4110 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 5, MAY 2017

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1 40 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 5, MAY 07 Trnsmit Power Control for DD-Underlid Cellulr Networs Bsed on Sttisticl Fetures Peng Sun, Kng G. Shin, Life Fellow, IEEE, Hilin Zhng, Member, IEEE, nd Ling He, Member, IEEE Abstrct By llowing two nerby mobile devices to communicte vi direct lin between them, device-to-device DD communictions cn efficiently increse the cpcity of DD-underlid cellulr networs, in which DD nd cellulr communictions shre the sme frequency bnd. However, the coexistence of DD nd cellulr communictions in the sme frequency bnd will cuse interference between the DD nd cellulr users, thus degrding their performnce. One my control the trnsmit power bsed on the rel-time chnnel-stte informtion CSI to mitigte this interference, but it is difficult to cquire the rel-time CSI between DD/cellulr trnsmitters nd DD receivers. To overcome this difficulty, we propose novel sttisticl-feture-bsed power control SFPC, which determines the trnsmit power bsed on sttisticl insted of rel-time CSI. The proposed SFPC combines the power control tht is wre of DD success lielihood with opportunistic ccess control to reduce the interference cused by DD communictions nd mximize the re spectrl efficiency of DD communictions. Specificlly, it ims to minimize the DD trnsmit power nd optimize the selection of ccess threshold. Our simultion results show tht SFPC cn increse both the cellulr communiction success probbility nd the energy efficiency of DD communictions, s well s reduce the verge DD trnsmit power. Index Terms Cellulr networs, device-to-device DD communictions, opportunistic ccess control, Poisson point process PPP, power control. I. INTRODUCTION DEVICE-TO-DEVICE DD communictions hve been studied extensively to meet the incresing demnd for wireless communiction between nerby devices/users/pplictions, e.g., socil networs or medi shring [] [5]. By llowing direct communictions between nerby devices without directing ll communictions through the BSs, Mnuscript received Jnury, 06; revised August 9, 06; ccepted September 30, 06. Dte of publiction October 4, 06; dte of current version My, 07. The wor of K. G. Shin ws supported in prt by the U.S. Ntionl Science Foundtion under Grnt CNS nd Grnt CNS The wor of P. Sun nd H. Zhng ws supported in prt by the Ntionl Nturl Science Foundtion of Chin No , the Project of Chin B08038, nd Chin Scholrship Council. This wor ws done when P. Sun ws visiting student with the University of Michign under the supervision of Prof. K. G. Shin. The review of this pper ws coordinted by Dr. D.-W. Mtol. P. Sun nd H. Zhng re with the Stte Key Lbortory of Integrted Service Networs, Xidin University, Xi n 7007, Chin e-mil: pengsun. xidin@gmil.com; hlzhng@xidin.edu.cn. K. G. Shin nd L. He re with the Deprtment of Electricl Engineering nd Computer Science, The University of Michign, Ann Arbor, MI USA e-mil: gshin@eecs.umich.edu; linghe@umich.edu. Color versions of one or more of the figures in this pper re vilble online t Digitl Object Identifier 0.09/TVT DD communictions offer severl potentil benefits, such s reduction of mobile devices energy consumption, improvement of spectrum utiliztion, nd cpcity. In spite of these potentil benefits, the coexistence of DD nd cellulr communictions in the sme frequency bnd is chllenging due to the difficulty of interference mngement. This is becuse cellulr users experience cross-tier interference from the DD trnsmitters, nd DD receivers experience both inter-dd interference nd cross-tier interferences from cellulr users. Trnsmit power control exploits rel-time chnnel-stte informtion CSI between communicting entities to mitigte the interference in wireless networs. However, due to dynmiclly chnging communiction environments nd inccurte chnnel estimtion t the receivers, it is difficult to obtin the ccurte rel-time CSI [6] [8], especilly in DD-underlid cellulr networs. Tht is, CSI frequently chnges due to the high mobility of cellulr nd DD users, nd DD receivers cnnot ccurtely estimte the time-vrying chnnel stte between multiple DD/cellulr trnsmitters nd DD receivers within the chnnel s coherence time. If outdted CSI is used to determine the trnsmit power, wireless users my experience severe performnce degrdtion nd/or outge. To overcome this problem, we propose SFPC, which cn determine the trnsmit power bsed on the sttisticl insted of the rel-time CSI. The sttisticl CSI ccounts for the effects of mobility nd time-vrying chnnel nd, thus, is estimted bsed on the PDF of user loctions nd fdings. The proposed SFPC combines the power control tht is wre of the DD success probbility with opportunistic ccess control to reduce the interference cused by DD communictions nd mximize the re spectrl efficiency of DD communictions. A. Relted Wor nd Motivtion There hs been extensive reserch on dynmic power control for DD-underlid cellulr networs to mitigte the interference cused by DD communictions. A dynmic power control method ws proposed in [9], focusing on the protection of existing cellulr lins by limiting the DD trnsmission power. A DD power lloction scheme ws proposed in [0] to mximize throughput for deterministic networs. Doppler et l. [] reduced the interference from DD trnsmitters to cellulr users by restricting the DD trnsmit power nd the distnce between DD pirs. The fixed booster nd bcoff fctors were proposed in [] to control DD trnsmit power nd mitigte the interference cused by DD communictions IEEE. 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2 SUN et l.: TRANSMIT POWER CONTROL FOR DD-UNDERLAID CELLULAR NETWORKS BASED ON STATISTICAL FEATURES 4 Most existing schemes for DD power control re bsed on the rel-time CSI to mitigte interference [], [9] []. However, the communiction environment is complex nd dynmic in DD-underlid cellulr networs, ming it difficult to obtin the ccurte rel-time CSI between multiple DD/cellulr trnsmitters nd DD receivers within the chnnel s coherence time. The sttisticl fetures of CSI were lso used in [] nd [3] for interference mngement. However, these schemes only involve two trnsmit powers: zero or pe power. To further decrese the interference nd improve the energy efficiency of DD communictions, we propose SFPC tht determines DD trnsmit power within the rnge from zero to pe power. Moreover, SFPC is different from the power control schemes in cognitive rdio cellulr networ, in which cognitive devices/users intelligently sense nd opportunisticlly ccess spectrum holes left unused by cellulr users to void interference. The power control lgorithm utilizes the informtion gthered from sensing to limit the interference from cognitive rdio users to cellulr users [4] [6], with no BS ssistnce. In contrst, the DD trnsmit power is controlled by the cellulr networ. Specificlly, SFPC utilizes the CSI sttisticl fetures provided by the BS for power control nd opportunistic ccess control. B. Advntges The proposed SFPC hs the following four min dvntges. Reduced ltency: A shorter rection time of power control reduces ltency. SFPC chieves this bsed on the CSI sttisticl fetures provided by the BS without complex interctions to mnge interference. Resilience to users movements: Users movements cuse CSI to vry. To cope with this problem, SFPC utilizes the sttisticl CSI insted of the CSI in prticulr deployment nd is thus robust to users movements. 3 Improved lin relibility: The DD success probbility is used s control threshold to ensure the DD communiction relibility. 4 Low overhed: There is no signling overhed for shring the rel-time CSI or loction informtion. This pper is orgnized s follows. We present the model for DD-underlid cellulr networs in Section II. DD success probbility-wre power control nd SFPC re presented in Sections III nd IV, respectively. The proposed pproches re evluted in Section V, nd the pper concludes with Section VI. II. SYSTEM MODEL Fig. shows the system model of n uplin DD-underlid cellulr networ, in which n uplin cellulr user communictes with the BS, while multiple DD lins re using the sme spectrum. This DD-underlid cellulr networ model is commonly used in the literture [], [3]. The uplin DD-underlid cellulr networ consists of cellulr nd DD tiers. The BS nd its ssocited cellulr user form the cellulr tier, the circulr dis C of rdius R represents the coverge region of the BS locted t the center. A cellulr uplin user is locted rndomly within the cell ccording to uniform distribution. The DD trnsmitters nd their intended receivers form the DD tier. The DD trnsmitters re rndomly distributed in the networ coverge re nd represented s homogeneous PPP, i.e., Φ, with density λ. We ssume tht the intended DD receivers re uniformly nd independently locted within the distnce R d of their ssocited DD trnsmitters, R d is the DD communiction rnge. The PDF of the communiction distnce, which is defined s the direct lin distnce between DD trnsmitter nd its corresponding DD receiver, is f d x = x R d, 0 x R d. Let K be the number of DD trnsmitters in C, which is Possion rndom vrible with men E[K] =λπr ccording to the bove model. Given prticulr reliztion of the PPP Φ, the received signls t the BS nd DD receiver re y 0 = h 0,0 d α/ 0,0 s 0 + y = h, d α/, s + K i= h i,0 d α/ i,0 s i + n 0 K i=0,i h i, d α/ i, s i + n 3 y 0 nd y represent the received signls t the BS nd DD receiver, respectively; s 0 nd s re the signls sent by the uplin cellulr user nd DD trnsmitter, respectively; 3 n 0 nd n re the dditive noises t the BS nd DD receiver, which re nown to hve complex norml distributions CN0,σ []. We ssume tht ll lins experience Ryleigh fding while ignoring the effect of slow fding [], [3], [7]. Let h 0,0, h i,0, h 0,, nd h i, be smll-scle fding from the cellulr user to the BS, from DD trnsmitter i to the BS, from the cellulr user to the DD receiver, nd from DD trnsmitter i to the DD receiver, which re independently distributed s CN0, [], [3]. A lrge-scle ttenution is ssumed s the stndrd pth-loss propgtion d α A,B, d A,B is the distnce from A to B nd α is the pth-loss exponent. Let d 0,0, d i,0, d 0,, nd d i, denote the distnce from the cellulr user to the BS, from DD trnsmitter i to the BS, from the cellulr user to DD receiver, nd from DD trnsmitter i to DD receiver. SINR is commonly used metric for the evlution of communiction qulity in cellulr networs. User communictions re successful if nd only if their corresponding receivers SINR re higher thn the trget SINR threshold. The SINR t the BS nd DD trnsmitter is SINR 0 p = h 0,0 d α 0,0 p 0 I0 d + 4 σ SINR p = h, d α, p I c + Id + σ 5

3 4 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 5, MAY 07 I d 0 = I d = K i= K i=,i h i,0 d α i,0 p i Fig.. h i, d α i, p i I c = h 0, d α/ 0, p 0 nd p =[p 0,p,...,p K ] T is the trnsmit power vector, with p 0 being the power of the cellulr user nd p i i 0 being the power of DD trnsmitter i; nd I0 d, Id, nd Ic re the interferences from DD trnsmitters to BS, from other DD pirs to DD receiver, nd from the cellulr user to DD receiver, respectively. Are spectrl efficiency is mesure of the number of users tht cn be simultneously supported by limited rdio frequency bndwidth per unit re [8] [0]. In DD-underlid cellulr networs, re spectrl efficiency of DD communictions cn be expressed s [3] System model of DD-underlid cellulr networs. TABLE I ABBREVIATIONS DEFINITION T γ = λip SINRp >γ log + γ 6 γ denotes the trget SINR threshold, IP SINRp > γ is the men of the DD success probbility, λ = P t λ denotes the effective DD lin density without ny inctive DD lin, nd P t is the men of the ccess probbility. The bbrevitions nd nottions used throughout this pper re summrized in Tbles I nd II for the ese of reference. III. DEVICE-TO-DEVICE SUCCESS PROBABILITY-AWARE POWER CONTROL This section presents DD success probbility-wre power control, ey component of SFPC. The proposed lgorithm significntly decreses the cross-tier interference from DD communictions to cellulr communictions by minimizing the DD trnsmit power, while stisfying the trget SINR requirements of DD communictions. For DD trnsmitter Abbrevitions DD BS PPP PDF SINR CSI SFPC Symbol R R d h A,B d A,B λ γ p 0 p p P t, Pt, G Mening Device-to-Device Bse Sttion Poisson Point Process Probbility Density Function Signl to Interference plus Noise Rtio Chnnel Stte Informtion Sttisticl-Feture-bsed Power Control TABLE II NOTATIONS DEFINITION Mening Cell rdius DD communiction rnge Fding from A to B Distnce from A to B DD lin density Pth-loss exponent Trget SINR threshold Trnsmit power of cellulr user Trnsmit power of DD trnsmitter Minimum trnsmit power of DD trnsmitter Access probbility of DD trnsmitter Optiml ccess probbility of DD trnsmitter Optiml ccess threshold of DD trnsmitter {,,..., K}, the minimum trnsmit power is obtined by solving the following optimiztion problem: min s.t. p h, d α, p h 0, d α 0, p 0 + K i=,i h i, d α i, p i + σ γ p i p mx,d, i {,,...,K} p 0 p mx,c 7

4 SUN et l.: TRANSMIT POWER CONTROL FOR DD-UNDERLAID CELLULAR NETWORKS BASED ON STATISTICAL FEATURES 43 p mx,d nd p mx,c re the mximum trnsmit power of DD nd cellulr communictions, respectively. Clerly, one DD trnsmitter cn lower its trnsmit power if the corresponding DD receiver s SINR is higher thn γ, reducing both the inter-dd interference nd cross-tier interference while stisfying the requirements of DD communictions. However, becuse the communiction environment is complex nd dynmic in DD-underlid cellulr networs, it is difficult to get ccurte rel-time CSI to estimte the SINR in rel wireless networs, especilly in DD-underlid cellulr networs. This is becuse CSI frequently chnges due to the high mobility of cellulr nd DD users, nd DD receivers my not ccurtely estimte the time-vrying chnnel between multiple DD trnsmitters cellulr user nd DD receivers within the chnnel s coherence time. If outdted CSI is used to determine the trnsmit power, users will experience severe performnce loss nd/or outge. Therefore, we estimte the DD success probbility the SINR complementry cumultive distribution function [] bsed on the sttisticl CSI nd, then, use the DD success probbility to determine the minimum DD trnsmit power. We estimte the DD success probbility s follows. For ny given p, the SINR t DD receiver is defined s in 4, nd the DD success probbility of DD receiver cn then be expressed s IP SINR p >γ p =e p p g p = σ γd, πλ [ ] = sinc E p i γ d, gx = + x γd, p 0. 8R 45π Proof: See Appendix A. We lso compute lower bound of DD success probbility to ensure the DD success probbility to be lwys higher thn the opertor-specified threshold even in the presence of the mximum interference. The lower bound of DD success probbility is computed by setting p i = p mx,d in to mximize the inter-dd interference, which cn be expressed s IP low SINR p >γ p =e p 3p 3 = πλ sinc p mx,d γ d,, g p nd IP low SINR p >γ p denotes the lower bound of the DD success probbility. 8 9 Let P th be the opertor-specified DD success probbility threshold. Thus, the problem in 7 cn be trnsformed to min s.t. p IP low SINR p >γ p P th p i p mx,d, i {,,...,K} p 0 p mx,c 0 nd then by solving e p 3 p g p P th = 0 we cn determine the minimum DD trnsmit power p for DD trnsmitter. Unsurprisingly, it is chllenging to find closedform solution for p in. For simplicity, we ignore the noise by ssuming σ = 0in. This is resonble becuse the interference is much stronger thn the noise in especilly dense DD-underlid cellulr networs. This simplifiction lso trnsforms to homogeneous eqution, which is solvble. Thus, the minimum DD trnsmit power cn be expressed s p = min 4 W = min 6 W e 3P th d, 5 6 e 5P th 6 3 P th 5 P th,p mx,d,p mx,d μ = min d,p mx,d, = fd, 3 4 = P th γd,p 0 8R 45π 5 = πλ sinc 6 = P th γp 0 μ = 6 W p mx,d γ 8R 45π e 5P th 6 5 P th 4 nd W denotes the Lmbert W function. In ddition, p = [p 0,p,...,p K ]T denotes the minimum trnsmit power vector, with p i i 0 being the minimum trnsmit power of DD trnsmitter i. Proof: See Appendix B. Note tht p depends on d, in 3. This is becuse for specific PPP reliztion, ech DD lin experiences different SINRs nd, thus, hs different trnsmit power levels, depending

5 44 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 5, MAY 07 Algorithm : DD Success Probbility-Awre Power Control. : BS computes μ ccording to 4; : BS brodcsts μ to DD trnsmitters; 3: for ech DD trnsmitter do 4: Estimte communiction distnce; 5: Compute the minimum trnsmit power in 3; 6: Set the trnsmit power being the minimum trnsmit power; 7: end for on its loction nd surrounding environments, i.e., the distnce between DD trnsmitter nd its intended receiver. In other words, DD trnsmitter with short communiction distnce hs lower trnsmit power thn DD trnsmitter with lrger communiction distnce, s it hs potentilly higher SINR. The proposed power control is bsed on the sttisticl CSI, which does not require the rel-time CSI. The sttisticl CSI is estimted bsed on the PDF of users loctions nd fdings. Therefore, the signling for shring CSI nd loction informtion is not needed. A DD trnsmitter selects the trnsmit power bsed solely on the nowledge of the communiction distnce nd μ. Remr : To relize the proposed power control lgorithm, ech DD trnsmitter needs to now the communiction distnce nd the vlue of μ. Ech DD trnsmitter cn obtin the communiction distnce through the feedbc from the corresponding DD receiver. For instnce, in multicrrier system, DD receiver cn relibly estimte the distnce-bsed pth loss using pilot signls sent on control chnnel by verging the effects of fdings over multiple resource blocs nd sends it bc to the DD trnsmitter vi feedbc chnnel []. As shown in 4, ech DD trnsmitter hs the sme μ, becuse the PDF of inter-dd interference nd the cross-tier interference re the sme for different DD receivers. Therefore, the vlue of μ cn be brodcst by the BS. In order to obtin the vlue of μ,thebs needs to now the DD lin density, the trget SINR threshold, the trnsmit power constrints, the cell rdius, nd the DD success probbility threshold. The DD lin density is estimted by the BS during the process of estblishing the DD lin [3], [4], [], [], nd the other informtion is set by the opertor. Therefore, the BS cn obtin the vlue of μ nd brodcst it to DD trnsmitters vi downlin control chnnel. Finlly, ech DD trnsmitter cn determine its minimum trnsmit power, depending on the communiction distnce nd μ. The DD success probbility-wre power control method is summrized in Algorithm. IV. STATISTICAL-FEATURE-BASED POWER CONTROL The inter-dd interference would be very high in the cse of dense DD lin deployment. As result, the DD success probbility threshold my not be stisfied, even when the mximum power p mx,d is dopted by the DD trnsmitter, especilly when the trget SINR threshold is high. Trgeting the cse of strong inter-dd interference, we propose SFPC which extends DD success probbility-wre power control by integrting it with opportunistic ccess control to mximize the re spectrl efficiency of DD communictions while decresing both inter-dd nd cross-tier interferences. Insted of llowing ll DD trnsmitters to ccess the chnnels, prt of DD pirs cnnot ccess the networ to decrese interferences in the proposed SFPC. Selecting proper ccess probbility nd ccess threshold ply n importnt role in our lgorithm. Choosing smll ccess probbility lrge ccess threshold reduces interferences t the cost of smller number of ctive DD trnsmitters in the cell. Therefore, it is importnt to find n optiml ccess probbility nd ccess threshold to mximize the re spectrl efficiency of DD communictions. In wht follows, we determine n optiml ccess probbility nd ccess threshold. We mximize re spectrl efficiency of DD communictions T γ by optimizing the men of the ccess probbility P t, which cn be expressed s mx P t T γ s.t. 0 <P t 5 T γ is defined in 6. Note tht P t is the verge ccess probbility. For specific PPP reliztion, ech DD lin experiences different SINR nd, thus, hs different ccess probbilities depending on the communiction distnce. Tht is, DD trnsmitter with short communiction distnce hs higher ccess probbility thn DD trnsmitter with lrger communiction distnce, becuse it hs potentilly higher SINR. Since the nlysis performed for typicl lin indictes the sptilly verged performnce of the networ by Slivny s theorem [3], [4], the mens of the DD success nd ccess probbilities cn be expressed s nd K IP SINRp = >γ= E[IPSINR p >γ] K = KE[IPSINR p >γ] K = E[IPSINR p >γ d, ] K = P t = E[P t,] K = E[P t, d, ] 6 P t, denotes the ccess probbility for DD trnsmitter. Therefore, for ny given d,, the problem in 5 cn be trnsformed to mx P t, P t, λipsinr p >γ log + γ 7 s.t. 0 <P t,.

6 SUN et l.: TRANSMIT POWER CONTROL FOR DD-UNDERLAID CELLULAR NETWORKS BASED ON STATISTICAL FEATURES 45 Bsed on 8, the bove objective function cn be trnsformed further to mx P t, P t, IPSINR p >γ mx P t, e p P t, b d, p gp P t, b = πλ [ ] sinc E p i γ 8 nd p i is the minimum DD trnsmit power of DD trnsmitter i identified by DD success probbility-wre power control, which cn be expressed s [ ] E p i = R d 0 fx x dx 9 R d R d is the DD communiction rnge, nd fx is defined in 3. The trnsformed problem cn be solved by d{p t, e p b d, P t,p g 3 p } = 0 dp t, nd thus b d,p t, p =. 0 Subsequently, the optiml ccess probbility for DD trnsmitter, denoted by Pt,, cn be expressed s { } { } Pt, p = min fd, b d, = min, b d,., Then, the optiml ccess threshold is designed ccording to the optiml ccess probbility; DD trnsmitter is ctive whenever its chnnel gin h, d, is bove its optiml ccess threshold. Since Pt, =IP h, d, >G, the optiml ccess threshold cn be obtined s G = lnp t, d α, G denotes the optiml ccess threshold for DD trnsmitter. A DD trnsmitter selects the trnsmit power bsed solely on the nowledge of its communiction distnce, chnnel gin, μ, nd the optiml ccess threshold. As shown in Fig., it cn be observed tht the SFPC improves the re spectrl efficiency of DD communictions over DD success probbilitywre power control nd the performnce gin increses s λ nd γ increse. The SFPC is summrized in Algorithm. V. SIMULATION We now use simultion to evlute the performnce of SFPC lgorithm for DD-underlid cellulr networs in terms of cellulr communiction success probbility, verge DD trnsmit power, energy efficiency of DD communictions, nd DD success probbility. The performnce of the proposed SFPC is compred with three other strtegies: Fig.. Are spectrl efficiency of DD communictions ccording to different DD trget SINR thresholds with set of prmeters p 0 = 00 mw, p = 0.mW,R = 500 m, R d = 50 m, nd P th = 85%. Algorithm : Sttisticl-Feture-Bsed Power Control. : BS computes μ nd b ccording to 4 nd 8; : BS brodcsts the vlues to DD trnsmitters; 3: for Ech DD trnsmitter do 4: Estimte its communiction distnce nd chnnel gin; 5: Compute the optiml ccess threshold ccording to ; 6: if The chnnel gin is bove the optiml ccess threshold 7: Crry out Algorithm nd set the trnsmit power being the minimum trnsmit power ccording to 3; 8: else 9: Set the trnsmit power being 0; 0: end if : end for conditionl SIR-wre ccess control Conditionl SIRwre AC [3]; ON OFF power control ON OFF PC []; 3 no PC: ll DD trnsmitters use p mx,d. The defult simultion settings re summrized in Tble III, unless otherwise specified, which re set bsed on the results in [] nd [3]. The BS is locted t the center, nd the cellulr user is uniformly locted in the cell of rdius R. DD trnsmitters re distributed in the cell ccording to PPP with density λ. Given the DD communiction rnge R d, ech intended DD receiver is uniformly nd independently locted within R d of its ssocited DD trnsmitter in the isotropic direction. We obtin the following results by verging 000 simultion runs. Fig. 3 shows the cellulr communiction success probbility s function of the DD lin density. From Fig. 3, one cn notice tht the proposed lgorithm gretly improves the

7 46 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 5, MAY 07 TABLE III DEFAULT SIMULATION SETTINGS Prmeter Vlue Cell rdius R 500 m DD communiction rnge R d 0m DD lin density on subchnnel λ from to Pth-loss exponent 4 The trnsmit power of the cellulr user p 0 = 00 mw The mximum DD trnsmit power p mx,d = 0.mW DD success probbility threshold P th 75%, 85% BS trget SINR threshold 3dB DD trget SINR threshold 4 db Noise vrince σ for -MHz bndwidth dbm The number of reliztions 000 geometry drop Fig. 4. Averge DD trnsmit power. Fig. 3. Cellulr communiction success probbility. cellulr communiction success probbility, implying the proposed lgorithm s efficiency in mitigting the interference cused by DD communictions vi power control. For exmple, when the DD lin density is E[K] =39., SFPC improves the cellulr communiction success probbility from 55.% ON OFF PC, No PC nd 57% conditionl SIR-wre AC to 65.6% SFPC P th = 85% nd 76.6% SFPC P th = 75%, respectively. Note tht the ON OFF power control yields the sme performnce s the cse of no power control becuse the ccess probbility is. The cellulr communiction success probbility decreses s the DD success probbility threshold increses becuse the DD trnsmit power increses monotoniclly s the DD success probbility threshold increses, thus incresing the interference from DD communictions. Fig. 4 plots the verge DD trnsmit power versus the DD lin density. SFPC cn reduce the trnsmit power significntly compred to other schemes, especilly when the DD lin density is low. For exmple, t λ = E[K] =3.5, the verge DD trnsmit power is 0. ON OFF PC, No PC, 0.09 conditionl SIR-wre AC, 0.04 SFPC P th = 85%, nd 0.03 SFPC P th = 75%, respectively. The verge DD trnsmit power monotoniclly increses s the DD success Fig. 5. Energy efficiency of DD communictions. probbility threshold increses. This is becuse DD trnsmitters hve to increse their trnsmit power to improve DD receivers SINR in order to stisfy the higher DD success probbility threshold. Since dense DD lin deployment cuses strong inter-dd interference, DD trnsmitters increse their trnsmit power to meet the DD success probbility threshold, nd thus, the verge DD trnsmit power monotoniclly increses s the DD lin density increses. Next, we evlute the energy efficiency of DD communictions, which is defined s the informtion-bits per unit of trnsmit energy nd very importnt for technologicl dvnces in current nd emerging cellulr networs. Clerly, our proposed scheme enhnces the energy-efficiency of DD communictions, s shown in Fig. 5, due to its reduction of inter-dd interference with power control. Energy-efficiency of DD communictions decreses monotoniclly s DD lin density increses s dense DD lin deployment ccompnies

8 SUN et l.: TRANSMIT POWER CONTROL FOR DD-UNDERLAID CELLULAR NETWORKS BASED ON STATISTICAL FEATURES 47 To overcome the difficulty in obtining rel-time CSI, SFPC utilizes sttisticl CSI, which is simple nd incurs low overhed. The performnce gin chieved by SFPC is evluted in terms of cellulr communiction success probbility, verge DD trnsmit power, nd energy efficiency of DD communictions. APPENDIX A The DD success probbility of DD receiver cn be expressed s Fig. 6. DD success probbility. strong inter-dd interference, forcing DD trnsmitters to rise their trnsmit power to mintin the sme SINR. Fig. 6 shows the DD success probbility versus the DD lin density. The figure shows tht SFPC cn ensure the DD success probbility to be higher thn the given threshold whenever possible. We cn observe tht the DD success probbility is higher thn the DD success probbility threshold under SFPC with P th = 75%. For exmple, t λ = E[K] = 70.6, the DD success probbility is ON OFF PC, No PC, 0.84 conditionl SIR-wre AC, 0.83 SFPC P th = 85%, nd SFPC P th = 75%, respectively. However, when P th = 85% nd λ , the DD success probbility chieved by SFPC cnnot stisfy the DD success probbility threshold due to the strong inter-dd interference nd the trnsmit power constrints. In this cse, the DD success probbility chieved by SFPC is close to tht of other schemes. In ddition, the DD success probbility increses s the DD success probbility threshold increses by SFPC lgorithm. All in ll, the proposed SFPC increses the cellulr communiction relibility nd energy efficiency. There is reciprocl reltionship between the cellulr communiction success probbility nd DD success probbility. Therefore, there is n inherent trdeoff between cellulr communiction success probbility nd DD success probbility. There re vrious services bsed on DD communiction such s vehicle-to-vehicle communictions, context shring, nd locl dvertising. Some services re given higher priority thn cellulr communictions, but others re not. The priority of DD communictions depends on the specific DD service. The priority of DD communictions cn be controlled by the opertor by setting proper DD success probbility threshold higher DD success probbility threshold indictes higher DD communiction priority. VI. CONCLUSION In this pper, we hve proposed SFPC for DD-underlid cellulr networs tht combines power control tht is wre of DD success probbility with opportunistic ccess control to reduce the interference cused by DD communictions nd mximize the re spectrl efficiency of DD communictions. IP SINR p >γ p h, d α, =IP p I c + >γ, Φ Id + σ =IP h, > γdα, Ic + Id + σ E I c,i d = [ exp p γdα, Ic + Id + σ p ] = e sσ L I c sl I d s 3 s = γdα, p, nd L I c s L I d s is the Lplce trnsform of rndom vrible I c Id. The equlity follows from h, exp []. L I d s cn be derived further s in [4] L I d s = E exp s p i h i, d α i Φ\ [ ] = exp πλ E[e sp i h/u ]udu = exp πλ [ sinc/ E p i L I c s cn be derived s 0 i, ] s. 4 L I c s = E[exp sp 0 h 0, d α 0, ] [ ] = E d0, + sp 0 d α. 5 0, For simplicity, we pproximte the expression L I c s by E d0, [ ] [ ] for []. Furthermore, E[d + d + / 0, ]= 0, E[d 0, ] 8R 45π s shown in [5], nd therefore, the Lplce trnsform of the rndom vrible I c cn be expressed s L I c s = = + sp 0 / E[d 0, ]. 6 + sp 0 / 8R/45π Plugging 4 nd 6 into 3, we cn derive the DD success probbility s given in 8

9 48 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 5, MAY 07 APPENDIX B For ny given DD success probbility threshold P th, we cn find the reltionship between minimum trnsmit power p d nd d,, which cn be expressed s e 3p = g P th p = P th + p 7 γmin d,p mx,c 45π. 8R For generl type of eqution e x+b = cx + d, x is the vrible to be solved;, b, c, d re constnts; nd, c 0, the solution by using Lmbert W function is W x = d c eb c d c 8 W denotes Lmbert W function. Using 8 s typicl solution for the type of 7, we cn obtin 3. REFERENCES [] K. Doppler, M. Rinne, C. Wijting, C. B. Ribeiro, nd K. Hugl, Device-todevice communiction s n underly to LTE-dvnced networs, IEEE Commun. Mg., vol. 47, no., pp. 4 49, Dec [] P. Jnis et l., Device-to-device communiction underlying cellulr communictions systems, Int. J. Commun. Netw. Syst. Sci., vol., pp , 009. [3] G. Fodor et l., Design spects of networ ssisted device-to-device communictions, IEEE Commun. Mg., vol. 50, no. 3, pp , Mr. 0. [4] M. S. Corson, R. Lroi, J. Li, V. Pr, T. Richrdson, nd G. Tsirtsis, Towrd proximity-wre internetworing, IEEE Wireless Commun., vol. 7, no. 6, pp. 6 33, Dec. 00. [5] X.Wu et l., Flshlinq: A synchronous distributed scheduler for peer-topeer d hoc networs, IEEE/ACM Trns. Netw.,vol.,no.4,pp.5 8, Aug. 03. [6] S. V. Hnly nd D. N. Tse, Power control nd cpcity of spred spectrum wireless networs, Automtic, vol. 35, no., pp , 999. [7] J. F. Chmberlnd nd V. V. Veervlli, Decentrlized dynmic power control for cellulr CDMA systems, IEEE Trns. Wireless Commun., vol., no. 3, pp , My 003. [8] K.Y.Wng,N.Jclin,Z.Ding,ndC.Y.Chi, RobustMISOTrnsmitoptimiztion under outge-bsed QoS constrints in two-tier heterogeneous networs, IEEE Trns. Wireless Commun.,vol.,no.4,pp , Apr. 03. [9] J. Gu, S. J. Be, B.-G. Choi, nd M. Y. Chung, Dynmic power control mechnism for interference coordintion of device-to-device communiction in cellulr networs, in Proc. 3rd Int. Conf. Ubiquitous Future Netw., Jun. 0, pp [0] C. H. Yu, K. Doppler, C. B. Ribeiro, nd O. Tironen, Resource shring optimiztion for device-to-device communiction underlying cellulr networs, IEEE Trns. Wireless Commun.,vol.0,no.8,pp , Aug. 0. [] P. Jnis, V. Koivunen, C. Ribeiro, J. Korhonen, K. Doppler, nd K. Hugl, Interference-wre resource lloction for device-to-device rdio underlying cellulr networs, in Proc. IEEE Veh. Technol. Conf., Apr. 009, pp. 5. [] N. Lee, X. Lin, J. G. Andrews, nd R. W. Heth, Power Control for DD underlid cellulr networs: Modeling, lgorithms, nd nlysis, IEEE J. Sel. Ares Commun., vol. 33, no., pp. 3, Jn. 05. [3] Z. Chen nd M. Kountouris, Distributed SIR-wre opportunistic ccess control for DD underlid cellulr networs, in Proc. IEEE Glob. Commun. Conf., Dec. 04, pp [4] S. Srinivs nd S. A. Jfr, Soft sensing nd optiml power control for cognitive rdio, IEEE Trns. Wireless Commun., vol. 9, no., pp , Dec. 00. [5] N. Hoven nd A. Shi, Power scling for cognitive rdio, in Proc. Int. Conf. Wireless Netw., Commun. Mobile Comput., Jun. 005, vol., pp [6] K. Hmdi, W. Zhng, nd K. B. Letief, Power control in cognitive rdio systems bsed on spectrum sensing side informtion, in Proc. IEEE Int. Conf. Commun., Jun. 007, pp [7] Q. Ye, M. Al-Shlsh, C. Crmnis, nd J. G. Andrews, Resource optimiztion in device-to-device cellulr systems using time-frequency hopping, IEEE Trns. Wireless Commun., vol. 3, no. 0, pp , Oct. 04. [8] M. S. Alouini nd A. J. Goldsmith, Are spectrl efficiency of cellulr mobile rdio systems, IEEE Trns. Veh. Technol.,vol.48,no.4,pp , Jul [9] L. Zhng, H. C. Yng, nd M. O. Hsn, Generlized re spectrl efficiency: An effective performnce metric for green wireless communictions, IEEE Trns. Commun., vol. 6, no., pp , Feb. 04. [0] Y. Kim, T. Kwon, nd D. Hong, Are spectrl efficiency of shred spectrum hierrchicl cell structure networs, IEEE Trns. Veh. Technol., vol. 59, no. 8, pp , Oct. 00. [] M. Peng, Y. Li, T. Q. S. Que, nd C. Wng, Device-to-device underlid cellulr networs under Ricin fding chnnels, IEEE Trns. Wireless Commun., vol. 3, no. 8, pp , Aug. 04. [] Fesibility Study for Proximity Services ProSe Relese, 3rd Genertion Prtnership Project; Technicl Specifiction Group SA, Aug. 0. [3] D. Stoyn, W. S. Kendll, J. Mece, nd L. Ruschendorf, Stochstic Geometry nd Its Applictions, vol., New Yor, NY, USA: Wiley, 987. [4] X. Lin, J. G. Andrews, nd A. Ghosh, Spectrum shring for device-todevice communiction in cellulr networs, IEEE Trns. Wireless Commun., vol. 3, no., pp , Dec. 04. [5] D. Moltchnov, Distnce distributions in rndom networs, Ad Hoc Netw., vol. 0, no. 6, pp , 0. Peng Sun received the B.S. degree in communictions engineering from Centrl South University of Forestry nd Technology, Chngsh, Chin, in 00. He is currently woring towrd the Ph.D. degree with the Stte Key Lbortory of Integrted Services Networs, Xidin University, Xi n, Chin. He ws visiting Ph.D. student under the supervision of Prof. K. G. Shin with the Deprtment of Electricl Engineering nd Computer Science, The University of Michign, Ann Arbor, MI, USA, from 04 to 06. His reserch interests include deviceto-device communictions nd heterogeneous networs. Kng G. Shin LF received the B.S. degree in electronics engineering from Seoul Ntionl University, Seoul, Kore, in 970, nd both the M.S. nd Ph.D. degrees in electronics engineering from Cornell University, Ithc, New Yor, in 976 nd 978, respectively. He is the Kevin nd Nncy O Connor Professor of computer science with the Deprtment of Electricl Engineering nd Computer Science, The University of Michign, Ann Arbor, MI, USA. His current reserch focuses on qulity-of-service-sensitive computing nd networing, s well s on embedded rel-time nd cyber-physicl systems. He hs supervised the completion of 77 Ph.D.s, nd uthored/couthored more thn 830 technicl rticles, textboo, nd more thn 30 ptents or invention disclosures. He ws co-founder of couple of strtups nd hs licensed some of his technologies to industry. Prof. Shin hs received numerous Best Pper Awrds, including those from the 0 ACM Interntionl Conference on Mobile Computing nd Networing, the 0 IEEE Interntionl Conference on Autonomic Computing, nd the 00 nd 000 USENIX Annul Technicl Conferences; the 003 IEEE Communictions Society Willim R. Bennett Prize Pper Awrd; nd the 987 Outstnding IEEE Trnsctions of Automtic Control Pper Awrd. He hs lso received severl institutionl wrds, including the Reserch Excellence Awrd in 989, the Outstnding Achievement Awrd in 999, the Distinguished Fculty Achievement Awrd in 00, nd the Stephen Attwood Awrd in 004 from The University of Michign the highest honor bestowed to Michign Engineering fculty; Distinguished Alumni Awrd from the College of Engineering, Seoul Ntionl University, in 00; the 003 IEEE RTC Technicl Achievement Awrd; nd the 006 Ho-Am Prize in Engineering the highest honor bestowed to Koren-origin engineers.

10 SUN et l.: TRANSMIT POWER CONTROL FOR DD-UNDERLAID CELLULAR NETWORKS BASED ON STATISTICAL FEATURES 49 Hilin Zhng M 98 received the B.S. nd M.S. degrees from Northwestern Polytechnic University, Xi n, Chin, in 985 nd 988, respectively, nd the Ph.D. degree from Xidin University, Xi n, in 99. In 99, he joined the School of Telecommunictions Engineering, Xidin University, he is currently Senior Professor nd Den of the school. He is lso currently the Director of Key Lbortory in Wireless Communictions sponsored by Chin Ministry of Informtion Technology, ey member of Stte Key Lbortory of Integrted Services Networs, one of the stte government specilly compensted scientists nd engineers, Field Leder in Telecommunictions nd Informtion Systems in Xidin University, nd n Associte Director for Ntionl Project. He hs published more thn 00 ppers in journls nd conferences. His current reserch interests include ey trnsmission technologies nd stndrds on brodbnd wireless communictions for Fifth-Genertion wireless ccess systems. Ling He S 09 M received the B.Eng. degree from Tinjin University, Tinjin, Chin, in 006, nd the Ph.D. degree from Nni University, Chin, in 0, both in computer science. From 009 to 0, he ws Visiting Reserch Student with the University of Victori, Victori, BC, Cnd. He is currently Reserch Fellow with the University of Michign, Ann Arbor, MI, USA. He ws Postdoctorl Fellow nd then Reserch Scientist with Singpore University of Technology nd Design during 0 04 nd Reserch Assistnt with the University of Victori, BC, Cnd, during His reserch interests include cyber-physicl systems, bttery mngement, nd networing. Mr. He received the Best Pper Awrds t the 0th Interntionl Conference on Heterogeneous Networing for Qulity, Relibility, Security nd Robustness; the 0 Interntionl Conference on Wireless Communictions nd Signl Processing; nd the 0 IEEE Globl Telecommunictions Conference.