Optimal Dual-Connectivity Traffic Offloading in Energy-Harvesting Small-Cell Networks

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng Optmal Dual-Connectvty Traffc Offloadng n Energy-Harvetng Small-Cell Network Yuan Wu Senor Member IEEE, Xaowe Yang, L Png Qan Senor Member IEEE, Habo Zhou Member IEEE, Xuemn Sherman) Shen Fellow IEEE, Mohamad Awad Member IEEE Abtract Traffc offloadng through heterogenou mall-cell network HSCN) ha been envoned a a cot-effcent approach to accommodate the tremendou traffc growth n cellular network. In th paper, we nvetgate an energy-effcent dual-connectvty DC) enabled traffc offloadng through H- SCN, n whch mall cell are powered n a hybrd manner ncludng both the conventonal on-grd power-ly and renewable energy harveted from envronment. To acheve a flexble traffc offloadng, the emergng DC-enabled traffc offloadng n 3GPP pecfcaton allow each moble uer MU) to multaneouly communcate wth a macro cell and offload data through a mall cell. In pte of avng the on-grd power conumpton, powerng traffc offloadng by energy harvetng EH) mght lead to qualty of ervce QoS) degradaton, e.g., when the EH power-ly fal to ort the requred offloadng rate. Thu, to reap the beneft of the DC-capablty and the EH power-ly, we propoe a jont optmzaton of traffc chedulng and power allocaton that am at mnmzng the total on-grd power conumpton of macro and mall cell, whle guaranteeng each erved MU traffc requrement. We tart by tudyng a repreentatve cae of one mall cell ervng a group of MU. In pte of the non-convexty of the formulated jont optmzaton problem, we explot t layered tructure and propoe an algorthm that effcently compute the optmal offloadng oluton. We further tudy the cenaro of multple mall cell, and nvetgate how the mall cell elect dfferent MU for maxmzng the ytemwe reward that account for the revenue for offloadng the MU traffc and the cot of total on-grd power conumpton of all cell. We alo propoe an effcent algorthm to fnd the optmal MU-electon oluton. Numercal reult are provded to valdate our propoed algorthm and how the advantage of our propoed DC-enabled traffc offloadng through the EHpowered mall cell. I. INTRODUCTION The pat decade ha wtneed an explove growth of mart moble devce and popularty of moble nternet Y. Wu, L. Qan, and X. Yang are wth College of Informaton Engneerng, Zhejang Unverty of Technology, Hangzhou, Chna emal: ewuy@zjut.edu.cn, lpqan@zjut.edu.cn). L. Qan the correpondng author. Y. Wu alo wth the State Key Laboratory of Integrated Servce Network, Xdan Unverty, Xan, 77, Chna. H. Zhou and X. Shen wth the Department of Electrcal and Computer Engneerng, Unverty of Waterloo, Waterloo, ON N2L 3G, Canada emal: h53zhou@uwaterloo.ca, xhen@bbcr.uwaterloo.ca). H. Zhou now wth the School of Electronc Scence and Engneerng, Nanjng Unverty, Nanjng, Chna. M. Awad wth the Department of Computer Engneerng, Kuwat Unverty, 36 Kuwat Cty, Kuwat emal: mohamad@eee.org). Th work ha been preented, n part, n IEEE Global Communcaton Conference GLOBECOM) 27. Th work wa orted n part by the Natonal Natural Scence Foundaton of Chna under Grant 657244, n part by the Zhejang Provncal Natural Scence Foundaton of Chna under Grant LR7F2 and LR6F3, n part by the Young Talent Cultvaton Project of Zhejang Aocaton for Scence and Technology under Grant 26YCGC, and n part by the Natural Scence and Engneerng Reearch Councl, Canada. ervce, whch have yelded a tremendou traffc burden on cellular network. By explotng the mult-ter tructure of rado acce network RAN), offloadng moble traffc through heterogenou mall-cell network HSCN) ha been wdely condered a a cot-effcent approach to releve traffc congeton n macro cell. Due to brngng RAN cloer to moble uer MU), traffc offloadng through HSCN can yeld mult-fold beneft, uch a enhancng throughput and mprovng reource utlzaton effcency. To facltate a flexble traffc offloadng, the recent 3GPP pecfcaton ha propoed a paradgm of mall-cell dualconnectvty DC) that enable a MU, by ung two dfferent rado nterface, to communcate wth a macro cell and multaneouly offload data through mall cell []. Wth a flexble traffc chedulng between macro and mall cell, the DC-enabled traffc chedulng expected to further enhance the beneft of traffc offloadng [2] [7]. However, the dene deployment of HSCN ha yelded a gnfcant energy conumpton n cellular RAN, whch ha attracted lot of attenton n realzng energy-effcent HSCN whle provdng guaranteed qualty of ervce QoS) [9] []. Vewng the mportant role of traffc offloadng, many reearch effort have alo been devoted to nvetgatng energy-effcent traffc offloadng through HSCN [2]. In partcular, wth the recent advance n collectng and torng renewable energy from envronment e.g., va the emergng mart grd [2]), traffc offloadng through mall cell whch are powered by energy-harvetng EH) ha been condered a a vable approach to reap the beneft of traffc offloadng and to reduce the on-grd power conumpton [2] [25]. However, due to the randomne n renewable energy ource, the EH power-ly uffer from ntermttency, whch adverely nfluence the performance of traffc offloadng. For ntance, evere offloadng outage e.g., packet lo) due to nuffcent receved gnal to noe and nterference rato SINR) wll occur f the mall cell blndly provde a large offloadng rate whle ufferng from a temporary valley of the EH power-ly. Several tude have been denoted to nvetgatng how to properly explot the ntermttent EH power-ly to accommodate the MU traffc. In partcular, the emergng paradgm of DC, whch allow the MU to multaneouly communcate wth the macro and mall cell, enable a flexble traffc chedulng between macro and mall cell [], [2] and thu provde an effectve approach to addre the ntermttent EH power-ly. For ntance, baed on the DC, the mall cell ufferng from the valley of EH power-ly can low down t offloadng rate to the MU, and correpondngly, the macro cell actvely ncreae t tranmon rate to the MU n order to mantan 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 2 the requred QoS e.g., throughput). Therefore, n th tudy, by explotng the EH power-ly and the DC-capablty, we nvetgate the DC-enabled traffc offloadng through the EH-powered mall cell. The man contrbuton of th paper are ummarzed a follow. We tart by tudyng the cenaro of one EH-powered mall-cell acce pont AP) whch offload traffc for a group of MU. Specfcally, gven the total number of erved MU, we formulate a jont optmzaton of the traffc chedulng and power allocaton for one targeted par of the AP and the MU. Our formulaton take nto account the offloadng outage due to the AP ntermttent EH power-ly and am at mnmzng the total on-grd power conumpton of macro and mall cell, whle atfyng the MU throughput requrement. Depte the non-convexty of the jont optmzaton problem, we explot t layered tructure and propoe an algorthm that can effcently compute the optmal offloadng oluton. Wth the optmal offloadng oluton for each AP- MU par, we further tudy the cenaro of multple AP, and nvetgate how the AP elect dfferent MU to execute the DC-enabled traffc offloadng. The formulaton am at maxmzng the total networkreward that account for the revenue of ervng the MU traffc requrement and the cot of the total ongrd power conumpton. Depte the nature of complcated nonlnear bnary programmng of the formulated optmzaton problem, we propoe an effcent layeredalgorthm to olve t and fnd the optmal MU-electon oluton. We preent extenve numercal reult to valdate our propoed algorthm for both the ngle-ap cae and the mult-ap cae). Moreover, we preent extenve reult to how the performance advantage of our propoed DC-enabled traffc offloadng through the EH-powered mall cell n avng the on-grd power conumpton and ncreang the total network-reward. The remander of th paper organzed a follow. We revew the related tude n Secton II. We preent the ytem model and problem formulaton for the ngle-ap cae n Secton III. An effcent algorthm to compute the optmal offloadng oluton propoed n Secton IV. In Secton V, we further tudy the mult-ap cae. We preent the numercal reult n Secton VI and fnally conclude th work n Secton VII. II. RELATED LITERATURE In th ecton, we frtly revew the related tude about the energy-effcent traffc offloadng n HSCN but wthout conderng the DC-capablty. We then revew the related tude that explot the DC-capablty for traffc offloadng. Stude about energy-effcent traffc offloadng through HSCN wthout DC: Wthout explotng DC, there have been many tude nvetgatng the energy-effcent traffc offloadng through HSCN, whch can be n general categorzed nto two man tream. The frt tream of tude focu on nvetgatng the optmal reource allocaton for energy-effcent traffc offloadng but wthout explotng the EH powerly) [2] [9]. For ntance, effcent cheme to optmze the heterogenou mall cell on/off mode have been propoed n [2] and [3]. Effcent cheme that optmze the tradeoff between the pectrum-effcency and energy-effcency have been propoed n [4] and [5]. Yu et. al. propoed a mult-objectve optmzaton framework that account for the energy-effcency n traffc offloadng [6]. Takng nto account the lmted capacty of backhaul lnk, Yang et. al. propoed a refundng cheme for the mall cell to accommodate the MU offloaded from macro cell [7]. An archtecture of vertcal offloadng ha been propoed n [8] to acheve the goal of energy-avng by actvely turnng off the redundant cell. In [9], an energy-effcent traffc offloadng cheme that explot devce-to-devce communcaton ha been propoed. The econd tream of tude explot the EH powerly for traffc offloadng [2] [25]. In [2], by explotng the tattc nformaton about the traffc ntenty and EH power-ly, Zhang et. al. propoed a cheme that jontly offload the MU to the EHpowered mall cell and adjut the mall cell on/off mode. In [22], to utlze the harveted energy, Han et. al. propoed a cell-ze adapton cheme that actvely offload the MU to the cell whch are powered by green energy. However, aggrevely offloadng traffc through the EH-powered cell mght lead to a evere congeton. The author of [23] propoed a jont energyaware and latency-aware cheme that offload the MU to the green-powered yet le congeted mall cell. In [24], by explotng the advanced mcrogrd, Cha et. al. propoed the data offloadng through the mcrogrdconnected mall cell whch are powered by EH. In [25], Chang et. al. propoed a wrele power tranfer cheme for enablng the data offloadng. In addton to the above tude targeted for traffc offloadng, there are many tude focung on the performance analy for the EH-powered mall cell [26] [28]. In [26], Gong et. al. propoed a jont optmzaton of the cell on-off tate, reource block allocaton, and renewable energy allocaton to mnmze the average on-grd power conumpton. In [27], Yu et. al. developed a tochatc model to analyze the throughput and coverage performance when the mall cell are powered by EH. In [28], Zheng et. al. nvetgated the optmal placement of the EH-ated relay for offloadng the cell-edge uer traffc. Takng nto account the ntermttency of EH ly a well a the envronmental condton, there have been many tude nvetgatng the tranmon outage mnmzaton [29] [3]. For ntance, n [29], Zhou et. al. tuded the onlne power control polce for outage mnmzaton n a fadng wrele lnk wth EH-powered tranmtter and recever. In [3], L et. al. propoed an optmal tranmon polcy for mnmzng the long-term tranmon outage probablty, when the ource node olar-powered and eqed wth 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 3 a fnte-zed battery. In [3], baed on the offlne performance analy, Ikman et. al. propoed a lowcomplexty onlne tranmon cheme for optmzng the outage probablty n an EH block-fadng communcaton ytem. Stude about the DC-enabled traffc offloadng: Due to the beneft of enablng a flexble traffc chedulng between macro and mall cell, the DC-enabled traffc offloadng ha attracted lot of reearch nteret [] [7]. The functonalty of DC and t performance gan have been llutrated n []. Explotng the multaneou communcaton wth macro and mall cell provded by the DC, the author of [2] llutrated the mportance of proper reource plttng n the DC-enabled tranmon. Power-capacty plttng cheme for the DC-enabled traffc offloadng wa propoed n [3], and the traffc plttng wa nvetgated n [4]. In [5], a jont reource allocaton cheme for the DC-enabled traffc offloadng ha been propoed to mnmze the overall reource conumpton cot whle atfyng each uer traffc requrement. Groupng dfferent macro and mall cell to execute the DC-enabled traffc offloadng ha been tuded n [6]. The mpact of backhaul delay n the DC-tranmon ha been tuded n [7]. However, to the bet of the author knowledge, few tude have nvetgated the DC-enabled traffc offloadng through mall cell whch are powered by EH. A we have explaned before, proper traffc chedulng and power allocaton are necetated for the DC-enabled traffc offloadng through the EH-powered mall cell, uch that we can jontly reap the beneft of the DC and the EH power-ly. III. SYSTEM MODEL AND PROBLEM FORMULATION FOR Drect-path from mbs p + q 6,r 6) 6 AP g 6 Solar Panel Offloadng path from AP ONE SMALL CELL MU 5 MU 6 Solar Panel g B6 MU p,x ) B6 Solar Panel AP 2 B6 mbs AP 4 MU 2 MU 3 MU 4 AP 3 Solar Panel Power Grd Power Lne Fg. : An llutraton of the condered DC-enabled traffc offloadng model contng of three AP whch are powered by the hybrd energy ource and one mbs whch powered by the on-grd power-ly. We frtly preent the overall ytem model condered n th work, a hown n Fgure. Specfcally, a group of AP S = {, 2,...,,..., S} are underlad to the coverage of a macro bae taton mbs). The mbs olely powered Depte enablng the flexble traffc chedulng, the DC necetate the coordnaton between the macro and mall cell, and thu conume addtonal reource for the gnalng exchange between the macro and mall cell, whch however out of the cope of our work. by the on-grd power-ly, and each AP powered by both the conventonal on-grd power-ly and the EH power-ly. The AP and the mbs provde the DCenabled downlnk traffc offloadng for a group of MU I = {, 2,...,,..., I}. In the followng Secton III to IV, we frt tudy the cae of one AP, by pecfcally focung on nvetgatng that one AP together wth the mbs) provde the DC-enabled traffc offloadng for one MU.e., one AP- MU par). Baed on the optmal offloadng oluton for each ndvdual AP-MU par, we further tudy the cenaro of multple AP n Secton V. A. Problem Formulaton for the Par of one AP and one MU We tart by tudyng the DC-enabled traffc offloadng of one AP. To preent a detaled problem formulaton, we focu on nvetgatng that the AP together wth the mbs) provde the DC-enabled traffc offloadng for one MU.e., one AP-MU par), aumng that the AP multaneouly offloadng traffc to a total number N MU. Notce that we frtly conder that the value of N predetermned, and the value of N wll be further optmzed for the cenaro of multple AP n Secton V. For the ake of clear preentaton, n the followng, we denote the condered AP a AP, and the MU a MU. MU ha a traffc requrement to acheve, whch denoted by. The DC enable the mbs to provde a fracton of MU traffc requrement and AP to offload the remanng part. We conder that the mbs and AP ue dfferent frequency channel to erve the MU, and thu there no co-channel nterference among the mbs tranmon and the AP tranmon. We ue p B) to denote the mbs tranmt-power to MU, when AP execute the DC-enabled offloadng notce that we nclude the ubcrpt n varable p B), nce the mbs tranmtpower to MU depend on whch AP execute the DCenabled offloadng). The downlnk tranmon-rate x B) from the mbs to MU can be wrtten a: x B) = W B log 2 + p ) B)g B, ) n B where parameter W B denote the mbs downlnk channel bandwdth to accommodate each MU, and g B denote the channel power gan from the mbs to MU. Parameter n B denote the power of the background noe at MU from the mbs tranmon, e.g., n B can be expreed a n B = W B n, where n the power denty of the background noe. AP ha both the on-grd power-ly and the EH power-ly. We ue p to denote AP tranmt-power to MU from t on-grd power-ly, and AP can flexbly adjut p [, p max ] where p max denote the maxmum on-grd tranmt-power). However, due to the ntermttency of renewable energy ource, AP harveted energy, whch denote by Q, a random varable. A mentoned before, gven the total number of N MU erved by AP, from the farne perpectve and tractablty perpectve, we conder that AP equally dvde Q for 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 4 all t erved MU. A a reult, the offloadng rate from AP to MU can be wrtten a: wrtten a: x = W log 2 + N ) p + Q )g, 2) N n where W denote the downlnk channel bandwdth ued by AP to erve each MU, and g denote the channel power gan from AP to MU. Parameter n denote the power of the background noe at MU from the tranmon of AP. In th work, to focu on our objectve n nvetgatng how to properly explot the DC-capablty to facltate the MU traffc offloadng and mtgate the mpact of the ntermttency n the EH power-ly, we adopt a relatvely mple aumpton on the utlzaton of EH power-ly.e., AP equally allocate t entre EH power-ly Q to the erved N MU). Therefore, our reult n th work provde a benchmark evaluaton on explotng the DC for traffc offloadng when ntegratng the EH power-ly. A we preent n th paper, uch a degn.e., our propoed jont traffc chedulng and power allocaton) already very challengng to olve, even under the current aumpton. In partcular, a an mportant drecton for our future tudy, we wll further conder that the AP can flexbly chedule t EH power-ly over dfferent tme lot and allocate dfferent amount of the EH power-ly for dfferent MU, and nvetgate the correpondng optmal degn of the DCenabled traffc offloadng. In th work, we conder the long-term average on-grd power conumpton and model Q n each hort chedulng perod a an ndependent and unform dtrbuton wthn [M low, M ]. The value of M low and M are aumed to be known baed on the htorcal data. The unform dtrbuton ha been ued to model uncertanty n EH power-ly over hort-term perod [27], [32] [34]. For ntance, n [32], baed on a tme-lotted tructure, the author adopted the mlar unform dtrbuton a well a other dtrbuton) to model the harveted energy from olar energy. [33] ued the ame lotted-tructure and the unform dtrbuton of the EH ly to nvetgate the network throughput maxmzaton for nk-baed wrele enor network. Neverthele, t worth notcng that the current aumpton about the EH-ly relatvely deal for ome pecfc cae. A an mportant drecton for our future work, we wll alo conder other more realtc aumpton on the EH-ly and nvetgate the correpondng optmal degn of DCenabled traffc offloadng. The uncertanty n Q ntroduce randomne to the achevable offloadng rate x from AP to MU. Let r denote AP agned offloadng rate to MU. Due to the randomne n x, r may not be atfed, whch lead to the offloadng outage. To capture th outage, we ntroduce functon P out p, r ) to denote the probablty that AP achevable offloadng rate x to MU fal to meet the agned offloadng rate r. Functon P out p, r ) can be P out p, r ) = Pr {r x } { } N p + Q )g ) = Pr r W log 2 + N n r ) N 2 W ) n g p M low, M M low f 2 r W ) n g M N p = 2 r W ) n g M low 3) N, f 2 r W ) n g, otherwe M low N < p Baed on P out p, r ), we formulate an optmzaton problem to mnmze the total on-grd power conumpton,.e., p B) + p when AP offload traffc to MU. The detal are hown n the followng total On-Grd Power Conumpton Mnmzaton OGPM) problem: OGPM) mn p B) + p Subject to: x B) + r Pout p, r ) ) = 4), p B) p max B, 5) p p max, 6) Varable: r, p ) and ) x B), p B). In Problem OGPM), we jontly optmze the followng varable: ) AP agned offloadng rate r and the tranmt-power p to MU, and ) the mbs tranmon rate x B) and the tranmt-power p B). Contrant 4) guarantee that MU receve a total ucceful throughput equal to t requrement, where the term of r P out p, r ) ) denote the ucceful throughput receved from AP. Parameter p max B denote the mbs maxmum on-grd tranmt-power for each MU, and p max denote AP maxmum on-grd tranmt-power for each MU. Accordng to [35], Problem OGPM) a non-convex optmzaton problem whch dffcult to olve. To addre th dffculty, we explot the layered-property of Problem OGPM), and equvalently tranform t nto an equvalent form that can lead to Problem OGPM) an effcent oluton. B. Layered Structure of Problem OGPM) We now conder the mot general cae of P out p, r ) [, ].e., the frt cae n 3)) 2. In th cae, we can 2 We wll analyze the cae of full offloadng outage at the end of th ecton and the cae of zero-offloadng outage n Secton IV-D. 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 5 equvalently tranform Problem OGPM) nto: OGPM) mn p B) + p Subject to: W B log 2 + p B) g B n B ) + M r 2 r W ) n + N p N 2 r W ) n g M M low M p g N =, 7) 2 r W ) n M low, 8) g N and contrant 5) and 6), Varable: r, p ) and p B). However, contrant 7) and 8) tll yeld a non-convex feable regon, leadng to that Problem OGPM) a nonconvex optmzaton problem. To olve Problem OGPM) effcently, we explot t layered-property. Specfcally, we ntroduce an auxlary varable ρ [, ] a follow: M ρ = r + N p N 2 r W ) n g M. 9) M low denote the porton of MU traffc re- Varable ρ qurement uccefully offloaded through AP, and t ntroduced to help u decompoe Problem OGPM) a hown n Fgure 2. Specfcally, we ue ρ to decompoe Problem OGPM) nto a top-problem.e., Problem OGPM-Top)) and two parallel ubproblem.e., Problem Sub-mBS) and Problem Sub-AP)). We next explan the detal about the decompoton a follow. Gven a fxed ρ, we can equvalently eparate Problem OGPM) nto two parallel ubproblem to mnmze the BS tranmt-power and the AP tranmt-power, repectvely. Subproblem to fnd the BS mnmum tranmt-power a a functon ρ : Gven ρ, the frt ubproblem am at fndng the BS mnmum tranmt-power ˆp B) ρ ) a follow: Notce that we denote the optmal oluton ˆp B) ρ ) namely, the BS mnmum tranmt-power) a a functon of ρ. Subproblem to fnd the AP mnmum tranmt-power a a functon ρ Gven ρ, the econd ubproblem am at fndng the AP mnmum tranmt-power ˆp ρ ) a follow: Sub-AP) ˆp ρ ), ˆr ρ ) ) = arg mn p M M low )ρ Subject to: p = + N r 2 r W ) n M, ) g N and contrant 6) and 8), Varable: p and r. Contrant ) tem from contrant 9). We denote the optmal oluton of th ubproblem.e., the tuple of AP mnmum tranmt-power and agnedoffloadng rate ˆp ρ ), ˆr ρ ) ) ) a a functon of ρ. By ung the optmal oluton of the two ubproblem at the bottom, we further optmze ρ [, ] to mnmze the total on-grd power conumpton, whch lead to Problem OGPM-Top) a follow: OGPM-Top) ρ = arg mn ˆp B) ρ ) + ˆp ρ ) Varable: ρ. Notce that after we olve Problem OGPM-Top) and fnd ρ. We can expre the optmal oluton of Problem OGP- M) by feedng ρ nto the two ubproblem,.e., p B), p, r ) = ˆpB) ρ ), ˆp ρ ), ˆr ρ ) ). 2) In addton, x B) = W B log + p B) g B n B ). Problem OGPM) Problem Sub-mBS) Problem OGPM-Top) p, p, r, x * * * * B) ) B) Problem Sub-AP) Fg. 2: Decompoton of Problem OGPM) nto a top-problem.e., Problem OGPM-Top)) and two ubproblem.e., Problem Sub-mBS) and Problem Sub-AP)). We wll preent the detaled algorthm to olve the above three problem n the next ecton. Before preentng the detal, we dcu a trval cae of the full offloadng outage,.e., P out p, r ) = n 3). In th cae, only the mbs can provde tranmon rate to MU, and no ucceful Sub-mBS) ˆp B) ρ ) = arg mn p B) offloadng rate provded by the AP. A a reult, we p B) g B ) can drectly derve the oluton of Problem OGPM) a: Subject to: W B log 2 + = ρ ) req, ) n B x,f = Rreq, and p R B),F = 2 W B ) n B g B ong that and contrant 5), p B),F pmax B ), and p,f =. Here, the ubcrpt F Varable: p B). denote Full Offloadng Outage. Due to the trvalty, we aume that the full offloadng outage wll not happen at the optmum of Problem OGPM). IV. PROPOSED ALGORITHMS TO SOLVE PROBLEM OGPM) In th ecton, we propoe algorthm to olve Problem Sub-mBS), Problem Sub-AP), and Problem OGPM-Top) n the above decompoton tructure hown n Fgure 2. A. Analytcal Soluton of Problem Sub-mBS) We frt olve Problem Sub-mBS). By takng nto account p max B, the vable nterval of ρ, whch can enure that Problem Sub-mBS) feable, ρ [ max{, ρ low,mbs }, ] where ρ low,mbs = W B log 2 + pmax B g B n B ). For each ρ 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 6 n th vable nterval, we can derve the optmal oluton of Problem Sub-mBS) a: ˆp B) ρ ) = ρ ) W 2 B ) n B, g B 3) ˆx B) ρ ) = ρ ). 4) B. Propoed Algorthm to olve Problem Sub-AP) Problem Sub-AP) dffcult to olve due to the nonconvexty of contrant ). To overcome th dffculty, we tranform Problem Sub-AP) nto the followng form wth a ngle decon-varable r : Sub-AP-E) Varable: ˆp ρ ) = mn M M low )ρ + N r 2 r W ) n M g N r ρ. 5) Notce that the frt n contrant 8) can be drectly atfed by ung ) to replace p, and the econd n 8) tranlate to 5). Compared wth Problem Sub-AP), we temporarly do not conder contrant 6) n Problem SubAP-E). Thank to th temporal relaxaton, Problem SubAP-E) become a convex optmzaton problem whch wll be explaned n Propoton below). Before that, we dcu the connecton between Problem Sub-AP) and Sub-AP- E). Remark : Connecton between Problem Sub-AP) and Problem Sub-AP-E): Problem Sub-AP-E) equvalent to Problem Sub-AP), except that we do not nclude contrant 6). A a reult, there wll be three poble outcome after we olve Problem Sub-AP-E). Frt, f the optmal oluton of Problem Sub-AP-E).e., ˆp ρ )) atfe ˆp ρ ) p max, then ˆp ρ ) uffce to be the optmal oluton of Problem Sub-AP). Second, f the optmal oluton of Problem Sub-AP-E).e., ˆp ρ )) atfe ˆp ρ ) > p max, then Problem Sub-AP) nfeable under the currently gven ρ. Thrd, f ˆp ρ ) <, then t mean that AP r can be completely orted by t harveted energy, and there no need for AP to ue a potve on-grd power. In th cae, addtonal operaton are requred uch that we can fnd ˆp ρ ) = we wll pecfy the detal later on). To olve Problem Sub-AP-E), we dentfy the followng mportant property. Propoton : Problem Sub-AP-E) a convex optmzaton problem. Proof: Let F r ) denote the frt-order dervatve of the objectve functon of Problem Sub-AP-E). We then can derve: F r ) = ln 2n W g 2 r W M M low N ρ r 2, 6) whch monotoncally ncreang n r. Moreover, the feable nterval of Problem Sub-AP-E) affne. Thu, Problem Sub-AP-E) a convex optmzaton problem [35]. Propoton enable u to ue the Karuh-Kuhn-Tucker KKT) condton [35] to compute the optmal oluton of Problem Sub-AP-E). Specfcally, we ue ˆr ρ ) to denote the optmal oluton of Problem Sub-AP-E), whch depend on the gven ρ. To fnd ˆr ρ ), we propoe SubSol-Algorthm the detal are hown n the next page). The key of SubSol-Algorthm to explot the ncreang property of F r ) accordng to the proof of Propoton ) and ue the becton-earch to fnd the crtcal value denoted by r opt,temp ) uch that F r opt,temp ) =. The WHILE-Loop from Step 7 to Step 7) how the becton-earch method. Snce r lower bounded by ρ accordng to 5), we drectly et r opt,temp = ρ f F CaeI ρ ) >,.e., Step 4-5 n SubSol-Algorthm. Fnally, SubSol-Algorthm output ˆr ρ ) = r opt,temp. SubSol-Algorthm: to compute ˆr ρ ) and ˆp ρ ) : Input: ρ. 2: MU et γ.e., the tolerable computaton-error ued n the bectonearch) a a very mall number and et flag =. 3: MU et r lower = ρ and et r er = r er where r er a very large number). 4: f F r lower ) > then 5: MU et r opt,temp = r lower. 6: ele 7: whle flag = do 8: f r er r lower ) γ then 9: MU et r opt,temp = 2 rlower + r er ) and flag =. : ele : f F 2 rlower + r er ) ) > then 2: MU et r er = 2 rlower + r er ). 3: ele 4: MU et r lower = 2 rlower + r er ). 5: end f 6: end f 7: end whle 8: end f 9: MU compute p opt,temp = ) n g M. N low M M )ρ N r opt,temp 2: f p opt,temp < then 2: MU et r = r opt,temp and r = r er. 22: whle r r) > γ do low 2M M 23: MU et v = )ρ N r+r) 24: f v > then 25: MU et r = r + r). 2 26: ele 27: MU et r = r + r). 2 28: end f 29: end whle 3: MU et r opt,temp = M low M )ρ r opt,temp N r opt,temp + 2 W 2 r opt,temp + 2 W +2 r+r 2W ) n M. g N r + r), and popt,temp = ) n g M. N 3: end f 32: Output: ˆr ρ ) = r opt,temp and ˆp ρ ) = p opt,temp. Notce that baed on ˆr ρ ), SubSol-Algorthm alo output the mallet tranmt-power requred by AP n Step 9.e., the optmal objectve functon value of Problem Sub-AP-E)) a follow: ˆp ρ ) = M M low N ˆr ρ ) )ρ + 2 ˆr ρ ) W ) n M. 7) g N Vablty of SubSol-Algorthm to olve Problem Sub-AP): We llutrate the vablty of SubSol-Algorthm to olve 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 7 Problem Sub-AP) by addreng the three cae n Remark. Frt, ˆp ρ ), ˆr ρ ) ).e., the output of SubSol- Algorthm) uffce to be the optmal oluton of Problem Sub-AP), f ˆp ρ ) atfe ˆp ρ ) p max. Second, Problem Sub-AP) nfeable under the gven ρ ), f ˆp ρ ) lead to ˆp ρ ) > p max. Thrd, f ˆp ρ ) <, t mean that there no need for AP to pend any potve on-grd power. In th cae, we need addtonal operaton to fnd the proper value of r opt,temp that yeld p opt,temp =. To th end, we degn the addtonal Step 2-3 n SubSol-Algorthm. low M M We explot the property that )ρ +2 r W M N N r ) n g, ] here, r thre equal to r opt,temp obtaned n Step 9 of SubSol- Algorthm). Hence, we ue the becton-earch to fnd the new r opt,temp that yeld p opt,temp =. ncreang for r [r thre C. Propoed Algorthm to olve Problem OGPM-Top) After olvng Problem Sub-mBS) and Problem SubAP) and obtanng ˆp B) ρ ) and ˆp ρ ), repectvely, we contnue to olve Problem OGPM-Top). In pte of t mple form, t dffcult to olve Problem OGPM-Top), - nce we tll cannot analytcally derve ˆp B) ρ )+ˆp ρ ). Fortunately, Problem OGPM-Top) only nvolve a nglevarable ρ wthn a fxed nterval,.e., ρ [, ]. Baed on th property, we propoe LS-Algorthm that perform a lnear-earch of ρ [, ] wth a very mall tep-ze) to olve Problem OGPM-Top) and fnd the optmal oluton r, p, x B), ) p B). The detal of LS-Algorthm are a follow. LS-Algorthm: output r, p, x B), p B)) for Problem OGPM) : Intalzaton: Set ρ = and a a uffcently mall number = 5 ). MU et the current bet value CBV = and the current bet oluton CBS =. 2: whle ρ do 3: If Problem ub-ap) feable, MU ue SubSol-Algorthm to compute ˆr ρ ), ˆp ρ )). Otherwe, turn to Step 9. 4: If Problem ub-mbs) feable, MU ue 3) and 4) to compute ˆx B) ρ ) and ˆp B) ρ ). Otherwe, turn to Step 9. 5: f ˆp ρ ) + ˆp B) ρ ) ) < CBV then 6: MU update CBV = ˆp ρ ) + ˆp B) ρ ). 7: MU et CBS = ˆr ρ ), ˆp ρ ), ˆx B) ρ ), ˆp B) ρ ) ) accordng to 2). 8: end f 9: Update ρ = ρ +. : end whle : Output: r, p, x B), B)) p = CBS. range of ρ over whch we can analytcally characterze the optmal oluton of Problem OGPM-Top). A a reult, we do not need to ue the above lnear-earch wthn th range. ) Zero-outage Cae and It Suffcent Condton to Occur: To fnd uch an nterval of ρ over whch we do not need to execute the lnear-earch, we dentfy a pecal cae of zero-outage, namely, P out p, r ) =. A an mportant property, we provde the followng propoton. Propoton 2: Gven ρ, f F ρ ), then the optmal oluton of Problem Sub-AP-E) yeld the zerooutage,.e., P out ˆp ρ ), ˆr ρ ) ) =. Proof: Baed on the convexty of Problem Sub-AP-E), f F ρ ), then the optmal oluton can be drectly, whch conequently lead expreed a ˆr ρ ) = ρ to req ˆp ρ ) = 2 ρ R W ) n M low. g N By ubttutng ˆr ρ ), ˆp ρ ) ) nto 3), we can obtan P out ˆr ρ ), ˆp ρ ) ) =. Furthermore, we dentfy the followng mportant property. Propoton 3: There ext a crtcal threhold ρ cr, whch gven by ρ cr = W ln 2 WM M low N g n ). 8) Here, functon W.) the Lambert W-functon [36],.e., the nvere functon of fx) = x exp x). Specfcally, f ρ cr <, then for each ρ [ρ cr, ], the correpondng optmal oluton ˆp ρ ), ˆr ρ ) ) of Problem Sub-AP- E) lead to the zero-outage. Proof: Baed on 6), we can derve F ρ ) = ln 2 W n req g 2 ρr W M low M N ρ, whch ncreang n ρ. Thu, there ext a unque ρ cr uch that F ρcr Rreq ) =. By olvng F ρ cr Rreq ) =, we can obtan ρ cr n 8). 2) Analytcal Soluton n Zero-outage Cae: The purpoe of analyzng the zero-outage cae that we can analytcally derve the optmal oluton of Problem OGPM). The detal are a follow. Wth P out p, r ) =, Problem OGP- M) can be equvalently re-wrtten nto the followng form where, the letter Z denote Zero ): OGPM-Z) mn p B) + p Subject to: Varable: W B log 2 + p B) g B n B ) + r = p 2 r W ) n M low 9) g N and contrant 5) and 6) {r, p } and p B D. Advanced Algorthm to olve Problem OGPM-Top) baed on the Cae of Zero-Outage The lnear-earch n LS-Algorthm requre a very mall tep-ze e.g., = 5 ), whch conequently requre at mot teraton. To reduce the number of teraton, we further propoe an advanced LS-Algorthm.e., ADLS- Algorthm) n th ubecton. The key dea to dentfy a We next analytcally derve the optmal oluton of Problem OGPM-Z). To th end, we frtly dentfy the followng two ubcae regardng the rght hand de of 9): Subcae-I whch baed on the pre-aumpton that r W log 2 + M low g N n ). Subcae-I mean that the agned offloadng rate r no larger than the rate that can be olely orted by AP mnmum EH 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 8 power-ly M low, whch thu enure the zero-outage to occur. Correpondngly, p hould be zero. Subcae-II whch baed on the pre-aumpton that r W log 2 + M low g N n ). Subcae-II mean that the agned offloadng rate r larger than the rate that can be olely orted by AP mnmum EH power-ly M low. A a reult, a potve p requred to enure the zero-outage to occur. Baed on the above Subcae-I and Subcae-II, we derve the optmal oluton of Problem OGPM-Z) under the two ubcae a follow. Soluton under Subcae-I: Baed on the ratonale of Subcae-I, the optmal oluton of Problem OGPM-Z) can be wrtten a: r,z-subi = mn { W log 2 + M low p,z-subi =, x B),Z-SubI = r,z-subi, g N n ), }, p B),Z-SubI = )n 2 x B),Z-SubI B. g B Notce that Subcae-I vald, only f p B),Z-SubI pmax B. Soluton under Subcae-II: Baed on the ratonale of Subcae-II, we can derve the optmal oluton of Problem OGPM-Z) a follow. Snce contrant 9) trctly bndng at the optmum n th cae.e., no addtonal on-grd power requred), we can equvalently tranform Problem OGPM-Z-SubII) nto a ngle-varable optmzaton problem a follow: OGPM-Z-SubII): mn 2 r W ) n M low + 2 g N Varable: r,z-subii low r r,z-subii. r W B In the above problem, the lower-bound r,z-subii low gven by: r,z-subii low = max { p max W B log 2 + B n B g B whch tem from 5) and p = 2 r W The er-bound r gven by: r,z-subii = mn { Z-SubII p max W log 2 + whch tem from p = 2 r W ) n g ) n g + M low N n M low N M low N. )g ), R req p max. Notce that Subcae-II vald, only f r,z-subii low. Otherwe, Subcae-II fal to hold. r,z-subii In partcular, we expre the optmal oluton of Problem OGPM-Z-SubII) n the followng propoton. Propoton 4: If r,z-subii low r,z-subii, the optmal oluton of Problem OGPM-Z-SubII) can be analytcally wrtten a: r,z-subii = r,z-subii low, f F Zr,Z-SubII low ) > r,z-subii, f F Zr,Z-SubII ) < W B W R req W B +W log 2 W Bg B n W g n B ) ), otherwe. W B }, 2) Here, F Z r ) = ln 2n W ln 2n B W W B g B 2 B the frt-order dervatve of the objectve functon of Problem OGPM-Z-SubII). Proof: It can be verfed that functon F Z r ) ncreang n r. Thu, conderng the affne feable nterval, Problem OGPM-Z-SubII) a trctly convex optmzaton problem. The convexty enable u to ue the KKT condton to derve the optmal oluton. Specfcally, by olvng F Z r ) =, we obtan the lat cae of 2). On the other hand, f F Z r,z-subii low ) > whch mean that the objectve functon ncreang for r [r,z-subii low, r,z-subii ]), we et r,z-subii = rlow,z-subii,.e., the frt cae of 2). Fnally, f F Z r,z-subii ) < whch mean that the objectve functon decreang for r [r,z-subii low, r,z-subii ]), we et r,z-subii = r,z-subii,.e., the econd cae of 2). By ung r,z-subii n 2), we derve the optmal oluton of Problem OGPM-Z-SubII) a follow: W g 2 r r p,z-subii = r,z-subii 2 W ) n M low, g N x B),Z-SubII = r,z-subii, x p B),Z-SubII W B),Z-SubII = 2 B ) n B. g B In ummary, by comparng the optmal oluton under Subcae-I and Subcae-II f they are feable), we can derve the optmal oluton of Problem OGPM-Z) a follow: r,z, p,z, x,z, p ) B),Z = r,,z-subˆθ p,,z-subˆθ x, ),Z-Subˆθ p B),Z-Subˆθ, 2) ) n B where ˆθ = arg mn θ {I,II} p,z-subθ g + p B),Z-Subθ. B 3) Propoed Advanced LS-Algorthm: Baed on Propoton 2 and 3, for the nterval of ρ [ρ cr, ] wthn whch the optmal oluton of Problem OGPM) alway lead to the zero-outage), we can drectly ue 2) to compute the optmal oluton of Problem OGPM), ntead of executng ), W log 2 + M low } g a lnear-earch ρ [ρ cr, ]. Explotng th mportant ), N n property, we further propoe the followng ADLS-Algorthm AD mean Advanced ) to olve Problem OGPM). The detal of ADLS-Algorthm are hown on the next page. Compared wth LS-Algorthm, ADLS-Algorthm ue 2) to compute the optmal oluton for the nterval ρ, ].e., Step 3-9), and thu avod the lnear-earch of ρ [ρ cr, ]. In partcular, let denote the tepze whch a very mall number, e.g., 5 ) ued by the lnear-earch n ADLS-Algorthm. Our propoed ADLS- Algorthm requre no more than 2 ρcr log r er ) 2 γ recall that γ denote the tolerable computaton-error ued by our SubSol-Algorthm before). In Secton VI, Fgure 5b) how the advantage of ADLS-Algorthm n reducng the number of teraton. Untl now, we have completed olvng Problem OGPM) and obtaned the optmal offloadng oluton for the targeted par of AP and MU, when AP ervng the total number of N MU. Notce that by ung our ADLS- Algorthm, we can fnd the optmal offloadng oluton for an arbtrary AP-MU par, whch facltate our extended tudy of the mult-ap cae n the next ecton. [ρ cr 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 9 ADLS-Algorthm: The optmal oluton r, p, x B), p B)) of Problem OGPM) : Intalzaton: Set ρ = and a a uffcently mall number = 5 ). MU et CBV = and CBS = 2: whle ρ do 3: f ρ ρ cr then 4: If r,z-subii low r,z-subii, MU compute r,z, p,z, x,z, ) p B),Z accordng to 2). Otherwe, break the Whle-Loop. 5: f p,z +, p ) < CBV then B),Z 6: MU update CBV = p,z +, p B),Z r,z, p,z, x,z, ) p B),Z. and CBS = 7: end f 8: Break the whole WHILE-LOOP. 9: end f : If Problem ub-ap) feable, MU ue SubSol-Algorthm to compute ˆr ρ ), ˆp ρ )). Otherwe, tart the next teraton. : If Problem ub-mbs) feable, MU ue 3) and 4) to compute ˆx B) ρ ) and ˆp B) ρ ). Otherwe, tart the next teraton. 2: f ˆp ρ ) + ˆp B) ρ ) ) < CBV then 3: MU update CBV = ˆp ρ ) + ˆp B) ρ ). 4: MU et CBS = ˆr ρ ), ˆp ρ ), ˆx B) ρ ), ˆp B) ρ ) ). 5: end f 6: Update ρ = ρ +. 7: end whle 8: Output: r, p, x B), B)) p = CBS. V. EXTENSION TO THE SCENARIO OF MULTIPLE SMALL CELLS A. Sytem Model and Problem Formulaton In th ecton, baed on the optmal offloadng oluton for the ngle AP cae n Secton IV, we further extend to nvetgate the cenaro of multple AP. A hown n the ytem model n Fgure, we conder a cenaro of a group of AP S = {, 2,..., S} provdng the DCenabled offloadng to a group of MU I = {, 2,...I}. Our objectve to nvetgate how the AP properly elect dfferent MU to provde the DC-enabled offloadng, wth the objectve of maxmzng the total network-reward. To model th problem, we ntroduce the bnary varable z {, }, I, S to denote whether AP elect MU or not. Specfcally, z = mean that AP elect MU to execute the DC-enabled traffc offloadng, whle z = mean the oppote. Recall that n Secton III and IV, by aumng that AP elect exactly N = I z MU to erve, we have propoed ADLS-Algorthm and LS-Algorthm) to compute the optmal traffc chedulng and power allocaton for the par of AP and MU, whch denoted by r, p, x B), ) p B). In other word, the optmal oluton r, p, x B), ) p B) of Problem OGPM) depend on the detaled value of N = I z. To explctly denote th mpact due to I z, n the followng, we re-denote the optmal oluton of Problem OGPM) about the par of AP and MU a follow: r, z), p I, z), I x ) B), z), p I B), I. 22) z) Baed on 22), we formulate the followng optmal MUelecton problem to nvetgate how dfferent AP optmally elect dfferent MU to provde the DC-enabled offloadng: MultMUSel): max µr req πp, I z ) + S I p B), z))) z I Subject to: S z, I 23) I z H max, S 24) z =, f Ω nf, I z), S, I 25) Varable: {z } S, I. In Problem MultMUSel), we am at maxmzng the total network-reward that take nto account the margnal reward λ for uccefully ervng a MU traffc requrement, and the cot due to the mbs and AP total on-grd power conumpton p, I z ) + p B), I )) when AP elect MU to provde the traffc offloadng. z Here, parameter π denote the margnal cot for the on-grd power conumpton. Contrant 23) mean that MU can only be erved by at mot one AP. Contrant 24) mean that AP can elect no more than H max MU to erve. Here, we conder that the mall cell ue the frequency dvon multple acce FDMA) to accommodate dfferent MU, and each AP ha H max avalable ub-channel to erve the MU. In contrant 25), et Ω nf, I z denote the ) ubet of the MU who cannot be erved by AP when AP elect total I z MU to erve 3. Problem MultMUSel) very challengng to olve, nce t a nonlnear bnary programmng problem due to the followng two reaon. Frt, n the objectve functon, for each par of AP and MU, the mnmum on-grd power p, I z ), ) p B), I z ) depend on the value of I z. Second, contrant 23) and 24) together lead to a reource-contraned generalzed agnment problem [38]. Specfcally, each AP.e., an agent) can accept no more than H max MU.e., the job), and each MU can only be agned to at mot one AP. To tackle th dffculty, we propoe an effcent algorthm to olve Problem MultMUSel) n the next ubecton. B. Layered Algorthm to Solve Problem MultMUSel) To olve Problem MultMUSel), we frt dentfy the followng property: n Problem MultMUSel), the objectve functon and contrant are eparable wth repect to ndvdual AP, except that contrant 23) couple all AP. To decouple 23), for each AP, we frt ntroduce et Λ I to denote the ubet of the MU who are agned to AP a the canddate-uer to be erved. Pleae notce that the MU n Λ are the canddate-uer to be elected by AP n other word, t mght be optmal for AP to only elect ome MU n Λ, ntead of all of them). In addton, we ntroduce Λ to denote the ubet of MU who are not 3 Notce that we can determne et Ω nf, I z a follow. Gven the ) value of I z, MU belong to et Ω nf, I z, f we fnd that ) Problem OGPM) nfeable for the par of AP and MU. 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng agned to any AP.e., the MU Λ wll be not erved by any AP). We mpoe the followng two contrant regardng {Λ } S {},.e., ) S {} Λ = I, and ) Λ Λ = for any two dfferent and. Baed on {Λ } S {}, our key dea to olve Problem MultMUSel) to vertcally decompoe t nto the followng two problem a hown n Fgure 3. We explan the detal about the decompoton a follow. ProblemMultMUSel) n Sec.V.A to olve ProblemMultMUSel-Top) n Sec.V.B to olve ProblemMultMUSel-AP) n Sec.V.B to olve ProblemAP-Top) n Sec.V.C ProblemAP-Sub) n Sec.V.C Fg. 3: Decompoton of Problem MultMUSel) nto Problem MultMUSel-Top) on the top and Problem MultMUSel-AP) for each AP at the bottom. Problem MultMUSel-AP) further decompoed nto Problem AP-Top) and Problem AP-Sub) n Secton V-C. ) Subproblem to optmze the MU-electon for each ndvdual AP under gven Λ : Soe that {Λ } S {} gven. We olve the followng ubproblem for each AP : MultMUSel-AP): RW Λ ) = max Λ µr req πp, Λ z) + p B), Λ z ) )) z Subject to: z H max 26) Λ z =, f Ω nf, Λ z 27) ) Varable: z = {, }, Λ. A we wll how later on, we can olve Problem MultMUSel-AP) and derve RW Λ ) effcently. 2) Top-problem to optmze {Λ } S for all AP: After olvng Problem MultMUSel-AP) and obtanng RW Λ ) for each AP, we then contnue to fnd the optmal {Λ } S {}, by olvng the followng optmzaton problem: MultMUSel-Top): max S RW Λ ) Subject to: S {} Λ = I Λ Λ =, Varable: {Λ } S {}. Notce that after obtanng {Λ } S {}, we can obtan the optmal MU-electon oluton for the orgnal Problem MultMUSel),.e., by olvng Problem MultMUSel-AP) for each AP agan under the gven Λ. In the followng, we provde the algorthm to olve Problem MultMUSel-AP) and Problem MultMUSel- Top), repectvely. C. A Further Decompoton of Problem MultMUSelAP) Frtly, we focu on olvng Problem MultMUSel-AP) under the gven Λ. However, Problem MultMUSel-AP) tll a nonlnear bnary programmng problem. To effcently olve Problem MultMUSel-AP), we further decompoe t nto two ubproblem a hown n Fgure 3). Specfcally, we ntroduce a varable n to denote the number of the MU elected by AP to erve, and the feable value of n wthn, 2,..., Λ here, Λ denote the cardnalty of et Λ whch gven n advance n Problem MultMUSel-AP)). By ung the newly ntroduced varable n, we preent the vertcal decompoton of Problem MultMUSel-AP) a follow. ) Subproblem AP-Sub) to optmze {z } Λ under gven n: Soe that the value of n gven n advance, whch mean that AP elect Λ z = mn{h max, n} MU n Λ. In th tuaton, we focu on olvng the followng ubproblem under the gven n a well a the gven Λ ): AP-Sub): RW ub Λ, n) = max µr req Λ πp,mn{h max,n}) + p B),mn{H max,n}) )) z Subject to: z = mn{h max, n}, Λ z =, f Ω nf,mn{h max,n}), Varable: z = {, }, Λ. Snce the value of mn{h max, n} known, Problem AP- Sub) a lnear bnary programmng problem, whch dffer from Problem MultMUSel-AP). We wll how that we can analytcally derve RW ub Λ, n) and thu olve Problem AP-Sub). 2) Top-problem AP-Top) to optmze n: After obtanng RW ub Λ, n) for the gven n, we then olve the followng problem to fnd the optmal n that can maxmze AP reward under the gven et Λ : AP-Top): RW Λ ) = max n={,,2,...,mn{ Λ,H max }} RWub Λ, n). 28) Notce that after olvng Problem AP-Top), we complete olvng the orgnal Problem MultMUSel-AP) D. Propoed Algorthm to Problem MultMUSel-AP) for each AP Baed on the decompoton of Problem MultMUSelAP) explaned n the prevou ubecton, we next olve Problem MultMUSel-AP). Specfcally, we frt analytcally olve Problem AP-Sub), and then propoe an algorthm to olve Problem AP-Top) by ung the analytcal oluton of Problem AP-Sub). ) Analytcal oluton of Problem AP-Sub): We frt focu on olvng Problem AP-Sub) and dervng Λ, n). Thank to the mple tructure of Problem AP-Sub), we can derve the optmal oluton a follow. RW ub 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng Specfcally, oe that the MU n Λ are ordered n the decendng order baed on the value of V m = µ πp m,mn{h max,n}) + p Bm),mn{H max,n})),.e. m V > V 2 > V 3 >... > V Λ. 29) In the remnder of th ecton, we aume that MU m n Λ ha been ordered accordng to 29) when we ue ubcrpt m to denote the MU. We provde the followng reult regardng the optmal oluton of Problem AP-Sub). Propoton 5: Baed on the orderng n 29), the optmal oluton of Problem AP-Sub) wth the gven n mn{ Λ, H max }}) can be gven by, f m / Ω nf zm,n) = j Λ,j=m j Λ,j=, otherwe,mn{h max,n}) and z j < mn{hmax, n} Pleae notce that the ubcrpt n) n zm,n) ndcate that the optmal oluton depend on the gven value of n. On the other hand, Problem AP-Sub) nfeable, f the followng condton hold: Λ Ω nf,mn{h max,n}) < mn{hmax, n}. 3) Proof: Due to the tructure of Problem AP-Sub), we can prove 3) by howng the contradcton. Let {zm} m Λ denote the optmal oluton of Problem AP-Sub) but beng ncontent wth 3). In other word, there ext two dfferent m and m wth m and m Λ, m > m, m and m / Ω nf,mn{h max,n}) ), and we have z m = and zm =, whch ncontent wth 3). In th tuaton, we can et zm = and zm = to ncreae the objectve functon of Problem AP-Sub) but wthout volatng any contrant. We thu fnh the proof. Baed on Propoton 5 and 3), we can expre the optmal objectve functon value of Problem AP-Sub) a follow RW ub Λ, n) = m Λ µr req πp m,mn{h max,n}) + p Bm),mn{H max,n}) )) z m,n). 3) 2) Solvng Problem AP-Top) and Problem MultMUSel-AP): Baed on 3) and 3), we then olve Problem AP-Top). Snce Problem AP-Top) only nvolve an nteger varable n = {,, 2,..., mn{ Λ, H max }}, we propoe APSol- Algorthm, whch baed on the enumeraton of n wthn {,, 2,..., mn{ Λ, H max }}, to fnd the optmal n that can maxmze the objectve functon RW Λ ). Notce that our propoed APSol-Algorthm alo olve Problem MultMUSel-AP) and output the optmal oluton {zm} m Λ a well a the correpondng RW Λ )). E. Propoed Algorthm to olve Problem MultMUSel-Top) By ung APSol-Algorthm a the ubroutne to compute RW Λ ) for each AP ) under the gven Λ, we then contnue to olve Problem MultMUSel-Top). Thank to the mple form, Problem MultMUSel-Top) can be condered a an optmal groupng problem that agn the MU nto APSol-Algorthm: to olve Problem MultMUSel-AP) and output {z m} m Λ and RW Λ ) : Input Λ for AP 2: Intalze CBV =, CBS =, and n =. 3: whle n mn{ Λ, H max } do 4: AP ue ADLS-Algorthm to compute p,n), p B),n) ) for each MU Λ, and obtan Ω nf,n). 5: f Problem AP-Sub) nfeable accordng to 3) then 6: AP et n = n + and tart the next round of teraton. 7: ele 8: AP ue 3) to compute {zm,n) } m Λ and ue 3) to compute RW ub Λ, n). 9: f RW ub Λ, n) > CBV then : AP et CBV = RW ub Λ, n), and et CBS = {zm,n) } m Λ. : end f 2: AP et n = n +. 3: end f 4: end whle 5: Output: RW Λ ) = CBV and {zm } m Λ = CBS. the et {Λ } S {}. We ue {Λ } S {} to denote the optmal oluton of Problem MultMUSel-Top). To fnd {Λ } S {}, we propoe the followng SelSol-Algorthm. The key of SelSol-Algorthm to execute a randomzed local earch baed on the dea of mulated annealng [39]. SelSol-Algorthm: to olve Problem MultMUSel-Top) and output {Λ } S {} : Intalzaton: agn the MU nto {Λ} S {} n a round-robn manner, et the teraton ndex t =, and et the ntal temperature T n =. 2: Each AP ue APSol-algorthm to compute RW Λ ), and the vrtual AP et RW Λ ) = drectly. 3: whle ) do 4: Randomly elect an AP let u ay ) wth nonempty Λ, and AP randomly elect a MU j Λ. AP further randomly elect another AP. 5: AP move MU j to AP. Correpondngly, AP et Λ = Λ \ {j}, and AP et Λ = Λ {j}. 6: f RW Λ ) + RW Λ ) > RW Λ ) + RW Λ ) then 7: AP update Λ = Λ, and AP update Λ = Λ. 8: ele 9: Wth probablty equal to exp{ } where = RW κt Λ ) + t RW Λ ) RW Λ ) RW Λ ), and T t = T n +αt 2 the ytem temperature at tme t, κ the Bolzmann contant. AP update Λ = Λ, and AP update Λ = Λ. : end f : f the et of {Λ } S do not change for conecutve teraton then 2: Reach convergence and break the WHILE-LOOP. 3: end f 4: Update t = t +. 5: end whle 6: Output Λ = Λ, S. In each round of teraton, a randomly elected AP randomly elect a MU j Λ and move th MU j to another another randomly elected AP. If uch a MU-wtch can mprove the total reward of AP and AP, then AP and AP accept uch a MUwtch by updatng Λ = Λ \{j} and Λ = Λ {j}. Pleae notce that for the ake of eay preentaton, we ntroduce AP a a vrtual AP whch manage Λ. To avod beng trapped n the local optmum, we adopt the dea of Smulated Annealng SA) [39], [4] to accept the non-mprovement MU-wtch wth a certan 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 2 probablty n Step 4). In partcular, the probablty to accept the non-mprovement MU-wtch depend on both the reward degradaton and the current temperature.e., T t ). Specfcally, we ue the coolng chedule T n +αt 2 T t = wth T n denotng the ntal temperature, α > beng a contant, and t denotng the teraton ndex) [4] 4. The hgher the temperature, the more lkely to accept the non-mprovement exchange. When the temperature decreae, the probablty to accept the non-mprovement MU-wtch decreae. After obtanng {Λ } S {}, we can fnally compute the optmal MU-electon oluton for the orgnal Problem MultMUSel) n Secton V-A), by executng APSol- Algorthm for each AP under the gven Λ. SelSol-Algorthm n Sec. V. E to olve ProblemMultMUSel-Top) { } for each AP APSol-Algorthm n Sec. V. D to olve MultMUSel-AP) ub nternal varable n RW, n) Propoton 5 and eq.3) n Sec. V. D to olve ProblemAP-Sub) ub RW ) Fg. 4: Connecton between SelSol-Algorthm, APSol-Algorthm, and Propoton 5 and eq. 3) A a ummary of n th ecton, we provde Fgure 4 to llutrate the connecton among our propoed algorthm, and more mportantly, how they work together to fnd the optmal oluton of Problem MultMUSel). VI. NUMERICAL RESULTS A. Numercal Reult for the Sngle AP Cae We frt valdate our analytcal reult and the propoed algorthm for the cae of one AP. We conder a cenaro n whch the mbs located at the orgn m, m), and AP located at 25m, m). The repreentatve MU, whch form the DC-par wth AP located at 22m, m) later on we wll pecfy the value of N,.e., the number of the MU erved by AP ). We et the channel power gan g B from the mbs to from MU accordng to the path-lo model,.e., g B = λd φ B, n whch parameter d B denote the dtance between the mbs and MU, parameter φ denote the calng-parameter we ue φ = 2.5), and λ follow an exponental dtrbuton wth the unt mean for capturng the mpact of channel fadng. The channel power gan g from AP to MU generated n a mlar way. Wth th 4 Th coolng chedule can yeld an aymptotc convergence to the global optmum oluton accordng to [42]. Specfcally, baed on Theorem n [42], a coolng cheme can yeld an aymptotc convergence to the global optmum oluton, f the followng condton are atfed,.e., ) lm t T t) =, and ) d t= exp[ T t) ] =, where d can be regarded a the dtance between the optmal oluton and other one. In partcular, n our Problem MultMUSel-Top), the value of d a fnte yet fxed number. Thu, we can how that the adopted coolng chedule T t = T n +αt 2 ft the two aforementoned condton, whch can yeld the aymptotc convergence to the global optmum oluton. ettng, the randomly generated channel power gan are g B = 6.383 7 and g = 8.62 5, whch are ued n the followng Fgure 5 to 7. In addton, we et p max B = W and p max =.4W [37], and et the bandwdth W B = MHz, W = 5MHz, and et n = 4 W. Verfcaton of ADLS-Algorthm: Fgure 5a) how the operaton of ADLS-Algorthm that enumerate ρ for olvng Problem OGPM). We et N = 3. Recall that for each enumerated ρ, we ue SubSol-Algorthm to compute ˆr ρ ), ˆp ρ )), and ue 3) and 4) to compute ˆx B) ρ ) and ˆp B) ρ ), repectvely. In addton, we ue 8) to compute ρ cr =.6228 whch marked out n Fgure 5a)). The top-ubplot of Fgure 5a) how that ˆr ρ ), ˆp ρ )) lead to the zero-outage when ρ ρ cr, whch thu valdate Propoton 2. The bottom-ubplot of Fgure 5a) how the on-grd power conumpton ˆp ρ )+ ˆp B) ρ ) when enumeratng ρ. Meanwhle, we ue 2) to compute p,z + p B),Z, whch marked out by the red crcle. In partcular, p,z + p B),Z exactly correpond to the mnmum of ˆp ρ ) + ˆp B) ρ ) for the nterval of ρ [ρ cr, ]. Th valdate our analy for the zerooutage cae and our propoed ADLS-Algorthm,.e., drectly calculatng p,z +p B),Z, ntead of ung the lnear-earch for ρ [ρ cr, ]. Advantage of of ADLS-Algorthm: Fgure 5b) how the advantage of ADLS-Algorthm n reducng the teraton, n comparon wth LS-Algorthm. A tated n Secton IV, by ung the analytcal oluton 2) for the zerooutage cae, ADLS-Algorthm can avod the lnear-earch of ρ [ρ cr, ], whch thu reduce the number of requred teraton. Specfcally, we plot the rato of reduced teraton.e., the value of ρ cr ) by ung ADLS-Algorthm n Fgure 5b). Fgure 5b) how that the reduced rato ncreae quckly n both MU traffc requrement and the number of the MU erved by AP. Th reult mean that our ADLS-Algorthm more computatonally effcent when the MU traffc requrement or the total number of the MU erved by the AP) larger. Illutraton of Optmal Offloadng Soluton: Fgure 6a) llutrate the optmal oluton of Problem OGPM) veru dfferent traffc requrement. Here, we et N = 7.e., the AP ervng 7 MU). The top-ubplot of Fgure 6a) plot AP optmal on-grd tranmt-power, the mbs optmal tranmt-power, and the mnmum total on-grd power conumpton. A hown n the top-ubplot of Fgure 6a), when the MU traffc requrement low, the mnmum total ongrd power conumpton zero. Th becaue that we can completely rely on the AP EH power-ly to power the offloadng n order to meet the MU traffc requrement. However, when the MU traffc requrement ncreae, the AP EH power-ly alone cannot atfy the MU requrement. Thu, the AP need to pend a non-zero ongrd power to afford the MU requrement, whch yeld the ncreae n the AP optmal on-grd power. Moreover, when the MU traffc requrement further ncreae, traffc offloadng through the AP wll conume a large on-grd power. A a reult, the mbs need to pend a non-zero ongrd power to afford part of the MU traffc requrement, whch yeld the ncreae n the mbs optmal on-grd 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 3 Value of Gradent On Grd Power Conumpton 2 x 9 5 5 5.4.5.6.7.8.9.8.5.4 F G ρ ) Suc. Prob ρ cr =.6228 ˆp,Gρ )+ ˆp B),G ρ ).3 the nterval ˆp,Z + ˆp B),Z =.32.2 requrng LS the nterval. wthout LS.4.5.6.7.8.9 ρ a) An llutratve example of executng ADLS-Algorthm. Example of F r ). Bottom: Total on-grd power..5.95.9.85 Value of Probablty Top: Reduced Rato of Total Iteraton.7.6.5.4.3.2. N =3 N =5 N =7 2 2.5 3 3.5 4 4.5 5 5.5 6 Traffc Demand x 7 b) Advantage of reducng the number of teraton ued by ADLS- Algorthm n comparon wth ung LS-Algorthm. Fg. 5: Performance of ADLS-Algorthm. Left: Example of executng ADLS-Algorthm. Rght: Advantage of ADLS-Algorthm. On Grd Power Dtrbuton Offloadng Rato.5.5 p p B) p +pb) 2 3 4 5 6 7 8.8.6 ρ.5.4 P out r,p ).2 2 3 4 5 6 7 8 Traffc Demand Succeful Prob Total On Grd Power Conumpton.6.5.4.3.2. Fxed offloadng 7% Fxed offloadng 8% Fxed offloadng 9% Fxed offloadng % ADLS Algorthm th cheme nfeable after > 45.5 th cheme nfeable after > 57.5 th cheme nfeable after > 5 25 3 35 4 45 5 55 6 Traffc DemandMbp) a) Illutraton of the optmal oluton of Problem OGPM). b) Advantage n avng the total on-grd power conumpton. Fg. 6: Illutraton of the optmal offloadng oluton and the advantage n reducng the total on-grd power conumpton. power conumpton. In th tuaton, the correpondng optmal offloadng-rato.e., the value of x B) /Rreq ) tart to decreae, a hown n the bottom-ubplot of Fgure 6a). In partcular, the bottom-ubplot of Fgure 6a) alo how that the ucceful offloadng probablty.e., the value of P out r, p )) gradually ncreae to one, when the MU traffc requrement ncreae. The reaon that the throughput offloaded through the AP ncreae, when the MU traffc requrement ncreae. A a reult, the AP need to be more conervatve n relyng on the EH powerly, but ung more on-grd power to ort the traffc offloadng. Th eentally becaue that a larger offloadng outage probablty wll lead to a larger wate of the AP on-grd power conumpton. Advantage of Optmal Offloadng Soluton: Fgure 6b) further how the advantage of the propoed optmal offloadng cheme n reducng the total on-grd power conumpton. For the purpoe of comparon, we alo conder another offloadng cheme n whch the MU offload a fxed porton of t traffc requrement to the AP we et uch a porton a 7%, 8%, 9%, and % n Fgure 6b)). The reult valdate the advantage of our propoed offloadng cheme,.e., t can mnmze the total on-grd power conumpton whle guaranteeng the erved MU traffc requrement. Th advantage eentally acheved by our formulated jont optmzaton of the traffc chedulng and power allocaton, whch able to jontly reap the beneft of DC-capablty to flexbly chedule the MU traffc between macro and mall cell) and the beneft of explotng EH power-ly to reduce the on-grd power conumpton). In comparon, the fxed offloadng cheme fal to acheve thee beneft. Specfcally, a hown n Fgure 6b), due to the fact the AP EH power-ly cannot accommodate a very large offloadng rate, offloadng too much of the MU traffc.e., the %-offloadng) wll lead to a quck ncreae n the total on-grd power conumpton when the MU traffc requrement ncreae. Impact of the EH power-ly: To evaluate the mpact of the EH power-ly, we plot the optmal oluton veru dfferent degree of the randomne of the EH powerly n Fgure 7a). We et N = 2 and M low =., and vary M from.5 to.25, whch correpond to a larger average EH power-ly. A hown n the topubplot of Fgure 7a), the MU optmal total on-grd power 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 4 Total On Grd Power.35.3.25 =23Mbp =25Mbp.5..5.2 Total On Grd Power.4.35.3.25 =23Mbp =25Mbp.2 4 5 6 7 8 9 Succeful Prob..9.8.7 =23Mbp =25Mbp.6.5..5.2.25 M a) Impact of the randomne of the EH power-ly. Succeful Prob..9.8 =23Mbp =25Mbp.7 4 5 6 7 8 9 The agned number of MU erved by AP N S ) b) Impact of the number of the MU erved by the AP. Fg. 7: Optmal oluton of Problem OGPM) under dfferent parameter-ettng. conumpton decreae a M ncreae. Such a decreae n the total on-grd power conumpton eentally tem from that we rely more on the EH power-ly to power the MU traffc offloadng, whch yeld a decreae n the ucceful probablty of traffc delvery, a hown n the bottom-ubplot of Fgure 7a). Impact of the Number of the Served MU: Due to harng the AP harveted energy, the number of the MU erved by the AP.e., the value of N ) wll nfluence the optmal offloadng oluton of Problem OGPM). To evaluate th mpact, we plot the optmal oluton veru dfferent value of N n Fgure 7b). A hown n the top-ubplot of Fgure 7b), the optmal total on-grd power conumpton ncreae when N ncreae, whch due to the fact each MU allocated a maller amount of harveted energy when N ncreae. Correpondngly, to atfy the MU traffc requrement, AP need to ue more on-grd power to ort the traffc offloadng, whch conequently yeld an ncreae n the ucceful probablty of traffc delvery, a hown n the bottom-ubplot of Fgure 7b). In partcular, Fgure 7b) alo ndcate that we need to carefully determne the number of the MU erved by each AP n the multap cenaro, B. Numercal Reult for the Cae of Multple AP We next evaluate our propoed algorthm for the cae of multple AP, and how the performance gan of the optmal MU-electon oluton of Problem MultMUSel). We conder a cenaro that the mbs located at the orgn m, m), and three AP are located at 22m, m), 22m, 8m), and 235m, 6m). The group of MU are randomly located wthn the plane whoe center 22m, m) and radu 2m,.e., the MU are geographcally cloer to the AP than the mbs th a favorable condton for traffc offloadng). The channel power gan and other parameter are randomly et a decrbed before. Illutraton of the Optmal MU-Selecton Soluton: We frt llutrate the optmal MU-electon oluton of Problem MultMUSel), whch yelded by our propoed SelSol- Algorthm. Fgure 8 how the optmal MU-electon oluton for two dfferent cae. Specfcally, Fgure 8a) how the cae of all AP wth a homogeneou EH-capacty.e., M low =. and M =.2, =, 2, 3). In th cae, the optmal oluton how that the AP elect dfferent MU to provde traffc offloadng n an almot balanced way, namely, both AP and AP 2 erve 6 MU, and AP 3 erve 8 MU. Fgure 8b) how the cae of the AP wth heterogenou EH-capacty. To llutrate the reult clearly, we et AP wth M low =. and M =.2, and AP 2 and AP 3 wth M low =. and M 2 =.4, M 3 =.6, namely, AP 3 ha a much larger EH power-ly than AP and AP 2. A a reult, to fully explot the EH powerly and reduce the total on-grd power conumpton for whole network, AP 3 elect 2 MU to offload traffc, a hown n Fgure 8b). Advantage of the Optmal MU-Selecton Soluton: We next how the performance advantage of our SelSol- Algorthm n Fgure 9. For comparon, we alo how the reult of a dtance-baed cheme n whch each MU aggrevely elect the AP wth the hortet dtance for traffc offloadng. Smlar to Fgure b), we ue the cae that the AP are of heterogeneou EH-capacty. Fgure 9a) how the reult under dfferent number of the MU. Specfcally, we fx 4 AP at 22m, m), 22m, 8m), 235m, 6m), and 25m, 3m). We vary the number of the MU from 6 to 3, and fx each MU traffc requrement a 4Mbp. In Fgure 9a), we mark out the relatve mprovement acheved by our propoed algorthm agant the dtance-baed cheme on the top of each teted cae. Fgure 9a) how that the acheved average reward 5 gradually ncreae a the number of the MU ncreae, nce the AP have a larger freedom n electng dfferent MU for executng the traffc offloadng. Fgure 9a) valdate that the average reward can be gnfcantly ncreaed by ung our propoed SelSol-Algorthm. A hown n Fgure 9a), our SelSol-Algorthm can mprove the reward up to 58.6% n comparon wth the the dtance-baed cheme. The performance advantage not only come from that we 5 Every pont n Fgure 9 repreent the average reult of 2 realzaton of the MU geographcal dtrbuton. 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 5 2 5 5 crcle:mu offloadng through AP trangle:mu offloadng through AP 2 AP AP3 2 5 5 crcle:mu offloadng through AP trangle:mu offloadng through AP 2 AP AP3 5 tar:mu offloadng through AP 3 AP2 5 tar:mu offloadng through AP 3 AP2 mbs located at,) 5 8 9 2 2 22 23 mbs located at,) 5 8 9 2 2 22 23 a) AP wth homogeneou EH-capablty. b) AP wth heterogeneou EH-capablty. Fg. 8: Example of the optmal MU-electon oluton of Problem MultMUSel) under µ =.25$/Mbp and π =.2/KW. Total Average Reward 5 4.5 4 3.5 3 2.5 2.5.5 58.6% OptmalHete.EH) HetertcHete.EH) 2.7% 8.2% 23.% 38.% 4.3% 6.8% 3.% The Average Reward.6.4.2.8.6.4.2 84.26% 35.8% 8.% 32.37% OptmalHete.EH) HetertcHete.EH) 23.5% 24.99% 6 8 2 22 24 26 28 3 The number of MU 3 35 4 45 5 55 6 65 Traffc DemandMbp) a) Performance comparon under dfferent number of MU. b) Performance comparon under dff. traffc requrement. Fg. 9: Performance advantage of the optmal MU-electon oluton. Average Total Reward 4.5 4 3.5 3 2.5 2.5.5 MU=8 MU=9 Average Total Number of Serverd MU 7 6 5 4 3 2 MU=8 MU=9.22.24.26.28.3.32.34.36.38.4 Unt Reward$/Mbp) a) The total reward veru dfferent µ.22.24.26.28.3.32.34.36.38.4 Unt Reward$/Mbp) b) The number of erved MU veru dfferent µ Fg. : Optmal MU-electon oluton under dfferent Margnal Reward. 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 6 explot the beneft of the DC-enabled traffc offloadng whch provde a flexble traffc chedulng and power allocaton, but alo come from that we properly explot the AP EH power-ly by avodng too many MU offloadng through a ame AP. Fgure 9b) how the reult under dfferent traffc requrement. Specfcally, we fx 4 AP and 8 MU, and vary each MU traffc requrement from 35Mbp to 6Mbp. The reult how that our propoed SelSol-Algorthm can gnfcantly mprove the average reward compared to the dtance-baed cheme. In partcular, Fgure 9b) how that the acheved total reward frtly ncreae when the traffc requrement ncreae, and then gradually decreae when the traffc requrement further ncreae beyond a threhold. Th phenomenon can be explaned a follow. When each MU traffc requrement low.e., < 35Mbp), t optmal for the AP to erve all MU, and the total reward ncreae when each MU ncreae. However, when each MU traffc requrement become very large.e., 45Mbp), the rapd ncreae n the total ongrd power conumpton cannot be covered by the AP acheved revenue to erve all MU traffc. A a reult, the AP need to properly elect part of the MU to provde the traffc offloadng, n order to reach a good balance between ervng the MU traffc and reducng the total on-grd power conumpton. Impact of the Margnal Reward for Servng the MU Traffc: Both the margnal reward µ for uccefully ervng the MU traffc)and the margnal cot π for the total ongrd power conumpton wll nfluence the optmal number of the MU elected by the AP. To how uch an mpact, n Fgure, we vary µ from.225$/mbp to.4$/mbp whle fxng π =.2$/KW) and plot the correpondng reult when the AP are of heterogenou EH-capacty. Smlar to Fgure 9, each pont n Fgure correpond to the average reult of 2 random realzaton of the MU geographcal dtrbuton. The left-ubplot of Fgure how that the total reward gradually ncreae n µ, nce we can gan more for uccefully ervng the MU requred traffc. Moreover, a larger µ encourage the AP to elect more MU.e., offloadng traffc for more MU), whch hown n the rght-ubplot. VII. CONCLUSION In th paper, we have nvetgated the energy-effcent DC-enabled traffc offloadng through the EH-powered mall cell. To reap the advantage of the DC-capablty and the EH power-ly, we have propoed the jont optmzaton of the traffc chedulng and power allocaton to mnmze the total on-grd power conumpton of macro and mall cell. We frtly focu on the ngle AP cae, and have propoed an effcent layered-algorthm to compute the optmal offloadng oluton for each ndvdual par of AP- MU. We then tudy the mult-ap cae and nvetgate how dfferent mall cell elect the MU for maxmzng the total network-reward. We have alo propoed an effcent algorthm to compute the optmal MU-groupng oluton. Extenve numercal reult have been provded to valdate our propoed algorthm and the performance advantage of the propoed DC-enabled traffc offloadng through the EHpowered mall cell. For our future work, we wll further conder that the AP can flexbly chedule t EH power-ly over dfferent tme lot and allocate dfferent amount of the EH power-ly for dfferent MU, and nvetgate the optmal degn of the DC-enabled traffc offloadng for mprovng the energy-effcency. REFERENCES [] C. Roa, K. Pederen, and H. Wang Dual connectvty for LTE mall cell evoluton: Functonalty and performance apect, IEEE Communcaton Magazne, vol. 54, no. 6, pp. 37-43, Jun. 26. [2] S. Jha, K. Svanean, R. Vannthamby, and A. Koc, Dual connectvty n LTE mall cell network, n Proc. of IEEE GLOBECOM 24 Workhop. [3] J. Lu, J. Lu, H. Sun, An enhanced power control cheme for dual connectvty, n Proc. of IEEE VTC 24-Fall. [4] M. Pan, T. Ln, C. Chu, and C. 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Wu, Demand repone management va real-tme electrcty prce control n mart grd, IEEE Journal on Selected Area n Communcaton, vol. 3, no. 7, pp. 268-28, 23. 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 7 [2] S. Zhang et. al., Energy-Aware traffc offloadng for green heterogeneou network, IEEE Journal on Selected Area of Communcaton, vol. 34, no. 5, pp. 6-29, May 26. [22] T. Han, and N. Anar, ICE: Intellgent cell breathng to optmze the utlzaton of green energy, IEEE Communcaton Letter, vol. 6, no. 6, pp. 866-869, Jun. 22. [23] T. Han, and N. Anar, Green energy aware and latency aware uer aocaton n heterogeneou cellular network, n Proc. of IEEE GLOBECOM 23 Workhop. [24] Y. Cha, C. Ho, and S. Sun, Data offloadng wth renewable energy powered bae taton connected to a mcrogrd, n Proc. of IEEE GlOBECOM 24. [25] Z. Chang et. al., Reource allocaton and data offloadng for energy effcency n wrele power tranfer enabled collaboratve moble cloud, n Proc. of IEEE INFOCOM 25 Workhop. [26] J. Gong, J. Thompon, S. Zhou, and Z. Nu, Bae taton leepng and reource allocaton n renewable energy powered cellular network, IEEE Tranacton on Communcaton, vol. 62, no., pp. 38-383, Nov. 24. [27] P. Yu, J. Lee, T. Quek, and Y. Hong, Traffc offloadng n heterogeneou network wth energy harvetng peronal cell network throughput and energy effcency, IEEE Tranacton on Wrele Communcaton, vol. 5, no. 2, pp. 46-6, Feb. 26. [28] Z. Zheng, L. Ca, R. Zhang, and X. Shen, RNP-SA: Jont relay placement and ub-carrer allocaton n wrele communcaton network wth utanable energy, IEEE Tranacton on Wrele Communcaton, vol., no., pp. 388-3828, Oct. 22. [29] S. Zhou, T. Chen, W. Chen, and Z. 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Hoan, On the battery recharge tme n a tochatc energy harvetng ytem, avalable onlne at http: //arxv.org/pdf/76.383.pdf, Oct. 27. [35] S. Boyd, and L. Vandenberghe, Convex Optmzaton, Cambrdge Unverty Pre, 24. [36] Weten, Erc W. Lambert W-Functon. From MathWorldA Wolfram Web Reource, http://mathworld.wolfram.com/ LambertW-Functon.html. [37] Natonal Intrument, Introducton to UMTS devce tetng tranmtter and recever meaurement for WCDMA devce, avalable onlne at http://download.n.com/evaluaton/rf/introducton to UMTS Devce Tetng.pdf. [38] J.B. Mazzola and A.W. Neebe, Reource-contraned agnment chedulng, Operaton Reearch, vol. 34, No. 4, Jul.-Aug., 986. [39] E. Talb, Metaheurtc: From degn to mplementaton, John Wley & Son Ltd, 29. [4] D. Bertma, and J. Ttkl, Smulated annealng, Statcal Scence, vol. 8, no., pp. -5, 993. [4] J.F. Martn and J.M, Serra, A comparon of coolng chedule for mulated annealng, Chapter of Encyclopeda of Artfcal Intellgence, 29, DOI:.48/978--5994-849-9.ch53. [42] B. Hajek, Coolng chedule for optmal annealng, Mathematc of Operaton Reearch, vol. 3, no. 2, pp. 3-329, May 988. Yuan Wu S 8-M -SM 6) receved the Ph.D degree n Electronc and Computer Engneerng from the Hong Kong Unverty of Scence and Technology, Hong Kong, n 2. He an Aocate Profeor n the College of Informaton Engneerng, Zhejang Unverty of Technology, Hangzhou, Chna. Durng 26-27, he wa wth the Broadband Communcaton Reearch BBCR) group, Department of Electrcal and Computer Engneerng, Unverty of Waterloo, Canada. H reearch nteret focu on reource management for wrele communcaton and network, and mart grd. Xaowe Yang currently purung her M.S. degree n College of Informaton Engneerng, Zhejang Unverty of Technology, Hangzhou, Chna. Her reearch nteret focue on reource management for wrele communcaton and network, and green communcaton. 澳 L Png Qan S 8-M -SM 6) receved the Ph.D. degree n nformaton engneerng from The Chnee Unverty of Hong Kong, Hong Kong, n 2. She wa wth Broadband Communcaton Reearch Laboratory, Unverty of Waterloo, from 26 to 27. She currently an Aocate Profeor wth the College of Informaton Engneerng, Zhejang Unverty of Technology, Chna. Her reearch nteret le n the area of wrele communcaton and networkng, cogntve network, and mart grd. Dr. Qan wa a co-recpent of the IEEE Marcon Prze Paper Award n wrele communcaton n 2. Habo Zhou receved the Ph.D. degree n nformaton and communcaton engneerng from Shangha Jao Tong Unverty, Shangha, Chna, n 24. Snce 24, he ha been a Pot-Doctoral Fellow wth the Broadband Communcaton Reearch Group, ECE Department, Unverty of Waterloo. He currently an aocate profeor wth the School of Electronc Scence and Engneerng, Nanjng Unverty, Nanjng, Chna. H reearch nteret nclude reource management and protocol degn n cogntve rado network and vehcular network. 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.

Th artcle ha been accepted for publcaton n a future ue of th journal, but ha not been fully edted. Content may change pror to fnal publcaton. Ctaton nformaton: DOI.9/TGCN.28.285843, IEEE Tranacton on Green Communcaton and Networkng 8 Xuemn Sherman) Shen IEEE M 97-SM 2- F 9) a Unverty Profeor and the Aocate Char for Graduate Stude, Department of Electrcal and Computer Engneerng, Unverty of Waterloo, Canada. Dr. Shen reearch focue on wrele reource management, wrele network ecurty, ocal network, mart grd, and vehcular ad hoc and enor network. He the IEEE Com- Soc VP Publcaton, wa an elected member of IEEE ComSoc Board of Governor, and the Char of Dtnguhed Lecturer Selecton Commttee. Dr. Shen erved a the Techncal Program Commttee Char/Co-Char for IEEE Globecom 6, Infocom 4, IEEE VTC Fall, and Globecom 7, the Sympoa Char for IEEE ICC, the Tutoral Char for IEEE VTC Sprng and IEEE ICC 8, the General Co-Char for ACM Mobhoc 5, and the Char for IEEE Communcaton Socety Techncal Commttee on Wrele Communcaton, and P2P Communcaton and Networkng. He alo erve/erved a the Edtor-n-Chef for IEEE Internet of Thng Journal, and IEEE Network, a Foundng Area Edtor for IEEE Tranacton on Wrele Communcaton; and an Aocate Edtor for IEEE Tranacton on Vehcular Technology and IEEE Wrele Communcaton, etc. Dr. Shen receved the IEEE ComSoc Educaton Award, the Joeph LoCcero Award for Exemplary Servce to Publcaton, the Excellent Graduate Supervon Award n 26, and the Premer Reearch Excellence Award PREA) n 23 from the Provnce of Ontaro, Canada. Dr. Shen a regtered Profeonal Engneer of Ontaro, Canada, an IEEE Fellow, an Engneerng Inttute of Canada Fellow, a Canadan Academy of Engneerng Fellow, a Royal Socety of Canada Fellow, and a Dtnguhed Lecturer of IEEE Vehcular Technology Socety and Communcaton Socety. Mohamad Khattar Awad S 2-M 9) receved the B.A.Sc. degree n electrcal and computer engneerng communcaton opton) from the Unverty of Wndor, Wndor, ON, Canada, n 24 and the M.A.Sc. and Ph.D. degree n electrcal and computer engneerng from the U- nverty of Waterloo, Waterloo, ON, n 26 and 29, repectvely. From 24 to 29, he wa a Reearch Atant wth the Broadband Communcaton Reearch Group, Unverty of Waterloo. In 29 to 22, he wa an Atant Profeor of electrcal and computer engneerng wth the Amercan Unverty of Kuwat, Kuwat Cty, Kuwat. Snce 22, he ha been an Atant Profeor of computer engneerng wth Kuwat Unverty, Kuwat Cty. H reearch nteret nclude wrele and wred communcaton, oftwaredefned network reource allocaton, wrele network reource allocaton, and acoutc vector-enor gnal proceng. Dr. Awad wa a recpent of the Ontaro Reearch and Development Challenge Fund Bell Scholarhp n 28 and 29; the Unverty of Waterloo Graduate Scholarhp n 29; a Fellowhp Award from Dartmouth College, Hanover, NH, USA, n 2; and the Kuwat Unverty Teachng Excellence Award n 25. 2473-24 c) 28 IEEE. Peronal ue permtted, but republcaton/redtrbuton requre IEEE permon. See http://www.eee.org/publcaton_tandard/publcaton/rght/ndex.html for more nformaton.