tansmission ate of the channel unde a total powe constaint. Only BS can adjust its powe level and all uses tansmit with a fixed powe. In this scenaio, we will deive the optimal tansmission powe at the BS in tems of maximizing the tansmission ate. A. Rate Maximization unde Total Powe Constaint The objective is to allocate s powe consumption constaint tot and P i unde a total, which is the maximum available tansmission powe fo channel i. The poblem is fomulated as an optimization poblem: max s, R i subject to s + tot. 6 In the achievable ate expession 5, the fist tem is the elay decoding ate and the second epesents the destination decoding ate. Fo any given P s i and P i, the lagest achievable ate is attained by optimally choosing β by the souce. Since the highest achievable ate is obtained when the elay decoding ate equals the destination decoding ate, ou optimal powe allocation scheme ties to balance these two ates by jointly designing P s i, P i and β. Depending on whethe elay decoding ate o destination decoding ate is the bottleneck, thee ae two powe allocation stategies fo the souce node. If the destination decoding ate is the bottleneck, the souce node can educe β until the elay decoding ate equals the destination decoding ate. If the elay decoding ate is the bottleneck, the souce node will set β =. Note that when β =, the souce node and the elay node will tansmit independent codes. Theefoe, the second coopeation mode between the souce and the elay is also known as the asynchonous case while the fist mode is efeed to as the synchonous case. Fo ou optimization poblem, we will jointly allocate P s i, P i and β fo both cases. Synchonous Case: The destination decoding ate is the bottleneck, and β<. Denote P s i = βp s i and P s i i = βp s as the two components of P s i. Since the signal eceived at the destination contains a combined stength, we fist maximize the destination decoding ate with fixed, Pi = P s i +. Then, we can allocate P s i powe constaint. The destination decoding ate is given by: IX si,x ; Y di = + log σ h si d i s + and unde the total h si d i P s i + h di P s i. Since 7 is a concave function of P s i, the fist-ode condition esults in the optimum powe allocation between P s i, which is given by and s = = h di + h di, 7 + h di, 8 and the destination decoding ate becomes: IX si,x ; Y di = log + 4 h si d i h di h si d i + h di + P s i. 9 Fo the optimization poblem 6, the optimum of ate R i is achieved when P s i + P s i + P i = tot and when the elay decoding ate equals the destination decoding ate, i.e., h si P s i σ = 4 h s id i h di + h di σ + h s id i P s i σ. The above constaints lead to the optimal solution when h si : σ s = h s id i + h di h si + h di tot, = h s i h si + h di tot. The highest achievable ate in the synchonous case is given by R sync i = log + h s i + h di h si + h di tot σ. If > h si, the souce-destination channel has a bette channel condition than the souce-elay channel. In this case, any diect tansmission is moe eliable than coopeative tansmission. Theefoe, the souce tansmits to the destination diectly to avoid the waste of esouces, and the highest end use ate channel capacity fo non-coopeative tansmission is R i di = log + h s id i tot σ. 3

5 ZHANG et al.: OPTIMIZING NETWORK SUSTAINABILITY AND EFFICIENCY IN GREEN CELLULAR NETWORKS 33 Asynchonous Case: In this case, the souce and the elay employ independent codes, so that β =. The achievable ate fo channel i becomes R i =min log { log + h s id i P s i + h s i P s i σ + h di σ, }. 4 By the same agument, the maximum achievable ate is obtained when the elay decoding ate equals the destination decoding ate, i.e., h si s = s + h di. 5 When h si, the optimal powe allocation in the asynchonous case is given by: s = = h di h si + h di tot, h si h si + h di tot, 6 and the highest achievable ate is given by R asyn + i = log h si h di h si + h di tot σ. 7 Remak. The optimal coopeation stategy and powe adaptation scheme to maximize the achievable ate depends on the channel conditions and the locations of the uses. Fo example, in the AWGN channel with path loss, if BS is close to the souce, the powe allocation in the synchonous case achieves highe ate; othewise, the powe allocation scheme in the asynchonous case achieves highe ate. B. Rate Maximization unde BS Powe Constaint Suppose all uses have a fixed tansmission powe P s i = P s and only the BS can adjust its powe level based on the havested enegy and the QoS equiement. Then, the ate maximization poblem unde BS powe constaint is fomulated as: R i max P i subject to P s i = P s P i P, 8 whee P is the maximum tansmission powe at the BS. Intuitively, the achievable ate R i impoves with the BS tansmission powe. Howeve, since the elay decoding ate is independent of P i, in this poblem, we ae inteested in how R i changes with BS tansmission powe P i. When the powe level at the BS is known, the souce node will adapt its tansmission powe accodingly by choosing pope β to maximize the achievable ate. As shown in Section III-A, when > h si, the souce tansmits to the destination diectly. Theefoe, we only discuss the powe adaptation scheme fo the souce and the BS to maximize the achievable ate when h si. In the synchonous case, the elay decoding ate is the dominant one, so the souce node will choose <β< to balance the elay decoding ate and the destination decoding, so the maximum is achieved when P i = P. In the asynchonous case, the elay decoding ate becomes the bottleneck, so β =. Synchonous Case: In this case, the maximum ate is achieved when P i = P and ate. In this case, R i inceases with h si βp s = βp s + βp s + h di P. 9 Solving 9 fo β, we can get β = h s id i h di h si 4 P s h si P s h di P h si h di + P The condition fo this case to happen is. P < h s i h di P s. Theefoe, the maximum ate is given by R sync i = log + h s id i h di h si σ h si P s h di P h si h di + P. Asynchonous Case: When P hs i h si d i h di P s, β =. Since the bottleneck is the elay decoding ate, impoving P i cannot incease the achievable ate. In this case, the maximum tansmission ate is a constant and given by R asyn i = log + h s i P s σ, 3 and the optimal tansmission powe at the BS is given by = h s i h di P s. 4 In conclusion, depending on the BS s powe output as well as its location, the maximum achievable ate fo the optimization poblem 8 is given by log + h s i d h i di R i = h si σ h si P s h di P h di + h si h si d P i, h si d i if P < hs i h si d i P h di s; log + hs i P s, if P σ hs i h si d i P h di s. 5

6 34 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO., FEBRUARY 4 IV. POWER ALLOCATION CONSIDERING ENERGY BUFFER DYNAMICS In geen cellula netwok, the BS is equipped with a echageable enegy battey to stoe and elease the havested enewable enegy. In this section, we take the dynamic enegy chaging/dischaging pocesses into consideation to allocate the maximum powe output P i fo each channel i. A. Enegy Buffe Model Since the enewable enegy is intinsically intemittent, the chaging pocess is a stochastic pocess. Denote Nt as the total havested enegy ove time [,t]. Nt is non-deceasing and its coesponding chaging ate is λt. Consideing the intemittency of the enewable enegy souces, we assume that the chaging ate changes ove time and the chaging pocess is descibed as a non-homogeneous andom pocess in this pape. As the tansmission time fo each channel is elatively shot compaed with the pocess, the chaging ate of the pocess duing channel i s tansmission can be appoximated as a constant λ i. The havested enegy at the BS is consumed fo signal pocessing, coding and fowading the infomation to the destination. The total tansmission enegy when channel i is active can be calculated by E i = P i T, 6 whee T is the tansmission time fo channel i. Suppose the enegy used fo signal pocessing and coding is a constant E fo all time peiods. Denote V t as the total enegy dischaged ove [,t]. Then, V t = E t t T + P sds, 7 whee P s =P i when channel i is active at time s. The dischaging ate of channel i is thus a constant given by μ i = P i + E /T. 8 Denote C as the battey capacity, which is assumed to be lage enough to stoe the enegy havested within a time peiod. Then, the enegy stoed in the buffe at time t is given by Qt = min[max[nt V t, ],C]. 9 Define DQ i as the enegy depletion time of the enegy buffe with initial buffe length Q i, DQ i =inft Qt =,Q = Qi, 3 whee inf{t T}denotes the infimum of set T. Ou objective is to design the maximum tansmission powe fo each channel while peventing the DD communication netwok fom battey enegy depletion. Specifically, we intend to avoid enegy buffe vacancy duing each tansmission peiod by deciding the tansmission powe at the beginning of the peiod. To achieve this goal, we investigate the elationship between the enegy depletion time of the enegy buffe DQ i dischaging ate μ i.letf D t; Q i and the denote the pobability density function of the enegy depletion time. Based on the stat up delay analysis in [6], we have f D t; Q i = d p Q q, tdq, 3 dt whee p Q q, t is the pobability density function of the buffe enegy stoage Qt at time t. In the following, we intend to obtain p Q q, t, whichis denoted as p Q q, t =E[δq Qt], 3 whee E[ ] calculates the expectation of the input function. Duing each tansmission peiod, the enegy buffe has a andom input and a constant ate output. Without loss of geneality, suppose the aival pocess duing channel i s tansmission is a andom pocess with a geneal distibution. Thus, the tempoal evolution of the enegy buffe duing a small time inteval Δ can be descibed by dqt =Qt +Δ Qt =ηδ μ i Δ, 33 whee ηδ = Nt +Δ Nt denotes the the summation of enegy chaged duing Δ. The chaging pocess with a geneal distibution can be appoximated as a Wiene pocess with a dift [7], [8]. The dift duing channel i s tansmission is at ate λ i.the vaiance of the chaging pocess ν i is detemined by the Wiene pocess. In a Wiene pocess, the incement within a time duation Δ is nomally distibuted with zeo mean and a vaiance, which is linealy popotional to the time duation Δ [9]. As a esult, let ν i =γδ, wheeγ is a scaling facto detemined by the specific chaging technology. The pobability density function fo ηδ = x+λ i Δ is given by p η x, Δ = 4πΔγ e x /4Δγ. 34 Since the analysis of pobability density function with a constant dift ate is complex, to facilitate analysis, we adopt the techniques in [3] to obtain p Q q, t though Fouie tansfom. Let F{ux} denote the Fouie tansfom of a function ux, wehave F{ux} := û ξ = uxe jξx dx, 35 whee û ξ is the tansfomed function, and ξ is the tansfom vaiable. The Fouie tansfom of the pobability density function is a chaacteistic function of the andom vaiable. Thus, the Fouie tansfom peseves all the andom vaiable s statistic infomation. This featue guaantees the accuacy of ou analysis. Let ˆp Q ξ t and ˆpη ξ Δ denote the Fouie tansfom of p Q q, t and p η x, Δ, espectively. Pefoming Fouie tansfom on 33 and taking Δ, we can get t ˆpQ ξ t =μi F{ q pq q, t} +ˆp Q ξ tφ ξ, 36 whee φ ξ = lim Δ Δ [ˆpη ξ Δ ]. 37

7 ZHANG et al.: OPTIMIZING NETWORK SUSTAINABILITY AND EFFICIENCY IN GREEN CELLULAR NETWORKS 35 To get ˆp η ξ Δ in 37, we pefom Fouie tansfom on the pobability density function p η x, Δ, which is given by 34, and obtain ˆp η ξ Δ = e γδξ e jξλi. 38 Thus, φ ξ is given by φ ξ = γξ jξλ i. 39 Based on the time deivative popety of Fouie tansfom, 36 could be futhe efomed as t ˆpQ ξ t =jξμi ˆp Q ξ t+ˆpq ξ tφ ξ =jξμ i + φ ξ ˆp Q ξ t. 4 To solve this fist ode odinay diffeential equation 4, we need to detemine initial values. The initial condition of 4 could be obtained at time t =. At time t =, the enegy buffe length is Q i, namely pq q = Q i, =. The Fouie tansfom of this condition is ˆp Q ξ = e jξqi. With this initial condition and 39, the solution to 4 can be obtained as ˆp Q ξ t =e jξqi e jξμ i λ i γξ t. 4 Finally, p Q q, t can be obtained by pefoming the invese Fouie tansfom on 4. Replacing p Q q, t in 3, the pobability density function of the enegy depletion time with initial buffe length Q i is given by { } f D t; Q i Qi = exp Qi +λi μ i t. 4γπt 3 4γt 4 B. Powe Allocation Schemes We have modeled the enegy buffe and povided the pobability density function of enegy depletion time in the pevious subsection. Based on ou theoetical analysis, in this subsection, we design powe allocation schemes to maximize the tansmission efficiency while ensuing the netwok sustainability. Assume that the initial enegy stoage in the buffe and the statistical paametes of the chaging pocess can be estimated and ae available at the beginning of each tansmission peiod. The BS can adjust the dischaging ate by choosing tansmission powe P i duing channel i s tansmission peiod. The objective of ou powe allocation scheme is to maximize each single channel s tansmission ate while maintaining the sustainability of the netwok at a cetain level. We still conside two diffeent netwok scenaios depending on whethe uses ae able to adjust the tansmission powe. In the fist netwok scenaio, both the BS and uses can adjust tansmission powe. Thus, ou scheme can allocate powe fo both the BS and uses to impove the tansmission efficiency. Then, we conside the case that uses can not adjust tansmission powe due to equipment constaints, which means that only the BS can choose vaious powes fo data tansmission. In the following, we pesent the tansmission powe allocation famewoks unde both total powe constaint and BS powe constaint cases. Powe Allocation unde Total Powe Constaint: We fist conside the situation that both the BS and uses can adjust thei tansmission powe levels. In the poposed netwok scenaio, since impoving the tansmission ate is at the expense of consuming moe tansmission powe, the communication netwok may not be sustainable ove time due to powe depletion. To tackle this issue, ou design objective is to impove the tansmission efficiency of each channel while maintaining the whole netwok s sustainability. Ou poposed scheme allocates both BS tansmission powe and use tansmission powe on a slot-by-slot basis. At the beginning of channel i s tansmission peiod, the emaining enegy in the buffe is Q i. In ode to maintain the netwok sustainability, the maximum tansmission powe P i fo the BS on channel i is detemined by numeically solving the following equation: E[DQ i ] = T + δ, 43 whee δ denotes a constant to guaantee the sustainability of geen wieless netwoks. δ is decided accoding to the toleance level of the tansmission o the available volume of backup enegy. If thee is sufficient backup enegy o the tansmission has high toleance level, i.e., the netwok toleates a high tansmission latency like data tansmission, δ can be set to a small value. If the available volume of the backup enegy is not enough and the tansmission does not toleate a high tansmission latency, such as voice/video, a lage δ is chosen. Based on ou analysis in Section IV-A, the expectation of the depletion time can be calculated by E[DQ i ] = Q i exp 4γπt { } Qi +λi P i + E /T t dt. 4γt 44 Then, we can obtain the optimal P s to maximize the tansmission efficiency based on the value of P i.inthe total powe constaint case, the use is able to adjust its own tansmission powe to coopeate with the BS to impove the tansmission efficiency. Based on 8 and in Section III-A, in the synchonous case, the optimal tansmission powe fo the use is given by P s i = + h di + h di h si + h di h si P i. 45 In the asynchonous case, accoding to 6, the optimal use tansmission powe is given by s = h di h si. 46 Powe Allocation unde BS Powe Constaint: We futhe conside the case that uses can not adjust thei tansmission powe level due to the device constaints. In this case, uses tansmit with fixed powe while BS adapts its tansmission powe to meet ou design objective.

8 36 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO., FEBRUARY Achievable ate bps/hz sync async non coopeative Achievable ate bps/hz BS sync, total async, total non coopeative Total tansmission powe tot /σ db Fig.. Rate compaison unde the total powe constaint fo a single-use channel. Accoding to 5, the maximum ate fo the optimization poblem 8 is achieved when P i = P if P < h si h si d i h di P s, and P i = hs i h si d i h di P s if P h si h si d i h di P s. Theefoe, the powe allocation scheme pefoms as follows: at the begining of channel i s tansmission peiod, based on the emaining buffe enegy Q i, the BS fist calculates a tansmission powe P i such that E[DQ i ] = T + δ, 47 which is the same as the fist step of the powe allocation scheme in the total powe constaint case. Then, the BS compaes P i with min{p, hs i h si d i h di P s } and chooses the minimum of the two values as the optimal tansmission powe. V. NUMERICAL RESULTS To veify the above theoetical analysis and to evaluate ou powe allocation schemes, we povide some numeical esults in this section. We assume that all wieless channels ae independent Rayleigh fading channels with path loss. Fistly, in ode to illustate the ate enhancement by the coopeative communication in a single-use channel, we compae the optimal ate achieved by ou poposed coopeative powe adaptation schemes with the non-coopeative tansmission ate unde the total powe constaint as shown in Fig.. The tansmission powe fo the non-coopeative communication is set to be P tot, i which is the maximum total tansmission powe fo channel i. Suppose P tot/σ i anges fom db to 3dB, and the path loss exponent α is. The distances between the souce and the BS, between the BS and the destination, and between the souce and the destination ae 75 metes, 8 metes and 5 metes, espectively. It can be obseved that coopeative tansmission can achieve highe ate than non-coopeative tansmission in both synchonous case and asynchonous case. In a high SNR envionment, the spectum efficiency can be doubled. Fig. 3 depicts the ate compaison employing diffeent powe adaptation schemes fo both total powe constaint and Fig P i /σ db Rate compaison fo a single-use channel. BS powe constaint poblems. Suppose P i /σ anges fom db to 4dB. Fo the total powe constaint poblem, the souce would adapt its own tansmission powe based on the available BS s tansmission powe. Fo the BS powe constaint poblem, the tansmission powe at the souce is set to be db and the maximum BS tansmission powe P is 4dB. The est of the simulation paametes emain unchanged. To illustate the ate impovement, we also set the capacity of the non-coopeative tansmission as a baseline fo compaison, whee the use tansmission powe is db. It can be obseved that the powe adaptation schemes unde the total powe constaint can achieve highe ate, which is at the expense of highe tansmission powe at the souce. Unde the BS powe constaint, the channel ate eaches a is lage, which is bounded by the limited tansmission powe at the souce. Secondly, we evaluate ou poposed powe allocation schemes consideing the enegy buffe dynamics. The cumulative distibution function CDF of enegy depletion time is shown in Fig. 4, whee Fig. 4a illustates the CDF with diffeent initial buffe stoage and Fig. 4b depicts the CDF with diffeent dischaging ate. It can be seen fom Fig. 4a that the CDF cuve of the enegy depletion time shifts ight as the initial buffe enegy Q i gows, which means that the BS is moe likely to povide constant when enegy output fo a longe time if Q i is lage. As shown in Fig. 4b, the CDF cuve shifts left as the dischaging ate μ i gows, which means that the BS is moe likely to deplete its enegy soon with the incease of the dischaging ate. ] of the geen enegy buffe model shown in Subsection IV-A is depicted in Fig 5. The chaging ate λ i is set to be 3.5. It can be seen that E[DQ i ] deceases with depletion ate μi and inceases The depletion time expectation E[DQ i with the initial enegy stoage Q i fom both analytical esults and simulation esults. Fig. 6 and Fig. 7 illustate the pefomance of ou poposed powe allocation schemes in a pactical netwok containing consecutive tansmissions. The use tansmission powe in the BS constaint case is set to be db and the maximum BS tansmission powe is db. The battey capacity is. The enewable enegy chaging ate at the BS duing

9 ZHANG et al.: OPTIMIZING NETWORK SUSTAINABILITY AND EFFICIENCY IN GREEN CELLULAR NETWORKS CDF of enegy depletion time Q i =3 Q i =6 Q i =9 Q i = Aveage use ate bps/hz Poposed Max sustainability Time unit a λ i =3.5, μ i = δ a Aveage channel ate CDF of enegy depletion time μ i =4.5 μ i =5.5 μ i =6.5 Enegy depletion pobability Poposed Max sustainability Time unit b Q i =, λ i = δ b Enegy depletion pobability Fig. 4. CDF of enegy depletion time. Fig. 6. Total powe constaint case channel numbe=. Expectation of enegy depletion time time unit sim, μ=4.5 ana, μ=4.5 sim, μ=5.5 ana, μ=5.5 sim, μ=6.5 ana, μ=6.5 5 i 5 3 Initial enegy stoate Q enegy unit Fig. 5. Expectation of depletion duation λ i =3.5. each tansmission peiod is andom and time-vaiant. Suppose that the enegy chaging ate can be foecasted based on some histoical data, e.g. data fom the pevious day o yea. To demonstate the enegy efficiency of ou poposed schemes, we compae with a max-sustainability scheme whee = Qi E T min{ Qi E T in total powe constaint case and =,P i,p } in BS powe constaint case. We calculate both the enegy depletion pobability and the aveage tansmission ate of all channels accoding to the efeence max-sustainability scheme and ou poposed powe allocation schemes deived in Subsection IV-B. The compaison in the total powe constaint case is shown in Fig. 6 and the esult in the BS powe constaint case is shown in Fig. 7. It can be obseved that ou poposed powe allocation schemes can impove the aveage tansmission ate dastically fo both total powe constaint case and BS powe constaint case. The eason is that ou schemes exploit the dynamic chaging pocess of the enewable enegy to impove the enegy efficiency. Compaed with the max-sustainability powe allocation scheme which has zeo enegy depletion pobability, ou poposed method is associated with vey low depletion pobability. VI. CONCLUSION In this pape, we have poposed seveal powe allocation schemes to maximize the thoughput while maintaining the netwok sustainability in a DD communication undelaying geen cellula netwok. The esults should shed some light on the geen wieless netwok design with enegy efficiency and enegy sustainability as citical design citeia. Fo the futue wok, we will conside moe netwok scenaios including vaious mobility pattens and QoS equiement of uses to optimize the netwok efficiency and sustainability in geen wieless communication netwoks. REFERENCES [] Global mobile statistics 3. Available: mobile-maketing-tools/latest-mobile-stats [] Z. Hasan, H. Boostanimeh, and V. K. Bhagava, Geen cellula netwoks: a suvey, some eseach issues and challenges, IEEE Commun. Suveys & Tutoials, vol. 3, no. 4, pp ,. [3] A. Fehske, G. Fettweis, J. Malmodin, and G. Biczok, The global footpint of mobile communications: the ecological and economic pespective, IEEE Commun. Mag., vol. 49, no. 8, pp. 55 6,.

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Hänggi, Genealized Fokke-Planck equation: deivation and exact solutions, The Euopean Physical J. B, vol. 68, no. 4, pp , 9. Xiaoxia Zhang eceived the B.E. degee fom Beijing Univesity of Posts and Telecommunications, Beijing, China in 8 and M.A.Sc. degee in Electical and Compute Engineeing fom the Univesity of Wateloo, Wateloo, ON, Canada in. She is cuently woking towads the Ph.D. degee at the Depatment of Electical and Compute Engineeing, Univesity of Wateloo, Wateloo, ON, Canada. He eseach inteests include esouce management fo boadband communication netwoks, coopeative communication, wieless senso netwoks and netwok infomation theoy. Zhongming Zheng eceived the B.Eng. 7 and M.Sc. degees fom City Univesity of Hong Kong. Cuently, he is pusuing his Ph.D. degee in Electical and Compute Engineeing at Univesity of Wateloo, unde Boadband Communication Reseach Goup. His eseach focuses on geen wieless communication, smat gid and wieless senso netwoks.

11 ZHANG et al.: OPTIMIZING NETWORK SUSTAINABILITY AND EFFICIENCY IN GREEN CELLULAR NETWORKS 39 Qinghua Shen eceived the B.Sc. degee and maste degee in Electical Engineeing fom Habin Institute of Technology HIT, China, in 8 and, espectively. He is cuently woking towad a Ph.D. degee in the Depatment of Electical and Compute Engineeing, Univesity of Wateloo, Canada. His eseach inteests include esouce allocation fo e- healthcae system, cloud computing and smat gid. Jing Liu eceived the B.S., M.S. and Ph.D. degees fom Xidian Univesity, Xi An, China, in 998, and 5. Since July 5, she joined the Depatment of Electonic Engineeing, Shanghai Jiao Tong Univesity, China, whee she is cuently an Associate Pofesso. Fom Jan. to Jan. 3, she is a Visiting Pofesso in Depatment of Electical and Compute Engineeing, Univesity of Wateloo, Canada. He cuent eseach inteests include Wieless body aea netwok, Wieless senso netwok, Coopeative communications, Cognitive communications, and Mobility management. Xuemin Sheman Shen IEEE M 97-SM - F 9 eceived the B.Sc. 98 degee fom Dalian Maitime Univesity China and the M.Sc. 987 and Ph.D. degees 99 fom Rutges Univesity, New Jesey USA, all in electical engineeing. He is a Pofesso and Univesity Reseach Chai, Depatment of Electical and Compute Engineeing, Univesity of Wateloo, Canada. He was the Associate Chai fo Gaduate Studies fom 4 to 8. D. Shen s eseach focuses on esouce management in inteconnected wieless/wied netwoks, wieless netwok secuity, social netwoks, smat gid, and vehicula ad hoc and senso netwoks. D. Shen seved as the Technical Pogam Committee Chai/Co- Chai fo IEEE Infocom 4, IEEE VTC Fall, the Symposia Chai fo IEEE ICC, the Tutoial Chai fo IEEE VTC Sping and IEEE ICC 8, the Technical Pogam Committee Chai fo IEEE Globecom 7, the Geneal Co-Chai fo Chinacom 7, the Chai fo IEEE Communications Society Technical Committee on Wieless Communications, and PP Communications and Netwoking. He also seves/seved as the Edito-in-Chief fo IEEE Netwok, Pee-to-Pee Netwoking and Application, andiet Communications; a Founding Aea Edito fo IEEE TRANSACTIONS ON WIRELESS COMMU- NICATIONS; an Associate Edito fo IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, Compute Netwoks, andacm/wieless Netwoks, etc.; and the Guest Edito fo IEEE JOURNAL ON SELECTED AREAS IN COMMUNI- CATIONS, IEEE Wieless Communications, IEEE Communications Magazine, and ACM Mobile Netwoks and Applications, etc. D. Shen eceived the Excellent Gaduate Supevision Awad in 6, and the Outstanding Pefomance Awad in 4, 7 and fom the Univesity of Wateloo, the Pemie s Reseach Excellence Awad PREA in 3 fom the Povince of Ontaio, Canada, and the Distinguished Pefomance Awad in and 7 fom the Faculty of Engineeing, Univesity of Wateloo. D. Shen is a egisteed Pofessional Enginee of Ontaio, Canada, an IEEE Fellow, an Engineeing Institute of Canada Fellow, a Canadian Academy of Engineeing Fellow, and a Distinguished Lectue of IEEE Vehicula Technology Society and Communications Society. Liang-Liang Xie IEEE M 3-SM 9 eceived the B.S. degee in mathematics fom Shandong Univesity, Jinan, China, in 995 and the Ph.D. degee in contol theoy fom the Chinese Academy of Sciences, Beijing, China, in 999. He did postdoctoal eseach with the Automatic Contol Goup, Linköping Univesity, Linköping, Sweden, duing 999- and with the Coodinated Science Laboatoy, Univesity of Illinois at Ubana-Champaign, duing -. He is cuently a Pofesso at the Depatment of Electical and Compute Engineeing, Univesity of Wateloo, Wateloo, ON, Canada. His eseach inteests include wieless netwoks, infomation theoy, adaptive contol, and system identification.