Energy Efficiency Resource Allocation for Device-to-Device. Communication Underlaying Cellular Networks

Transcription

1 Energy Effcency Resource Allocaton for Devce-to-Devce Communcaton Unerlayng Cellular Networks AO-ZHOU YU AND QI ZHU The Key Wreless Laboratory of Jangsu rovnce School of Telecommuncaton an Informaton Engneerng Nanng Unversty of osts an Telecommuncatons Nanng 13 Chna Key Laboratory on Weban Wreless Communcatons an Sensor Network Technology of Mnstry of Eucaton Jangsu Nanng 13 Chna E-mal: Abstract: The energy effcency (EE) of Devce-to-Devce (DD) communcaton unerlay cellular networks has become a sgnfcant ssue because of ncreasng the resource utlzaton an etenng the battery lfe of user equpment. However the nterference cause by sharng the same resources wth the cellular users wll escen the performance of the system. Therefore DD users shoul be allocate reasonable sub-carrer an sutable power to mprove the performance of the cellular networks. In ths paper DD communcaton can rectly transmt nformaton or transmt ates through an assste relay base on the outage probablty of DD users. Meanwhle we propose an algorthm to stuy the problem of EE of DD communcaton uner the conton of the requre QoS (Qualty of Servces) of both cellular users an DD users an the mamum transmsson power threshol of DD users. To solve the problem effcency we ve the algorthm nto two stages to allocate sub-carrer an optmze power respectvely. y numercal smulaton we also prove the goo performance of the propose algorthm. Keywor: energy effcency evce-to-evce communcaton relay selecton outage probablty resource allocaton 1. INTRODUCTION Devce-to-Devce (DD) communcaton [1][] where the users n close promty transmt nformaton wth each other rectly has gane much attenton because of ts potental for mprovng the spectrum effcency an reucng the power consumpton of the cellular networks. These DD users (DUEs) reuse the rao resources of cellular users (CUEs) uner the careful control of the evolve Noe (en) [3]. However DUEs communcaton unerlay cellular networks wll cause the nterference for sharng the resources of CUEs. Therefore the reasonable resources occupe by the CUEs shoul be allocate to DUEs to ecrease the nterference an mprove the performance. To mprove the performance of cellular networks varous technques have been put forwar to cope wth the above mentone problem. In LTE-A cellular networks sub-carrer allocaton an power control schemes are the two wely use nterference management technques [4][5]. Furthermore energy effcency of DD communcaton n cellular networks s an ncreasng concern [6]-[8] for ts reucng power consumpton of the cellular networks. However when DD communcaton reuse the sub-carrer occupe by a CUE the CUE wll ncrease the transmsson power to guarantee ts QoS (Qualty of Servces). In [6] authors nvestgate a system moel of mult-hop DD communcatons where one UE may help other one potental DD par to echange nformaton. They also analyze the average energy effcency an spectral effcency of the mult-hop DD communcatons an get close analytcal appromatons through Taylor-seres epanson. In [7] energy-effcent resource allocaton problem for DD communcaton unerlayng cellular networks s stue. Authors am to mamze the mnmum weghte energy effcency of DD lnks whle guaranteeng mnmum ata rates for Receve on September 16; revse on March 17; accepte on March Communcate by Q Zhu.

2 cellular lnks. Etensve numercal stues emonstrate that the propose algorthm acheve superor performance an sgnfcantly outperform a conventonal algorthm. A ont resource allocaton an power control for energy-effcent DD communcatons unerlayng cellular networks are nvestgate n [8] whch proposes an effcent teratve resource allocaton an power control scheme to fn the optmum at each teraton. Smulaton results emonstrate the remarkable mprovements n terms of energy-effcent by usng the propose scheme. However the lterature [6] assumes the stuaton of one cellular user or one DD par. An the papers [7][8] o not conser ont optmzaton of energy effcency an moe selecton of users. In ths paper we conser the stuaton of multple DD users sharng the multple sub-carrers occupe by cellular users. An a selecton communcaton moe [9] an resource assgnment algorthm s propose to optmze the energy effcency of DUEs uner the conton of guaranteeng the QoS of orgnal CUEs an DUEs. An when DUEs nten to echange nformaton wth each other there are two fferent communcaton moes that can be consere: Moe A (Drect DD communcaton) an Moe (Two-hop DD communcaton through le CUE). Meanwhle the man contrbutons of ths paper are summarze as follows: 1) We take the outage probablty of CUEs an DUEs nto conseraton to manage the nterference between CUEs an DUEs. An base on the outage probablty DUEs that nten to echange nformaton coul select Moe A or Moe. However f one DUE can t meet the contons of above communcaton moes the DUE o not transmt nformaton n the pont. ) We construct an analyss moel of EE of DUEs unerlayng the cellular networks where the avantages n spectrum utlzaton the energy savng the verse QoS requrements of users an both transmsson power an the crcut power consumpton are characterze quanttatvely. 3) We put forwar a novel algorthm for solvng the resource strbuton problem. We esgn a two-stage scheme the frst stage copes wth sub-carrer allocaton an the secon stage copes wth power control. Meanwhle the propertes of the propose algorthm nfluence by the system parameters are scusse. The remaner of ths paper s organze as follows. In Secton II we brefly ntrouce the network moel an energy effcency analyss. In secton III the sub-carrer allocaton an power control problem as an optmal problem are formulate. We also propose a two-steps algorthm an analyze ts mportant propertes. In Secton IV smulaton results are prove. Fnally we conclue ths paper wth a summary n Secton V.. SYSTEM MODEL AND OUTAGE ROAILITY ANALYSIS.1 System Moel We conser a sngle cell that contans two types of users n Fg. 1 whch are the cellular users (CUEs) an the DD users (DUEs). An the CUEs only can communcate wth the cellular communcaton moe where CUEs communcate through the S (base staton). However the DUEs have two fferent communcaton moes. One s the Moe A where the DUE (one DD par) communcate wth each other rectly. The other s the Moe where DD communcaton wth relay selecte from le CUEs s use for the outage probablty of DUE gong beyon the threshol efne by the system. We only conser the ntra-cell nterference for a sngle cell system moel. Meanwhle n the system moel we also assume a fully loae cellular network [1] where all the sub-carrers are allocate to CUEs. An M actve CUEs occupy M orthogonal uplnk sub-carrers an there s no

3 atonal uplnk sub-carrer for N DUEs n the cell where DUE communcates by reusng the uplnk (UL) spectrum resources of an actve CUE whch s calle pare CUE. The sets a CUE 1... M an = DUE 1... N onate the DUEs n the cell respectvely. From Fg 1 we assume that there are relay of DUEs wth Moe. Furthermore we employ the set cell. K M actve CUEs an N le CUEs as the canate to ncate the le CUEs wthn the S CUE DUE Date lnk Moe Fg. 1. Network moel of DUE communcaton unerlayng cellular network where one CUE an one DUE share UL resources. In Moe A the pare CUE causes nterference to the recever of DUE an the transmtter of DUE causes nterference to S. In Moe relay (RN) s selecte from le CUEs whch o not transmt nformaton n ths pero. eses the transmtter of DUE communcates wth RN rectly an t s the same as RN communcates wth the recever of DUE. The relay les close to both the transmtter an the recever of DUEs. The transmtter of DUEs echanges nformaton wth the relay through reusng the sub-carrer of CUEs whch s the same as the relay an the recever of DUEs. We also assume the system UL frequency resources have been allocate to the actve CUEs unformly an the transmsson power of CUEs s constant whch s enote as C. We conser the etreme case that all of the DUEs communcate wth Moe. Thus atonal le CUEs at least are requre to serve as the relay. Therefore we assume there are K le CUEs n the system an K. Outage robablty Analyss N N. For Moe A DUE wll echange nformaton through rect one-hop communcaton. The pare CUE transmts a sgnal 1 to S an a sgnal s the transmsson sgnal between DUE. Thus the receve sgnal of S an the recever of DUE can be formulate as

4 y g g n (1) S C 1 1 y g g n () C 1 In above epressons enotes the transmsson power of DUE reusng the channel of CUE. The channel gan between S an the CUE can be wrtten as g h where s the stance between CUE eponent respectvely. h an S an represents the fang coeffcents wth CUE are the path loss constant an the path loss. Smlarly the channel gan between the S an DUE s g g s the channel gan between the transmtter an recever of DUE an g s the channel gan between the actve CUE an DUE. n 1 an n ncate the atve whte Gaussan nose (AWGN) for S an the recever of DUE respectvely. Wthout loss of generalty we assume that all communcaton lnks receve the same AWGN power assume the DUE reuse the subcarrer of CUE Sgnal-to-Interference-an-Nose-Rato (SINR) of pare CUE N. We to transmt the nformaton. An then the an DUE can be formulate as c g N g C (3) g N g C (4) The rate of DUE by Shannon capacty formula. sharng the sub-carrer of CUE can be formulate as (5) whch can be got r log (1 ) (5). The energy effcency (EE) of DUE lnk can be efne as the rato between throughput an total power of DUE. As mentone n [11] transmsson power an average crcut power are mportant of energy effcency. Therefore the EE of DUE reusng the sub-carrer of CUE can be epresse as u MoeA r cr (6) Where an cr are the transmsson power an the average crcut power respectvely. Smlar to [11] [1] the EE of the total DUEs unerlay cellular network can be efne as ee MoeA N u (7) The outage probablty of pare CUE whch equals the Cumulatve Dstrbuton Functon (CDF) c of can be formulate as 1 MoeA f F (8) C c c c out r c c

5 Where ncates the SINR threshol of pare CUE an c f c s the robablty Densty Functon (DF). We can get the epresson of outage probablty of CUE Lemma 1 n [11] g N 1 ep c C out C g g g C accorng to the (9) Smlarly the outage probablty epresson of DUE s wrtten as N out 1 ep g c g g g (1) Where s the SINR threshol of DUE Appen A. an the proof of formulas (9) an (1) are presente n Comparng wth Moe A Moe s an etenson of Moe A.e. two hops of Moe A. An we assume the le CUE RN k DUE k as the relay of DUE where the transmtter of DUE an the relay reuse the sub-carrer of pare CUE n two tme slots. In the frst tme slot the transmtter of communcates wth RN k. In the secon tme slot DUE. Therefore the outage probabltes of DUE to the epresson (9) an (1). RN k communcates wth the recever of wth Moe relate to every hop are smlar 3. ROLEM FORMULATION AND RESOURCE ALLOCATION ALGORITHM 3.1 Constructon of Optmzaton roblem The prorty of CUE s hgh than the DUE that s to say the QoS of pare CUE shoul be guarantee. ase on the secton II when the outage probablty of the pare CUE or the DUE oversteps the threshol efne by the system Moe nten to be use. Hence we can ve the DUEs nto fferent parts accorng to the followng epresson c out out (11) Where The DUE an are the outage probablty threshols of pare CUE an DUE respectvely. communcate wth Moe A when t satsfes the epresson (11). Otherwse the DUE wll communcate wth Moe. Hence the DUE nee a relay to realze the communcaton. For all le CUE k f there s any le CUE as relay of DUE makng both the DUE an the relay meetng the conton (11) the DUE transmt wth Moe. Otherwse the DUE can t transmt at ths pero. Therefore the set followng epresson can be ve nto A an O accorng to the c A out & out a c n c out & out & out & out a n O other (1) The DUEs n sets A an O correspon to the communcaton moe of Moe A Moe an Moe O respectvely. Where the DUE wth Moe O onates the DUE can t transmt nformaton snce there s no more sub-carrer for the DUE communcatng wth orgnal cellular moe. We also

6 efne to ncate the sub-carrer reuse eponent where 1 epresses the DUE reuse the sub-carrer of CUE an ncates the DUE can t reuse the sub-carrer of CUE. We also assume that each DUE can reuse the only one sub-carrer of CUEs an each sub-carrer of CUEs can be reuse by one DUE. Thus the total EE of DUEs can be acheve as follows k Where MoeA Moe ee ee ee 1 k log 1 log 1 log 1 k A a cr a k k cr cr s the CUE sharng the sub-carrer wth the DUE an relay n two fferent tme slots. An onates the relay selecte from the le CUEs. The man work s selectng the reasonable pare CUE for DUE wth Moe A an the reasonable pare CUE an relay for DUE wth Moe. Therefore we establsh the followng optmal problem: Subect to Moe k k k A a a (13) MoeA 1 ma u + u (14) k a 1 (15) 1 (16) (17) ma Where u k log 1 log 1 Moe = k k cr cr an obect functon ncates mamzng the EE of total DUEs. The constrants (15) an (16) guarantee each DUE can reuse the only one sub-carrer of DUE an each sub-carrer of actve CUE can be reuse by only one DUE. The epresson (17) restrct the transmsson power of DUE to guarantee the QoS of pare CUE. From the constrants we fn the optmal problem can be consere as an assgnment problem whch contans one more constrant (17) compare to the stanar assgnment problem. Meanwhle the above optmal problem s non-conve whch can t be solve by the general methos. Therefore the orgnal optmal problem s ve nto two sub-problems. To begn wth we use the Hungaran algorthm to allocate the reasonable sub-carrer of CUEs to DUEs. An then we optmze the transmsson power of DUE to mprove the EE of the total DUEs. 3. Sub-carrer Allocaton for DUE Fg. llustrates the sub-carrer allocaton problem n (14) wth the constrants (15) an (16). In ths fgure the set of DUEs wth Moe A an Moe an the reuse canate sub-carrer set are the two groups of vertces n the bpartte graph. If the sub-carrer of CUE s a reuse canate for DUE an the verte connects to verte MoeA Moe by an ege. Meanwhle u an u k s the weght of ege of DUEs wth Moe A an Moe respectvely.

7 DD par... 1 N-1 N Reuse canate M- M-1 M Fg.. partte graph for DUEs an the reuse canates matchng problem We employ Hungaran algorthm [1] to solve ths problem. The algorthm s an effcent bpartte allocaton scheme. In general N M perfectly symmetrc. To meet ths requrement we a but the Hungaran algorthm emans the bpartte graph to be M N vrtual vertces to the set of DD pars n the orgnal graph. The obect functon of optmal problem mamze the EE of total DUEs. However the stanar Hungaran algorthm s use to solve the mnmum weghte matchng problem on the transforme bpartte graph. Therefore we transform the orgnal obect functon to be mnmzng the EE through usng a suffcently large constant subtract the EE of each DUE. An the transforme optmal problem s equvalent to the orgnal problem. The etal steps are presente n Table 1. Algorthm 1 Optmal Sub-carrer Allocaton Algorthm Input: The sets of actve an le CUEs n the cell Table 1. Optmal sub-carrer allocaton algorthm a The set of DUEs the stance between DUEs The set of DUEs wth Moe A an Moe The set of relay canates of DUEs RN an R A an The set of stance between the CUEs an DUEs st T st Output: The set of sub-carrer reuse eponent 1. Step 1. For all a an o R 3. Calculate the outage probablty c out an out by formula (9) an (1) 4. If c out && out 5. Then put nto A : A A MoeA 6. Calculate u by formula (6) 7. Else 8. For all o 9. Calculate st T st 1. If T R R st st R

8 11. Then RN k k an / 1. For all a o 13. If && c out out c k out out 14. Then put an k nto : k 15. Calculate u u MoeA MoeA k by formula (6) to get u Moe k 16. Else 17. En f 18. En for 19. En f. En for 1. En f. En for 3. Step 4. For all a an o 5. If A or 6. Construct symmetrc bpartte graph by Vm u whch V m s a enough large value 7. Use the Hungaran algorthm to obtan 8. Else 9. There s no sub-carrer for DUE an the algorthm ens 3. En f 31. En for 3.3 Optmal ower Control for DUE The sub-carrer occupe by the pare CUEs has been allocate to the DUEs so we can smplfy optmal problem (14) as the followng optmal problem ma u + k 1 u (18) MoeA Moe k k A a a Subect to ma (19) For smplfcaton we onate A as A N g g C. Thus the EE of DUE wth Moe A an Moe can be respectvely onate as u MoeA log 1 A cr ()

9 A A u log 1 log 1 u u Moe 1 k k 1 MoeA MoeA = k k cr k cr (1) The form of epressons () an (1) are smlar to the functon of f a whch can be efne f a as log (1 a) where b b s a constant. The sub-carrers reusng by DUEs are nepenent the solutons of (18) s the same as the sum of mamum EE of each DUE. That s to say f we acheve the mamum value of f a we get the optmal solutons of (18). Therefore we brefly analyss the characterstc of f a. To begn wth seekng the ervatve of f a corresponng to the varable. f a 1 a b 1 log 1 a g a b ln 1 a b () An then seekng the ervatve of g a corresponng to the varable. ln 1 a g a a b (3) Accorng to the (3) we know that g a s a monotoncally ecreasng functon n an ab ln ga g a a b + lm log 1 a ln 1 a. Therefore wth the ncreasng of there s a makng g a. An g a s greater than zero on the nterval an less than zero on the nterval. So the functon f a s * monotoncally ecreasng on the nterval an monotoncally ascenng on the nterval *. That s to say * s the mamum value pont of functon f a. secton metho s use to solve the mamum of functon f a wth the constrant of mamum transmsson power ma an the etale steps are llustrate n Table. Table. secton metho for optmal power of DUE Algorthm secton metho for optmal power of DUE Input: gven the mamum transmsson power the tolerance an suffcently small value l = an suffcently large value 8 v =1. Output: the optmal transmsson power of DUE. ma

10 1. for. f 1 to A N ; then 3. whle v l t l v u MoeA t 6. f l t ; else v t 7. en f 8. en whle l v f ma ma ; else en 11. else f 1. for 13. en f 14. en for ; then an corresponng relay power of DD users k an k eecute steps 3-1. An then gettng the optmal k 4. SIMULATION RESULTS In ths secton we present the smulaton results of the propose sub-carrer allocaton an power control algorthm an analyze the EE performance of DUEs wth the fferent communcaton moe of the DUEs the stance between DUEs an the mamum transmsson power of DUEs. We conser a sngle solate crcular cell an the raus s fe. The locaton of en s n the center of the cell where CUEs are unformly strbute an each transmtter an recever of DUEs are locate n a unformly strbute wthn a raus R. In ths secton we present etensve smulaton of EE for DUEs of fferent transmsson moe. Table 3 summarzes the lst of smulaton parameters an ther efault value.

11 Table 3. Smulaton parameters arameter Values Cell raus ( R ) 5m AWGN power ( N ) -114m ath-loss constant ( ).1 ath-loss eponent ( ) 4 Actve CUE transmt power ( Ma. DUE transmt power( UE crcut power ( cr ma c ) 4m ) 1m ) 17m Req. SINR of CUE ( ) 3 Req. SINR of DUE ( ) 3 The stance between DUE ( R ) 3 1m Number of actve CUEs ( M ) 4 Number of le CUEs( K ) 4 Number of DUEs ( N ) 1% % 1% of actve CUEs Outage probablty threshol of CUE ( ).1 Outage probablty threshol of DUE ( ).1 We wll show the capacty of DUEs an CUEs an the EE of DUEs n the followng Fg As a comparson we compare the performance of our propose algorthm to the locaton-base algorthm (LA) n [13]. The authors of [13] prove that the EE of the DD lnk s manly etermne by the locaton of the CUE that shares sub-carrer wth the DUE. On ths bass a LA s propose to mamze the sum EE of DUEs. Snce the LA gets the transmsson power by converson formula of SINR the transmsson power may not be the optmal. However the propose algorthm optmze the transmsson power of DUEs. Specfcally when a DUE has been allocate sub-carrer occupe by CUE the transmsson power of DUEs on the sub-carrer s optmze usng secton methos. We also nvestgate the performance of our algorthm wth fe transmsson power at 17m. 5 The capacty of total users (bts/s/hz) CUEs of ropose DUEs of ropose CUEs n [13] DUEs n [13] The number of CUEs Fg. 3. The capacty of DUEs an CUEs wth the ncreasng number of DUEs where R=5m

12 Fg. 3 shows the capacty of total DUEs an CUEs wth the ncreasng number of DUEs. The number of actve CUEs s. Note that we assume the number of CUEs equals the number of sub-carrers snce each sub-carrer s occupe by one CUE. Wth the ncreasng number of DUEs the capacty of total DUEs ncrease whle the capacty of total CUEs escen. Ths s because the more DUEs wll reuse the more sub-carrers of actve CUEs an cause more nterference to the actve CUEs. From Fg. 3 we can see that the capacty of DUEs of our propose algorthm s less than the LA n [13] whle the capacty of CUEs s much hgher than the LA n [13]. Snce the LA oes not conser the QoS of the CUEs whch causes more nterference to the CUEs an escens the capacty of total CUEs. Energy effcency of total DUEs (bts/s/hz/w) ropose Algorthm Algorthm n [13] ropose Algorthm(fe power) The number of DUEs Fg. 4. Energy effcency of total DUEs wth the ncreasng number of DUEs where R=5m M= We present the EE of DUEs wth the fferent number of DUEs n Fg. 4. We can see that EE mproves wth the ncreasng number of DUEs whch ncates that wth onng of more DUEs more DUEs can echange nformaton through sharng sub-carrers occupe by actve CUEs. Therefore the EE of total DUEs s ncrease. Meanwhle our propose algorthm behaves better than the algorthm n [13]. Snce the algorthm n [13] acheves transmsson power by converson formula of SINR whch coul not be the optmal. However the transmsson power of our propose algorthm s optmal. The propose algorthm wth fe power acheves a lower EE for t transmts more power.

13 Energy effcency of total DUEs (bts/s/hz/w) ropose Algorthm Algorthm n [13] ropose Algorthm(fe power) The number of CUEs Fg. 5. Energy effcency of total DUEs wth the ncreasng number of CUEs where R=5m. In Fg. 5 we present the EE of DUEs wth the number of actve CUEs (sub-carrers). An the number of DUE s 1. We observe that wth the ncreasng number of sub-carrers the EE of DUEs ncrease slowly. Wth more sub-carrers DUEs have more sub-carrers to choose from an thus the performance s mprove. However the ncrease of EE of DUEs s slow whch mples that the DUE can reuse only one sub-carrer occupe by CUE an the CUEs o not have maor mpact on the performance of DUEs. Energy effcency of total DUEs (bts/s/hz/w) ropose Algorthm Algorthm n [13] ropose Algorthm(fe power) Crcut power of DUE(W) Fg. 6. Energy effcency of total DUEs wth crcut power of DUEs Fg. 6 shows the EE of total DUEs wth the crcut power of the DUE. It can be seen that our propose algorthm offers better performance than the other two algorthms. For small crcut power the EE of the propose algorthm s about 5% hgher than the algorthm n [13] an about 4% hgher than the propose algorthm wth fe power respectvely. However when crcut power

14 ncreases the performance gap between the propose algorthm an the other two schemes s reuce snce the total consume power s omnate by the crcut power. 5. CONCLUSIONS In ths paper we analyze the sub-carrer allocaton an power control uner the conton of mamum transmsson power constrant of DUEs to optmze the EE of fferent communcaton moe of DUEs unerlayng cellular networks. We apply the relay selecte from the le CUEs to DD communcaton when the outage probabltes of CUE an DUE whch share the same sub-carrer ecee the threshol efne by the system. Numercal smulatons show the EE of fferent types of communcaton moes an revel the avantage of DUE wth relay moe n average by comparng wth rectly DD communcaton moe. ACKNOWLEDGMENT Ths work s supporte by Natonal Natural Scence Founaton of Chna ( ) Natonal asc Research rogram of Chna (973 program: 13C395). AENDIX Wth the help of [14 eq. (5-18)] the DFs of an y are epresse as 1 1 y 1 1 f ep U an f y y ep U y respectvely. Net the DF of z = /y can be evaluate as follows: [14 eq. (6-59)] 1 z fz z yf yz y y z z From (4) the CDF can be epresse as ep 1/ y (4) Fz z a a Usng the ntegraton by parts the rght term n (5) can be evaluate as z e e (5) z e z 1 = e e z e 1 z z z z e e (6) We can get the followng epresson by substtutng (6) nto (5)

15 Let = g C F z 1 ep z z z 1 y = N g an =. The esre result (9) can be obtane. Smlarly the N esre formula (1) can be obtane. (7) REFERENCES 1. K. Doppler M. Rnne C. Wtng C. Rbero an K. Hugl Devce-to-evce communcaton as an unerlay to LTE-avance networks IEEE Communcaton Magazne vol. 47 no. 1 pp December 9.. G. Foor et. al Desgn aspects of network assste evce-to-evce communcatons IEEE Communcaton Magazne vol. 5 no. 3 pp March X. Ln J. G. Anrews A. Ghosh an R. Ratasuk An overvew of 3G evce-to-evce promty servces IEEE Communcaton Magazne vol. 5 no. 4 pp Aprl Kaufman J. Llleberg an. Aazhang Spectrum sharng scheme between cellular users an a-hoc evce-to-evce users IEEE Transactons on Wreless Communcatons vol. 1 no. 3 pp March H. Meshg D. Zhao an R. Zheng Jont channel an power allocaton n unerlay multcast evce-to-evce communcatons IEEE Internatonal Conference Lonon 15 pp W. Ll Y. Qan an G. Wu Energy-Effcency an Spectrum-Effcency of Mult-hop Devce-to-Devce Communcatons Unerlayng Cellular Networks IEEE Transactons on Vehcular Technology vol. 65 no. 1 pp January H. Tuong Duc L. Long ao an T. Le-Ngoc Energy-Effcent Resource Allocaton for DD Communcatons n Cellular Networks IEEE Transactons on Vehcular Technology vol. 65 no. 9 pp September J. Yanang L. Qang Z. Fuchun an C. Xq Energy-Effcent Jont Resource Allocaton an ower Control for DD Communcatons IEEE Transactons on Vehcular Technology vol. 68 no. 8 pp August H. Mn W. Seo J. Lee S. ark an D. Hong Relablty mprovement usng receve moe selecton n the evce-to-evce uplnk pero unerlayng cellular networks IEEE Trans. Wreless Communcaton. vol. 1 no. pp February S. Alamout an A. Sharafat Resource Allocaton for Energy-Effcent Devce-to-Devce Communcaton n 4G Networks Internatonal Symposum on Telecommuncatons 14 pp G. Mao N. Hmayat G. Y. L an S. Talwar Dstrbute Interference-Aware Energy-Effcent ower Optmzaton IEEE Transactons Wreless Communcaton vol. 1 no. 4 pp Aprl D. Feng L. Lu Y. Yuan-Wu G. Y. L G. Feng an S. L Devce-to-evce communcatons unerlayng cellular networks IEEE Transactons on Communcatons vol. 61 no. 8 pp August C. Yn Y. Wang L. Wenuan an X. Wang Energy-Effcent Channel Reusng for Devce-to-Devce Communcatons Unerlayng Cellular Networks Vehcular Technology Conference (VTC Sprng) Seoul 14 pp A. apouls an S. U. lla robablty Ranom Varables an Stochastc rocess 4 th eton. McGraw-Hll.

16 ao-zhou Yu ( 于宝舟 ) was born n Jangsu rovnce Chna n He receve the.e. egree n Communcaton Engneerng from Nantong Unversty Nantong n 14. He s now pursung master's egree n the epartment of Communcaton an Informaton Engneerng. He researches on the area of resource management an power control of DD communcaton unerlayng cellular networks. Q Zhu ( 朱琦 ) was born n Suzhou Jangsu Chna n She receve the M.S. egree n rao engneerng from Nanng Unversty of osts an Telecommuncatons n Now she s a professor n the Department of Telecommuncaton an Informaton Engneerng Nanng Unversty of osts an Telecommuncatons Jangsu Chna. Her research nterests focus on technology of net generaton communcaton broaban wreless access OFDM channel an source cong ynamc allocaton of rao resources.