QoE-based Resource Allocation for Multi-cell NOMA Networks

Transcription

1 1 QoE-based Resource Allocaion for Muli-cell NOMA Neworks Jingjing Cui, Suden Member, IEEE, Yuanwei Liu, Member, IEEE, Zhiguo Ding, Senior Member, IEEE, Pingzhi Fan, Fellow, IEEE and Arumugam Nallanahan, Fellow, IEEE, Absrac Qualiy of experience (QoE) is an imporan indicaor in he fifh generaion (5G) wireless communicaion sysems. For characerizing user-base saion (BS) associaion, subchannel assignmen and power allocaion, we invesigae he resource allocaion in muli-cell mulicarrier non-orhogonal muliple access (MC-NOMA) neworks. An opimizaion problem is formulaed wih he objecive of maximizing he sum mean opinion score (MOS) of users in he neworks. To solve he challenging mixed ineger programming problem, we firs decompose i ino wo subproblems, which are characerized by combinaional variables and coninuous variables, respecively. For he combinaional subproblem, a hree-dimensional (3D) maching problem is proposed for modelling he relaion among users, BSs and subchannels. A wo-sep approach is proposed o aain a subopimal soluion. For he coninuous power allocaion subproblem, he branch and bound (BB) approach is invoked o obain he opimal soluion. Furhermore, a low complexiy subopimal approach based on successive convex approximaion (SCA) echniques is developed for sriking a good compuaional complexiy-opimaliy radeoff. Simulaion resuls reveal ha: i) he proposed NOMA neworks is capable of ouperforming convenional orhogonal muliple access (OMA) neworks in erms of QoE; and ii) he proposed algorihms for sum-mos maximizaion can achieve significan fairness improvemen agains he sum-rae maximizaion scheme. Index Terms Muli-cell mulicarrier non-orhogonal muliple access (MC-NOMA), qualiy of experience (QoE), resource allocaion, hree-dimensional (3D) maching, he branch and bound (BB) approach. I. INTRODUCTION Mulicarrier ransmission echniques such as orhogonal frequency division muliple access (OFDMA), have been widely adoped in broadband wireless communicaion sysems such as LTE and LTE-Advanced [2]. In convenional mulicarrier sysems, a given radio frequency band is divided ino muliple orhogonal subcarriers and each subcarrier is allocaed o a mos one user o avoid muliuser inerference (MUI). The work of Jingjing Cui and Pingzhi Fan was suppored by he Naional Science Foundaion of China (NSFC, No ), and he 111 Projec (No ). The work of Z. Ding was suppored by he UK EPSRC under gran number EP/L025272/1 and by H2020-MSCA-RISE-2015 under gran number J. Cui and P. Fan are wih he Insiue of Mobile Communicaions, Souhwes Jiaoong Universiy, Chengdu , P. R. China. ( cuijingj@foxmail.com, p.fan@ieee.org). Y. Liu and A. Nallanahan are wih he Deparmen of Informaics, Queen Mary Universiy of London, London E1 4NS, U.K. ( {yuanwei.liu, a.nallanahan}@qmul.ac.uk). Z. Ding is wih he School of Elecrical and Elecronic Engineering, The Universiy of Mancheser, Mancheser, M13 9PL, UK. ( zhiguo.ding@mancheser.ac.uk). Par of his work was presened in IEEE Global Communicaion Conference (GLOBECOM) workshop, Dec. Singapore, 2017 [1]. However, he fifh generaion (5G) wireless communicaion sysem is expeced o provide high daa raes and massive conneciviy o mee he rapid growh of wireless daa services and requiremens. Non-orhogonal muliple access (NOMA) is recognized as a promising candidae ha provides an effecive soluion o address he challenging requiremens of 5G mobile neworks, such as massive conneciviy, high daa speed and low laency [3, 4]. Compared o he convenional orhogonal muliple access (OMA), NOMA allows muliple users complexed in he same orhogonal resources (e.g., ime/frequency) by exploiing superposiion coding in he power domain a ransmiers and successive inerference cancellaion (SIC) echniques a receivers. The advanages behind his approach lies in he fac NOMA can opporunisically explore users channel condiions [5]. Driven by he requiremens of high qualiy video services such as embedded video conens in he webpages, video calls, online TVs, ec, an appropriae level of qualiy of experience (QoE) in 5G mobile neworks is desired. QoE is a subjecive assessmen of media qualiy of users and has recenly become an essenial indicaor in 5G wireless communicaion sysems [6, 7]. Due o he various video characerisics, he users may experience differen QoE even if he daa raes are same, which implies ha effecive QoE-based resource allocaion is essenial o provide beer user saisfacion wih limied radio resources. By aking advanage of NOMA feaures, his paper esablishes he poenial of QoE-based resource allocaion in muli-cell NOMA neworks. A. Relaed Works 1) Sudies on NOMA: Prior research conribuions have sudied he advanages of NOMA over OMA in differen scenarios. In [8], he auhors invesigae he performance of NOMA in a cellular downlink cell wih randomly deployed users. The impac of user pairing on he sum rae performance was sudied in NOMA sysems [5]. Sparked by he characerisics of CR, he applicaion of NOMA in large-scale CR neworks was sudied in [9] wih carefully considering he channel ordering issue. To address he power allocaion problem, a general power allocaion scheme was sudied in [10], which designed he power allocaion based on he channel sae informaion. In [11], he cooperaive NOMA scheme was invesigaed by invoking simulaneous wireless informaion and power ransfer (SWIPT) echnique, where a nearby user is regarded as an energy harvesing relay o assis a disan user. Driven by he parial CSI feedback, a power allocaion sraegy for downlink NOMA sysems based on he

2 2 average CSI was developed in [12] and an opimal decoding order is considered in [13]. In [14], a dynamic user clusering and power allocaion for uplink and downlink NOMA sysems was invesigaed. Regarding he resource allocaion works in mulicarrier NOMA (MC-NOMA), he auhors developed a join subcarrier and power allocaion algorihm in [15], where a near opimal soluion was developed based on Lagrangian dualiy and dynamic programming. In [16], he auhors ook he user-specific rae characerisics, which are calculaed for each subchannel, as he preference and build a many o many maching game wih exernaliies model o solve he user scheduling and subchannel assignmen problem. On he oher hand, for fullduplex MC-NOMA sysems, he auhors in [17] exploied he monoonic opimizaion heory for he power allocaion and user scheduling problem, and an opimal soluion was developed o maximize he weighed sum sysem hroughpu. Furhermore, in [18], he energy efficiency of MC-NOMA was considered, where a low-complexiy subopimal algorihm based on maching heory was developed. 2) Sudies on QoE-based resource allocaion: In [19], a QoE-based evaluaion mehodology is proposed o assess he LTE sysems video capaciy, where he proposed QoE-based radio resource allocaion (RRA) scheme can enhance he video capaciy. The auhors in [20], proposed a user-oriened join subcarrier and power allocaion algorihms for he downlink of a heerogeneous OFDMA sysem, where he bes possible QoE for each user is opimized. Sparked by he game heory, a QoE-oriened sraegy for OFDMA RRA was sudied in [21], where he goal is o achieve he bes possible QoE by search a saisfacory equilibria hrough marke-like resource exchanges. To saisfy he heerogeneous service requiremens in muli-cell OFDMA neworks, a QoE-based proporional fair (PF) scheduling was invesigaed in [22],which considered he nework-wide users QoE maximizaion as well as fairness among users. To miigae he co-iered inerference, a join maching-coaliion game heoreical scheme was proposed o solve a QoE-based mulichannel allocaion problem in heerogeneous cellular neworks in [23]. On he oher hand, in [24], he QoE oriened resource allocaion problem in OFDMA based muli-cell neworks was invesigaed, where he muliple BSs cooperaed for inerference miigaion. In addiion, a game based join specrum sharing, power allocaion and user scheduling approach was developed in [25], where he objecive is o maximize he users saisfacion across he nework for providing beer QoE. B. Moivaions and Conribuions As menioned above, NOMA has received remarkable aenion boh in he world of academia and indusry. However, so far few works consider he resource allocaion for MC-NOMA in muli-cell neworks. Moreover, here is sill a pauciy of research conribuions on invesigaing he QoE issues of NO- MA, which moivaes his reaise. Noe ha he employmen of NOMA on he BS, muliple users can be muliplexed on a specific subchannel, which makes he resource allocaion of MC-NOMA differen from ha of OMA. The moivaion and he challenges of his work is concluded as follows: Muli-cell MC-NOMA is no well invesigaed, especially for he problem boh considering user associaion and resource allocaion. In his reaise, we specifically consider he muli-cell neworks, where he BS cooperaion is performed o reduce he iner-cell inerference. QoE is no considered for NOMA, especially for user- BS cooperaion. Mos exising work addresses fairness issue only by using nework-level crieria like max-min bu neglecs he specific requiremens of individual users. Noe ha he QoE is a user-cenric measure demonsraing he user saisfacion, which has received many aenions from many enerprises and researchers. QoEdriven echniques will bring abou he improvemen of fairness and efficiency, bu i does no add any cos of addiional resource invesmen [24]. Therefore, we model he problem of resource allocaion for MC-NOMA in muli-cell neworks o improve he user QoE insead of hroughpu, which can provide poenial performance gains saisfying he user demands [26]. Specifically, in his paper, we employ BS cooperaion o solve he QoE-based resource allocaion problem in he muli-cell MC-NOMA neworks, which consiss of user-bs associaion, subchannel assignmen and power allocaion. I involves a join opimizaion decision by BSs. Furhermore, in he aggressive frequency reuse deploymen, he co-channel inerference makes he resource allocaion among cells coupled and correlaed. In addiion, he non-convexiy of QoE makes he problem more complicaed. The primary conribuions of his paper are concluded as follows: 1) We invesigae he applicaion-oriened QoE in mulicell MC-NOMA neworks. We use he mean opinion score (MOS) o evaluae he QoE of users. Wih his aim, we formulae he sum MOS maximizaion problem by joinly designing user-bs associaion, subchannel assignmen and power allocaion, which is a combinaorial opimizaion problem. 2) To solve he challenging opimizaion problem, we decompose he join resource allocaion problem ino wo subproblems as : i) he problem of user-bs associaion and subchannel assignmen; and ii) power allocaion opimizaion. We consruc a hree-dimensional (3D) maching problem o model he allocaion among users, BSs and subchannels. Then, we also propose a wo-sep approach by solving wo wo-dimensional (2D) maching subproblems: UE-BS maching problems and (UE,BS)- SC maching problems, which provides a low-complexiy soluion of he user-bs associaion and subchannel assignmen. 3) For he non-convex power allocaion problem, we propose a global opimal power allocaion sraegy based on he branch and bound (BB) approach, which provides an upper bound for power allocaion. Moreover, we also propose a low-complexiy subopimal soluion based on successive convex approximaion (SCA) echniques. 4) We demonsrae ha he proposed low-complexiy soluion by leveraging he maching heory based wo-sep approach and he SCA algorihm is capable of achieving

3 Power 3 User 1 User 2 BS Power User 4 User 6 User 5 User 4 User 3 User 2 User 1 User 3 User 9 User 8 User 7 User 6 User 5 User 4 BS User 3 User 2 User 1 User 9 User 8 User 7 User 5 User 6 Frequency/Time User 7 User 8 Web browsing Audio Video Applicaion Display BS User 9 Fig. 1: An exemplary user-bs associaion and subchannel assignmen in downlink muli-cell NOMA scenarios. a good performance comparing wih he global opimal soluion wih exhausive search and he BB algorihm. Moreover, we demonsrae ha he proposed mulicell MC-NOMA framework ouperforms he convenional muli-cell MC-OMA framework wih he aid of boh of he proposed algorihms. C. Organizaion The res of he paper is organized as follows. In Secion II, we presen nework model consiss of he problem formulaion for he QoE-based resource allocaion. In Secion III, we propose a low complexiy algorihm for user-bs associaion and subchannel assignmen using maching heory. Soluion o power allocaion opimizaion problem is presened in Secion IV, where a global opimal soluion based on BB is provided and a low complexiy power allocaion based SCA are proposed. Simulaion resuls are presened in Secion V, which is followed by conclusions in Secion VI. A. Sysem Descripion II. NETWORK MODEL Consider a muli-cell downlink NOMA ransmission scenario as shown in Fig. 1, where muliple T base saions (BSs) communicae wih K cellular users, denoed by T = {1,, T } and K = {1,, K}, respecively. We assume ha each cell is served by a BS and BSs are emporally synchronized 1. Boh BSs and users equip wih one ransmi and one receive anenna. The enire bandwidh W is pariioned ino N subchannels, each wih W N. The index se of all subchannels is denoed by N = {1,, N}. We consider he universal frequency reuse deploymen in which every cell is available o he whole bandwidh. Invoked by he NOMA proocol, each subchannel can be shared by muliple 1 I is assumed ha a user can be associaed o one BS. If a user can connec o muliple BS simulaneously, hen he BSs can serve he user cooperaively. The cooperaion beween he BSs may furher enhance he sum MOS of he sysem considered, hence our fuure research would consider invesigaing cooperaive muli-cell NOMA sysems. users associaed o he same BS. Considering he deecion complexiy of SIC receiver, we assume ha he maximum number of users allocaed in he n-h subchannel, denoed by SC n, of BS, denoed by BS, is L. Paricularly, inspired by specral aggregaion, we consider ha each cellular user k K, denoed by UE k, can poenially aggregae daa from all available subchannels of he conneced BS. Moreover, we assume ha he BSs cooperae o joinly serve he users where he CSI of he direc link and he cross link channels are available a he BSs. This is employed o design he user scheduling and power allocaion sraegies, which enhances he reliabiliy of daa recepion a each user by exploiing he muliple-base-saion diversiy. In his paper, we consider a quasi-saic channel, ha is he channel condiion remains consan wihin a ime slo and varies independenly from one o anoher. In he following, we inroduce he following ses: Kn, Nk, and T k n denoe he ses of users associaed o BS on SC n, he se of subchannels occupied by UE k associaed o BS and he se of BSs associaed o UE k on SC n, respecively. B. Signal Model Denoe ν,k and ξ n, as he user-bs indicaor and he subchannel-bs indicaor, respecively. ν,k = 1 indicaes he k-user is served by he -h BS, ν,k = 0 if oherwise; ξ n, = 1 indicaes ha he n-h subchannel is allocaed o he -h BS; ξ n, = 0 if oherwise. Noe ha ν,k ξ n, = 1 indicaes UE k is conneced o BS and allocaed wih SC n, and ν,k ξ n, = 0 if oherwise. Thus, he superposiion coded symbol x n o be ransmied a BS on channel n is given by K x n = ν,k ξ n, Pn,k x k,n, (1) k=1 where x n,k is he ransmi signal of BS in SC n, Pn,k is he allocaed power of UE k associaed wih BS on SC n. In SC n, UE k, k K receives inerference from oher users in he same subchannel. As a consequence, he received signals of UE k associaed wih BS on SC n is given by yn,k = fn,kx n + In,k + ηn,k, (2) where η n,k is he addiive whie Gaussian noise (AWGN) a UE k on SC n wih variance σ 2, fn,k is he channel coefficiens beween BS and UE k on SC n. And In,k is he accumulaive inerference o UE k from oher BSs on SC n excep BS, which is given by In,k = T fn,k s P s n x s n, (3) s=1,s and Pn s is he oal power consumpion of BS s on SC n, K Pn s = ν s,k ξ n,spn,k, s (4) k=1 To proceed furher, we inroduce an auxiliary erm g n,k as g n,k = ν,k ξ n,h n,k T s=1,s hs n,k P s n + σ 2, k, j K n, (5) where h n,k = f n,k 2 is he channel gain coefficien and g n,k can be viewed as an equivalen channel gain beween BS and UE k on SC n. In each subchannel, NOMA proocol is invoked. Specifically, consider a pair of wo users (k, j) served by BS, in which UE k wans o decode and remove UE j s signal by SIC on

4 4 SC n, hen he inequaliy holds: gn,k g n,j. In fac, in NOMA, SIC can be carried ou a he users wih sronger equivalen channel gains. Wihou loss of generaliy, i is assumed ha all he channels on SC n of BS follows he order as gn,π(1) g n,π(2) g π( Kn ), where π(k) denoes he k-h decoded user s index and Kn denoes he cardinaliy of Kn. Therefore, UE π(k) firs decodes he messages of all he (k 1) users, and hen successively subracs hese messages o decode is own informaion. Following he principle above, he received signal-o-inerference-plus-noise-raio (SINR) for he k-h decoded user on SC n is given by γ ν,π(k) ξ n,h n,π(k)p n,π(k) n,π(k) = K n ν,π(k) ξ n,h n,π(k) P n,π(i) +. h s n,π(k) P n s + σ 2 i=k+1 s (6) Then we focus on he daa rae of UE on SC n a BS, which is given by Rn,π(k) = W N log ( 1 + γn,π(k)). Hence, he overall daa rae of user k can be compued as T N R k = Rn,π(k). (7) =1 n=1 C. MOS Model for Web Browsing Inspired by he widely used QoE meric, MOS model is used as a measure of he user s QoE for he services like video sreaming, file download, or web browsing. As one of he mos popular applicaion in wireless neworks, we focus on web browsing applicaions in his paper. I maps he subjecive human percepion of qualiy for web browsing applicaions o he objecive merics 2. In [27], he MOS model for web browsing applicaions is defined as follows: MOS web = C 1 ln(d(r web )) + C 2, (8) where R web is he daa rae. MOS web represens he real score ranging from 1 o 5, which reflecs he user perceived qualiy. The higher score means ha he human percepion qualiy is he beer. C 1 and C 2 are consans deermined by analyzing he experimenal resuls of he web browsing applicaions, which are se o be and , respecively. d(r web ) is he delay ime beween a user sen a reques for a web page and he enire web conens displayed. The delay ime depends on muliple facors such as he web page size (e.g. he round rip ime (RTT)) and he effecs of he proocols (e.g., TCP and HTTP). In his paper, we adop TCP and HTTP proocols for he muli-cell NOMA sysems, where he funcion d(r web ) in [28] is modelled as d(r web ) =3RTT + FS R web + L( MSS (9) + RTT) 2MSS(2L 1), R web R web where RTT [s] is he round rip ime, FS [bi] is he web page size and MSS [bi] is he maximum segmen size. The parameer L = min{l 1, L 2 } represens he number of slow sar cycles wih idle periods. L 1 denoes he number of cycles he congesion window akes o reach he bandwidh-delay produc and L 2 is he number of slow sar cycles before he web page size is compleely ransferred, which are defined as follows [28]. ( Rweb RTT ) L 1 = log , and MSS ( FS ) (10) L 2 = log 2 2MSS Noe ha he relaionship beween he daa rae and he QoE for differen applicaions were modelled by differen MOS models [20 22]. The proposed algorihm is capable of being exended o oher applicaions wih necessary modificaions, which we may include in our fuure work. As discussed in [27], he impac of he RTT on he MOS funcion is minor compared o he daa rae and he file size of web pages, especially for shor ranges of RTT. In addiion, as he 3GPP echnical specificaion of he LTE release 8 proposed, i is expeced ha he fuure advanced LTE sysems achieve even lower RTT [29] han he currenly suppored 10 ms. Thus, i is reasonable o assume RTT = 0 ms 3. Based on his assumpion (9) is simplified as d(r web ) = FS R web. Then he mapping for user π(k) from he user daa rae o he MOS funcion can be simplified as ( T = C1 ln N ) + C π(k) 3, (11) MOS π(k) web where C π(k) 3 = C 2 + C 1 ln D. Problem Formulaion R n,π(k) =1 n=1 ) W N FS π(k) ( is a consan. In his secion, we formulae he problem o opimize he cross-layer QoE aware resource allocaion based on designing he user-bs associaion, subchannel assignmen and power allocaion. The opimizaion problem can be expressed as follows: max {{ν,π(k) }, {ξ n, },{P n,π(k) }} U = π(k) K MOS π(k) web (12a) s.. g n,π(k) gn,π(j), k > j, (k, j),, n, (12b) ν,π(k) ξ n,p n,π(k) P,, (12c) π(k) K n N 2 π(k) K ν,π(k) L, ν,π(k) 1,, k, T ξ n, S, ξ n, T n,, n, n N T P n,π(k) 0, π Π, ν,π(k), ξ n, {0, 1}, n, k,, (12d) (12e) (12f) where Π represens he se of oal possible decoding orders. Consrains (12b) is o guaranee ha SIC can be performed successfully for a specific order. (12c) is a power consrain for BS wih he maximum power allowance P. Consrains (12d) is a NOMA muliplexing consrain where L indicaes he maximum number of muliplexed users conneced o BS. Moreover, we consider each each user is capable of connec one BS a each subchannel. Consrains (12e) represen each BS can occupy S subchannels a maximum and each subchannel can be shared by T n BSs a maximum In his paper, we assume ha he NOMA scheme is applied among he users in he same frequency band and ime slo, which has been sudied in [24] and [30]. The use of more sophisicaed reuse schemes may furher enhance he aainable performance of he sysems considered, bu his is beyond he scope of his reaise. In addiion, regarding he case where we allow a BS someimes serves only one user, he muli-cell nework will work in a hybrid muliple access mehod. In his case, he performance of he hybrid nework maybe improved by opimizing resource allocaion. However, he performance opimizaion of he hybrid nework becomes more challenging especially in selecing he muliple access mehod. Our fuure work will invesigae he resource allocaion of he hybrid 3 In his paper, we assume ha he nodes are saic, or slow moving in he considered neworks. Therefore, he channels migh say he same for a quie long ime period, and hence we can use he assumpion ha he channels are quasi-saic such as in [24 27], or someimes ermed block-fading.

5 5 nework, perhaps wih he aid of he resuls derived in his work. The sum MOS opimizaion problem (12) by joinly designing user-bs associaion, subchannel assignmen and power allocaion for a muli-cell NOMA nework is a combinaorial opimizaion ask, which generally yields unaccepable compuaion burden wih brue-force search. Noe ha he opimizaion problem (12) includes he binary opimizaion variables for he user-bs associaion and subchannel assignmen and he coninuous variables for he power allocaion coefficiens. To solve problem (12) effecively, we propose o decompose i ino wo subproblems: 1) he problem of he user-bs associaion and subchannel assignmen and; 2) he problem of power allocaion among users. Fig. 2 gives an overview of he developmen in he paper, paricularly he connecions beween key opimizaion problems and he algorihms. In Fig. 2, he key reformulaed problems and he algorihm sudied in his paper are illusraed in differen boxes: The ones wih solid boundaries are he reformulaed problems, he ones wih doed boundaries are he designed algorihms, and he ones wih rounded recangle are he generaed soluions. Due o he combinaorial feaures of he user-bs associaion, subchannel assignmen, exhausive search provides a sraighforward mehod o find he globally opimal combinaion for a small-scale nework when he power allocaion coefficiens are fixed. In addiion, we propose a low-complexiy maching heory based algorihm which will be discussed in Secion III. Furhermore, when he user- BS associaion, subchannel assignmen are fixed, finding he opimal soluion is sill nonrivial due o he non-convex propery of problem (12) in erms of he power allocaion coefficiens. BB echniques provide an efficien approach o solve he non-convex opimizaion problem [31 33], which moivaes us he applicaion of he BB algorihm o obain he opimal power allocaion coefficiens. Moreover, an lowcomplexiy power allocaion algorihm is also developed o avoid he huge complexiy of he BB algorihm. The proposed opimal and subopimal power allocaion algorihm will be discussed in Secion IV. III. USER-BS ASSOCIATION AND SUBCHANNEL ASSIGNMENT USING 3D MATCHING In his secion, we focus on solving he user-bs associaion and subchannel assignmen problem in (12), which can be expressed as max {ν,k },{ξ n, } K k=1 MOS k web (13) s.. (12d) (12f). Problem (13) is a combinaional opimizaion problem a- mong users, BSs and subchannels. From he poin of he graphical, he muual relaionship among among users, BSs and subchannels can be represened in he lef op par of Fig. 3. To furher presen he relaionship among users, BSs and subchannels, a bi-parie graph based represenaion is shown in he lef boom par of Fig. 3. As illusraed in Fig. 3, UE k is associaed o BS, hey compose an associaion uni (UE k, BS ). When SC n is allocaed o he associaion uni (UE k, BS ), we say UE k, BS and SC n are mached wih Fig. 2: Overview of he proposed approach o he sum MOS maximizaion problem. We obain boh he global opimal and subopimal algorihms. Fig. 3: Graphical expressions of 3D maching among users, BSs and subchannels. each oher, denoed by a maching riple (UE k, BS, SC n ). Nex, we firs inroduce he definiion of 3D maching. Definiion 1. An insance of 3D maching involves hree disjoin finie ses K, T and N, where he cardinaliies are K, T and N, correspondingly, which are he size of he problem insance. A maching riple is denoed by (UE k, BS, SC n ) K T N. A maching is a se of user-bs-subchannel assignmen. I is proved ha 3D maching is NP-hard and here is no polynomial-complexiy algorihm o find he opimal soluion [34]. To solve he challenging problem, we propose a lowcomplexiy subopimal algorihm by decomposing he 3D maching problem ino wo 2D maching subproblems-ue- BS maching problems and (UE,BS)-SC maching problems. Then, we solve he wo subproblems individually as shown in he righ par of Fig. 3. Specifically, he firs subproblem is o selec a served BS for each user o ransmi desired signals,

6 6 which is a many-o-one maching problem beween users and BSs, i.e, muliple users can be served by one BS using he NOMA proocol. Then, subchannel sharing for each BS is considered in he second subproblem, which is a many-omany maching problem beween BSs and subchannels, i.e., one BS o S subchannels and one subchannel o T n BSs. A. Preliminaries for Maching Theory In a 2D maching, here are wo finie and disjoin ses denoed by M = {m 1, m 2,, m n } and W = {w 1, w 2,, w p }, respecively. Each m i M has a preference lis over he se of W In his paper, we build he preferences by he rae raher han he MOS value. Since he MOS value is a user-cenric measure, i canno be calculaed in he formulaed (UE,BS)-SC maching problem for subchannel assignmen. In addiion, in he formulaed user-bs associaion maching problem, he preference buil by he rae value is equivalen o ha based on he MOS value, since a user s MOS value is he logarihm of he user s sum rae over all subchannels. Analogously, each w j W has preferences over M. The individual preferences represen he prioriies of is selecion among differen alernaives. If m i prefers w 1 o w 2, we express i as w 1 mi w 2. In his paper, we assume ha he preference lis of each player has he following properies: 1) complee ordering: each player will never confron wih an indeerminable choice, i.e., any wo alernaives can be compared for an player o ge a preferred one. 2) ransiive: i can be express as if w 1 mi w 2 and w 2 mi w 3 hen w 1 mi w 3. Based on he above descripions, we give he following definiions: Definiion 2. A many-o-many (one) maching ϕ is a funcion from he se M W ino he se of unordered families of elemens of M W {0} such ha 1) ϕ(m) q w for every m M; 2) ϕ(w) = q m for every w W; 3) ϕ(m) W if and only if ϕ(w) M; 4) m = ϕ(w) w = ϕ(m); where q w and q m are posiive ineger quoas. The noaion ϕ has differen meanings depending on he parameer. If he parameer is m, hen ϕ(m) maps o he mached W se. If he parameer is w, hen ϕ(w) gives he se of mached player of M. Noe ha is q w = 1, one can obain he definiion of many-o-one maching. In a many-o-many (one) maching wih exernaliies, i is no sraighforward o define a sabiliy concep because he gains from a maching pair depends on which players he oher agens have. Sparked by he definiion of exchange sable sabiliy, i is convenien o define a swap maching [35]. Specifically, a swap maching is defined as ϕ j i = {ϕ \ {(i, m), (j, n)} {(j, m), (i, n)}}, where ϕ(i) = m and ϕ(j) = n. Based on he swap operaion, we inroduce he wo-sided exchange sabiliy [35] as follows. Definiion 3. A maching ϕ is wo-sided exchange-sable if and only if here does no exis a pair of players (i, j) wih m = ϕ(i) and n = ϕ(j), such ha 1) x {i, j, m, n}, U m (ϕ j i ) U m(ϕ); 2) x {i, j, m, n}, such ha U m (ϕ j i ) > U m(ϕ), hen he swap maching ϕ j i is approved, and (k, j) is called a swap-blocking pair in ϕ. where U m (ϕ) denoes he uiliy for player m under maching ϕ. In general, he pair of players saisfying condiion 1) and condiion 2) is called a swap-blocking pair. The feaures of he swap-blocking pair ensure ha if a swap maching is approved, he achievable raes of any user involved will no decrease and a leas one of he user s rae will increase. Furhermore, he definiion indicaes ha a swap maching is wo-sided exchange-sable when all players are indifferen. B. User-BS Associaion Problem As discussed above, he user-bs associaion problem is a many-o-one maching problem. Due o he inerference in (6), he SINR of user UE n,k over each subchannel is relaed o he se of users sharing wih he same subchannels. Furhermore, each BS no only considers which users o mach wih, bu also ha he inner-relaionship among he subse of users due o he power domain muliplexing. Thus, more specifically, he formulaed user-bs associaion problem is a many-o-one maching problem wih exernaliies. To model he exernaliies, he preference can be formulaed as he rae of each user over all subchannels, where he rae of UE k associaed o BS can be expressed as Pk = log 2 (1 + γn,π(k)). (14) n N Then he preference of BS on a se of users ϕ() can be defined as P = k ϕ()pk. (15) Specifically, for a given UE k, any wo BS and BS, any wo machings ϕ and ϕ, we have he following relaions, (, ϕ) UEk (, ϕ ) Pk(ϕ) > Pk(ϕ ), (16) which indicaes ha UE k prefers BS in ϕ o BS in ϕ only if UE k can achieve a higher rae on BS han BS. Analogously, for any BS, T, is preference over he user se can be described as follows. For any wo subses of users K 1 and K 2 wih K 1 K 2, any wo machings ϕ and ϕ wih K 1 = ϕ() and K 2 = ϕ () are defined as (K 1, ϕ) (K 2, ϕ ) P (ϕ) > P (ϕ ). (17) I implies ha BS prefers he se of users K 1 o K 2 only when BS can ge a higher rae from K 1. Based on he esablished preference liss, we uilize a exend deferred accepance (EDA) based algorihm proposed in [36] o consruc a iniial maching sae beween users and BSs. Then, he swap operaion procedure is employed o furher enhance he uiliy. In he EDA based iniializaion procedure, he BS firs allocaes he ransmi power equally o he users. Hence, he users and he BSs can consruc heir own preference liss based on (16) and (17), respecively. Then each user proposes o he mos preferred BS based on is preference lis. A he BS accepance phase, each BS acceps he users wih prior preferences and rejecs he ohers. The algorihm erminaes when all users are mached o he BSs or every unmached users has been rejeced by every BS.

7 7 C. Subchannel Assignmen As discussed above, he problem o assign subchannels o (UE,BS) unis is a many-o-many maching problem. Due o one subchannel can assign muliple BSs, he rae of each (UE,BS) uni over each subchannel is relaed o he oher BSs sharing wih he same subchannels. Thus, he formulaed subchannel assignmen problem is a many-o-many maching problem wih exernaliies. Similar o Subsecion III-B, we formulae he preference as he sum rae of he users associaed o he BSs on each subchannels. Specifically, he sum rae of users associaed o BS on SC n can be expressed as P n = log 2 (1 + γn,π(k)). (18) k K Analogously, suppose φ and φ are wo differen machings, for a given BS, any wo subchannels SC n and SC n, we have he following relaions, (n, φ) BS (n, φ ) P n (φ) > P n (φ ), (19) which indicaes ha BS prefers SC n in φ o SC n in φ only if BS k can achieve a higher rae on SC n han SC n. For any SC n, n N, is preference over he user se can be described as follows. For any wo subses of BSs T 1 and T 2 wih T 1 T 2, any wo machings φ and φ wih T 1 = φ(n) and T 2 = φ (n) are defined as (T 1, φ) (T 2, φ ) P n (φ) > P n (φ ). (20) I implies ha SC n prefers he se of BSs T 1 o T 2 only when SC n can ge a higher rae from T 1. Now based on he esablished preference liss, an iniial maching sae can be obained by uilizing EDA based algorihm beween (UE,BS) unis and subchannels, where we assume ha he (UE,BS) uni propose o subchannels. Specifically, similar o he process of EDA based user-ba associaion, he subchannels and he (UE,BS) unis can consruc heir own preference liss based on (19) and (20), respecively. Then each (UE,BS) uni proposes o he mos preferred subchannel based on is preference lis. A he subchannel accepance phase, each subchannel acceps he (UE,BS) uni wih prior preferences and rejecs he ohers. The algorihm erminaes when all (UE,BS) unis are mached o he subchannels or every unmached users has been rejeced by every subchannel. Furhermore, we can conclude he complee procedure for solving user-bs associaion and subchannel assignmen problem in Algorihm 1. In Sep-I, user-bs associaion is performed, which consiss of an iniializaion procedure in line 1 and a swap procedure in line 2 o line 9. EDA based algorihm is adoped for he iniializaion procedure. Then, all possible swap operaions beween users and BSs are checked o furher enhance he sysem uiliy. A wo-sided sable maching will be reached beween users and BSs. In Sep- II, he maching beween (UE,BS) unis and subchannels are performed. Similar o Sep-I, he iniializaion algorihm can be realized by EDA based algorihm, where he preference liss for (UE,BS) unis and subchannels are consruced from (18). We assume ha (UE,BS) unis propose o subchannels in he iniializaion algorihm. Then he swap procedure is conduced in line 12 o line 19 o furher improve he uiliies. Algorihm 1 Two-sep Algorihm Based User-BS Associaion and Subchannel Assignmen Sep-I: Many-o-one maching based UE-BS associaion 1: Consruc he iniial UE-BS maching se A by EDA based algorihm. Le A I = A. 2: repea 3: For any user k A I, i searches for anoher user j A I \ A I(ϕ(k)). 4: if k, j is a swap-blocking pair hen 5: ϕ = ϕ j k 6: else 7: Keep he curren maching sae 8: end if 9: unil No swap-blocking pair is found 10: Oupu he sable maching denoed as ϕ I and he corresponding objecive value U 0 = U(ϕ I). Sep-II: Many-o-many maching based SC assignmen 11: Consruc he iniial (UE,BS)-SC maching se A II = A by EDA based algorihm. 12: repea 13: For any (UE,BS) uni A II, i searches for anoher (UE,BS) uni s wih s A II \ A II(ϕ()). Le U = {U 0}. 14: For a given, calculae he candidae U s for he swapping pair (, s). 15: if, s is a swap-blocking pair hen 16: U = U {U s }. 17: end if 18: Keep he swapping-blocking pair wih, s = arg max U s U, hen ϕ = ϕ s. Se U 0 = U s. 19: unil No swap-blocking pair is found. 20: Oupu he sable maching ϕ II. D. Analysis of he Proposed Two-Sep Algorihm 1) Complexiy: The compuaional complexiy of he proposed wo-sep algorihm based user-bs associaion and subchannel assignmen in Algorihm 1 is relied on he wo 2D maching procedures. In he following, we will analyze he compuaional complexiy of each 2D maching procedure. The iniializaion algorihm in Sep-I requires each user o propose o one BSs and each BS can accep muliple users based on is preference lis. Assume ha he wors case ha he proposing number of each user is T. The complexiy is O(KT 2 ). For he swap procedure in Sep-I, here are a mos T L users can perform swap operaion. In each ieraion, for UE k, he maximum swap operaion number is L (T 1), since each user associaes wih one BS. Therefore, a swap operaion for K users in each ieraion is 1 2 KL (T 1). For a given number of oal ieraion V, he complexiy can be presened as O(V KL T ). The iniializaion algorihm in Sep-II requires (UE,BS) unis o propose o muliple subchannels and each subchannel makes a decision o accep muliple (UE,BS) unis based on is preference lis. The wors case ha he proposing number of (UE,BS) uni is N S. The complexiy is O(N 2 T 2 ). For he swap procedure in Sep-II, here are T (UE,BS) unis a N subchannels can perform swap operaion. We consider he wors case ha each (UE,BS) uni occupies S subchannels and each subchannel is shared by T n

8 8 (UE,BS) unis. Therefore, in each ieraion, for (UE, BS) he maximum swap operaion number is S (N S ). In each ieraion, T (UE,BS) unis require a mos 1 2 T T ns (N S ) swap operaions. For a given number of oal ieraion V, he complexiy is approximaed as O(V T T n S N). As a resul, he complexiy of Algorihm 1 can be calculaed as O((K + N 2 )T 2 + (V KL + V T n S N)T ). 2) Sabiliy and Convergence: Afer performing Sep-I in Algorihm 1, any user UE k wih k K canno find anoher BS BS, T o form a swap-blocking pair under he curren maching. Hence, a wo-sided exchange-sable maching is formed beween users and BSs. Then, by performing Sep-II in Algorihm 1 while reaing he mached user and BS as a complee (UE,BS) uni, one can obain a wo-sided exchangesable maching among (UE,BS) unis and subchannels based on Definiion 2. Since he uiliy funcion will increase monoonically by he swap operaion in Algorihm 1 and he uiliy funcion is bounded due o he ransmi power consrain, Algorihm 1 will erminae o a local soluion afer finie swap operaion. Since he formulaed wo 2D maching subproblems are many-wo-one maching wih exernaliies and many-o-many maching wih exernaliies, respecively, he proposed approaches in Sep-I and Sep-II converge o a wo-sided exchange-sable saus [35]. Noe ha no all wosided exchange-sable maching are local opimal. The reason can be given by a simple example for Sep-I: In a wosided exchange-sable saus, here exiss possibiliy ha user k associaed o BS refuses a swap as is uiliy would decrease, bu user j associaed o BS involved will benefi a lo from his swap operaion and he uiliy of BS and BS will increase. In his case, a forced swap will furher increase he oal uiliy compared o an approved swap maching. A similar case also exis for Sep-II. IV. SOLUTIONS FOR POWER ALLOCATION OPTIMIZATION PROBLEM In his secion, we ry o solve he power allocaion problem for given user-bs associaion and subchannel assignmen. In his case, Kn, Nk, and T k n is known o BSs. For noaion simpliciy, we assume ha π(k) = k in he following. We firs propose an opimal power allocaion sraegy based on BB approach. To obain some useful insighs, we derived he opimal power sraegy when he power equally disribued among subchannels. Based on (12), power allocaion opimizaion problem can be formulaed as: max (21a) MOS k {P n,k } web k K s.. g n,k g n,j, k > j, (k, j) K n,, n, (21b) Pn,k P,, n, k, (21c) where P = {Pn,k n N k K P n n,k P, Pn,k 0, n, }, N denoes he se of subchannels allocaed o BS. Noe ha (21b) can be equivalenly expressed as ( ) h n,kh s n,j h n,jh s n,k Pn s s (22) + ( h n,k h n,j) σ 2 0, k > j, (k, j),, n. Though he consrain (22) is linear and hus convex. However, problem (21) is sill non-convex due o he non-convex objecive funcion. A. Opimal Power Allocaion Sraegy Using BB In his subsecion, we ry o solve problem (21) over a M- dimensional simplex, where M = K T N k=1 =1 n=1 ν,kξ n, is he oal number of variables. The key idea of BB approach can be described as follows: 1) ransform he consrain ses ino a muli-dimensional simplex; 2) compue upper and lower bounds. Firs we inroduce a se of variables Γ = {Γ n,k,, n, k} such ha Γ n,k γ n,k in (6). Then, problem (21) can be ransformed as max U(Γ) s.. Γ D, (23) {P n,k }{Γ n,k } where U(Γ) = ( )) k K C 1 ln Tkn N log k 2 (1 + Γ n,k. In addiion, he consrains D is defined as D = { Γ R M Γ n,k γ n,k, k, n,, (21c) & (22) }. (24) Lemma 1. U(Γ) is an monoonically increasing funcion. More specifically, U(Γ) a concave funcion. Proof: See Appendix A. Proposiion 1. Problem (23) have he same opimal soluion o he opimizaion problem in (21). Proof: See Appendix B. Le Γ be he larges possible SINR se. Noe ha U(Γ) (, U( Γ)], where he minimum of U(Γ) is unbounded. To ackle he difficuly, we inroduce a new funcion Ũ(Γ) Ũ(Γ) = ( (C 1 log Γ ) ) n,k, (25) k K T k n N k which such ha Ũ(Γ) [0, Ũ( Γ] and U(Γ) = ln ( Ũ(Γ) ). Then, he ransformaion of problem (23) is max Ũ(Γ) s.. Γ D, (26) {P n,k }{Γ n,k } Problem (26) and problem (23) has he same opimal soluion due o he monooniciy of logarihm funcion. Nex we ry o solve problem (26) using BB algorihm. 1) Consrucion of muli-dimensional simplex S: Le S = [v 1, v 2,, v M+1 ] be an M-simplex in R M saisfying D S. The iniial S should be a simple polyope ighly enclosing D wih a small number of verices. Because he feasible se D in (24) is an recangular wih removing some margins, a simple mehod o consruc S is given as follows S = {Γ R M 0 Γ n,k Γ n,k} (27) wih Γ n,k = h n,k P σ denoing he larges possible SINR for 2 UE k on SC n associaed o BS. The verex se of S is V (S) = {v 1, v 2,, v M+1 } wih v 1 = 0, v j = Γ n,k e j, where e j is he j-h basis vecor of R M. By consrucing he muli-dimensional simplex, problem (23) has been ransformed ino a maximizaion of non-convex funcion U(Γ) over an M-simplex S. 2) Compue lower and upper bounds: To compue lower and upper bound, we firs consruc a bounding funcion, which is defined as { Ũ(Γ), if Γ D, g(γ) = (28) 0, oherwise.

9 9 Noe ha for he feasible se D and he M-simplex S wih D S, we have ψ min(s) = inf g(γ) = inf Ũ(Γ). (29) Γ S Γ D which implies ha he funcion Ũ(Γ) is a lower bound of g(γ). For S = {ˆΓ Γ Γ}, we now have he lower bound and upper bound funcions as { ψ lb (S Ũ( Γ), if ˆΓ D, ) = 0, oherwise. { ψ ub (S Ũ(ˆΓ), if ˆΓ (30) D, ) = 0, oherwise. From he definiion of (28), one can know ha ψ lb (S ) = ψ min (S ) = ψ ub (S ) = 0, if ˆΓ / D. Consequenly, for any S S, we have ψ lb (S ) ψ min (S ) ψ ub (S ). Based on he definiion of lower and upper bounding funcions in (30) and (30), he key sep o compue he bounding funcions is o check ˆΓ D. I can be formulaed as Find {Pn,k} (31a) s.. γn,k ˆΓ n,k, (31b) ( ) s h n,kh s n,j h n,jh s n,k Pn s + ( ) h n,k h n,j σ 2 (31c) 0, k > j, (k, j) Kn,, n, P n,k P, n,, k. (31d) which is a convex problem on power allocaion coefficiens {P n,k }. Proposiion 2. Problem (31) can be ransformed ino a compac marix form as follows: Find p n, n N (32a) s.. A np n b n, H np n θ n, P n,k P, n,, k, (32b) where A n = I (Λ n + D n G n ) and b n = D n σ 2. Proof: See Appendix C. Problem (32) is a linear programming (LP) feasibiliy, which can be described as follows. Define wo ses P 1 = {A n p n b n, P n,k P, n,, k} and P 2 = { H n p n θ n, P n,k P, n,, k}. The disance of he wo ses is defined as dis(p 1, P 2) = inf{ x 1 x 2 x 1 P 1, x 2 P 2}. (33) If he wo ses inersec, he disance is zero. To find he disance beween P 1 and P 2, we can solve he following QP min x 1 x 2 s.. (32b). (34) The opimal value is zero if and only if he wo ses inersec. This problem is infeasible if and only if one of he ses is empy. Oherwise, he problem will reurn he opimal poins x 1 and x 2 in P 1 and P 2, respecively, ha are close o each oher. One can verify ha he marix Λ n + D n G n is irreducible nonnegaive marix. As in [37], a posiive soluion o p n ha saisfies A n p n = b n exiss if and only if he Perron- Frobeniuous eigenvalue of Λ n + D n G n, denoed as ρ(λ n + D n G n ) < 1. Therefore, we can check if ˆΓ D by he following proposiion. Proposiion 3. For any ˆΓ, he following saemens hold: i) If i exiss one n N wih ρ(λ n + D n G n ) 1 or ρ(i + H n ) 1, we have ˆΓ / D; ii) If n N wih ρ(λ n + D n G n ) < 1 or ρ(i + H n ) < 1, bu n N such ha k K n N p n,ik > P, we have ˆΓ / D; iii) If n N wih ρ(λ n + D n G n ) < 1, one need o check he LP feasibiliy problem in (34). 3) Opimal power allocaion based on BB algorihms: Based on he above discussions, he procedures of he proposed BB algorihm for opimal power allocaion is described as follows. Le S(v) = {A 1 n,k (v),, AT N,K (v)} denoe he se of box subses A n,k (v) = {ˆΓ n,k (v) Γ n,k Γ n,k (v)} for all n, k and a he v-h ieraion. S(0) is he iniial recangular consrain se, on he roo node of he binary ree, which is define (27). A he v-h ieraion, we spil S(v) ino wo subses Q I and Q II along one of is longes edges, removing S(v) and adding he wo new subses o R(v). Nex, we solve (31) based on Proposiion 3 over each subse Q l, l {I, II}. A lower bound and an upper bound can be obained. Then, we choose he minimum over all upper bounds as f ub (v) and choose he minimum over all lower bounds as f lb (v), i.e., aking he minimum over all he upper and lower bounds a each leaf node across all he levels in he binary ree. Removing he leaf node S such ha ψ lb (S ) f ub (v), which will no affec he opimaliy of he BB ree. Repea he above procedures unil i saisfies he accuracy ɛ which is he difference beween he global upper bound and he global lower bound. In he procedure of generaing he BB ree, a sequence of subses will be generaed from S(0). The deails are given in Algorihm 2 ha capures he global opimal soluion of (12). Algorihm 2 The opimal power allocaion algorihm based on BB 1: Iniializaion for BB: 1) Consruc he iniial simplex S(0) such ha D S(0), which was described in Secion IV-A1. 2) Compue f lb (1) = ψ lb (S 0) and f ub (1) = ψ ub (S(0)), by (30) and (30), respecively. 3) Se R(1) = {S 0}, opimal upper bound U = U(1), olerance ɛ > 0 and v = 1. 2: while f ub (v) f lb (v) > ɛ do 3: Pick S R(v) for which φ lb (S ) = f lb (v) and se S(v) = S. 4: Subdivide S(v) along one of is longes edges ino Q I and Q II. ( ) ( ) 5: Compue ψ lb QI, ψub QII by solving problem (31). 6: Updae he upper bound f ub (v) and he lower bound f lb (v) as follows: f lb (v) = min ψ lb(s ); S R(v+1) f ub (v) = ψ ub (S ) ; min S R(v+1) updae fub = min(fub, f ub (v)). 7: Updae R(v + 1) by removing all S for which ψ lb (S ) f ub (v + 1). 8: v := v : end while 10: Oupu he value Ũ = fub and he opimal power allocaion P. Remark 1. A he v-h ieraion of Algorihm 2, f ub (v) and f lb (v) are he minimums over all he upper bounds and lower bounds a each leaf nodes in he BB ree, respecively, which give a global upper bound and lower bound on he opimal value of (25). The sopping crierion for Algorihm 2 can be

10 10 f ub (v) f lb (v) ɛ for given a small ɛ. Accordingly, i means ha U ln ɛ U op. The overall complexiy of Algorihm 2 is deermined by he complexiy of each ieraion and he number of ieraions required for achieving he desired olerance. During each ieraion, i requires o solve a LP problem for he wors case. Since he formulaed LP problem in (32) can be solved using an inerior-poin mehod, he compuaional complexiy of LP is upper bounded by O((NKT ) 2 (NKT + T + NT L )) [32], where erm N KT denoes he number of variables and erm NKT + T + NT L is he number of consrains. In addiion, he wors case compuaional complexiy of Algorihm 2 is exponenial in he number of variables. Assume ha 2 KNT is he oal number of ieraions required o obain he ɛ- approximaion soluion. The complexiy of BB algorihm can be approximaed as O(2 (KNT )4 ). B. Low-Complexiy Power Allocaion Sraegies Though BB approaches can find he opimal power allocaion, he high compuaional complexiy makes i difficul o realize. In his subsecion, we proposed a subopimal power allocaion sraegy based on he SCA echniques. We firs consider he MOS funcion in (12a), which can be rearranged as follows. T N C 1 ln( k K (a) C 1 k K N (b) = =1 n=1 T n T C k 3 Rn,k) + n=1 k K N ln(rn,k) + C3 k k K =1 n=1 C k 3, (35) C 1 ln(rn,k) + k K k K n where (a) follows he Jenssen s inequaliy [32] and (b) is based on he propery of polynomials. As a resul, problem (21) can be equivalenly reformulaed as max {P n,k }{R n,k } s.. R n,k log N n=1 T n k K n ( 1 + K n C 1 ln(r n,k) h n,k P n,k h n,k P n,i + h s n,k P n s+σ2 i=k+1 s ), (36a) (36b) (21b) & (21c) & (22). where he relax rae consrain in (36b) will be sricly equal a he opimal soluion. Problem (36) is non-convex due o he he consrain in (36b). To solve i, we propose a convex approximaion mehod in he following. To illusrae he approximaion, le us firs consider he following change of variables: e y n,k = 2 R n,k 1, e z n,k = Pn,k, (37) for k K, n N, and T, where x n,k and y n,k are slack variables. By subsiuing (37) ino (36), one can obain he following problem: max {P n,k },{R n,k }, {x n,k },{y n,k } N n=1 T n k K n C 1 ln(r n,k) (38a) s.. ( K n,k e y n,k z n,k n N k K n i=k+1 e zn,i + s P n,k(z) P, Rn,k log 2 (1 + e y n,k), h s n,k h n,k s h n,jh s n,kp s n(z) + (h n,j h n,k)σ 2 s k K, n N, T, P s n(z) + σ2 h n,k ) 1, h n,kh s n,jp s n(z), (38b) (38c) (38d) (38e) (38f) where Pn(z) s = K s n i=1 ezs n,k. Noice ha we have replaced he equaliies in (36b) and (37) wih inequaliies as in (38b) and (38d). Due o he monooniciy of he objecive funcion, all inequaliies in (38b) and (38d) would hold wih equaliies a he opimal soluion. I is observed ha he objecive funcion is concave and he consrains in (38b) and (38c) are convex. Consrains (38d) and (38e) are no convex. Nex, we use he firs-order Taylor approximaion o approximae he lower bound of he non-convex pars in (38d) and (38e). Le { P n,k } and { R n,k } be a se of feasible soluion of (38). Then, we have ỹn,k = ln 2 R n,k 1, z n,k = ln(pn,k). (39) As a resul, he lower-bound approximaion for (38d) and (38e) can be given by log 2 (1 + e y n,k) = log 2 (1 + eỹ n,k) + eỹ n,k(yn,k ỹn,k) ln(2) ( ), (40a) 1 + e y n,k h n,kh s n,jpn(z) s = h n,kh s n,jpn( z) s s s + (40b) K s s h n,k hs n e zs n,j i=1 n,i(zn,i s zs n,i ), Consequenly, by replacing (38d) and (38e) wih (40a) and (40b), we obain he following approximaion of problem (38): max {P n,k },{R n,k }, {x n,k },{y n,k } s.. N n=1 T n k K n C 1 ln(r n,k) (38b) & (38c) & (38f), Rn,k log 2 (1 + ỹ n,k ) + ỹ n,k (y n,k ỹ n,k ( ) ), ln(2) 1+e y n,k s h n,jh s n,kpn(z) s + (h n,j h n,k)σ 2 h n,kh s n,jpn( z) s s (41a) (41b) + s h n,k hs n,j K s n i=1 e zs n,i(z s n,i zs n,i ). (41c) Problem (41) is a convex opimizaion problem; i can be efficienly solved by sandard convex solvers such as CVX [38]. Problem (41) is formulaed by approximaing (38) a a feasible soluion ({Rn,k }, {P n,k }), as described in (39). Noe ha for a fixed poin ({Rn,k }, {P n,k }), he obained objecive of (41) is no less han ha obained in he fixed poin. Therefore, he approximaion can be improved by successively approximaing problem (38) based on he opimal soluion ({Rn,k }, {P n,k }) obained by solving (41) in he previous approximaion. The compleed procedure of he proposed successive approximaion approach is described in Algorihm 3. In paricular, in each ieraion of Algorihm 3, he objecive funcion of problem (41) will be improved successively. However, due o he oal power consrain, he generaed sequence

11 11 is bounded, which implies he convergence of Algorihm 3. Algorihm 3 SCA algorihm for solving (38) 1: Given a se of soluion ({ R n,k [0]}, { P n,k [0]}), which is feasible o (38). 2: Compue he opimal objecive value of problem (38), denoed as Φ(0). Se v = 1. 3: while Φ[v] Φ[v 1] Φ[v 1] ɛ, where ɛ is a given sopping crierion, do 4: v := v : Obain ỹn,k (v 1) and z n,k (v 1) by (39), and solve problem (41) o obain he opimal soluion ({ R n,k [v]}, {ỹ n,k (v)}, { z n,k [v]}). 6: end while 7: Oupu he opimal {R n,k } and {P n,k = ln(z n,k )}. Due o he relaxaion in (35), (38) provides a lower bound of problem (21). Furhermore, problem (41) is a lower bound approximaion of problem (38) because of he approximaion in (40). Consequenly, he soluion obained is subopimal. However, he complexiy of Algorihm 3 is lower han Algorihm 2. Assume ha he number of ieraions of Algorihm 3 is V, hen V is less han O((NKT ) 2 ) [39]. V. SIMULATION RESULTS In his secion, he simulaion and he performance resuls are evaluaed o he performance of he muli-cell NOMA sysem wih proposed resource allocaion scheme. In he simulaions, he locaions of he BSs are assumed o be fixed, and he locaions of he users o be uniformly and independenly disribued in a disk space wih radius R = 500 m, if i is no specified. The bandwidh of each subchannel is W N = 75 khz. h n,k = f n,k 2 is he channel power gain from BS o user UE k on subchannel SC n, which is expressed as h n,k = (d,k) α χ n,k, where d,k is he disance beween BS and user UE k, α is he pah loss exponen and χ n,k is he fading coefficien wih χ n,k CN (0, 1). We assume ha he small scale fading pars of all channels follow from independen idenically disribued (i.i.d) Rayleigh disribuion. A oal of 100 differen channel realizaions were used in he simulaions, if i is no specified. The pah loss exponen is 3.7 [24] and he noise experienced a each user is assumed idenical. The noise power is σ 2 = log 10( W N ) dbm. Moreover, we consider ha he sysem consiss of K = 6 users, T = 3 BSs and N = 3 subchannels, if i is no specified. For a web browsing applicaion, he web page sizes are deermined according o he web raffic saisics colleced and analyzed in he previous sudy [40]. In simulaions, web users ypically access he web page size wih he average average web page size of 320 KB [27], if i is no specified. To invesigae he performance of he proposed muli-cell NOMA sysem, hree differen algorihms are simulaed for he muli-cell NOMA sysem and he muli-cell OMA sysem, respecively. Firsly, we consider he global opimal resource allocaion algorihm called Exhaus+BB. In Exhaus+BB, for each combinaion among users, BSs and subchannels, he BB approach is invoked o aain he opimal power allocaion scheme; Then, an exhaus search is exploied over all combinaions of he user-bs associaion and subchannel assignmen. Furhermore, for he subopimal algorihm- Mach+BB, he proposed maching approach is firsly invoked o obain a subopimal scheme of user-bs associaion and subchannel assignmen; Then, he power allocaion procedure is performed by applying BB approaches. In addiion, for he low-complexiy subopimal algorihm- Mach+SCA, he proposed SCA-based power allocaion scheme is applied afer performing he proposed maching approach. Moreover, we also consider an muli-cell OMA sysem wih TDMA, where an BS communicaes wih a mos one user in one ime slo. Since he BS applying NOMA can serve muliple users simulaneously in he same subchannel, he BS applying OMA requires muliple ime slos o serve he same number of users in NOMA. In Fig. 4, we invesigae he sum MOS versus he maximum ransmi power a each BS, P, for differen algorihms menioned above where L = 2, T n = 2, and S n = 2. As i can be observed from Fig. 4, he sum MOS aained by differen algorihms increases wih he maximum ransmi power of BSs P. This is because he received SINR a he users can be improved by opimally allocaing he ransmi power via he proposed algorihms which leads o an improvemen of he sysem sum MOS. However, here is a diminishing rend in he sum MOS when P is higher han 10 dbm. In fac, as he P increases, he iner-cell inerference becomes more severe, which degrades he received SINR a users. As a resul he sum MOS of he sysems will decrease. Besides, i can be observed from Fig. 4, he sum MOS of he global opimal algorihm- Exhaus+BB grows faser han Mach+SCA and Mach+BB. Table I compares various algorihms from he perspecive of compuaional complexiy. I shows ha he complexiy of Mach+SCA is grealy less han ha of Exhaus+BB and Mach+BB. From Fig. 4 and Table I, we can observe ha hough some performance is suffered in he proposed low-complexiy subopimal algorihm- Mach+SCA, is compuaional complexiy will be reduced grealy compared o Exhaus+BB and Mach+BB, which indicaes ha he proposed Mach+SCA is efficien o solve he opimizaion problem (12). Furhermore, noe ha he proposed muli-cell NOMA sysem ouperforms he convenional muli-cell OMA sysem in erms of he sum MOS. In Fig. 5, we sudy he performance of he sysem sum MOS and he sysem sum rae over differen P wih K = 6. We assume he 6 users run page applicaions wih he F S = [50, 100, 200, 320, 400, 500] KB. For comparison, we consider he fixed power allocaion scheme in NOMA, called as FNOMA, as a baseline, which has been widely adoped in [5, 41]. Correspondingly, we erm he proposed lowcomplexiy subopimal power allocaion scheme based on SCA as DNOMA. To validae he effeciveness, we compare he proposed Mach+DNOMA wih he corresponding OMA scheme, ermed as Mach+DOMA, and Mach+FNOMA. In Mach+FNOMA, we assume ha he BS allocaes is power uniformly over he occupied subchannels. Besides, L = 2 is assumed and he power allocaion coefficiens beween he users associaed he BS on a specific subchannel is assumed o

12 12 TABLE I: Comparison of various algorihms Algorihm Complexiy Opimaliy Exhaus+BB O(2 (NKT )2(KNT )2 ) Global opimal Mach+BB O((K + N 2 )T 2 + (V KL + V T ns N)T ) + O(2 (KNT )2 )) Subopimal Mach+SCA O((K + N 2 )T 2 + (V KL + V T ns N)T ) + O( V (NKT ) 3 ) Subopimal be p 1 and p 2 for he users wih he beer equivalen channel gain and he poorer equivalen channel gain, respecively. As can be observed from Fig. 5, boh he performance of sum MOS can be grealy enhanced by Mach+DNOMA compared wih Mach+FNOMA and Mach+DOMA. Moreover, he curves of sum MOS and sum rae have similar increasing rends. I is because ha one user s MOS funcion is a monoonically increasing funcion wih is rae. In paricular, as can be observed in (11), one user s MOS funcion is relaed wih he logarihm of is rae and he applied web page size, which resuls in Mach+FNOMA can obain a beer sum-rae performance compare o Mach+DNOMA. In Fig. 6, we invesigae he sum-mos performance of he proposed muli-cell NOMA neworks for K = 6, T = 3 and N = 4. Three differen schemes are illusraed in Fig. 6: Mach+DNOMA, Mach+FNOMA and P- Mach+DNOMA. The impac of he subchannel assignmen is sudied, where maching operaion only performed for user- BS associaion and he subchannels randomly assigned o he BS saisfying he consrains in problem (12). I can be ermed as P-Mach+DNOMA for simpliciy. In addiion, for compleeness, he corresponding OMA schemes are also simulaed. As can be observed from Fig. 6, Mach+DNOMA is capable of increasing he sum MOS compared o he oher schemes. Moreover, he sum-mos performance of P- Mach+DNOMA is worse han ha of Mach+DNOMA and Mach+FNOMA, which indicaes ha he subchannel assignmen has imporan impac on he nework uiliies. Combined wih he observaions from Fig. 4, i can be concluded ha Mach+SCA srikes a balance beween he performance gain and he compuaional complexiy. In Fig. 7, we invesigae he performance of he proposed muli-cell MC-NOMA neworks versus differen number of users in he sysem. Here he number of users associaed wih one BS is defined as he average number of he oal users over he number of BSs, L = K T. Moreover, hree differen NOMA-based schemes are compared: Mach+DNOMA, Mach+FNOMA, and P-MAch+DNOMA. For comparison, wo OMA schemes are also compared in Fig. 7: Mach+DOMA and P-Mach+DOMA. As can be observed from Fig. 7, for all schemes, he sum-mos performance will be enhanced wih increasing he number of he number of users in he sysem. Besides, Mach+DNOMA is capable of ouperforming he oher schemes. To illusrae he impac of sum MOS on he user fairness of muli-cell NOMA sysems, we invesigae he fairness of he proposed schemes and he baseline schemes based on Jain s fairness index (JFI) [42], which is an imporan indicaor of measuring he performance meric. In paricular, JFI is calculaed as J QOE = ( k K MOSk web) 2 /K k K (MOSk web) 2. Noe ha he JFI Sum MOS Mach+SCA:NOMA Mach+SCA:OMA 10 Mach+BB:NOMA Mach+BB:OMA 5 Exhaus+BB:NOMA Exhaus+BB:OMA Tx power (dbm) Fig. 4: Comparisons of sum MOS over differen algorihms, where K = 6, T = 3, N = 3, L = 2, T n = 2, and S n = 2. Sum MOS Sum MOS:Mach+DNOMA Sum MOS:Mach+FNOMA Sum MOS:Mach+DOMA Sum Rae:Mach+DNOMA Sum Rae:Mach+FNOMA Sum Rae:Mach+DOMA Tx power (dbm) Fig. 5: Comparisons of sum MOS and sum rae wih differen ransmi power, where K = 6, T = 3, N = 3, L = 2, T n = 2, S n = 2 and [ p 1, p 2] T = [1/4, 3/4] T. ranslaes a se of MOS vecor {MOS 1 web,, MOS K web} ino a score in he inerval of [ 1 K, 1] and higher JFI means he resource allocaion is fairer. Fig. 8 illusraes he evaluaion of JFI versus he number of users in he nework. Here, he JFIs in erms of he opimizaion objecive wih sum-mos based maximizaion and sum-rae based maximizaion, where he proposed Mach+DNOMA scheme was employed. The JFI of sum- MOS based maximizaion is higher han ha of sum-rae based, because he sum MOS funcion reduces he gap beween users raes. Moreover, he JFIs in erms of he wo schemes decrease wih he oal number of users since he compeiion among users becomes more enser when here are more users in he sysem Sum Rae (bis/s/hz)

13 13 Sum MOS Mach+DNOMA P Mach+DNOMA Mach+FNOMA Mach+DOMA P Mach+DOMA Tx power (dbm) Fig. 6: Comparisons of sum MOS wih differen maching schemes, where K = 6, T = 3, N = 4, L = 2, T n = 2, and S n = 2. Sum MOS Mach+DNOMA Mach+FNOMA P Mach+DNOMA Mach DOMA P Mach+DOMA Number of users Fig. 7: Comparisons of sum MOS wih differen number of users, where T = 3, N = 4, T n = 2, and S n = 3. Jains Fairness Index Number of users Max sum MOS Max sum rae Fig. 8: Comparisons of he JFI beween QoE-based and sum raebased scheme wih differen number of users, where T = 3, N = 4, T n = 2, and S n = 3. VI. CONCLUSIONS In his paper, we sudied he QoE-based resource allocaion algorihm design of an muli-cell MC-NOMA sysem in erms of user-bs associaion, subchannel assignmen and power allocaion. The algorihm design was formulaed as a combinaorial non-convex opimizaion problem of maximizing he sum MOS of he sysem. By formulaing he user-bs associaion and subchannel assignmen as a 3D maching problem, we proposed a low-complexiy wo-sep approach based on 2D maching. Then, we developed an opimal power allocaion sraegy based on BB approaches o derive an upper bound for he sum MOS of he sysem. Besides, a subopimal algorihm based on SCA was also developed o achieve a rade-off beween compuaional complexiy and performance. Simulaion resuls has revealed ha he proposed subopimal algorihm obain a good performance compared o he opimal algorihm. In addiion, a subsanial improvemen of he sum MOS can be achieved by employing he proposed MC-NOMA scheme in muli-cell neworks. Furhermore, he proposed QoE-based muli-cell MC-NOMA scheme was shown o provide a good balance beween improving he sum MOS and mainaining fairness among users. In addiion, i is promising direcion o invesigae a general algorihm o improve he user QoE for various services such as web browsing, voices, sreaming audio and video, and so on. Therefore our fuure work will consider a general algorihm for MOS models wih various services wih he aid of he algorihms developed in his work. APPENDIX A: PROOF OF LEMMA 1 Since {Γ} is coninuous on R M, U(γ) is differeniable on Γ n,k, n N k, T k and k K. The firs-order derivaives on Γ n,k can be derived as U(Γ) Γ n,k = C 1 T k n N log k 2 1 ), (1 + Γ n,k 1 + Γ n,k (A.1) ) n N log k 2 (1 + Γ n,k is he effecive Noe ha T k rae for UE k. In he sysem, we assume ha all users are scheduled where each user k such ha R k > 0. Noe ha he gradien of U(Γ) 0, U(Γ) is an monoonically increasing funcion. Then we can compue he second-order derivaives of U(Γ) as 2 U(Γ) ( ) 2 = Γ n,j ( C 1 T k (( ) 1 + Γ n,k T k n N log ( k Γ n N k log 2 ) ) n,k + 1 )) 2 (1 + Γ n,k (A.2) Obviously, 2 U(Γ) 0, which implies ha U(Γ) is concave (Γ) 2 [32]. APPENDIX B: PROOF OF PROPOSITION 1 The objecive funcion in problem (21) can be wrien as k K MOS k web = ( ( ( C 1 ln log Γ ) ) ) n,k + C3 k k K T n N = k KC ( ( 1 ln log Γ ) ) n,k + k KC 3 k T n N } {{ } U (Γ) }{{} Consan (B.1) Noe ha k K Ck 3 is consan, which will no affec he opimal soluion. In addiion, based on Lemma 1, we have

14 14 proved ha U (Γ) is a monoonically increasing funcion of Γ. Based on he propery, a he opimum he sric equaliy will be saisfied for Γ n,k γ n,k, n, k, and. Therefore, he relaxaion is igh. Problem (23) will have he same opimal soluion wih problem (21). APPENDIX C: PROOF OF PROPOSITION 2 By rearranging (31b) as P n,k Γ n,k K n i=k+1 P n,i Γ n,k h n,k s fn,k s 2 Pn s Γ n,k σ 2. h n,k (C.1) For any subchannel SC n, (C.2) can be expressed as ( I (Λn + D ) ng n) p n D nσ 2, (C.2) where Λ n =diag ([ ]) Λ 1 n, Λ 2 n,, Λ Tn n, D n =diag ([ ]) D 1 n, D 2 n,, D Tn n, p n =[p 1 n, p 2 n,, p Tn n ], G n = [ ] G 1 n, G 2 n,, G Tn n. and Λ n is an upper riangle marix wih he elemen in he i-h row and he j-h column Λ n[i, j] = Γ n,i wih j > i. ([ ]) D Γ n =diag n,1, Γ n,2,, Γ n,l, (C.4a) h n,1 h n,2 h n,l p n = [ ] Pn,1, Pn,2,, Pn,L, (C.4b) G n = [ ] h 1 n,11 L,, h 1 n,1 1 L, 0 L, h +1 n,1 1 L,, h Tn n,l 1 L (C.4c) For example, we assume ha L = 2 and T n = 3, for = 2, we have [ 0 Γ Λ 2 2 ] [ Γ ] n,1 n,1 n =, D 2 0 n = h n,1, p 2 n = [ Pn,1, P n,2], G n = [ ] h 1 n,1, h 1 n,2, 0, 0, h 3 n,1, h 3 n,2 Analogously, for a pair of users UE k and UE j, wih k > j, we can rewrien consrains in (31c) as follows. H n p n θ n (C.6) where H n = [ H1 n, H ] 2 Tn n,, H n, θn = [ θn, 1 θn, 2, θn Tn, ], p n = [ ] Pn, 1 Pn, 2, Pn Tn, H n = [ h1 ] 1 +1 Tn n,, h n, 0, h n,, h n h s n = f n,k 2 f s n,j 2 f n,j 2 f s n,k 2, s, θ n =( f n,k 2 f s n,k 2 )σ 2. Subsiuing (C.2) and (C.6) ino opimizaion problem (31), we can aain problem (32). REFERENCES [1] J. Cui, Y. Liu, P. Fan, and A. Nallanahan, A QoE-aware resource allocaion sraegy for muli-cell NOMA neworks, in IEEE Global Commun. Conf. (GLOBECOM) Workshop, 2017, pp [2] A. Ghosh, R. Raasuk, B. Mondal, N. Mangalvedhe, and T. Thomas, LTE-advanced: nex-generaion wireless broadband echnology [invied paper], IEEE Wireless Commun., vol. 17, no. 3, pp , Jun [3] Z. Ding, Y. Liu, J. Choi, Q. Sun, M. Elkashlan, C. L. I, and H. V. Poor, Applicaion of non-orhogonal muliple access in LTE and 5G neworks, IEEE Commun. Mag., vol. 55, no. 2, pp , Feb [4] Y. Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanahan, and L. Hanzo, Nonorhogonal muliple access for 5G and beyond, Proceedings of he IEEE, vol. 105, no. 12, pp , Dec [5] Z. Ding, P. Fan, and H. V. Poor, Impac of user pairing on 5G nonorhogonal muliple-access downlink ransmissions, IEEE Trans. Veh. Technl., vol. 65, no. 8, pp , Aug [6] H. Shao, H. Zhao, Y. Sun, J. Zhang, and Y. Xu, QoE-aware downlink user-cell associaion in small cell neworks: A ransfer-maching game heoreic soluion wih peer effecs, IEEE Access, vol. 4, pp , [7] W. Wang, Y. Liu, Z. Luo, T. Jiang, Q. Zhang, and A. Nallanahan, Toward cross-layer design for non-orhogonal muliple access: A qualiyof-experience perspecive, IEEE Wireless Commun., o appear in [8] Z. Ding, Z. Yang, P. Fan, and H. V. Poor, On he performance of non-orhogonal muliple access in 5G sysems wih randomly deployed users, IEEE Signal Process. Le., vol. 21, no. 12, pp , Dec [9] Y. Liu, Z. Qin, M. Elkashlan, Y. Gao, and L. Hanzo, Enhancing he physical layer securiy of non-orhogonal muliple access in large-scale neworks, IEEE Trans. Wireless Commun., vol. 16, no. 3, pp , Mar [10] Z. Yang, Z. Ding, P. Fan, and N. Al-Dhahir, A general power allocaion scheme o guaranee qualiy of service in downlink and uplink noma sysems, IEEE Wireless Commun., vol. 15, no. 11, pp , Nov [11] Y. Liu, Z. Ding, M. Elkashlan, and H. V. Poor, Cooperaive nonorhogonal muliple access wih simulaneous wireless informaion and power ransfer, IEEE J. Sel. Areas Commun., vol. 34, no. 4, pp , Apr [12] S. Timoheou and I. Krikidis, Fairness for non-orhogonal muliple access in 5G sysems, IEEE Signal Process. Le., vol. 22, no. 10, pp , Oc [13] J. Cui, Z. Ding, and P. Fan, A novel power allocaion scheme under ouage consrains in noma sysems, IEEE Signal Process. Le., vol. 23, no. 9, pp , Sep [14] M. S. Ali, H. Tabassum, and E. Hossain, Dynamic user clusering and power allocaion for uplink and downlink non-orhogonal muliple access (noma) sysems, IEEE Access, vol. 4, pp , [15] L. Lei, D. Yuan, C. K. Ho, and S. Sun, Power and channel allocaion for non-orhogonal muliple access in 5G sysems: Tracabiliy and compuaion, IEEE Trans. Wireless Commun., vol. 15, no. 12, pp , Dec [16] B. Di, L. Song, and Y. Li, Sub-channel assignmen, power allocaion, and user scheduling for non-orhogonal muliple access neworks, IEEE Trans. Wireless Commun., vol. 15, no. 11, pp , Nov [17] Y. Sun, D. W. K. Ng, Z. Ding, and R. Schober, Opimal join power and subcarrier allocaion for full-duplex mulicarrier non-orhogonal muliple access sysems, IEEE Trans. Commun., vol. 65, no. 3, pp , Mar [18] F. Fang, H. Zhang, J. Cheng, and V. C. M. Leung, Energy-efficien resource allocaion for downlink non-orhogonal muliple access nework, IEEE Trans. Commun., vol. 64, no. 9, pp , Sep [19] S. Singh, O. Oyman, A. Papahanassiou, D. Chaerjee, and J. G. Andrews, Video capaciy and QoE enhancemens over LTE, in IEEE Proc. of Inernaional Commun. Conf. (ICC), Jun. 2012, pp [20] M. Rugelj, M. Volk, U. Sedlar, J. Serle, and A. Kos, A novel user saisfacion predicion model for fuure nework provisioning, Telecommunicaion sysems, vol. 56, no. 3, pp , [21] C. Sacchi, F. Granelli, and C. Schlegel, A QoE-oriened sraegy for OFDMA radio resource allocaion based on min-mos maximizaion, IEEE Commun. Le., vol. 15, no. 5, pp , May [22] Y. H. Cho, H. Kim, S. H. Lee, and H. S. Lee, A QoE-aware proporional fair resource allocaion for muli-cell OFDMA neworks, IEEE Commun. Le., vol. 19, no. 1, pp , Jan [23] D. Wu, Q. Wu, Y. Xu, J. Jing, and Z. Qin, QoE-based disribued mulichannel allocaion in 5G heerogeneous cellular neworks: A machingcoaliional game soluion, IEEE Access, vol. 5, pp , [24] J. Zheng, Y. Cai, Y. Liu, Y. Xu, B. Duan, and X. Shen, Opimal power allocaion and user scheduling in mulicell neworks: Base saion cooperaion using a game-heoreic approach, IEEE Trans. Wireless Commun., vol. 13, no. 12, pp , Dec [25] N. Zhang, S. Zhang, J. Zheng, X. Fang, J. W. Mark, and X. Shen, QoE driven decenralized specrum sharing in 5G neworks: Poenial game approach, IEEE Trans. Veh. Technol., vol. 66, no. 9, pp , 2017.

15 15 [26] Z. Du, Q. Wu, P. Yang, Y. Xu, J. Wang, and Y. D. Yao, Exploiing user demand diversiy in heerogeneous wireless neworks, IEEE Trans. Wireless Commun., vol. 14, no. 8, pp , Aug [27] M. Rugelj, U. Sedlar, M. Volk, J. Serle, M. Hajdinjak, and A. Kos, Novel cross-layer QoE-aware radio resource allocaion algorihms in muliuser OFDMA sysems, IEEE Trans. Commun., vol. 62, no. 9, pp , Sep [28] QoE oriened cross-layer design of a resource allocaion algorihm in beyond 3G sysems, Compuer Communicaions, vol. 33, no. 5, pp , [29] G. T.. v11.0.0, Feasibiliy sudy for furher advancemens for E-UTRA (LTEAdvanced), Sep. Sophia-Anipolis, France,2012. [30] S. Tomida and K. Higuchi, Non-orhogonal access wih SIC in cellular downlink for user fairness enhancemen, in In. Sym. Inell. Signal Process. Commun. Sys. (ISPACS), Dec. 2011, pp [31] R. Hors and H. Tuy, Global opimizaion: Deerminisic approaches. Springer Science & Business Media, [32] S. Boyd and L. Vandenberghe, Convex opimizaion. Cambridge universiy press, [33] P. C. Weeraddana, M. Codreanu, M. Lava-aho, and A. Ephremides, Weighed sum-rae maximizaion for a se of inerfering links via branch and bound, IEEE Trans. Signal Process., vol. 59, no. 8, pp , Aug [34] C. Ng and D. S. Hirschberg, Three-dimensional sable maching problems, SIAM Journal on Discree Mahemaics, vol. 4, no. 2, pp , [35] E. Bodine-Baron, C. Lee, A. Chong, B. Hassibi, and A. Wierman, Peer effecs and sabiliy in maching markes, in Inernaional Symposium on Algorihmic Game Theory. Springer, 2011, pp [36] J. Cui, Y. Liu, Z. Ding, P. Fan, and A. Nallanahan, Opimal user scheduling and power allocaion for millimeer wave NOMA sysems, IEEE Trans. Wireless Commun., o be published. [37] R. A. Horn and C. R. Johnson, Marix analysis. Cambridge universiy press, [38] M. Gran and S. Boyd, CVX: Malab sofware for disciplined convex programming, version 2.1, hp://cvxr.com/cvx, Mar [39] W. C. Li, T. H. Chang, and C. Y. Chi, Mulicell coordinaed beamforming wih rae ouage consrain-par ii: Efficien approximaion algorihms, IEEE Trans. Signal Process., vol. 63, no. 11, pp , Jun [40] M. Molina, P. Caselli, and G. Foddis, Web raffic modeling exploiing TCP connecions emporal clusering hrough HTML-REDUCE, IEEE Nework, vol. 14, no. 3, pp , May [41] Z. Ding, F. Adachi, and H. V. Poor, The applicaion of MIMO o nonorhogonal muliple access, IEEE Trans. Wireless Commun., vol. 15, no. 1, pp , Jan [42] R. Jain, D.-M. Chiu, and W. R. Hawe, A quaniaive measure of fairness and discriminaion for resource allocaion in shared compuer sysem. Easern Research Laboraory, Digial Equipmen Corporaion Hudson, MA, 1984, vol. 38. Jingjing Cui (S14) received he B.S. degrees in communicaion engineering from Tibe universiy, Lhasa, China, She is currenly pursuing he Ph.D. degree in he Insiue of Mobile Communicaions, Souhwes Jiaoong Universiy, Chengdu, China. She was a Visiing Ph.D. Suden a he School of Compuing and Communicaions, Lancaser U- niversiy, U.K., from November 2016 o November Her research ineress include Non-orhogonal Muliple Access for 5G neworks, machine learning for 5G neworks, convex opimizaion. Yuanwei Liu (S 13, M 16) received he Ph.D. degree in Elecrical Engineering from he Queen Mary Universiy of London, U.K., in Before ha, He received he B.S. and M.S. degrees from he Beijing Universiy of Poss and Telecommunicaions in 2011 and 2014, respecively. He has been a Lecurer (Assisan Professor) wih he School of Elecronic Engineering and Compuer Science, Queen Mary Universiy of London, since He was wih he Deparmen of Informaics, King s College London, from 2016 o 2017, where he was a Pos-Docoral Research Fellow. His research ineress include 5G wireless neworks, Inerne of Things, s- ochasic geomery, and maching heory. He received he Exemplary Reviewer Cerificae of he IEEE WIRELESS COMMUNICATION LETTERS in 2015 and he IEEE TRANSACTIONS ON COMMUNICATIONS in He has served as a TPC Member for many IEEE conferences, such as GLOBECOM and ICC. He currenly serves as an Edior of he IEEE COMMUNICATIONS LETTERS and he IEEE ACCESS. Zhiguo Ding (S 03-M 05) received his B.Eng in Elecrical Engineering from he Beijing Universiy of Poss and Telecommunicaions in 2000, and he Ph.D degree in Elecrical Engineering from Imperial College London in From Jul o Aug. 2014, he was working in Queen s Universiy Belfas, Imperial College and Newcasle Universiy. Since Sep. 2014, he has been wih Lancaser Universiy as a Chair Professor. From Oc o Sep. 2019, he has also been an academic visior in Princeon Universiy. Dr Ding research ineress are 5G neworks, game heory, cooperaive and energy harvesing neworks and saisical signal processing. He is serving as an Edior for IEEE Transacions on Communicaions, IEEE Transacions on Vehicular Technology, and Journal of Wireless Communicaions and Mobile Compuing, and was an Edior for IEEE Wireless Communicaion Leers, IEEE Communicaion Leers from 2013 o He received he bes paper award in IET Comm. Conf. on Wireless, Mobile and Compuing, 2009, IEEE Communicaion Leer Exemplary Reviewer 2012, and he EU Marie Curie Fellowship Pingzhi Fan (M93-SM99-F15) received his Ph.D. degree in Elecronic Engineering from he Hull Universiy, UK. He is currenly a professor and direcor of he insiue of mobile communicaions, Souhwes Jiaoong Universiy, China. He is a recipien of he UK ORS Award, he NSFC Ousanding Young Scienis Award, and he chief scienis of a naional 973 research projec. He served as general chair or TPC chair of a number of inernaional conferences, and is he gues edior-in-chief, gues edior or ediorial member of several inernaional journals. He is he founding chair of IEEE VTS BJ Chaper and ComSoc CD Chaper, he founding chair of IEEE Chengdu Secion. He also served as a board member of IEEE Region 10, IET(IEE) Council and IET Asia- Pacific Region. He has over 200 research papers published in various academic English journals (IEEE/IEE/IEICE, ec), and 8 books, and is he invenor of 20 graned paens. His research ineress include high mobiliy wireless communicaions, 5G echnologies, wireless neworks for big daa, signal design and coding, ec. He is an IEEE VTS Disinguished Lecurer ( ), and a fellow of IEEE, IET, CIE and CIC.