Stable Throughput Region of Downlink NOMA Transmissions with Limited CSI

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1 Stable Throughput Regio of Dowlik NOMA Trasmissios with imited CSI Yog Zhou ad Vicet W.S. Wog Departmet of Electrical ad Computer Egieerig The Uiversity of British Columbia, Vacouver, Caada {zhou, Abstract No-orthogoal multiple access (NOMA) has recetly bee proposed as a key eablig techology for the fifth geeratio (5G) wireless etworks. Differet from the existig works which focus o the performace aalysis of NOMA with backlogged traffic, i this paper, we aalyze the stable throughput regio of dowlik NOMA trasmissio with dyamic traffic arrival for users with differet priorities. By utilizig limited istataeous chael state iformatio (CSI) at the base statio, we propose a opportuistic NOMA scheme to ehace the etwork performace. Cosiderig both NOMA ad dyamic traffic arrival leads to iteractig queues, which complicate the performace aalysis. By usig tools from stochastic geometry ad queueig theory, we decouple the iteractig queues ad characterize the stable throughput regio of the proposed opportuistic NOMA scheme i terms of the threshold to trigger NOMA ad trasmissio power allocatio coefficiets. Numerical results show that, compared to the orthogoal multiple access scheme, the proposed opportuistic NOMA scheme ca sigificatly ehace the stable throughput regio whe the desig parameters are appropriately selected. I. INTRODUCTI To meet the icreasig traffic demad due to the proliferatio of smart devices ad data hugry applicatios, oorthogoal multiple access (NOMA) has recetly bee proposed as a promisig multiple access techique to ehace the spectrum efficiecy of the fifth geeratio (5G) wireless etworks [], []. The base statio usig NOMA ca serve multiple users simultaeously by exploitig the power domai rather tha the time/frequecy/code domai i orthogoal multiple access (OMA). By appropriately allocatig the trasmissio power of the base statio to multiple users with diverse chael coditios, NOMA ca also achieve a balace betwee etwork throughput ad user fairess. The research o NOMA has recetly received cosiderable attetio [3] [9]. The -level performace of dowlik NOMA trasmissio is evaluated i [3], which shows that user pairig ad trasmissio power allocatio are importat desig aspects of NOMA. The outage probabilities of NOMA with radomly deployed users ad cooperatio amog users are aalyzed i [4] ad [5], respectively. The authors i [6] study the performace of NOMA with multiple-iput multipleoutput (MIMO) for both dowlik ad uplik trasmissio, i which sigal aligmet is utilized to mitigate the cochael iterferece amog differet user pairs. The impact of user pairig o the performace of NOMA is aalytically ivestigated i [7], which shows that NOMA achieves better performace whe the paired users have more diverse chael coditios. The applicatios of NOMA i Iteret of Thigs ad cogitive radio etworks are studied i [8] ad [9], respectively. owever, all the aforemetioed studies focus o the performace aalysis of NOMA with backlogged traffic, which caot be directly exteded to the sceario with dyamic traffic arrival. This work is motivated by the followig three aspects. First, with dyamic traffic arrival, queue stability is a importat quality of service (QoS) requiremet. To guaratee the stability of a queue, NOMA caot always be performed as its average service rate ca be degraded due to the sharig of frequecy chael ad trasmissio power with other users. Secod, cosiderig dyamic traffic arrival together with NOMA complicates the performace aalysis by itroducig iteractig queues. I particular, the service process of a queue depeds o the status of other queues, which determies whether NOMA or OMA should be eabled. Third, chael state iformatio (CSI) plays a importat role i desigig user pairig ad trasmissio power allocatio strategies, which have sigificat impact o the performace of NOMA. As full CSI is difficult to obtai i practice, the impact of limited CSI o the performace of NOMA should be ivestigated. I this paper, we ivestigate the performace of dowlik NOMA trasmissio with dyamic traffic arrival for all users. I such a sceario, the stable throughput regio [], [] is a importat performace metric, which is defied as the set of maximum achievable packet arrival rates give that all queues are stable. We propose a opportuistic NOMA scheme to ehace the stable throughput regio, where NOMA for users with differet priorities is eabled oly if the chael gai betwee the high-priority user ad the base statio does ot fall below a certai threshold. The mai cotributios of this paper are three-fold: ) We develop a theoretical performace aalysis framework for dowlik NOMA trasmissio with dyamic traffic arrival ad spatially radom users. This framework provides a better uderstadig of the beefits ad limitatios of NOMA. ) By usig limited istataeous CSI at the base statio, we propose a opportuistic NOMA scheme to serve users with differet priorities. We characterize the stable throughput regio of the proposed opportuistic NOMA scheme by utilizig tools from stochastic geometry ad queueig theory. 3) Numerical results show that the stable throughput re-

2 r D r D m D 3 r m r S D s Q... M Q FIFO s i s k S D D k SIC for sigal s Detectio of sigal s Detectio of sigal s k D D M Fig. : Illustratio of the queueig model for dowlik NOMA trasmissio with dyamic traffic arrival. Fig. : Illustratio of the etwork topology for dowlik NOMA trasmissio with spatially radom users. gio of opportuistic NOMA is sigificatly larger tha that of OMA. The impact of importat desig parameters (e.g., threshold to trigger NOMA ad trasmissio power allocatio coefficiets) o the performace of NOMA is also illustrated. The remaider of this paper is orgaized as follows. We describe the etwork topology, queueig model, ad sigal receptio model i Sectio II. Sectio III presets a opportuistic NOMA scheme ad characterizes the correspodig stable throughput regio. Numerical results are illustrated i Sectio IV. Fially, Sectio V cocludes this paper. II. SYSTEM MODE A. Network Topology ad Queueig Model Cosider a dowlik commuicatio sceario cosistig of oe base statio ad M + users, as show i Fig.. Base statio S locates at the ceter of the circular etwork coverage area with radius r. Users are categorized ito two groups with differet priorities. User D has a high priority to be served, while other users (i.e., {D m,m M= {,...,M}}) have the same low priority. Over a sigle frequecy chael, the time is slotted ito costat duratios. The locatios of lowpriority users are assumed to follow a biomial poit process (BPP). Specifically, M low-priority users at each time slot are idepedetly ad uiformly distributed withi a circle cetered at base statio S (i.e., origi) with radius r <r. O the other had, the distace betwee base statio S ad highpriority user D is fixed ad deoted as r (r,r]. Extesio to multiple high-priority users ad radom distaces betwee the base statio ad the high-priority users is possible at the expese of complicatig the derived expressios. Base statio S is equipped with two queues of ifiite size, deoted as Q ad Q, which store the packets to be trasmitted to high-priority user D ad M low-priority users, respectively, as show i Fig.. The packet arrival at base statio S for user D m follows a idepedet ad idetically distributed (i.i.d.) Beroulli process with a average arrival rate of m (packets/time slot). ece, the average arrival rate of queue Q is = P M m= m. Base statio S ad all users have a sigle atea. All packets have equal legth ad each packet is trasmitted i oe time slot. The packets of the same priority are served i a first-i first-out (FIFO) maer. At the ed of each time slot t Z +, the locatios of lowpriority users are chaged accordig to a high mobility radom walk model withi the circle with radius r as i [], [3]. The chael betwee ay two trasceivers suffers from path loss ad Rayleigh fadig. The fadig coefficiets are assumed to remai ivariat durig oe time slot ad vary idepedetly over differet time slots ad amog differet liks, as i [], []. Due to chael impairmets ad iterferece, a packet ca be successfully decoded if the received sigalto-iterferece-plus-oise ratio (SINR) is ot smaller tha the required receptio threshold. Upo successfully or erroeously receivig a packet from base statio S, the correspodig receiver seds a ackowledgemet (ACK) or egative ACK (NAK) frame via a error-free ad delay-free cotrol chael. After receivig the ACK frame, the packet is removed from the queue at base statio S. Otherwise, base statio S retrasmits the packet util it is successfully decoded. The protocol overhead due to ACK ad NAK feedback is much smaller tha the packet size ad is ot cosidered i this paper. We deote Q (t) ad Q (t) as the queue legth of Q ad Q at time slot t, respectively. A queue is said to be stable if its queue legth has a limitig distributio as time goes to ifiity [4]. If the arrival ad service processes of a queue are joitly statioary ad ergodic, by oyes theorem [5], the sufficiet coditio for the stability of queue Q is that <µ, where = ad µ (packets/time slot) deotes the average service rate of queue Q. The etwork is stable whe both queues Q ad Q are stable. The stable throughput regio is defied as the set of maximum arrival rates {, }, which ca stabilize the etwork. B. Sigal Receptio Model NOMA has the potetial to ehace the spectrum efficiecy by exploitig the power domai to simultaeously serve multiple users. To reduce the implemetatio complexity, we cosider the case that two users are paired to perform NOMA. Such a two-user NOMA scheme is specified i og Term Evolutio Advaced (TE-A) [6] ad cosidered i [6], [7]. We pair high-priority user D with low-priority user D k, which is the iteded receiver of the first packet from queue Q. Whe NOMA is performed to trasmit the packets from both queues Q ad Q at time slot t, the superpositioed sigal trasmitted by base statio S ca be expressed as p p PS s (t) + PS s k (t), where P S deotes the total trasmissio power of base statio S, ad deote the power allocatio coefficiets for high- ad low-priority users,

3 respectively, ad s k (t) deotes the sigal iteded for user D k at time slot t. Without loss of geerality, s k (t) s are assumed to be i.i.d. Gaussia radom variables with zero mea ad uit variace. As r m <r, 8 m M, accordig to the desig priciple of NOMA, we have > ad + =. Over the block fadig chael, the sigal received by user D m at time slot t is give by y m (t)=( s (t)+ s k (t)) p P S h m (t) p` (x m )+ m (t), () where h m (t) deotes the Rayleigh fadig chael gai betwee base statio S ad user D m with zero mea ad uit variace at time slot t, m (t) deotes the additive white Gaussia oise at user D m with zero mea ad variace at time slot t, `(x m )= +r m deotes the o-sigular path loss betwee base statio S ad user D m, x m deotes the locatio coordiate of user D m, ad deotes the path loss expoet. After receivig the sigal from base statio S, user D treats the sigal iteded for user D k as co-chael iterferece ad decodes its ow sigal based o the SINR give by (t, )= P S h (t) ` (x ) P S h (t) ` (x )+, () where (t, ) deotes the SINR of sigal s (t) observed by user D whe pairig with a low-priority user at time slot t. O the other had, user D k first tries to decode the sigal iteded for user D with the SINR give by!k(t, )= P S h k (t) ` (x k ) P S h k (t) ` (x k )+, (3) where!k(t, ) deotes the SINR of sigal s (t) observed by user D k at time slot t. et th deote the threshold for successful packet receptio. If user D k successfully decodes sigal s (t), i.e.,!k(t, ) th, user D k removes sigal s (t) from received sigal y k (t) by applyig successive iterferece cacellatio (SIC), ad the decodes its ow sigal with the sigal-to-oise ratio (SNR) give by k(t, )= P S h k (t) ` (x k ), (4) where k(t, ) deotes the SNR of sigal s k (t) observed by user D k at time slot t. Based o the above discussios, by usig NOMA, users D ad D k ca successfully decode their ow sigals if the evets { (t, ) th} ad {!k (t, ) th \ k(t, ) th} occur, respectively. O the other had, by usig OMA (e.g., time divisio multiple access (TDMA)), user D k ca successfully decode its ow sigal if evet { k (t, ) th} occurs. By usig NOMA, base statio S ca serve users D ad D k simultaeously, at the cost of reducig the probability of successful packet receptio at user D. Specifically, by sharig the frequecy chael ad splittig the trasmissio power, the received SINR at user D decreases, i.e., (t, ) < (t, ) = P S h (t) `(x )/. As a result, to guaratee the stability of queue Q, NOMA caot always be eabled, especially whe the average arrival rate is large. III. STABE TROUGPUT REGI I this sectio, we preset a opportuistic NOMA scheme by utilizig limited istataeous CSI at base statio S ad a baselie OMA scheme, ad derive their stable throughput regios. A. Opportuistic NOMA We cosider that limited istataeous CSI is available at base statio S. First, whe queue Q is o-empty at time slot t, oe-bit iformatio is fed back from user D to base statio S. I particular, user D feeds back to base statio S if the istataeous chael gai, h (t) ` (x ), is ot less tha a threshold,, ad feeds back to base statio S otherwise. Secod, whe queue Q is empty at time slot t, the iteded receivers of the first two packets from queue Q feed back their distace iformatio to base statio S. Based o limited istataeous CSI, NOMA ca be opportuistically eabled by base statio S to ehace the stable throughput regio. The opportuistic NOMA, deoted as, is described as follows. As user D has a high priority to be served, base statio S trasmits a packet from queue Q wheever it is o-empty. Without loss of geerality, the iteded receiver of the secod packet from queue Q at time slot t, whe available, is deoted as user D i. Depedig o the status of queues Q ad Q at time slot t, the packet trasmissios i opportuistic NOMA ca be categorized ito the followig three cases: Case : If Q (t) > ad Q (t) >, the base statio S trasmits the first packet from queue Q ad the first packet from queue Q to users D ad D k, respectively, usig NOMA with fixed power allocatio coefficiets (, ) whe h (t) `(x ), ad trasmits the first packet from queue Q to user D usig OMA with power P S whe h (t) `(x ) <. Case : If Q (t) > ad Q (t) =, the base statio S trasmits the first packet from queue Q to user D usig OMA with power P S. Case 3: If Q (t) =ad Q (t) >, the base statio S trasmits the first ad secod packets from queue Q to users D k ad D i, respectively, usig NOMA whe the first two packets are iteded for differet users (i.e., D k 6= D i ), ad trasmits the first packet from queue Q to user D k usig OMA with power P S whe D k = D i or Q (t) =. Based o the opportuistic NOMA described above, the average service rate of queue Q depeds o the status of queue Q. I particular, whe queue Q is empty, base statio S trasmits a packet from queue Q to user D usig OMA. O the other had, whe queue Q is o-empty, base statio S trasmits the first packet from queue Q ad the first packet from queue Q to users D ad D k usig NOMA with proba- +r bility P h (t) `(x ) =exp. Note that the probabilities of successful packet receptio at user D

4 usig OMA ad NOMA are differet. Similarly, the average service rate of queue Q also depeds o the status of queue Q. As a result, queues Q ad Q are iteractig with each other ad their average service rates caot be directly calculated. Stochastic domiace [4] ca be used to decouple the iteractig queues ad to facilitate the characterizatio of the stable throughput regio. By usig stochastic domiace, we costruct two domiat s ad based o the origial opportuistic NOMA. The domiat s, as a modificatio of the origial (i.e., ), esure that their queue legths are always ot less tha those i the origial by eablig the empty queues to trasmit dummy packets. The trasmissio of dummy packets reduces the probability of successful packet receptio by geeratig co-chael iterferece, but does ot cotribute to the throughput. ece, the stability coditio of domiat s is sufficiet for the stability of the origial. The stable throughput regios of the costructed two domiat s are discussed as follows. ) Stable throughput regio i domiat : I, if queue Q is empty, the queue Q domiat cotributes a dummy packet whe user D feeds back to base statio S, while queue Q acts the same as i the origial. I this case, the service process of queue Q ca be divided ito two cases: a) base statio S trasmits oe packet to user D usig OMA whe h (t) `(x ) <; b) base statio S trasmits oe packet to user D usig NOMA whe h (t) `(x ). As a result, the average service rate of queue Q i domiat, deoted as µ, ca be expressed as µ = P (t, ) th, h (t) `(x ) < + P (t, ) th, h (t) `(x ). (5) The probability of successful packet receptio at user D usig OMA (i.e., the first term of the right-had side of (5)) is deoted as q OMA (). For simplicity of otatio, we deote = th /P S. If apple, we have q OMA () =. Otherwise, we have q OMA () =P `(x apple h ) (t) < `(x ) (a) =exp +r exp +r, (6) where (a) follows from the Rayleigh fadig chael. The probability of successful packet receptio at user D usig NOMA (i.e., the secod term of the right-had side of (5)), deoted as q (,), ca be expressed as q (,)=P h (t) max =exp max th, th, `(x ) +r, (7) where > th. Otherwise, we have q (,)=. After derivig the average service rate of queue Q, by oyes theorem, queue Q is stable if <µ = ( q (,), if apple, q OMA ()+q (,), if >. O the other had, the service process of queue Q ca also be categorized ito two cases: a) if queue Q is oempty, base statio S trasmits oe packet to user D k usig NOMA whe h (t) `(x ) ; b) if queue Q is empty, base statio S trasmits two packets to users D k ad D i usig NOMA whe D k 6= D i (which occurs with probability M ), ad trasmits oe packet to user D k usig OMA whe D k = D i (which occurs with probability M ). Note that, for ease of presetatio, the average arrival rates of low-priority users are set to be the same, i.e., m = /M, 8 m M, but the aalysis ca be easily exteded to a geeral sceario with diverse average arrival rates. As all low-priority users follow the same locatio distributio, the average probability of successful packet receptio at each low-priority user is the same. ece, the average service rate of queue Q i domiat µ, deoted as µ, ca be expressed as = P(Q (t) > )P( h (t) `(x ) )q ( ) + P(Q (t) = ) q + M M qoma, (9) where the probability of queue Q beig o-empty is P(Q (t) > ) = /µ, q ( ) deotes the probability of successful packet receptio at user D k with power allocatio coefficiet whe pairig with user D, q is the summatio of the probabilities of successful packet receptio at users D k ad D i usig NOMA, ad q OMA is the probability of successful packet receptio at user D k usig OMA. The probability of successful packet receptio at user D k whe pairig with user D is give by q ( )=P (!k (t, ) th, k(t, ) th) = P h k (t) ( th ) `(x k), h k(t) `(x k) = E xk [exp ( " /`(x k ))], () o where " = max, ad E th xk [ ] deotes the expectatio of user D k s locatio x k. Due to the uiform distributio of low-priority users withi a circle with radius r, the probability desity fuctio (PDF) of user D k s locatio is give by f(x k )=/. ece, we have q ( )= = Z exp " / exp ( " ) " +r k r k dr k (8)," r, () where (u, v) = R v e z z u dz is the lower icomplete Gamma fuctio [7]. Whe queue Q is empty ad D k 6= D i, base statio S trasmits the first ad secod packets from queue Q usig NOMA accordig to the distaces of their iteded users. I particular, amog these two users, the ear ad far users are deoted as D ad D f with distaces r ad r f, respectively, ad r apple r f. Users D k ad D i have the same probability (i.e.,

5 .5) to be the ear or far user. For istace, if r k apple r i, we have D = D k ad D f = D i, ad we have D = D i ad D f = D k otherwise. I additio, we set f ad + f =. Due to the uiform distributio of users D ad D f [8], the PDF of the distace of far user D f is give by f(r f )=4r 3 f r 4, apple r f apple r. () The probability of successful packet receptio at user D f usig NOMA, deoted as qf ( f), ca be expressed as qf ( f)=p f (t, f ) th = E xf [exp ( " /`(x f ))] 4 4 Z exp " 4/ exp ( " ) " +r f rf 3 dr f 4," r, (3) where " = ad f th f > th. The PDF of the distace of ear user D is give by f(r )=4 r r, apple r apple r. (4) The probability of successful packet receptio at user D usig NOMA, deoted as q f ( ), is give by q f ( )=P ( f! (t, f ) th, (t, ) th) = E x [exp ( " 3 /`(x ))] r Z 4 r 4 exp " 3 +r " / 3 exp ( " 3 ) " 4/ 3 exp ( " 3 ) r r 3,"3 r dr 4,"3 r, (5) o where " 3 = max, f th ad f > th. Based o (3) ad (5), we have q = q f ( f)+q f ( ). (6) Similarly, the probability of successful packet receptio at user D k usig OMA ca be expressed as q OMA = P ( k (t, ) th) = / exp( ),. (7) By substitutig (), (6), ad (7) ito (9), the average service rate of queue Q i domiat ca be derived. By oyes theorem, queue Q is stable if < µ = µ exp +r q ( ) + q + M M qoma. (8) µ Based o (8) ad (8), the stable throughput regio i domiat is give by R ( ) o = (, ): µ + <, for apple <µ, (9) where = M qf ( f)+q f ( ) + M qoma ad =exp +r q ( ). Accordig to (9), stable throughput regio R depeds o the values of threshold ad power allocatio coefficiets (, ). I domiat, some would make queue Q always o-empty. As log as queue Q always has packets to trasmit, the behaviour of domiat is idetical to that of the origial opportuistic NOMA. ece, domiat ad the origial are idistiguishable at the boudary poits of the stable throughput regio. ) Stable throughput regio of domiat : I domiat, if queue Q is empty, the queue Q cotributes a dummy packet, while queue Q acts the same as i the origial. The average service rate of queue Q i domiat, deoted as µ, ca be expressed as µ = exp +r q ( ), where q ( ) is give i (). ece, queue Q is stable if <µ. The service process of queue Q ca also be categorized ito two cases: a) if queue Q is empty, the base statio S trasmits oe packet to user D usig OMA; b) if queue Q is o-empty, the base statio S trasmits oe packet to user D usig NOMA whe h (t) `(x ), ad trasmits oe packet to user D usig OMA whe h (t) `(x ) <. As a result, the average service rate of queue Q i domiat, deoted as µ, ca be expressed as µ = P(Q (t) = )q OMA () + P (Q (t) > ) q OMA ()+q (,), () where the probability of queue Q beig empty is P(Q (t) = ) = /µ, ad q OMA () ad q (,) are give by (6) ad (7), respectively. After derivig the average service rates of queues Q ad Q, by oyes theorem, the stable throughput regio i domiat R = for apple (, ) : <µ ca be expressed as q OMA () + µ q OMA () <, o =exp +r q ( ), () where = q OMA () q OMA () q (,). Similarly, stable throughput regio R depeds o the values of threshold ad power allocatio coefficiets (, ), ad domiat ad the origial are idistiguishable at the boudary poits of the stable throughput regio. Based o the above discussios, the stable throughput regio of the origial opportuistic NOMA is equal to the uio of the stable throughput regios i domiat s ad, i.e., R = R [R. B. Orthogoal Multiple Access I this subsectio, we preset a TDMA-based OMA, OMA, as a baselie, where base statio S trasmits oe packet i oe time slot. As queues Q ad Q are ot iteractig whe OMA is utilized, the stability coditio of

6 Average arrival rate of queue Q θ = ρ θ =.3ρ Domiat System Φ Domiat System Φ OMA System Φ OMA θ =.5ρ θ =ρ θ =ρ Average arrival rate of queue Q (.7,.3) (.75,.5) Domiat System Φ Domiat System Φ OMA System Φ OMA (.8,.) (.9,.) Average arrival rate of queue Q Fig. 3: Stable throughput regio with differet values of threshold ad parameters (, )=(.8,.) ad th =. these two queues ca be separately aalyzed. As user D has a high priority to be served, the average service rate of queue Q is µ OMA =exp +r. O the other had, whe queue Q is empty, base statio S trasmits a packet from queue Q to the correspodig user. The average service rate of queue Q is give by µ OMA = P (Q = ) P ( k (t, ) th) = /µ OMA q OMA, where q OMA is give i (7). Based o the above discussios, the stable throughput regio of the OMA ca be expressed as R OMA = (, ) : + <, +r for apple exp < exp IV. NUMERICA RESUTS q OMA +r o. () I this sectio, we evaluate the stable throughput regios of the proposed opportuistic NOMA ad baselie OMA schemes. The radius of the etwork coverage area is r =.5 km. igh-priority user D is located at r =.km away from base statio S, ad M = low-priority users are radomly distributed withi a circle with radius r =km cetered at base statio S. Trasmissio power P S ad oise power are set to be W ad dbm, respectively. We cosider Rayleigh fadig chaels ad the path loss expoet is set to be 4. The power allocatio coefficiets of far ad ear users of queue Q, ( f, ), are set to be (.8,.). Fig. 3 shows the impact of threshold o the stable throughput regio of the opportuistic NOMA whe (, ) = (.8,.) ad th =. The stable throughput regio of opportuistic NOMA is the uio of that of ad domiat s, give by (9) ad (), respectively. Whe threshold = = th /P S, the achievable i domiat is much larger tha that i OMA OMA, while the maximum achievable i domiat is smaller tha that i OMA OMA. This is due to the fact that the opportuistic NOMA scheme provides more trasmissio opportuities to low-priority users, at the cost of reducig the average service rate of high-priority user D. Whe =.5, the maximum Average arrival rate of queue Q Fig. 4: Stable throughput regio with differet values of power allocatio coefficiets (, ) ad parameters = ad th =. achievable i domiat ad OMA are the same, which shows that the opportuistic NOMA scheme ca ehace the performace of low-priority users without sacrificig the performace of high-priority user D by appropriately selectig the value of threshold. By further icreasig the value of threshold, the achievable i domiat s ad decreases, as the opportuity to perform NOMA decreases. The opportuistic NOMA ehaces the stable throughput regio whe compared with the OMA, i.e., R R OMA. Fig. 4 illustrates the impact of power allocatio coefficiets (, ) o the stable throughput regio of opportuistic NOMA with parameters = ad th =. Stable throughput regio R [R chages sigificatly with power allocatio coefficiets (, ). Whe, =(.7,.3), the achievable i domiat s ad is less tha that i OMA OMA whe >.6, as low-priority user D m, 8 m M, is bottleecked by successful decodig of the sigal iteded for high-priority user D, which is the prerequisite of performig SIC. By icreasig, the maximum achievable ad i domiat s ad icreases ad decreases, respectively, as more trasmissio power is allocated to highpriority user D. By eablig NOMA to serve the packets from queue Q, the maximum achievable i domiat is much greater tha that i OMA OMA. By appropriately selectig the power allocatio coefficiets, the stable throughput regio of opportuistic NOMA ca always be larger tha that of the OMA OMA. Fig. 5 plots the impact of receptio threshold th o the stable throughput regio of opportuistic NOMA whe = ad, = (.8,.). With a decrease of receptio threshold th, the maximum achievable ad i both opportuistic NOMA ad OMA OMA icrease, as the probability of successful packet receptio at each user icreases. With a smaller receptio threshold, the probability of queue Q beig empty is higher, which leads to more time slots available for the base statio to serve queue Q usig NOMA. ece, the performace gap betwee domiat ad OMA OMA

7 Average arrival rate of queue Q Γ th = Domiat System Φ Domiat System Φ OMA System Φ OMA Γ th = Average arrival rate of queue Q Fig. 5: Stable throughput regio with differet values of receptio threshold th ad parameters = ad (, )=(.8,.). Average service rate of queue Q Threshold θ (α, α )=(.8,.) (α, α )=(.9,.) Fig. 6: Average service rate of queue Q i opportuistic NOMA versus threshold ad power allocatio coefficiets (, ) whe =.3 packets/time slot ad th =. becomes larger whe receptio threshold th is smaller. Fig. 6 shows the impact of threshold ad power allocatio coefficiets (, ) o the average service rate of queue Q whe =.3 ad th =. With the variatio of threshold, there exists a optimal poit of the average service rate of queue Q. The average service rate of queue Q ca be greater tha as NOMA is eabled to simultaeously serve two packets from queue Q whe queue Q is empty. If (, )=(.8,.), the average service rate of queue Q icreases with whe <.5. By eablig NOMA whe the chael gai betwee base statio S ad user D is larger, less packet retrasmissios are required to guaratee the stability of queue Q, which i tur provide more trasmissio opportuities to low-priority users. The average service rate of queue Q decreases with whe >.5 ad coverges to.87, as the probability of eablig NOMA becomes smaller. By icreasig to.9, the optimal threshold that ca maximize the average service rate of queue Q becomes smaller, as allocatig more trasmissio power to user D allows NOMA to be eabled whe the chael gai is lower. V. CCUSI I this paper, we studied the stable throughput regio of dowlik NOMA trasmissio with dyamic traffic arrival for users with differet priorities. To reduce the adverse effect of chael sharig ad trasmissio power splittig due to NOMA o the high-priority user, we proposed a opportuistic NOMA scheme by usig limited istataeous CSI at the base statio. 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