Downlink Power Allocation for CoMP-NOMA in Multi-Cell Networks

Transcription

1 Downn Power Aocaton for CoMP-NOMA n Mut-Ce Networs Md Shpon A, Eram Hossan, Arafat A-Dwe, and Dong In Km arxv: v [eess.sp] 6 Dec 207 Abstract Ths wor consders the probem of dynamc power aocaton n the downn of mut-ce networs, where each ce utzes non-orthogona mutpe access NOMA-based resource aocaton. Aso, coordnated mut-pont CoMP transmsson s utzed among mutpe ces to serve users experencng severe nter-ce nterference ICI. More specfcay, we consder a two-ter heterogeneous networ HetNet consstng of a hgh-power macro ce underad wth mutpe ow-power sma ces each of whch uses the same resource boc. Under ths CoMP-NOMA framewor, CoMP transmsson s apped to a user experencng hgh channe gan wth mutpe base statons BSs/ces, whe NOMA s utzed to schedue CoMP and non-comp users over the same transmsson resources,.e., tme, spectrum and space. Dfferent CoMP-NOMA modes are dscussed, but focus s prmary on the jont transmsson CoMP-NOMA JT-CoMP-NOMA mode. For the JT-CoMP-NOMA mode, an optma jont power aocaton probem s formuated and the souton s derved for each CoMP-set consstng of mutpe cooperatng BSs.e., CoMP BSs. To overcome the substanta computatona compexty of the jont power optmzaton approach, we propose a dstrbuted power optmzaton probem at each cooperatng BS whose optma souton s ndependent of the souton of other coordnatng BSs. The vadty of the dstrbuted souton for the jont power optmzaton probem s provded and numerca performance evauaton s carred out for the proposed CoMP- NOMA modes ncudng JT-CoMP-NOMA and coordnated schedung CoMP-NOMA CS-CoMP-NOMA. The obtaned resuts revea sgnfcant gans n spectra and energy effcency n comparson wth conventona CoMPorthogona mutpe access CoMP-OMA systems. Index Terms Non-orthogona mutpe access NOMA, coordnated mut-pont CoMP transmsson, mut-ce downn transsson, heterogeneous networs HetNets, dynamc power aocaton, spectra effcency, energy effcency. M. S. A and E. Hossan are wth the Department of Eectrca and Computer Engneerng at Unversty of Mantoba, Canada emas: ams@myumantoba.ca, eram.hossan@umantoba.ca. A. A-Dwe s wth Eectrca and Computer Engneerng Department, Khafa Unversty, UAE ema: arafat.dwe@ustar.ac.ae. D. I. Km s wth the Schoo of Informaton and Communcaton Engneerng at Sungyunwan Unversty SKKU, Korea ema: dm@su.ac.r.

2 2 I. INTRODUCTION A. Premnares Due to ts potenta to sgnfcanty enhance the rado spectra effcency, non-orthogona mutpe access NOMA s consdered as a promsng mutpe access technoogy for ffth generaton 5G and beyond 5G B5G ceuar systems []-[8]. The fundamenta dea of NOMA s to smutaneousy serve mutpe users over the same transmsson resources,.e., tme, spectrum and space, at the expense of nter-user nterference. Athough severa NOMA technques have been actvey nvestgated over the ast few years, majorty of the efforts have been focused on power-doman NOMA [6], [7], whch expots sgna power dversty for each NOMA user at each NOMA recever end. In a downn transmsson under powerdoman NOMA, a base staton BS transmtter schedues mutpe users to use the same transmsson resources by superposng ther sgnas n the power doman. The superposton s performed n such a way that each NOMA user can successfuy decode the desred sgna by appyng successve nterference canceaton SIC technque at the correspondng recever. In ths paper, we consder power-doman NOMA and thus the term NOMA w refer to power-doman NOMA, uness t s mentoned otherwse. To maxmze the sum-rate for downn transmsson wth NOMA, BS power aocaton enabes the NOMA users to perform SIC accordng to the ascendng order of ther channe gans [8]. That s, pror to decodng the desred sgna, each NOMA user w cance sgnas of other NOMA users wth ower channe gans than the consdered NOMA user. Wthn the same NOMA custer, a NOMA user wth hgher channe gan s sad to have a hgher SIC order compared to a NOMA user wth ower channe gan. The sgnas for other NOMA users wth hgher channe gans than the consdered user w act as nter-noma-user nterference INUI. As a resut, a ce-edge NOMA user generay experences INUI due to sgnas for the ce-center users. Snce wth downn transmsson a NOMA user experences the desred sgna and the INUI sgna over the same wreess channe, the correspondng sgna-to-nterference pus nose rato SINR depends on the transmt power aocated to a partcuar user n comparson wth the sum of transmt powers aocated to the other NOMA users wth hgher SIC orderng [8]. In a mut-ce networ, co-channe downn transmssons to ce-edge users strongy nterfere wth each other, whch may resut n ow receved SINR for ce-edge users. The nterference coud be more severe n a mut-ce heterogeneous networ HetNet scenaros. In a co-channe HetNet, nterce nterference ICI generated from a hgh power macro ce serousy affects on the SINR performance of the underad ow power sma ces, whch may mae tradtona NOMA appcaton neffcent for HetNets. Therefore, advanced ICI management w be cruca for mut-ce downn NOMA systems. To mtgate ICI for tradtona downn orthogona mutpe access OMA-based 4G ceuar systems,

3 3 thrd generaton partnershp project 3GPP has adopted coordnated mut-pont CoMP transmsson technque n whch mutpe ces coordnatey schedue/transmt to the ICI-prone users [9]. In ths paper, we focus on the appcaton of CoMP to NOMA-based mut-ce downn transmssons n a two-ter HetNets n order to mprove the networ spectra effcency. B. Termnooges and Assumptons In ths paper, we consder snge BS at each ce.e., no ce sectorzaton and thus the terms CoMP-BS and CoMP-ce are used nterchangeaby. A CoMP-set defnes the set of ces/bss whch cooperate/coordnate to serve a user, where each coordnatng ce/bs s defned as a CoMP-ce/CoMP- BS. The term CoMP-user refers to a user whose desred sgna s transmtted after coordnaton among CoMP-BSs beongng to a partcuar CoMP-set, whe a non-comp-user refers to a user whose desred sgna s transmtted by ony one BS wthout coordnaton wth other BSs. The term CoMP-NOMA s used to ndcate the appcaton of CoMP n a NOMA system n whch a CoMP-BS forms a NOMA custer by ncudng both CoMP-users and non-comp-users, accordng to the apped CoMP scheme. In addton, custer-head of a partcuar NOMA custer defnes a user who can cance a INUI due to other users n the consdered NOMA custer. For mut-ce downn transmsson, a two-ter HetNet s consdered wth fu frequency reuse where one macro ce s underad wth severa sma ces.e., a ces use same resource boc. The mathematca dervatons and correspondng numerca anayss performed n ths paper consder a partcuar resource boc consstng of tme and spectrum resource, e.g., resource boc n an LTE system. A Rayegh fadng rado channe s consdered where fadng gan s assumed to be fat over a consdered NOMA resource boc. Snge transmt and receve antennas are consdered at both user and BS ends. NOMA custers wthn each ce use orthogona resource bocs.e., no nter-noma-custer nterference wthn a snge ce. In the NOMA custers served by dfferent CoMP-BSs wthn a CoMP-set, a common CoMP-user s served by the CoMP-BSs usng the same resource bocs. C. Exstng Research on CoMP-NOMA In spte of tremendous research nterests n NOMA, very few exstng wors nvestgate NOMA n mut-ce networs. Here, we brefy revew the exstng research on resource aocaton and ICI mtgaton/modeng n downn mut-ce NOMA networs. In [], the outage probabty and achevabe data rates are derved for upn and downn NOMA n a mut-ce homogeneous networ. A jont probem for spectrum aocaton and power contro s formuated n [2] for downn n HetNets, where a many-to-one matchng game s utzed for spectrum aocaton and a non-convex optmzaton probem s

4 4 formuated for power contro. In [3], under a partcuar rate constrant, the authors formuate a dstrbuted optmzaton approach for sum transmt power mnmzaton among a number of BSs n a downn mutce networ. By utzng CoMP technoogy among mutpe ces, a downn CoMP-NOMA mode s studed n [4]. The authors dscuss the appcaton of varous CoMP schemes n a mut-ce homogeneous networ n whch each ce utzes 2-user NOMA for downn transmsson. In [5], Aamout code s utzed for jont downn transmsson to a ce-edge user under a CoMP framewor consstng of two ces n a homogeneous networ. In [5], a CoMP-user forms a NOMA custer wth a non-comp-user,.e., forms 2-user NOMA custers at each coordnatng ce. Aso, an appcaton of NOMA n a downn CoMP transmsson scenaro can be found n [6], where NOMA s opportunstcay used for a group of ce-edge users recevng CoMP transmsson from mutpe coordnatng ces. The authors derve the outage probabty for the proposed opportunstc NOMA system by consderng a jont mut-ce power aocaton among the CoMP-users. The authors n [7] aso study a CoMP-NOMA system for downn transmsson and propose a suboptma schedung strategy for NOMA users under CoMP transmsson. In [8], a downn CoMP- NOMA system s utzed for the purpose of reayng a sgna to a remote user who s unabe to receve drect transmsson from any coordnatng ce. The authors derve the outage probabty for ther proposed CoMP-NOMA system by consderng a fxed power aocaton strategy. In [9], dynamc power contro s used for mut-ce downn NOMA for sum-power mnmzaton and sum-rate maxmzaton. The authors consder CoMP transmssons from the ces n a homogeneous networ, where each ce consders two users n each NOMA custer. On the other hand, by utzng massve mutpe-nput mutpe-output MIMO-enhanced macro ce and NOMA-enhanced sma ce, a hybrd HetNet system s studed n [20], where the authors derve the coverage probabty of NOMA-enhanced sma ces under the mpact of MIMO-enabed macro ce. The probem of resource aocaton and sum-rate optmzaton for NOMA n a downn mut-ce MIMO networ are nvestgated n [2]-[23]. D. Motvaton and Key Contrbutons Athough dynamc power aocaton s crtca to acheve performance gan n a NOMA system, most of the extng research on CoMP-NOMA consders fxed power aocaton strateges and/or snge-ce scenaros. Moreover, to be usefu for practca scenaros, performance modeng, anayss and optmzaton of NOMA shoud consder mut-ce scenaros ncudng HetNets. Snce the performance of a mut-ce networ s prone to ICI, appcaton of CoMP woud be hghy desrabe, partcuary when NOMA s used. Motvated by these, we nvestgate the dynamc power aocaton probem for sum-rate maxmzaton

5 5 n downn CoMP-NOMA n a mut-ce scenaros under mnmum rate constrants for users n a NOMA custer. In the proposed CoMP-NOMA mode, each BS can form a NOMA custer by ncudng one/mutpe CoMP-users and one/mutpe non-comp-users. The system categorzes users nto CoMP-user and non- CoMP-user accordng to ther receved SINR. The CoMP-set s determned for each CoMP-user whch n turn yeds the number of CoMP-users n each CoMP-set. Wthn a CoMP-set, each coordnatng ce,.e., a CoMP-ce, forms NOMA custer consstng of ther non-comp-users and CoMP-users, based on the apped CoMP scheme. After formng NOMA custers, dynamc power aocaton s performed for each NOMA custer at each CoMP-ce. Fg. demonstrates the proposed CoMP-NOMA mode for a mut-ce two-ter HetNet scenaro consstng of one hgh power macro base staton MBS, whch s denoted as an enb n LTE termnoogy, underad by two ow power sma ce base statons SBSs. The fgure shows two CoMP-sets: one 3-BS CoMP-set and one 2-BS CoMP-set. In the 3-BS CoMP-set, UE,m, UE,s, and UE,s2 are the non-compuser equpment UE served ony by MBS, SBS- and SBS-2, respectvey, wthout any coordnaton among the CoMP-BSs, whe CoMP-UEs UE,mss2 and UE 2,mss2 are served by a three CoMP-BSs n a coordnated manner. Smary, n the 2-BS CoMP-set, UE 2,m and UE 2,s are the non-comp-ues served ony by enb and SBS-, respectvey, whe CoMP-UE UE,ms s served by both the CoMP-BSs,.e., enb and SBS-. Note that Fg. demonstrates the jont transmsson JT-CoMP-NOMA scenaro where the CoMP-UEs receve mutpe transmssons from the CoMP-BSs. However, sgna transmssons to a CoMP-UE depends on the apped CoMP scheme whch w be dscussed n deta n Secton III. In [24], we presented the concept of downn CoMP-NOMA n a homogeneous mut-ce networ scenaro. The ey contrbutons of ths paper can be summarzed as foows: Formuate a convex power optmzaton probem for sum-rate maxmzaton n a snge-ce downn NOMA system under constraned mnmum rate requrements for users n a NOMA custer and dscuss the necessary condtons for goba optmaty. Ths serves as a bass to formuate and sove the power aocaton probem for CoMP-NOMA n a mut-ce/hetnet scenaros. Provde a nove system and sgna mode for downn CoMP-NOMA n a mut-ce networ a two-ter HetNet scenaro n partcuar. We derve the achevabe rate formuas for CoMP-UEs and non-comp-ues consderng 2-ce and 3-ce CoMP-sets. A jont power optmzaton probem across mutpe ces s formuated for CoMP-NOMA sumrate maxmzaton consderng both 2-ce and 3-ce CoMP-sets. The souton of the jont power Throughout the paper, we w use the terms user and UE nterchangeaby.

6 6 NOMA custer non-comp-user MBS UE 2,m UE,m UE,ms UE 2,mss2 UE 2,s SBS UE,s UE,s2 UE,mss2 CoMP-user SBS 2 Fg.. An ustraton of the proposed downn JT-CoMP-NOMA mode n a two-ter HetNet. optmzaton probem s aso provded. A ow-compexty dstrbuted power optmzaton approach for each CoMP-ce s presented, whch avods the hgh computatona compexty of the jont power optmzaton probem nvovng a the CoMP-ces beongng to a CoMP-set. Fnay, provde a comprehensve performance evauaton of the proposed CoMP-NOMA system. Numerca resuts demonstrate the gan n spectra and energy effcency due to the proposed CoMP- NOMA mode n comparson wth tradtona CoMP-OMA systems. E. Paper Organzaton The rest of the paper s organzed as foows: Secton II presents the power optmzaton probem formuaton and souton for the downn n a snge-ce NOMA system. Secton III dscusses varous CoMP schemes and ther appcabty n the downn of NOMA-based mut-ce networs. Aso, t presents the system mode, assumptons and achevabe rate formua for the proposed downn JT- CoMP-NOMA mode n a two-ter HetNet. The jont and dstrbuted power optmzaton approaches for the proposed downn JT-CoMP-NOMA mode are presented n Sectons IV and V, respectvey. Secton VI provdes the necessary condtons to vadate the dstrbuted souton for the jont power optmzaton probem and aso provdes nsghts nto the energy effcency performance of CoMP-NOMA system. Secton VII evauates the performance of the proposed soutons numercay. Fnay, Secton VIII concudes the paper.

7 7 II. OPTIMAL POWER ALLOCATION FOR SINGLE-CELL DOWNLINK NOMA Consder a snge-ce networ.e., no ICI wth M 2 users havng dstnct channe gans whch form an M-user NOMA custer for downn transmsson. Aso, assume that the SIC orderng for ths NOMA custer foows the users ndces,.e., sgna for UE s decoded frst, sgna for UE 2 s decoded second, and so on. Thus, UE can decode ts desred sgna by treatng a other users sgnas as nterference.e., INUI, whe UE M can decode ts desred sgna after canceng a INUI sgnas by appyng SIC technques. In such a downn NOMA custer, the achevabe rate for any user can be wrtten as foows: R = B og 2 + M j=+ p γ, =, 2,, M p j γ + where γ denotes channe power gan at the recever wth a normazed nose power for user, and p denotes the transmsson power for user. The rado channe s assumed to be fat fadng Rayegh channe over NOMA bandwdth B for each resource boc. For successfu SIC operaton at the recever ends, the necessary condtons for power aocaton are: p γ M j=+ p j γ θ, =,2,,M =,+,,M. 2 The term θ denotes the mnmum dfference between the decoded sgna power and the non-decoded INUI sgna pus nose power [8]. Ths mnmum dfference s requred to decode a NOMA user s sgna n the presence of sgnas pus nose for other NOMA users wth hgher SIC orderng 2. To maxmze the sum-rate n a NOMA custer, the SIC orderng needs to foow the ascendng order of the NOMA users channe gans. That s, the aforementoned SIC orderng w provde maxmum sum-rate f the channe gans for the NOMA users are as foows: γ M > γ M > > γ. In such an optma scenaro, the SIC constrants n 2 coud be smpfed as [8] n p γ p j γ θ, =, 2,, M. 3 j=+ It s worth notng that, for an M-user NOMA wth any partcuar SIC orderng, the number of SIC constrants w be reduced to exacty M, and t can be smpfed by foowng a procedure smar to [8, eq. 5]. 2 User havng a hgher SIC order than user j means that user can cance INUI from user j before decodng the desred sgna, whe user j cannot cance INUI from user.

8 8 Now, the power optmzaton probem for sum-rate maxmzaton over unt NOMA bandwdth n an M-user downn NOMA havng channe gans γ M > γ M > > γ can be formuated as foows: subject to: C : max p M p p t = C2 : og 2 + C3 : p γ + M og 2 + = M j=+ M j=+ M j=+ p γ p j γ + p γ R, =, 2,, M p j γ + p j γ + θ, =, 2,, M where C and C3 represent NOMA power budget and SIC constrants, respectvey, whe C2 represents the constrant on each NOMA user s rate requrement. In ths paper, each NOMA user s mnmum rate requrement s consdered to be equa to ther achevabe rate n an OMA system. For exampe, n the case of equa spectrum and power aocaton among M users n an OMA system, R = B M og 2 +pt γ, =, 2,, M. Lemma. For an M-user M 2 downn NOMA system wth ascendng channe gan-based SIC orderng, the sum-rate s a strcty concave functon of the transmt powers for NOMA users. 4 Proof. See Appendx A. Lemma 2. A the constrants n downn NOMA sum-rate maxmzaton probem formuated n 4 are convex/concave functon of the transmt powers for NOMA users. Proof. For an M-user downn NOMA sum-rate maxmzaton probem, there are 2M constrants: one constrant for the power budget C, M constrants for the SIC C3, and M other constrants for the rate requrements of M NOMA users C2. In the optmzaton probem n 4, the power budget constrant C and the SIC constrants C3 a are affne functons of NOMA users power aocaton, and thus they are convex/concave. In the foowng, we prove that the constrants C2 are aso convex/concave functon of NOMA users power aocaton.

9 9 Consder the rate constrant for user as foows: og 2 + p γ M R, =, 2,, M. 5 p j γ + j=+ By ettng ζ = 2 R, 5 can be wrtten as M p γ ζ p j γ ζ 0 6 j=+ whch s an affne functon of p = [p, p 2,, p M ] T. Because a NOMA users rate requrements foow a smar form, then they are a affne functons,.e., convex/concave functon of p. Accordng to Lemma and Lemma 2, the sum-rate maxmzaton probem n 4 s a convex optmzaton probem. Aso, Lemma 2 ndcates that a the nequaty constrants are affne, and therefore, the Sater s condton hods [25, p. 227]. Therefore, accordng to Sater s theorem, the KKT condtons are both necessary and suffcent for the optma souton to the probem formuated n 4. Hence, the cosed-form soutons for the downn NOMA proposed n [8] w be the goba optma souton for the probem n 4. III. DOWNLINK COMP-NOMA IN A TWO-TIER HETNET Ths secton dscusses the appcaton of varous CoMP schemes n downn NOMA and provde power aocaton strategy for each COMP-NOMA mode for downn transmsson n a two-ter HetNet. Then, the focus w be on the jont transmsson CoMP-NOMA JT-CoMP-NOMA downn mode and present the achevabe rate formuas. Athough the anayss s carred out for HetNets, t s aso vad for homogeneous networs. A. CoMP-NOMA n Mut-ce Downn Networs In [24], dfferent CoMP-NOMA modes for mut-ce networs are dscussed. A ey observaton from [24] s that the power aocaton for coordnated schedung CoMP-NOMA CS-CoMP-NOMA system n downn transmsson s exacty the same as the power aocaton n snge-ce NOMA, when the NOMA custers n dfferent CoMP-ces, whch beong to a CoMP-set, utze dfferent resource bocs. In downn CS-CoMP-NOMA, a CoMP-UE receves transmsson from ony one CoMP-BS n a channe whch s orthogona to other channes where the other CoMP users receve transmssons from other CoMP-BSs beongng to the same CoMP-set. Thus, under downn CS-CoMP-NOMA transmsson, the

10 0 NOMA custers do not experence ICI, and hence, power aocaton n downn CS-CoMP-NOMA s smar to that n a snge-ce NOMA system as presented n Secton II. The downn transmsson for dynamc pont seecton DPS-CoMP scheme s smar to that under CS-CoMP scheme except that the former requres the CoMP UEs data to be avaabe at each CoMP-BS. Both schemes seect one CoMP-BS to transmt to a CoMP-UE at a tme nstant whe other CoMP-BSs beongng to the same CoMP-set does not use that spectrum [9]. Thus, at each schedung tme nterva, the power aocaton for downn DPS-CoMP NOMA s aso same as the power aocaton for snge-ce NOMA. It s aso noted that, under CS-CoMP/DPS-CoMP scheme, a CoMP-BS whch does not transmt to a CoMP-UE, may use the same spectrum to serve a ce-center user wth a ow power to mnmze ICI. Due to the possbe nfeasbty of MIMO precodng and/or decodng, coordnated beamformng CB-CoMP scheme s usuay not appcabe to downn NOMA systems [24]. On the contrary to the other CoMP schemes, jont transmsson JT-CoMP scheme enabes mutpe CoMP-BSs to transmt to a snge CoMP-user smutaneousy, and thus the power aocaton n JT-CoMP- NOMA s dfferent from that n snge-ce NOMA. In the foowng sectons, we w focus on the dynamc power aocaton for JT-CoMP-NOMA n mut-ce downn HetNets scenaros. B. JT-CoMP NOMA System Mode Consder a HetNet consstng of a snge hgh power enb underad by X ow transmt power SBSs from the set X = {, 2,, X}. For downn transmsson n ths HetNet, each BS uses NOMA to schedue ts users, whe JT-CoMP transmsson by mutpe CoMP-BSs s apped to serve ICI-prone CoMP-users. We aso assume that the number of coordnatng BSs s no more than three. Therefore, the number of 2-BS CoMP-set Y = X and the number of 3-BS CoMP-set Z X 2. It s aso assumed that Y = {, 2,, Y } s the set of 2-ce CoMP-set, and Z = {, 2,, Z} s the set of three-ce CoMP-set. Based on the receved SINR, users are categorzed nto the foowng sets: set of non-comp-ues served by the enb, denoted as U M = {, 2,, U M }; set of non-comp-ues served by the x-th SBS, denoted as U SX = {, 2,, U Sx }; set of CoMP-UEs under a 2-BS CoMP-set formed by the enb and the x-th SBS, denoted as U MSX = {, 2,, U MSx }; and set of CoMP-UEs under a 3-BS CoMP-set formed by the enb, x-th SBS, and x -th SBS, denoted as U MSX S X = {, 2,, U MSxSx }, x x. Under ths JT-CoMP-NOMA mode, a CoMP-UE receves mutpe transmssons from the CoMP-BSs beongng to a CoMP-set and forms dstnct NOMA custers wth non-comp-ues served by each of these CoMP-BSs of the consdered CoMP-set. On the other hand, a non-comp-ue receves her desred sgna ony from the BS t s assocated wth, whch can be a member of ony one NOMA custer. It s

11 worth notng that each CoMP-UE smutaneousy forms dfferent NOMA custers at mutpe CoMP-ces beongng to a CoMP-set, and hence, ts SIC orderng at each NOMA custer shoud foow Lemma 3. Lemma 3. The SIC orderng for a CoMP-user w be same n a NOMA custers formed at each CoMPce of a CoMP-set. Proof. See [24, p. 3]. In the proposed CoMP-NOMA mode, each NOMA custer must ncude at east one non-comp-ue and the SIC orderng for the non-comp-ues w be foowed by the SIC orderng for the CoMP-UEs,.e., each non-comp-ue can cance INUI due to the CoMP-UEs whe none of the CoMP-UE can cance INUI due to the non-comp-ues. Ths SIC orderng for CoMP-UEs s due to ther ocatons at the ce-edge area and hence ow channe gan. Note that ths SIC orderng aso reduces the overhead of SIC sgnfcanty when compared to the opposte SIC orderng [24]. In addton, we adopt the downn NOMA system proposed n [8] where the users are ntay grouped nto custers and then dynamc power aocaton s performed for each NOMA custer. For the sae of smpcty, we assume that a CoMP-UEs n a partcuar CoMP-set w be grouped nto a snge NOMA custer formed at each CoMP-ce. Aso, the mnmum number of NOMA custers n a partcuar ce/bs s assumed to be equa to the number of CoMP-sets n whch the consdered BS s a member. In the foowng, the dynamc power aocaton method s presented for our proposed CoMP-NOMA mode consderng a partcuar CoMP-set. C. Achevabe Data Rate n JT-CoMP-NOMA System Consder a partcuar 2-BS CoMP-set y Y, where the number of non-comp-ues n the MBS and SBS x are Φ y,m and Φ y,sx, respectvey, and the number of CoMP-UEs s Φ y,msx. Wthn ths y-th 2- BS CoMP-set, the set of non-comp-ues {,, Φ y,m } n the MBS, the set of non-comp-ues j {,, Φ y,sx } n the x-th SBS, and the set of CoMP-UEs {,, Φ y,msx } a are assumed to foow SIC orderng accordng to ther subscrpts. For the non-comp-ues at each ce, the subscrpts foow the ascendng order of ther channe gans wth ther respectve servng BS. On the other hand, for the CoMP-UEs, ther subscrpts may not foow the ascendng order of ther channe gans wth any partcuar CoMP-BS.

12 2 Under the above assumptons, the achevabe rate over unt resource boc for non-comp-ue, whch s n CoMP-set y and served by the enb, can be expressed as where γ m and γ sx R = og 2 + Φ y,m =+ p m γ m + p m γ m p sx j γ sx + represent -th non-comp-ue s channe gan wth enb desred channe and SBS x ICI channe, respectvey. The term p m denotes the downn transmt power aocated by the enb for the non-comp-ue.e., transmt power for the desred sgna, Φ y,m =+ pn represents the downn transmt power for other non-comp-ues served by the enb who are n the same NOMA custer as user but has hgher SIC orderng than user.e., transmt power correspondng to INUI sgna. Aso, p sx j = Φ y,sx j= p j represents the downn transmt power for non-comp-ues n SBS x whch form dfferent NOMA custers wth the common CoMP-UEs n the same NOMA custer as user.e., transmt power for ICI sgna. Over the same unt resource boc used n 7, the achevabe rate for a non-comp-ue j n SBS x can be expressed as where γ sx j and γ m j R j = og 2 + Φ y,sx j =j+ p sx j p sx j γ sx j + γ sx j p m γ m j + represent the j-th non-comp-ue s channe gan wth SBS x desred channe and enb ICI channe, respectvey. The term p sx j and Φ y,sx j =j+ psx j are smary defned as for 7, but for non-comp-ue j n SBS x n ths case. Here, p m = Φ y,m = p represents the downn transmt power for non-comp-ues served by the MBS, whch form dfferent NOMA custers wth the common CoMP-UEs n the same custer as user j.e., transmt power for ICI sgna. Aso, over the same unt resource boc used n 7 and 8, the achevabe rate for a CoMP-UE can be expressed as where γ m and γ s R = og 2 + Φ y,msx =+ p T γ + p m p T γ γ m + p sx j γ sx + represent -th CoMP-UE s channe gan wth enb and SBS x, respectvey, and CoMP-UE receves desred sgna over both channes. The term p T γ = p m γ m p sx γ sx represents the desred sgna for CoMP-UE jonty transmtted from both CoMP-BSs enb and SBS x, where

13 3 p = [p m, p sx ] T, γ = [γ m, γ sx ] T and p T ndcates the transpose of p. The term Φ y,msx =+ p γ represents INUI due to other CoMP-UEs of CoMP-set y whch form NOMA custer wth CoMP-UE but have hgher SIC orderng than UE. The terms p sx and p m are smary defned as n 7 and 8, respectvey, but act as INUI from the non-comp-ues of SBS x and MBS, respectvey, whch form dfferent NOMA custers wth CoMP-UE. Note that a CoMP-UE experences INUI from both the CoMP-BSs due to ts ncuson n both the NOMA custers and havng a ower SIC orderng than the non-comp-ues. j IV. SUM-RATE MAXIMIZATION IN JT-COMP NOMA: JOINT POWER OPTIMIZATION APPROACH Consder the same 2-BS CoMP-set y that are consdered n Secton III. Therefore, the number of non- CoMP-UEs served by the enb, non-comp-ues n the x-th SBS, and CoMP-UEs n CoMP-set y are Φ y,m, Φ y,sx and Φ y,msx, respectvey. Aso, assume that p m t and p sx t are the NOMA power budget at the enb and the x-th SBS, respectvey, for CoMP-set y. For CoMP-set y, f R, R j, and R are the rate requrements for non-comp-ue served by the enb, non-comp-ue j n the x-th SBS, and common CoMP-UE, respectvey, then the sum-rate maxmzaton probem for the 2-BS CoMP-set y can be formuated as foows 3 : subject to: C : C2 : Φ y,m = Φ y,sx j= C3 : R R, Φ y,msx p m + = Φ y,msx p sx j + = max p m,p sx p m p sx p m t Φ y,m = p sx t =,, Φ y,msx R + Φ y,sx j= R j + Φ y,msx = R 0 C4 : R R, =,, Φ y,m C5 : R j R j, C6 : p T γ Φ y,msx =+ j =,, Φ y,sx p T γ p m γ m p sx j γ sx θ, { =,,Φy,msx =,,Φ y,msx 3 Note that, smar formuatons can be done for hgher order CoMP-sets such as for 3-BS CoMP-sets.

14 4 C7 : p m γ m C8 : p sx j γ sx + Φy,m p m γ m p + s x j γ sx + θ, =,, Φ y,m =+ j+ Φy,sx j =j+ p sx j γ sx p + m γ m j+ θ, j =,, Φ y,s x where R, R j and R are defned n 7, 8 and 9, respectvey, Aso, the vector p, p, p m, p sx j and γ are defned smary as n 9. The optmzaton varabe vector p m and p sx are defned as p m = [p m,, p m Φ y,m, p m Φ y,m+,, pm Φ y,m+φ y,msx ] T and p sx = [p sx,, p sx Φ y,sx, p sx Φ y,sx +,, psx Φ y,sx +Φ y,msx ] T. Constrants C and C2 represent the power budget for NOMA custer at enb and SBS x, respectvey, under CoMP-set y. Constrants C3, C4, and C5 represent the ndvdua rate requrements for CoMP-UEs, non-comp-ues served by the enb, and non-comp-ues served by the SBS, respectvey, whch form NOMA custers n CoMP-set y. The SIC appcaton requrements for CoMP-UEs and non-comp-ues n CoMP-set y are represented by constrants C6, C7, and C8, respectvey. Snce SIC orderng for the non-comp-ues foows ther ascendng channe gan order, we use SIC constrant 3 for non-comp-ues. On the other hand, the SIC constrant n 2 s used for CoMP-UEs as they may not foow ascendng channe gan order at both the CoMP-BSs smutaneousy. The sum-rate maxmzaton probem for JT-CoMP-NOMA formuated n 0 s a jont optmzaton probem among the CoMP-BSs. Each CoMP-BS needs to sove probem 0 by consderng a the possbe soutons for other CoMP-BSs of the consdered CoMP-set. That s, for each feasbe power aocaton souton at SBS x, the enb maxmzes 0 by optmzng p m under constrants C, C3, C4, C6, and C7. For each feasbe p sx,.e., constant p sx, the optmzaton of p m n 0 s smar to the optmzaton of p n 4, and thus the souton 4 can be obtaned by usng the KKT condtons [8]. On the other hand, SBS x maxmzes 0 by optmzng p sx under constrants C2, C3, C5, C6, and C8, for each feasbe souton at the MBS. In addton, snce the CoMP-UEs SIC orderng may not foow ther ascendng channe gan order, the jont optmzaton shoud be soved for a possbe SIC orderng for the CoMP-UEs. Therefore, sovng the jont power optmzaton probem 0 to obtan the optma souton w ncur substanta computatona compexty. To reduce the compexty, n the foowng secton, we w present a method for dstrbuted power optmzaton at each CoMP-BS whch s ndependent of the power aocatons at other CoMP-BSs. V. DISTRIBUTED POWER ALLOCATION IN JT-COMP NOMA Ths secton provdes a suboptma souton for the optmzaton probem 0 by deveopng another optmzaton probem that can be soved dstrbutvey at each CoMP-BS wthout consderng power 4 Ths souton coud be a goba or oca maxma dependng on the SIC orderng of non-comp-ues and CoMP-UEs.

15 5 aocatons at the other CoMP-BSs. In the proposed souton, each CoMP-BS optmzes ts power aocaton for the NOMA custer wthout consderng ICI and the mpact of CoMP transmsson. However, note that, due to JT-CoMP transmsson, a of the CoMP-BSs smutaneousy transmt the same message sgna to the CoMP-users by usng the power aocaton souton presented n Secton II. Consder the same CoMP-set y that s consdered n Secton IV. In CoMP-set y, the NOMA custer served by the MBS contans Φ y,m non-comp-ues and Φ y,msx CoMP-UEs, and the NOMA custer served by SBS x contans Φ y,sx non-comp-ues and Φ y,msx CoMP-UEs. In CoMP-set y, et Ψ y,m = Φ y,m +Φ y,msx denote the tota number of users n the NOMA custer served by the MBS and Ψ y,sx = Φ y,sx + Φ y,msx denotes the tota number of users n the NOMA custer served by SBS x. For any CoMP-BS n {m, s x } n CoMP-set y, the achevabe rate formua for a NOMA user {, 2,, Ψ y,n } ether a non-comp-ue or a CoMP-UE can be wrtten as where γ n ˆR = og 2 + Ψ y,n =+ p n γ n p n γ n + represents channe gan for NOMA user wth servng BS n. The terms p n and Ψ y,n =+ pn, respectvey, denote the downn transmt power for user.e., transmt power for desred sgna and downn transmt power for other users n BS n whch form NOMA custer wth user but have hgher SIC orderng than user.e., transmt power for INUI sgna. Then, the dstrbuted sum-rate maxmzaton probem for CoMP-BS n {m, s x } can be formuated as subject to: Ĉ : Ψ y,n = p n p n t max p n Ψ y,n = ˆR 2 Ĉ2 : ˆR R, =, 2,, Ψ y,n Ĉ3 : p n γ q n Ψ y,n =+ { p n γ n q θ, =,2,,Ψy,n q=,+,,ψ y,n where Ĉ represents the power budget constrant for NOMA custer at CoMP-BS n, whe Ĉ2 and Ĉ3, respectvey, denote each of the NOMA user s rate requrement and SIC requrement n a NOMA custer at CoMP-BS n whch beongs to CoMP-set y. The optmzaton probem n 2 s exacty the same as the optmzaton probem n 4. Thus, the KKT optmzaton method [8] can be utzed to obtan the optma souton see footnote 2 for the dstrbuted optmzaton approach. Note that, for 3-BS CoMP-sets, the

16 6 dstrbuted power optmzaton approach s the same as 2, but t shoud be soved at each of the three CoMP-BSs. VI. VALIDITY OF THE DISTRIBUTED POWER OPTIMIZATION APPROACH AND INSIGHTS A. Vadty of the DPO Approach for JT-CoMP-NOMA A souton for the dstrbuted power optmzaton DPO approach n 2 w be a feasbe souton for the jont power optmzaton JPO approach n 0 f a the constrants n 2 beong to the feasbe souton regon of 0. Note that, the KKT optmaty mode n [8] can be used to obtan the optma souton for both the JPO and DPO approaches. Accordng to [8], the optma power aocaton souton for a downn NOMA aways provdes the mnmum power to a NOMA users except the custer-head; however, that mnmum power must satsfy each user s rate requrement and the SIC requrement. After satsfyng a the requrements for non-custer-head NOMA users, the rest of the avaabe power budget s aocated to the custer-head. Under ths souton technque, the necessary condtons, under whch a souton obtaned usng the DPO approach w be a feasbe souton for the JPO approach, are as foows: Power Budget Constrant: The NOMA power budget constrant for the DPO approach 2 and the JPO approach 0 are exacty the same, whch can be easy verfed by settng n = m,.e., constrants Ĉ and C are same, and by settng n = s x,.e., constrants Ĉ and C2 are same. Note that Ψ y,n = Φ y,n + Φ y,msx, n {m, s x }. 2 Data Rate and SIC Constrants: In JT-CoMP-NOMA, each CoMP-BS forms a NOMA custer by ncorporatng both CoMP-UEs and non-comp-ues, where the non-comp-ues are dfferent at each CoMP-BS but CoMP-UEs are the same wth smar SIC orderng at each CoMP-BS beongng to a partcuar CoMP-set. The achevabe rate formua for a CoMP-UE and a non-comp-ue are dfferent n the JPO approach 0, whe the achevabe rate formuas for a NOMA users ether CoMP-UE or non-comp-ue are the same n the DPO approach 2. The condtons under whch the NOMA users rate and SIC constrants under the DPO approach 2 w satsfy the respectve constrants under the JPO approach 0 are as foows: If the ICI for non-comp-ues s neggbe, then the non-comp-ues achevabe rate formua under the JPO and DPO approaches are exacty the same,.e., 7 and are smar when the ICI component n 7 s neggbe. If the ICI s not neggbe for non-comp-ues, then wth the DPO approach, the mnmum rate requrement for the non-comp-ues except the custer-head cannot be met. By ntroducng an offset ICI nto the achevabe rate formua for a non-comp-ue under DPO approach, the mnmum rate

17 7 requrement can be easy satsfed. The offset ICI, denoted as În, to a NOMA user for nterferng BS n can be expressed as where γ n set of CoMP-UEs, p n p n t Î n = p n t K p n γ n 3 s the power gan of nterferng channe normazed wth respect to nose power, K s the s the dstrbutvey aocated power to CoMP-UE from CoMP-BS n, and denotes the NOMA power budget at CoMP-BS n. Snce each CoMP-BS ndvduay meets the rate requrement for a common CoMP-UE, t can easy determne În power budget p n t s nown to a CoMP-BSs n. for any CoMP-BS n f the Accordng to Lemma 4 beow, the rate constrant for a CoMP-UE under the DPO approach aways satsfes the constrant under the JPO approach. In a JT-CoMP-NOMA mode, snce the CoMP-UEs receve smutaneous transmssons from a CoMP-BSs, ther correspondng SIC constrants under the DPO approach satsfy the SIC constrants under the JPO approach smar to Lemma 4. For a non-comp-ue, by addng the offset ICI of 3 nto the SIC constrant n 2, the correspondng SIC constrants n 0 can be satsfed. It can be easy verfed by notng the constrants. Lemma 4. The achevabe rate for a CoMP-UE under the DPO approach 2 s hgher than the rate that can be acheved under the JPO approach 0. The data rate of a CoMP-UE under the DPO approach w be exacty equa to that under the JPO approach f the nose power n ther SINR expressons s dvded by the number of CoMP-BSs,.e., f s modfed as ˆR = og 2 + Ψ y,n =+ p n γ n p n γ n + /N where N s the number of CoMP-BS and K s the set of common CoMP-users., K 4 Proof. See Appendx B. Accordng to Lemma 3, the SIC orderng for each CoMP-UE shoud be the same for the dstrbuted power aocaton approach n 2 used at each CoMP-BS. On the other hand, Lemma restrcts the convexty of probem 2 for ony ascendng channe gan-based SIC orderng. Therefore, the optma SIC orderng may not be possbe at a the CoMP-BSs smutaneousy. For maxmum sum-rate across a the CoMP-BSs, a the possbe combnatons of CoMP-UEs channe gan orders shoud be checed exhaustvey. In the secton on numerca resuts, the rate performance of dfferent decodng orders for

18 8 the CoMP-UEs w be nvestgated and we w expan the nsghts generated through the resuts. Note that, at each CoMP-BS, non-comp-ues have a hgher SIC orderng than CoMP-UEs. B. Insghts on Energy Effcency Performance of CoMP-NOMA JT-CoMP s an effectve rate mprovement technque for ICI-prone users n downn OMA systems. Under an OMA system, sgna transmtted to a CoMP-UE by each CoMP-BS does not contan any nterference and thus the resutant SINR sgnfcanty mproves.e., SINR = SNR. On the other hand, wth NOMA, sgna transmtted to a CoMP-UE by each CoMP-BS contans INUI, and thus the resutant SINR may not mprove sgnfcanty. Under dstrbuted power aocaton, Lemma 4 shows that each CoMP-BS ndvduay needs to meet the same rate requrement for each CoMP-UE. In addton, under the JT-CoMP-NOMA mode, a CoMP-UE has a ower SIC orderng. Thus, accordng to the achevabe rate formua n, the SINR for each CoMP-UE n each NOMA custer can be approxmated to the rato of desred transmt power to INUI power gan,.e., f Ψ y,n =+ pn γ n + Ψ y,n =+ pn Ψ y,n =+ p n γ n p n γ n + Ψ y,n pn =+ p n 5 γ n, Φ y,msx. Therefore, the average energy requrement for transmttng each bt coud be sgnfcanty hgh for downn JT-CoMP-NOMA. Wth JT-CoMP-NOMA, snce each CoMP-BS ndvduay meets the rate requrements for CoMP- UEs, we can appy ether DPS-CoMP or CS-CoMP nstead of JT-CoMP to acheve smar rate of JT- CoMP-NOMA. In such a DPS/CS-CoMP scheme, a of the CoMP-BSs use the same resource boc for NOMA custer under a partcuar CoMP-set but ony one CoMP-BS ncudes the CoMP-UEs nto her NOMA custer, whe the others form NOMA custers ncudng ony non-comp-ues. However, under the proposed JT-CoMP-NOMA mode, snce a of the CoMP-BSs use the same resource boc, the CoMP- BSs ony transmttng to the non-comp-ues coud cause sgnfcant nterference to the CoMP-UEs. By controng the transmt power at the CoMP-BSs transmttng ony to non-comp-ues, the nterference caused to the CoMP-UEs under the DPS/SC-CoMP coud be mnmzed. In such a case, the sum-rate under DPS/SC-CoMP-NOMA may decrease to some extent n comparson wth JT-CoMP-NOMA. VII. NUMERICAL ANALYSIS In ths secton, we examne the spectra effcency SE for JT-CoMP-NOMA under the proposed JPO and DPO approaches and aso compare the resuts wth those for JT-CoMP-OMA. We aso examne the energy effcency EE gan for the proposed JT-CoMP-NOMA system over ther OMA counterparts. The

19 9 SE s measured n bts/sec/hz whe EE s measured n Mb/J. The SE and EE for a CoMP-set s taen as a summaton over a the users served by that CoMP-set, whe the SE and EE for a CoMP-BS s taen as a summaton over a the users at the consdered BS. A the numerca resuts are generated usng MATLAB. A. Smuaton Assumptons We consder a fu frequency reuse n a two-ter HetNet consstng of one macroce underad by two partay overapped sma ces, whch s smar to Fg.. Each BS n the correspondng ce s ocated at the center of the correspondng crcuar coverage area. We manuay sove both optmzaton probems,.e., JPO and DPO, and obtan the optma soutons by utzng the KKT optmaty condtons [8]. For JPO, the optma power aocaton s obtaned by searchng ten thousand ponts over the feasbe power range n each CoMP-BS,.e., search step sze s p t /0000. For DPO, we use and 4 to obtan the achevabe data rate for non-comp users and CoMP users, respectvey. In each NOMA custer, we use one/mutpe CoMP-UE but the number of non-comp-ues s restrcted to one, and thus no offset ICI s used under the DPO approach. Note that an offset ICI expressed n 3 needs to be used for a non-comp-ues except the custer-head under the DPO approach. TABLE I SIMULATION PARAMETERS. Parameter Vaue enb to SBS dstance SBS to SBS dstance System effectve bandwdth, B Bandwdth of one resource boc Transmt power budget at enb, p m t Transmt power budget at SBS x, p sx t 0.75 Km 0.30 Km 8.64 MHz 80 Hz 46 dbm 25 dbm Number of antennas at BS/UE end Antenna gan at BS/UE end SIC detecton threshod, θ Recever nose spectra densty densty, N 0 0 db 0 dbm 69 dbm/hz In the smuatons, the wreess channe s assumed to experence ony path-oss. The path-oss for a user at a dstance d Km from BS s modeed as: og 0 d. User categorzaton.e., seecton of CoMP-UE and non-comp-ue and NOMA custerng, whch are done based on the dstances of the users from the dfferent BSs, are assumed to be nown a pror before power aocaton s performed.

20 20 Snce power aocaton s performed n order to mtgate the effects of arge-scae fadng, ony path-oss s consdered. ICI from a BS outsde the CoMP-set s gnored.e., assumed to be part of the nose power. The smuaton parameters are consdered n accordance of the 3GPP standards and the major parameters are shown n Tabe I. The number of resource boc bocs RB s consdered to be equa to the number of users n a NOMA custer. In case of orthogona mutpe access OMA, the transmt power and spectrum RB are assumed to be equay aocated among the OMA users. Note that EE s cacuated by averagng sum-rate over the transmt power. Perfect channe state nformaton CSI s assumed to be avaabe at the BS ends. For convenence, we use the term n:m: to ndcate an JT-CoMP NOMA system consstng of n CoMP-BS a snge enb and n SBS each of whch havng ndvdua NOMA custer of m users and each custer contans common number of CoMP-UEs wth the same SIC orderng at each custer and m non-comp-ues who are dfferent for dfferent NOMA custers. B. Spectra Effcency Performance JT-CoMP NOMA under JPO JT-CoMP NOMA under DPO JT-CoMP OMA JT-CoMP NOMA under JPO JT-CoMP NOMA under DPO JT-CoMP OMA JT-CoMP NOMA under JPO JT-CoMP NOMA under DPO JT-CoMP OMA Spectra effcency bts/s/hz Spectra effcency bts/s/hz Spectra effcency bts/s/hz Dstance for CoMP-user from SBS m a Dstance for SBS custer-head m b Dstance for MBS custer-head m c Fg. 2. Spectra effcency for JT-CoMP-NOMA mode 2:2: and JT-CoMP-OMA: a each non-comp-ue s at a dstance of 50 m from ts servng BS, b non-comp-ue of macroce s at a dstance of 50 m from the enb and the CoMP-UE s at a dstance of 50 m from SBS, c non-comp-ue of SBS s at a dstance of 50 m from SBS and the CoMP-UE s at a dstance of 50 m from SBS. The SE performance of the proposed JT-CoMP-NOMA system s anayzed by smuatng three dfferent JT-CoMP-NOMA modes: 2:2:, 3:2: and 2:3:2, and the correspondng smuaton resuts are shown n Fg. 2, Fg. 3, and Fg. 4. Each ndvdua fgure aso conssts of three dfferent resuts demonstratng SE performance n terms of dstance for CoMP-UE, non-comp-ues served by SBS, and non-comp-ues served by the enb, respectvey n a, b and c. Whe the dstance for a non-comp-ue s measured wth respect to ts servng BS, the dstances of the CoMP-UEs are measured wth respect to the SBS. In

21 JT-CoMP NOMA under JPO JT-CoMP NOMA under DPO JT-CoMP OMA JT-CoMP NOMA under JPO JT-CoMP NOMA under DPO JT-CoMP OMA Spectra effcency bts/s/hz JT-CoMP NOMA under JPO JT-CoMP NOMA under DPO JT-CoMP OMA Spectra effcency bts/s/hz Spectra effcency bts/s/hz Dstance for CoMP-user from SBS- m a Dstance for SBS- custer-head m b Dstance for MBS custer-head m c Fg. 3. Spectra effcency for JT-CoMP-NOMA mode 3:2: and JT-CoMP-OMA system: a each non-comp-ue s at a dstance of 50 m from ts servng BS, b the non-comp-ues of macroce and SBS-2 are at a dstance of 50 m from ther servng BSs, whe the CoMP-UE s at dstance of 50 m from SBS-, c non-comp-ues of SBS- and SBS-2 are at a dstance of 50 m from ther servng BSs, whe the CoMP-UE s at a dstance of 50 m from the SBSs. Spectra effcency bts/s/hz JT-CoMP-NOMA SBS orderng JT-CoMP-NOMA MBS orderng JT-CoMP-OMA Spectra effcency bts/s/hz JT-CoMP-NOMA SBS orderng JT-CoMP-NOMA MBS orderng JT-CoMP-OMA Spectra effcency bts/s/hz JT-CoMP-NOMA SBS orderng JT-CoMP-NOMA MBS orderng JT-CoMP-OMA Dstance for CoMP-user- from SBS m a Dstance for SBS custer-head m b Dstance for MBS custer-head m c Fg. 4. Spectra effcency for JT-CoMP-NOMA mode 2:3:2 and JT-CoMP-OMA system: a each non-comp-ue s at a dstance of 50 m from ts servng BS and CoMP-UE-2 s at a dstance of 50 m from SBS, b non-comp-ue of macroce s at a dstance of 50 m from enb, whe CoMP-UE- s at a dstance of 00 m and CoMP-UE-2 s at a dstance of 50 m from SBS, c non-comp-ue of SBS s at a dstance of 50 m from SBS whe the CoMP-UEs are at dstance as n b. the case of mutpe SBSs n a CoMP-set e.g., 3-BS CoMP-set, SBS- s consdered to determne the dstance for the CoMP-UEs. A three fgures,.e., Fg. 2, Fg. 3, and Fg. 4, demonstrate a sgnfcant mprovement of SE gan for JT-CoMP NOMA systems over ther OMA counterparts. However, f we compare the resuts n Fg. 2a and Fg. 3a, we observe that the range of dstance for CoMP-user whch n turns determnes the range of varaton of CoMP-user s channe power gan to form NOMA custer wth non-comp-user s reduced as the number of BS n a CoMP-set ncreases. As the number of BSs n a CoMP-set ncreases,

22 22 the desred sgna power for CoMP-UE aso ncreases addtvey under JT-CoMP-OMA. On the other hand, for a CoMP-UE under JT-CoMP-NOMA, the desred sgna power and INUI power both addtvey ncrease as the number of BSs n a CoMP-set ncreases. Aso, the data rate for a CoMP-UE n a NOMA custer s proportona to the rato of power aocated to that CoMP-UE and the power aocated to a other NOMA users whch have hgher SIC orderng. Thus, to acheve the same data rate that a CoMP-UE woud acheve wth OMA n Fg. 3a, the transmsson power avaabe for a CoMP-UE n each NOMA custer coud be nsuffcent. Fg. 2b, 3b, 2c and 3c demonstrate a sgnfcanty arge range of non-comp-ue s channe varaton to form NOMA custer wth CoMP-UEs. Ths s because, the non-comp-ue n each NOMA custer s the custer-head and has very hgh channe power gan due to coser dstance to ther servng BS, and thus unt ther channe gans decrease sgnfcanty, they can acheve a hgher data rate even-though they are aocated a sma porton of the transmt power. Fg. 2a and Fg. 3a aso show the performance gap between the proposed JPO approach and the owcompexty DPO approach. It can be found that the performance gap s very sma around the mdde ponts m n Fg. 2a and m n Fg. 3a over the range of CoMP-UEs channe varatons. In JT-CoMP, each CoMP-BS ndvduay needs to meet the rate requrement for the common CoMP-UEs. On the other hand, under the JPO approach, to aocate power to a CoMP-UE, a CoMP-BS consders a the possbe combnatons of NOMA power aocaton used by other CoMP-BSs, and thus obtan goba optma power aocaton over a CoMP-BSs. On the other hand, under the DPO approach, each CoMP-BS ndependenty aocates power to CoMP-UE and non-comp-noma users, and thus obtans a ocay optma power aocaton at each CoMP-BS. However, the resutant SE performance gap s not sgnfcant and t can be consdered as the cost of the compexty reducton of JT-COMP-NOMA. Note that the computatona compexty of the JPO approach s of O2 n, where n and are the number of CoMP-BSs and CoMP-UEs, respectvey, wthn a CoMP-set. Fg. 4 ustrates the SE gan for the proposed JT-CoMP-NOMA mode under DPO approach over JT-CoMP-OMA. Fg. 4a shows that the range for non-comp-ues channe varaton decreases to much ower vaues n comparson wth Fg. 2 a and 3a. Snce two CoMP-UEs are ncuded n each NOMA custer, the rate requrement for CoMP-users may not factate suffcent fexbty for ther channe varaton under JT-CoMP-NOMA. Moreover, as the power budget of enb s sgnfcanty hgher than that of SBS, the CoMP-users SIC orderng accordng to ther ascendng channe gan wth SBS provdes more fexbty for JT-CoMP-NOMA, whch s ndcated n Fg. 4a.

23 JT-CoMP NOMA under DPO CS-CoMP NOMA at SBS CS-CoMP NOMA at MBS JT-CoMP OMA Engergy effcency Mb/J Dstance for MBS custer-head m Fg. 5. Energy effcency for JT-CoMP-NOMA mode 2:2:, correspondng CS-CoMP-NOMA and JT-CoMP-OMA. Non-CoMP-UE of SBS s at a dstance of 50 m from SBS whe the CoMP-UE s at a dstance of 00 m from SBS. Spectra effcency bts/sec/hz JT-CoMP NOMA under DPO CS-CoMP NOMA at SBS CS-CoMP NOMA at MBS JT-CoMP OMA Spectra effcency for CoMP-user bts/sec/hz Dstance for MBS custer-head m a Dstance for MBS custer-head m b Fg. 6. Spectra effcency for JT-CoMP-NOMA mode 2:2:, correspondng CS-CoMP-NOMA and JT-CoMP-OMA. a SE over CoMP-set, b SE for CoMP-UE. Non-CoMP-UE of SBS and CoMP-UE are at a dstance of 50 m, and 50 m, respectvey, from SBS. C. Energy Effcency Performance The EE performance of the proposed CoMP-NOMA system under both JPO and DPO approaches and ts comparson wth the CoMP-OMA system are demonstrated n Fg. 5. As dscussed n Secton VI, under a JT-CoMP NOMA system, a the CoMP-BSs need to ndvduay satsfy the rate requrements for CoMP-users whose SINRs depend on the rato of desred sgna power and INUI power. As a resut, the EE performance gan for JT-CoMP NOMA n Fg. 5 ndex vew does not show sgnfcant mprovement

24 24 over JT-CoMP-OMA. However, n the case of the CS-CoMP-NOMA dscussed n Secton VI.A, the EE gan dramatcay ncreases when the CoMP-user s served by an SBS. The reasons ncude the hgh channe gan for CoMP-UE wth the SBS, ow transmt power budget of an SBS, and hgh transmt power of enb. When the CoMP-UE s served by the SBS, t uses ts fu power budget whe the enb ony uses the mnmum power that t needs to fuf the non-comp-ues mnmum rate requrements. Fg. 6a shows the SE for the proposed CS-CoMP-NOMA CoMP-set n comparson wth JT-CoMP OMA and JT-CoMP-NOMA mode 2:2:. Under CS-CoMP, a the CoMP-BSs except one, whch serves the CoMP-UE, utze power contro, thus the offset ICI n 5 coud not be utzed. As a resut, a ndvdua user s achevabe data rate under CS-JT-CoMP transmsson may not meet the rate requrement that coud be obtaned n JT-CoMP-OMA. In partcuar, a CoMP-UE s date rate decreases as the channe gans for the non-comp-ues served by the enb decease, whch s shown n Fg. 6b. Ths can be ntutvey expaned as foows: as the dstance of a non-comp-ue served by the enb ncreases wth respect to the enb tsef, then the effect of channe gan n the SINR formua decreases and thus the requred amount of transmt power ncreases. Increase n the transmt power for non-comp-ues served by the enb sgnfcanty ncreases ICI to CoMP-UEs and thus the SINR and hence the achevabe data rate decreases. The ICI for non-comp-ues served by the SBS aso ncreases; however, ths mpact can be sma f ts channe gan s suffcenty hgh. VIII. CONCLUSION We have modeed and anayzed the probem of dynamc power aocaton for downn CoMP-NOMA n a two-ter HetNet. For a CoMP-set, we have formuated the optma power aocaton for downn CoMP- NOMA as a jont power optmzaton probem among the coordnatng BSs. Due to the hgh computatona compexty assocated wth the proposed jont power optmzaton approach, a ow-compexty dstrbuted power optmzaton method has been proposed for each coordnatng BS. The optma power aocaton souton for each coordnatng BS under the dstrbuted approach s ndependent of the soutons at other coordnatng BSs. We have aso derved the necessary condtons under whch the dstrbuted power optmzaton souton becomes a vad souton for the jont power optmzaton probem. Fnay, through rgorous numerca anayss, we have demonstrated the gan n spectra effcency for the proposed CoMP- NOMA system n comparson wth ther CoMP-OMA counterparts. The performance gap between the proposed jont power optmzaton and dstrbuted power optmzaton approaches has been consdered as we. Insghts on the energy effcency performance of the proposed CoMP-NOMA modes have been aso dscussed. The proposed dynamc power aocaton mode for CoMP-NOMA n a two-ter HetNet s aso vad for any mut-ce downn system.