Non-Orthogonal Random Access for 5G Mobile Communication Systems

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1 This artile has been aepted for publiation in a future issue of this journal, but has not been fully edited. Content may hange prior to final publiation. Citation information: DOI.9/TVT.8.86, IEEE Non-Orthogonal Random Aess for G obile Communiation Systems Jun-Bae Seo, ember, IEEE, and Bang Chul Jung, Senior ember, IEEE, Hu Jin, ember, IEEE Abstrat This paper proposes two non-orthogonal random aess NORA) tehniques for G mobile ommuniation networks, where user equipments UEs) make use of the hannel inversion tehnique suh that their reeived power at the base station BS) an be one of two target values. It enables the BS to deode two pakets simultaneously with suessive interferene anellation SIC) tehnique if different power level is hosen. We propose two NORA systems; that is, UEs hoose one of two target power levels based on the hannel gain, or the region where they are. The performane of the proposed systems is analyzed in terms of aess delay, throughput, and energy effiieny. Through analysis and extensive omputer simulations, we show that the maximum throughput of the proposed NORA tehniques an exeed.7 whih is a signifiant improvement ompared to the maximum throughput of onventional random aess.368. Index Terms G mobile ommuniations, uplink NOA, random aess, suessive interferene anellation. I. INTRODUCTION To improve the spetral effiieny SE) for the th generation G) mobile ommuniation systems, non-orthogonal multiple aess NOA) has been proposed, in whih the reeiver separates the super-imposed signals via suessive interferene anellation SIC) tehnique. When it is used for the downlink, a base station BS) onstruts the super-imposed signal for a group of users in the same radio resoure and alloates different transmission powers to eah user equipment UE). The multiplexed signal experienes the same smallsale) fading and path-loss olletively over the downlink, and then it an be suessfully separated by eah UE with SIC tehnique if the BS properly alloates different levels of powers to the UEs. For the uplink, in ontrast, the BS reeives the super-imposed signals from different UEs, eah of whih may experiene independent fading and path-loss due to their different loations. As prior work for the uplink NOA, the outage probability and sum-rate were investigated, 3, in whih UEs utilize the transmit power ontrol TPC) tehnique to ompensate the path-loss, but only two or three UEs 3 are onsidered. The uplink NOA was also analyzed when UEs are deployed based on Poisson point proess or a lustered point proess, respetively. In, dynamis of users retransmissions and hannel inversion 6 were not onsidered. Copyright ) IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. This work was supported in part by the grant RP3G and in part by the National Researh Foundation of Korea NRF) Grant funded by the Korea Government SIT) NRF-8RCB686 and NRF- 6RAB83). Corresponding author: Hu Jin.) J.-B. Seo is with the Department of Eletrial Engineering, Indian Institute of Tehnology Delhi, New Delhi, 6, India jbseo@iitd.a.in). B. C. Jung is with the Department of Eletronis Engineering, Chungnam National University, Daejeon, 33, South Korea bjung@nu.a.kr) H. Jin is with the Division of Eletrial Engineering, Hanyang University, Ansan, 88, South Korea hjin@hanyang.a.kr). In 7, 8, the SIC tehnique was integrated with splitting algorithm for ontention resolution. In partiular, 8 proposed a dual power multiple aess DPA) system, where UEs exploit hannel inversion; that is, UEs transmit their paket so that their reeived power an be one of two power levels and the BS deodes the reeived pakets with the SIC. In ontrast with, 3, this paper onsiders a random aess network with UEs, where the BS adopts the SIC tehnique to separate the reeived pakets from multiple UEs in power domain, alled non-orthogonal random aess NORA). As in DPA 8, in our proposed tehnique, UEs utilize the hannel inversion as well. However, the proposed NORA fundamentally is different: DPA allows UEs to target at one of two power levels randomly, while our sheme asks UEs to opportunistially hoose their target power level based on their hannel gains whih may further improve the energy effiieny EE). As main ontribution, we propose two NORA systems and analyze their throughput pakets/slot), the average aess delay, and EE pakets/slot/joule), where Rayleigh fading and path-loss are taken into aount. II. SYSTE ODEL Suppose an uplink time division duplex TDD) wireless network, where a BS is at the enter of a irular overage area with radius R and UEs share the wireless uplink. Time is divided into slots of a onstant size; eah slot is equal to one paket transmission time. We assume that eah UE an hold only one paket and that at eah slot the probability of a new paket arrival to UE is σ. One a UE has a paket to send, it measures its hannel gain Y = hr α through the downlink referene signal with hannel reiproity of TDD. Here, h indiate a short-term fading, whih is assumed to be exponentially distributed random variable with unit mean, whereas r and α denote the distane from the BS to the UE, and the path-loss exponent, respetively. In NORA systems, UE makes the reeived power at the BS either P or P for P > P by utilizing hannel inversion. If P T,i denotes the transmission power of the UE whih targets at P i, we have P T,i = Pi hr = Pi α Y for i {, }. With the target reeived powers P and P, we onsider the SIC-based reeiver at the BS. It is always suessful for the BS to deode one paket, if it reeives only one paket with P i. When the BS reeives more than one pakets inluding the one with P, it an deode the paket with P suessfully, if P kp + N γ for k =,,..., ) where N and γ denote noise power and SINR threshold for the suessful deoding, respetively. In ), k indiates the number of reeived pakets with P. We assume that 8-9 ) 8 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See for more information.

2 This artile has been aepted for publiation in a future issue of this journal, but has not been fully edited. Content may hange prior to final publiation. Citation information: DOI.9/TVT.8.86, IEEE depending on target power P i, the referene signal for the BS to perform hannel estimation is differently loated, whih also failitates the BS s deteting and deoding the pakets reeived. oreover, the hannel estimation at the BS is assumed to be perfet. Let k be the maximum number of the pakets with P so that the paket with P is suessfully deoded. Using ), we an get k as k = P /γ N ) /P = SNR γ) /γsnr ), ) where SNR i P i /N for i = and. For the paket with P to be deoded suessfully, we have two ases. As mentioned before, the BS reeives a single paket with P, where SNR γ is satisfied. The seond one is when two pakets are reeived at the BS, eah of whih targets at P and P, respetively, i.e., k = in ). After the paket with P is deoded, it is removed with the SIC tehnique and the paket with P is also suessfully deoded provided that SNR γ. Note that if there exist more than one pakets with P, no pakets an be deoded. We assume that the BS notifies the outome of a paket transmission to the UE just before the beginning of the next slot. The UEs that do not have the feedbak shall regard themselves as baklogged. It is important to note that instead of allowing UEs to target at P or P randomly and independently, a higher throughput is expeted if the system inreases a joint probability or orrelation) that one UE targets at P and the other at P in a distributed and energy-effiient way. To do this, we onsider two systems, say NORA-A and -B: In NORA-A, if the UE finds Y β, it sends its paket with probability µ by adjusting its transmission power so that the reeived power at the BS is equal to P. If β Y < β, it transmits its paket with probability µ as well, but the BS reeives the paket with power P. The UE does not re)transmit the paket if Y < β, where β is alled outage threshold. On the other hand, in NORA-B, the overage area is divided into two regions: One is a small irular region with radius r, say region, and the other is the region with r for r < r R, say region. In the two regions, we assume that and UEs are randomly deployed in eah region, respetively. At eah slot, a new paket is generated at UEs in region and with probability σ and σ, respetively. Unlike NORA-A, UEs in NORA-B have a speifi threshold β i for region i. If the UE in region i finds Y β i for i =,, it transmits the paket at the next slot with probability µ i by adjusting its transmission power suh that the reeived power at the BS is equal to P i. III. ANALYSIS AND DESIGN Before analyzing the throughput, average aess delay, and EE of NORA-A and -B, we examine the probability that a hannel gain exeeds the threshold in both systems. Lemma : In NORA-A, the probability that a UE finds Y y for α =, i.e., a typial value of pathloss exponents for urban area, is expressed as PrY y = F Y y) = π R y erf yr ), 3) where F Y y) is the umulative distribution funtion CDF) of Y, and erfx) = x π dt. e t Proof: Sine F Y y) = PrY y, we an write it as F Y y) = Pr hr α y = = e yrα) f R r)dr e yrα f R r)dr, ) where f R r) is the probability density funtion pdf) of a UE being randomly in the overage area of NORA-A, whih is f R r) = r R for r R. For α =, we have F Y y) = R R rdr = π e yr R y erf ) yr. We then have 3) using PrY y = F Y y). Corollary : For NORA-B, let q β ) denote the probability that a UE in the region transmits its paket by targetting at P if finding its hannel gain Y β. For α =, we have q β ) = PrY β = r π β erf β r ). ) Proof: With slight abuse of notation, let F Y y) be the CDF of Y in the region, whereas f R r) denotes the pdf of a UE in the region, i.e., f R r) = r r for r r. We an get ) by replaing f R r) with f R r) in ). Corollary : Let q β ) be the probability that a UE in the region transmits its paket by targetting at P when Y β. For α =, it is obtained as q β ) = π erf β R ) erf β r ) R r ) β. 6) Proof: Let F Y y) be the CDF of Y of a UE in the region. In ), by replaing f R r) with f R r) = r/r r ) for r r R, we an get F Y y) and q β ) = F Y β ) Now, let us haraterize the performane of NORA-A. Note that the number of baklogged UEs n hanges at eah slot boundary, the system state an be aptured by a disrete-time arkov hain. To do this, let φ = φ n for n {,,..., } be the steady) state probability row vetor of length +, where φ n denotes the probability that the system has n baklogged UEs in steady state. Furthermore, S denotes the state transition probability matrix whose element s n,m is the state transition probability that state n at time t hanges into m at time t+. Then, based on theory of disrete-time arkov proess, we an get φ as φ = φ S and φ e =, where e is a olumn vetor of all ones, whose length orresponds to φ. We an find first s,m = Bm σ), where a binomial distribution, B n mx) = n m) x m x) n m, but it is zero if m < or m > n. For m max, n ) and n, we have k + s n,m = Bϑ)B n p o )B n m n ) σ) + Bϑ)B k k n p o ) + B n p o ) B n m n ) σ) + B n m n σ) B n p o ) + + k + n k=k + B n k p o ) B k ϑ) ) Bk n p o ) + Bϑ))B n p o ), 7) where p o is the probability that a baklogged UE re)transmits its paket. Using Lemma, we an get p o = µ PrY β = µ R π β erf β R ). In 7), ϑ indiates the probability that 8-9 ) 8 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See for more information.

3 This artile has been aepted for publiation in a future issue of this journal, but has not been fully edited. Content may hange prior to final publiation. Citation information: DOI.9/TVT.8.86, IEEE 3 the UE with Y β will re)transmit its paket by targeting r PrY β at P, i.e., ϑ = p o. Eq. 7) an be read as follows: For instane, the first term shows that the transition from n baklogged UEs i.e., n nonbaklogged UEs) to m ours in the system, if two out of n baklogged UEs transmit suessfully with probability Bϑ)B n p o ), whereas m n ) out of n UEs join the baklogged UEs newly with probability B n m n ) σ). The first term in the first braket indiates that the paket with P an be suessfully deoded as long as the number of pakets targetting at P is less than k. The seond term in the braket indiates that one paket suessfully is reeived with either P or P if only one is transmitted. Due to lak of spae, we explain the last term in 7), whih means that two UEs aess with probability B n p o ) and both of them hoose either P or P with probability Bϑ). If m n out of n UEs join, the system has m baklogged UEs at the next time. To get the throughput pakets/slot) of NORA-A, let τ a denote the throughput, whih an be obtained as τ a = n= k + ) Bϑ)B n p o ) + Bϑ)B k k n p o ) + B n p o ) φ n. The first term onsiders the ase that two out of n baklogged UEs transmit with probability p o. In this, both of them make a suessful transmission if one hooses P with probability ϑ and the other does P with probability ϑ. The seond term means that if there are aessing UEs more than two, the one with P an transmit its paket suessfully if the number of UEs with P is less than or equal to k. The last term implies that if only one UE transmits whether it hooses P or P ), it will make a suessful transmission. Using Little s result, we obtain the average aess delay of NORA-A as d a = N a /τ a, and N a = N n= nφ n. Let us onsider EE of NORA-A, defined as E a = τ a /P a, where P a is the average transmission power onsumption of NORA-A. We an write P a = µp a, +P a, )N a, where P a,i denotes the average transmission power onsumption of a UE aiming at P i for i =,. Lemma : In NORA-A, P a,i for α = is obtained as P a, = P Y a β ) and P a, = P Y a β ) Y a β )), where Y a y) is given in the proof. Proof: Based on P T,i = Pi Y, we an write P a, as P a, = EP T, = P β y f Y y)dy = P Y a β ) 9) π = P R y erf yr ) y e R y dy, β where we have f Y y) = R r e yr dr from ). Similiarly, β we get P a, = P β y f Y y)dy = P Y a β ) Y a β )). Let us move onto the performane of NORA-B. The system state an be aptured by n, n ), where n and n denote the number of baklogged UEs in region and at time t, respetively. Thus, its state spae is {n, n ) n {,,..., }, n {,,..., }}. Let π = π n,n be the steady state probability row vetor of length + ) + ), where π n,n is the steady state probability that the system has n and n baklogged UEs in region and 8), respetively. If the state transition probability matrix Q is obtained, whose element q n,n ),m,m ) denotes the state transition probability that state n, n ) at time t hanges into m, m ) at time t+, we an get π as π = π Q and π e =, where the length of e orresponds to that of π. For n = n =, we an have q,),m,m ) = Bm σ )Bm σ ). For m n, n and n =, we have q n,),m,m ) =B m σ ) B n θ )B n m σ n ) ) + B n θ ))B n m n σ ), ) where θ i = µ i q i β i ) for i =, is the probability that a baklogged UE in region i re)transmits its paket. In ), the region has m baklogged UEs from zero with probability Bm σ). eanwhile, the region has m baklogged UEs from n, if one out of n UEs transmits suessfully and m n ) newly join the baklogged. Otherwise, it has m baklogged UEs, if m n newly join the baklogged. Similarly, for m n, n and n =, we get q,n),m,m ) =Bm σ ) B n θ )B n m σ n ) ) + B n θ ))Bm n n σ ). ) For m n, m n, n, n, q n,n ),m,m ) is given in 6) on the top of the next page. The system throughput of NORA-B is then τ b = j= n = n = π n,n τ b,j,n,n, ) where τ b,,n,n = B n θ ) k i= Bn i θ ), and τ b,,n,n = B n θ ) i= Bn i θ ) denote the expeted number of pakets suessfully transmitted in region and, respetively. Let d b,i slots) denote the average aess delay of a UE in the region i in NORA-B. As in NORA-A, we also get d b,i = n = n + n )π b,n,n = N b /τ b,i, where N b = n = N + N. We an get EE of NORA-B as E b = τ b /P b, in whih we have the average transmission power onsumption P b = ) n = n r = P b, n + r P b, n πn,n. Corollary 3: Let P b,i be the average transmission power onsumption of a UE aiming at P i for i =, in NORA-B. For α =, we have π P b, = P and β P b, = P R r r erf ) yr y β y e r y dy, 3) π y erf yr ) erf yr )) y R e Ry r e r y) dy. ) Proof: We an write P b, as P b, = P β y f Y y)dy = P Y b, β ), ) 8-9 ) 8 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See for more information.

4 This artile has been aepted for publiation in a future issue of this journal, but has not been fully edited. Content may hange prior to final publiation. Citation information: DOI.9/TVT.8.86, IEEE q n,n ),m,m ) = B n θ )B n m σ n ) ) Bm n n σ ) { n B n i θ )+B n θ ) i= n i=k + k i=,i ) B n i θ ) Bm n n σ ) + B n θ ) B n i θ ) + B n θ )B n m σ n ) ) + Bm n n σ ) 6) B n θ )B n m n ) σ ) + B n θ ))B n m n σ ) }. τa pakets/slot) τb pakets/slot).6.. optimal a) NORA-A S-ALOHA subopt. µ =. µ =. 3 6 b) NORA-B.7.6 optimal. subopt.. S-ALOHA µ i =. NORA-A, subopt. µ i =. 3 6 Fig.. Throughput of NORA-A and -B: k = in whih we an get f Y y) = df Y y) dy from ). For α =, we an rewrite Y b, β ) in ) as Y b, β ) = β y f Y y)dy = yr r z e z dzdy β y so that we have 3). Likewise, the average transmission power of UEs for P is expressed as P b, = P β y f Y y)dy = P Y b, β ), where f Y y) is obtained from 6). We now disuss how the system parameters an be seleted. First, to maximize the throughput of the system in ongestion, we onsider retransmission probabilities for UEs to use in both systems. Suppose that NORA-A has n baklogged UEs for n, say ongested at time t. Then, the throughput is maximized when we maximize the term in the parenthesis in 8) with respet to µ. However, even for k =, it is not easy to find a losed form of µ. Therefore, let us fous on maximizing the term Bϑ)B n p o ) and we have a maximizer µ = min n PrY β, ). Now onsider NORA-B when it has n and n baklogged UEs in region and at time t. To maximize the system throughput, UEs in region i should use µ i of maximizing τ b,,n,n + τ b,,n,n, whose solution an not be obtained as a losed form. When fousing on the term B n θ )B n θ ), the re)transmission probability employed in region i is µ i = min n i PrY β, i ). We all µ and µ i a suboptimal retransmission probability under ongestion, whih later help us to estimate the throughput limit. Let us disuss how to set other system parameters suh as the thresholds for hannel gain, and target reeived powers. In determining β i, we an onsider three methods as follows. The first one is to restrit aess opportunity based on hannel gain suh that Prhr α β i = q i β i ) = ɛ i. If ɛ i =, UEs an re)transmit their paket with probability µ or µ i regardless of hannel gain. Suh a β i an be numerially obtained as β i = q i ɛ i ). Notie that a higher ɛ i an give more frequent aess opportunities in expense of the transmission power onsumption. For ɛ = ɛ, it an be said that UEs in region and have equal aess opportunities, but different transmission power onsumptions. The seond method is that one we set β as the outage threshold of region, we set β suh that either the throughput, or EE an be maximized. The last one is to onstrain the average transmission power onsumption by a value δ i, i.e., Y i β i ) = δ i. Given δ i, numerially we an find β i = Y i δ i ). If δ = δ, UEs in the region and have equal transmission power onsumption, but unequal aess opportunity. Aordingly, a tradeoff is expeted between aess opportunity and the average transmission power onsumption. Finally, let us onsider how P and P an be hosen. Given a bandwidth B, we an set P as SNR = P /N = R/B ) γ, where R is the required data rate of UEs aiming at P. Then, P an be set as P = θp for θ >. For SNR = γ, i.e., the minimum power P to meet R, we write ) as k = γ θ ) for θ >. IV. NUERICAL RESULTS Throughout this setion, unless otherwise stated, we use the parameters as r =, R =, and α =, whereas γ =., θ = 3. and N = in ), whih gives k =. Notie that the symbols in eah figure denote simulation results, while the lines indiate analysis. In Figs. and, our analysis is verified against simulations, where the throughputs, EE and aess delay of NORA-A and -B are presented. For NORA-A, we set σ =., while = +, =, and σ = σ =. for NORA-B. Note that the produt σ an be alled the average traffi intensity to the system. When we inrease and at the same time redue σ by keeping σ onstant, the same throughput as shown in Fig. an be observed. We set two thresholds β = , and β =.93 9 for both systems as follows: For a given β arbitrarily seleted here, but determined with ell overage in pratie), we hoose β suh that EE of NORA-A for = and µ =. an be maximized. This implies in NORA-B that UEs in region have the aess opportunity ɛ = q β ) =.8 and ɛ =.3 in region. First of all, in Figs. and, it is demonstrated that our analysis agrees well with simulation, while τ a and τ b very similarly hange upon the inrease in. One differene with µ and µ i is that τ b is slightly higher than τ a for a larger, and vie versa for a smaller. This is beause two UEs an hoose P or P rather independently with µ, whih makes both UEs target at P or P aidentally. This leads to more ollisions than in NORA-B. To find the maximum throughput supported by eah system marked as optimal in Fig. ), we numerially find exhaustive searh) the optimal retransmission probability of maximizing the term 8-9 ) 8 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See for more information.

5 This artile has been aepted for publiation in a future issue of this journal, but has not been fully edited. Content may hange prior to final publiation. Citation information: DOI.9/TVT.8.86, IEEE slots -9 3 a) Energy Effiieny NORA-A, µ =. NORA-A, µ =. NORA-B, µ i =. NORA-B, µ i = NORA-A, µ =. b) Aess Delay NORA-A, µ =. 3 NORA-B, µ i =. NORA-B, µ i = Fig.. EE and average aess delay of NORA-A and -B: k = in the parenthesis in 8) for NORA-A and τ b,,n,n +τ b,,n,n for NORA-B, respetively. For k =, the maximum throughput with the optimal retransmission probability is.6 and.6 in NORA-A and -B, respetively. Using the suboptimal retransmission probabilities under ongestion, we an ahieve.6 throughput of NORA-B. When θ is inreased up to 7 not shown here), whih yields k =, the optimal retransmission probability shows.777 throughput. As a omparison, we depit throughput of the system without SIC, i.e., S-ALOHA, for µ =. or µ i =.), where no pakets an be deoded upon transmissions of more than one pakets. While NORA is better, it shows also that ill-designed retransmission probability an make it even worse than S-ALOHA. As well known, the maximum throughput of S-ALOHA is.368 whih an also be observed from Fig. approximately. As inreases, it an be seen that the throughput with the suboptimal retransmission probability meets the optimal one. Sine a higher retransmission probability yields a higher throughput for the system with a smaller population size, a dynami retransmission probability depending on the baklog size) is needed in order to ahieve and maintain the maximum throughput over time. Fig. shows EE and aess delay with two retransmission probabilities used in Fig.. As expeted, as inreases, it is shown that EE dereases due to more ollisions. Furthermore, NORA-B shows better EE than NORA-A, whih is due to its higher throughput. Notie that the aess delay of NORA-A is smaller than that of NORA-B for 3. In Figs. and, it an be onluded that NORA-B is better than NORA-A if NORA-B has the same average traffi intensity of region and. While it is simple to run NORA-A in pratie, for NORA-B it is needed to make UEs aware of two regions so that they an realize hannel inversion with β i in eah region. Notie that although not presented here, the equal aess opportunities, ɛ = ɛ shows the same average aess delay of UEs in two regions, i.e., d = d in NORA-B. Fig. 3 illustrates the throughput and EE of two NORA-B systems: One is that the number of UEs deployed in region,, is four times larger than ; the other is that is one quarter of, and = +. The throughput of both systems in Fig. 3 is found lower than NORA-B in Fig., where is equal to. oreover, the throughput of the system with = drops drastially as exeeds 3 in omparison with the other system while it is slightly higher for < 3. This shows that UEs in region an have aess priority for a lightly loaded system, but deteriorate the overall τb pakets/slot) optimal a) Throughput <,k = >,k = <,k = >,k = 3 6 b) Energy Effiieny -8 <,k = >,k = -9 <,k = >,k = 3 6 Fig. 3. Throughput and EE of NORA B: k =, and µ i =. system if they are dominantly ative or baklogged. EE shows similar behavior. When θ is inreased from 3. to., whih gives k =, the throughput of the system having a larger is muh more improved than that of the other system. Suh throughput gains result from that the system of employing a higher P is more robust to the interferene from aessing UEs with P, whih gives a higher suess probability for UEs with P. Notie that even if EE of the system with < is muh lower than the other system for < 3, it beomes improved along with the enhaned throughput for > 3. The optimal throughput shown in Fig. 3a) is obtained for the system with > and the optimal retransmission. V. CONCLUSIONS We proposed two NORA tehniques: NORA-A and NORA- B, where UEs aim at two levels of target reeived powers aording to their hannel gain or loation. It has been shown that NORA-B is better than NORA-A in general, and it an partiularly ahieve the maximum throughput above.7 with propor retransmission ontrol. In other words, NORA-B an make use of power-domain NOA fully over the uplink if only one user in eah region is allowed to aess by retransmission ontrol and targets at a speifi power level assoiated with eah region. We leave a dynami retransmission sheme in NORA to maximize the system throughput and NORA with multilevel target powers as future work. REFERENCES S.. R. Islam, N. Avazo, O. A. Dobre, and K.-S. 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