Performance Analysis of a Hybrid Downlink-Uplink Cooperative NOMA Scheme
Zhiqiang Wei, Linglong Dai, Derrick Wing Kwan Ng, Jinhong Yuan
aa r X i v : . [ c s . I T ] M a r Performance Analysis of a Hybrid Downlink-UplinkCooperative NOMA Scheme (Invited Paper)
Zhiqiang Wei, Linglong Dai, Derrick Wing Kwan Ng, and Jinhong Yuan
Abstract —This paper proposes a novel hybrid downlink-uplink cooperative NOMA (HDU-CNOMA) scheme to achievea better tradeoff between spectral efficiency and signal receptionreliability than the conventional cooperative NOMA schemes.In particular, the proposed scheme enables the strong user toperform a cooperative transmission and an interference-freeuplink transmission simultaneously during the cooperative phase,at the expense of a slightly decrease in signal reception reliabilityat the weak user. We analyze the outage probability, diversityorder, and outage throughput of the proposed scheme. Simulationresults not only confirm the accuracy of the developed analyticalresults, but also unveil the spectral efficiency gains achieved bythe proposed scheme over a baseline cooperative NOMA schemeand a non-cooperative NOMA scheme.
I. I
NTRODUCTION
Recently, non-orthogonal multiple access (NOMA) hasdrawn a lot of attentions as an important enabling techniqueto fulfill the challenging requirements of the fifth-generation(5G) communication systems, such as massive connectivity,high spectral efficiency, and ultra-low latency [1], [2], [3].In the literature, different schemes, such as power domainNOMA and code domain NOMA, have been proposed tofacilitate multiuser multiplexing [3]. Power domain NOMA isparticularly appealing as it can be integrated with the existingfourth-generation communication systems. The fundamentalidea of power domain NOMA is to exploit the power domainfor multiuser multiplexing via using superposition coding attransmitters and successive interference cancellation (SIC) atreceivers [4]. In particular, NOMA allows a strong user (withbetter channel condition) concurrently accessing the spectrumresources assigned for a weak user (with worse channel con-dition) to increase the system spectral efficiency. To alleviatethe inter-user interference (IUI) at the weak user, a largeramount of power is allocated to the weak user while a smallerfraction of power is provided for the strong user. Meanwhile,SIC technique is adopted at the receiver of the strong userto remove the IUI. It has been shown that NOMA providessubstantial performance gains over conventional orthogonalmultiple access (OMA) in terms of spectral efficiency [5], [6],[7] and fairness [8], [9].In wireless communications, the system performance issignificantly limited by channel fading raised from multi-path propagations. This issue is more prominent in NOMA
Zhiqiang Wei, Derrick Wing Kwan Ng, and Jinhong Yuan are with theSchool of Electrical Engineering and Telecommunications, the Universityof New South Wales, Australia (email: [email protected];[email protected]; [email protected]). Linglong Dai is with the De-partment of Electronic Engineering, Tsinghua University, China (email:[email protected]). Derrick is supported under Australian Research Coun-cil’s Scheme Discovery Early Career Researcher Award funding scheme(project number DE170100137). scenarios. Specifically, weak users become more vulnerableto channel fading due to not only the severe path loss, butalso the IUI caused by the simultaneous communication tostrong users. Traditionally, cooperative diversity is an effectivetechnique to combat channel fadings in wireless networks[10]. Among different cooperative strategies proposed in theliterature [11], [12], [13], cooperative relaying is an attractivetechnique to increase the range of communication systems andto enhance the link reliability without incurring the high costof additional base station deployment. Therefore, a cooperativeNOMA (CNOMA) scheme was proposed in [14] to improvethe signal reception reliability for the weak user by exploitingthe prior information obtained at the strong user during SICprocess. Particularly, in addition to the downlink NOMAtransmission phase, the strong user acts as a decode-and-forward (DF) relay to deliver messages to the weak userin the cooperative phase. The extensions of this scheme tomultiple-antenna relaying networks and full-duplex relayingnetworks were investigated in [15] and [16], respectively. Notethat the aforementioned CNOMA schemes enhance the signalreception reliability at the price of reduced spectral efficiencydue to the duplicate transmission during the cooperative phase.More recently, a non-orthogonal relaying strategy is applied inCNOMA systems to improve the spectral efficiency, where abase station (BS) and a relay transmit their messages at thesame time in the same frequency. Nevertheless, a dedicatedrelay is required in most of existing schemes [17], [18]. Also,these schemes do not fully exploit the BS in the cooperativephase which lead to potential loss in spectral efficiency.In this paper, we propose a new hybrid downlink-uplinkCNOMA (HDU-CNOMA) scheme to improve the spec-tral efficiency. Different from the conventional CNOMAscheme[14], our proposed scheme enables the uplink trans-mission from the strong user to the BS during the cooperativephase. Hence, it is expected that our proposed scheme is ableto improve the achievable system sum rate at a price of aslightly decrease in the signal reception reliability at the weakuser. Besides, we derive the closed-form expressions of thesystem outage probability and the diversity orders to character-ize the performance of the proposed scheme. Numerical resultsare shown to verify our analytical results and to demonstratethe effectiveness of our proposed scheme.II. S
YSTEM M ODEL
Consider a communication scenario including downlink anduplink transmission with one BS and two users , as shown The extension to the case with more than two users is straightforward byfollowing a similar approach as [14]. ase station UE 2UE 1SIC First time slot (Downlink NOMA)Third time slot (Uplink NOMA)Memory unitDecoding methodSecond time slot (Cooperative phase)Decode
Side Information ( ) , s s s u s U E U E
11 1 2 2 p u p s + tUE1 y tBS y SIC tBS y u ( ) , u u U E pu MRC s tUE2 y tUE2 y B S B S p s p s + B S B S p s p s + U E p u Fig. 1. The proposed HDU-CNOMA scheme with one BS and two users. in Figure 1. All the transceivers are equipped with a singleantenna and operate in half-duplex mode, i.e., they cannottransmit and receive a signal at the same time in the same fre-quency. Furthermore, we assume a time division duplex (TDD)protocol for facilitating downlink and uplink transmission. Wedenote h BS , UE1 as the channel coefficient between the BS anduser 1 (UE 1), h BS , UE2 as the channel coefficient between theBS and user 2 (UE 2), and h UE1 , UE2 as the channel coefficientbetween UE 1 and UE 2. We assume that perfect channel stateinformation (CSI) is available at receivers for signal detection,while only statistical CSI is available at transmitters. All thelinks considered here are assumed to experience independentquasi-static fading, where the channel coefficients are constantfor each time slot but vary independently between differenttime slots for different links. Besides, we assume that thechannel coefficients are Rayleigh distributed: h δ ∼ CN (0 , β δ ) , δ ∈ { (BS , UE1) , (BS , UE2) , (UE1 , UE2) } , where CN (0 , β δ ) denotes the circularly symmetric complex Gaussian distribu-tion with zero-mean and variance β δ , and the variance β δ captures the effect of large scale fading for the link δ . Then, thecumulative distribution function (CDF) and probability densityfunction (PDF) for the channel gain of link δ , i.e., | h δ | , aregiven by F | h δ | ( x ) = 1 − exp( − xβ δ ) , x ≥ , and (1) f | h δ | ( x ) = 1 β δ exp( − xβ δ ) , x ≥ , (2)respectively, where |·| denotes the absolute value of a complexscalar. Meanwhile, we consider the user with the larger β δ as the strong user and without loss of generality, we assume β BS , UE1 > β BS , UE2 . In other words, UE 1 is selected toperform SIC and to assist UE 2 in our proposed scheme[19],[20]. Note that this may not be the optimal SIC decoding orderto minimize the system outage probability under statistical CSIassumption[19], [21], because β BS , UE1 > β BS , UE2 does notguarantee | h BS , UE1 | > | h BS , UE2 | . However, it is a simplebut effective strategy under statistical CSI[19]. To facilitateour performance analysis, we focus on this specific schemewith UE 1 as the strong user and serving as a relay to assistUE 2.As shown in Figure 1 and Figure 2(a), in our proposedHDU-CNOMA scheme, one time frame is partitioned intothree time slots with equal duration for downlink NOMA BS UE1, UE 2 fi UE1, UE 2 BS fi UE1 BS, UE 2 fi (a) Proposed HDU-CNOMA scheme. BS UE1, UE 2 fi UE1 UE 2 fi UE1, UE 2 BS fi (b) Conventional CNOMA scheme[14]. BS UE1, UE 2 fi UE1, UE 2 BS fi (c) Non-cooperative NOMA scheme.Fig. 2. Illustrations for: a) proposed HDU-CNOMA scheme; b) conventionalCNOMA scheme[14]; c) non-cooperative NOMA scheme. phase, cooperative phase, and uplink NOMA phase. Note thatfixed power allocation is adopted for in this paper. Althoughoptimizing the power allocation during different phases canfurther improve the performance of our proposed scheme, itis beyond the scope of this paper and will be considered inour future work. In the following, we present our proposedscheme. A. Proposed HDU-CNOMA Scheme
In the first time slot, i.e., the downlink NOMA phase, thetransmitted signal from the BS is given by x t BS = q α t UE1 P s + q α t UE2 P s , (3)where superscript t denotes the 1-st time slot, P denotes themaximum transmit power for the BS, s and s denote themodulated downlink symbols for UE 1 and UE 2, respectively,and α t UE1 and α t UE2 denote the power allocation factors forUE 1 and UE 2 in t , respectively. According to the NOMAprotocol[5], we allocate more power to the weak user, thuswe have α t UE1 ≤ α t UE2 and α t UE1 + α t UE2 = 1 . For notationalsimplicity, we assume the same maximum transmit power forthe BS, UE 1, and UE 2 in our model . Subsequently, thereceived signals at UE 1 and UE 2 in t are given by y t UE1 = h BS , UE1 (cid:18)q α t UE1 P s + q α t UE2 P s (cid:19) + z UE1 and (4) y t UE2 = h BS , UE2 (cid:18)q α t UE1 P s + q α t UE2 P s (cid:19) + z UE2 , (5)respectively, where z UE1 ∼ CN (0 , σ ) and z UE2 ∼ CN (0 , σ ) denote the additive white Gaussian noise (AWGN) at UE 1 andUE 2, respectively, with the same noise power σ .Then, UE 1 will first decode message of UE 2 s , subtractit from its observation y t UE1 , and then decode its own message s . The signal-to-interference-plus-noise ratio (SINR) for UE1 to decode the message of UE 2 is given by SINR t UE1 , UE2 = | h BS , UE1 | α t UE2 | h BS , UE1 | α t UE1 + 1 /ρ . (6)where ρ = P σ denotes the transmit signal-to-noise ratio(SNR). For a given target data rate of downlink transmissionof UE 2, R DLUE2 , if log (cid:16) t UE1 , UE2 (cid:17) ≥ R DLUE2 , themessage s is decodable and can be cancelled at UE 1, Note that it is straightforward to extend the results of this paper to thecase with different transmit powers. therwise the SIC process is failed. Note that a pre-log factorof is introduced which takes into account the loss of spectralefficiency as one time frame is partitioned into three timeslots. Meanwhile, we assume that UE 1 will not decode itsown message s if the SIC process is failed. Therefore, with asuccessful SIC, the SINR for UE 1 to decode its own messagesis given by SINR t UE1 = | h BS , UE1 | α t UE1 ρ. (7)On the other hand, UE 2 will directly decode its ownmessage s by treating the signal of UE 1 as noise. Thereby,the SINR for UE 2 to decode its own message is given by SINR t UE2 = | h BS , UE2 | α t UE2 | h BS , UE2 | α t UE1 + 1 /ρ . (8)In the second time slot t , i.e., the cooperative phase, UE1 will broadcast the superimposed signal of s and u , where s is the message for UE 2 obtained during SIC processin the first time slot and u is its own message for uplinktransmission. The transmitted signal from UE 1 in the secondtime slot is given by x t UE1 = q α t BS P u + q α t UE2 P s , (9)where α t BS and α t UE2 denote the power allocation factors forthe messages for the BS and UE 2 in t , respectively, with α t BS + α t UE2 = 1 . As a result, the received signal at the BSand UE 2 in t are given by y t BS = h BS , UE1 (cid:18)q α t BS P u + q α t UE2 P s (cid:19) + z BS and (10) y t UE2 = h UE1 , UE2 (cid:18)q α t BS P u + q α t UE2 P s (cid:19) + z UE2 , (11)respectively, where z BS ∼ CN (0 , σ ) denotes the AWGN atthe BS.Since the BS knows exactly the downlink message s in advance, it can subtract it directly from its observation y t BS and decode the uplink message u . In other words, thedownlink message s stored at the BS serves as a piece of sideinformation which benefits the decoding of the uplink message u . Therefore, our proposed scheme enables an interference-free uplink transmission and can significantly increase thesystem spectral efficiency. On the other hand, compared tothe conventional CNOMA scheme, it is expected that thereis a slightly decrease in the signal reception reliability atUE 2 as a portion of transmit power at UE 1, q α t UE2 P ,is used for uplink transmission for UE 1. In fact, allocatinga small fraction of power for the uplink transmission ofUE 1 can enable a noticeable system performance gain inspectral efficiency owing to its good channel condition andthe interference-free transmission. Therefore, in the proposedscheme, one can use the power allocation factor α t UE2 tocontrol the tradeoff between system spectral efficiency and sig-nal reception reliability. Note that the conventional CNOMAscheme is a subcase of our proposed scheme which can beobtained by setting α t UE2 = 0 . More importantly, unlike theSIC process in t at UE 1, the downlink message s can always be cancelled disregard the target data rate of the downlinktransmission of UE 2.At the BS, after eliminating s from y t BS , the SINR for theBS to decode the uplink message u is given by SINR t BS , UE1 = | h BS , UE1 | α t BS ρ. (12)On the other hand, at UE 2, the maximum ratio com-bining (MRC) is adopted to decode the message s fromtwo independent observations y t UE2 and y t UE2 with weights h ∗ BS , UE2 q α t1UE2 P | h BS , UE2 | α t1UE1 P + σ and h ∗ UE1 , UE2 q α t2UE2 P | h UE1 , UE2 | α t2BS P + σ , respectively,where ∗ denotes the conjugate operation. Therefore, the SINRfor UE 2 to decode s with MRC is given by SINR t , t UE2 − MRC = SINR t UE2 + SINR t UE2 , (13)where SINR t UE2 denotes the SINR for UE 2 to decode s in t , and it is given by SINR t UE2 = | h UE1 , UE2 | α t UE2 | h UE1 , UE2 | α t BS + 1 /ρ . (14)In the third time slot t , i.e., the uplink NOMA phase, UE1 and UE 2 transmit their uplink messages u and u to theBS simultaneously. Note that the different large scale fadingexperienced by both users results in different received signalpowers from UE 1 and UE 2, which can inherently facilitatethe SIC process. Therefore, we simply assume that both userstransmit their messages with their maximum transmit powersfor notation simplification. The received signal at the BS inthe third time slot is given by y t BS = h BS , UE1 p P u + h BS , UE2 p P u + z BS . (15)According to the uplink NOMA principle[22], the BS will firstdecode the user with higher received power. If | h BS , UE1 | ≥| h BS , UE2 | , the SINR for the BS to decode the uplink mes-sages of UE 1 and UE 2 are given by SINR t BS , UE1 = | h BS , UE1 | | h BS , UE2 | + 1 /ρ and (16) SINR t BS , UE2 = | h BS , UE2 | ρ, (17)respectively. On the other hand, if | h BS , UE1 | < | h BS , UE2 | ,the SINR for the BS to decode the uplink messages of UE 1and UE 2 are given by SINR t BS , UE1 = | h BS , UE1 | ρ and (18) SINR t BS , UE2 = | h BS , UE2 | | h BS , UE1 | + 1 /ρ , (19)respectively. Here, we assume that the BS will not decodethe message of the user with lower received power if the SICprocess is failed. Remark 1:
For comparison, two baseline schemes, the con-ventional CNOMA scheme and the non-cooperative NOMAscheme, are illustrated in Figure 2(b) and Figure 2(c), respec-tively. For a fair comparison, the time duration of the framefor all the schemes illustrated in Figure 2 are identical. Similarto our proposed scheme, the CNOMA scheme also requiresthree time slots to accomplish the downlink transmission,ooperative transmission, and uplink transmission. Differentfrom the CNOMA scheme, UE 1 in our proposed scheme willbroadcast the superposition of downlink symbols for UE 2 anduplink symbols of itself in the cooperative phase. In contrast,the non-cooperative NOMA scheme needs two time slots fordownlink NOMA and uplink NOMA transmissions.III. P
ERFORMANCE A NALYSIS
To characterize the reception reliability and system spectralefficiency of our proposed scheme, three performance metricsare discussed in this section. Firstly, we analyze the outageprobability for individual link for a given the target datarate, from which the diversity order achieved by the proposedscheme is obtained. Then, the system outage throughput isderived to demonstrate the improvement of spectral efficiency.Given the target data rate for downlink and uplink trans-missions of UE 1 and UE 2 as R DLUE1 , R DLUE2 , R ULUE1 , R ULUE2 ,respectively, an outage occurs when the achievable rate is lessthan that of the corresponding target data rate. Accordingly, theoutage probability of downlink and uplink transmissions of UE1 and UE 2 are given by (20)-(24) at the top of next page. Notethat we assume the same target data rate R ULUE1 for the uplinktransmissions of UE 1 in t and t . Correspondingly, theiroutage probability are denoted as P UE1 , ULout , t and P UE1 , ULout , t ,respectively.The outage probability of UE 1 for downlink NOMAtransmission has been derived in [17] as follows: P UE1 , DLout = (cid:26) − exp( − φ β BS , UE1 ρ ) , if α t UE2 − α t UE1 γ DLUE2 > , otherwise (25)where φ = max (cid:26) γ DLUE2 ( α t1UE2 − α t1UE1 γ DLUE2 ) , γ DLUE1 α t1UE1 (cid:27) , γ DLUE1 =2 R DLUE1 − , and γ DLUE2 = 2 R DLUE2 − . It is notable that thepower allocation factors should satisfy α t UE2 − α t UE1 γ DLUE2 > ,otherwise P UE1 , DLout will always be one.Based on (21), the outage probability of UE 2 for downlinkNOMA transmission is derived as (26) at the top of next page,where Q and Q can be easily obtained as Q = 1 − exp( − φ β BS , UE1 ρ ) and Q = 1 − exp( − φ β BS , UE2 ρ ) , (27)respectively, and φ = γ DLUE2 ( α t1UE2 − α t1UE1 γ DLUE2 ) . Again, the prereq-uisite α t UE2 − α t UE1 γ DLUE2 > should be satisfied, otherwise P UE2 , DLout will always be one.For Q , we first derive the distributions of SINR t UE2 and
SINR t UE2 , respectively, and then obtain Q via the followingintegration: Q = Z Z
SINR t1UE2 +SINR t2UE2 <γ DLUE2 f SINR t2UE2 ( x ) f SINR t1UE2 ( y ) dy dx. (28)The CDF of SINR t UE2 is defined as F SINR t1UE2 ( x ) = Pr (cid:8) SINR t UE2 < x (cid:9) , (29) thereby, if < x < α t1UE2 α t1UE1 , the CDF and PDF of SINR t UE2 aregiven by F SINR t1UE2 ( x )= F | h BS , UE2 | x (cid:0) α t UE2 − α t UE1 x (cid:1) ρ ! and (30) f SINR t1UE2 ( x )= f | h BS , UE2 | x (cid:0) α t UE2 − α t UE1 x (cid:1) ρ ! α t UE2 (cid:0) α t UE2 − α t UE1 x (cid:1) ρ , (31)respectively. Similarly, for < x < α t2UE2 α t2BS , the CDF and PDFof SINR t UE2 can be obtained as F SINR t2UE2 ( x )= F | h UE1 , UE2 | x (cid:0) α t UE2 − α t BS x (cid:1) ρ ! and (32) f SINR t2UE2 ( x )= f | h UE1 , UE2 | x (cid:0) α t UE2 − α t BS x (cid:1) ρ ! α t UE2 (cid:0) α t UE2 − α t BS x (cid:1) ρ , (33)respectively. Then, Q can be obtained by solving: Q = Z φ Z γ DLUE2 − x f SINR t2UE2 ( x ) f SINR t1UE2 ( y ) dy dx, (34)where φ = min (cid:16) γ DLUE2 , α t2UE2 α t2BS (cid:17) .It is difficult to directly solve the above integration. Toobtain more insights from P UE2 , DLout in (26), we apply theGauss-Chebyshev integration[23] to obtain Q via a closed-form approximation as follows : Q ≈ F SINR t2UE2 ( φ ) − α t UE2 φ β UE1 , UE2 ρ n X i =1 πn (cid:12)(cid:12)(cid:12)(cid:12) sin 2 i − n π (cid:12)(cid:12)(cid:12)(cid:12) g ( l i ) , (35)where n is the number of Gauss-Chebyshev integral approx-imation terms, l i = φ + φ cos i − n π , and g ( x ) is givenby g ( x ) = 1 (cid:0) α t UE2 − α t BS x (cid:1) exp − x (cid:0) α t UE2 − α t BS x (cid:1) β UE1 , UE2 ρ − (cid:0) γ DLUE2 − x (cid:1)(cid:0) α t UE2 − α t UE1 γ DLUE2 + α t UE1 x (cid:1) β BS , UE2 ρ ! . (36)Substitute Q , Q , and Q into (26), if α t UE2 − α t UE1 γ DLUE2 > ,the outage probability for the downlink transmission of UE 2can be derived as (37) at the top of next page.In t , since the interference of the weak user can beperfectly cancelled at the BS, the outage probability of UE1 for uplink NOMA transmission can be easily obtained by P UE1 , ULout , t = 1 − exp( − γ ULUE1 β BS , UE1 α t BS ρ ) , (38)where γ ULUE1 = 2 R ULUE1 − .For the uplink NOMA transmission phase, the outage prob-ability is complicated since the integral area in (23) and (24)depends on the target data rates of uplink transmissions of both The tightness of the adopted approximation will be verified in thesimulation section.
UE1 , DLout =Pr (cid:26)
13 log (cid:16) t UE1 , UE2 (cid:17) 13 log (cid:16) t UE1 , UE2 (cid:17) ≥ R DLUE2 , 13 log (cid:0) t UE1 (cid:1) 13 log (cid:16) t UE1 , UE2 (cid:17) < R DLUE2 , 13 log (cid:0) t UE2 (cid:1) < R DLUE2 (cid:27) +Pr (cid:26) 13 log (cid:16) t UE1 , UE2 (cid:17) ≥ R DLUE2 , 13 log (cid:0) t , t UE2 (cid:1) < R DLUE2 (cid:27) , (21) P UE1 , ULout , t =Pr (cid:26) 13 log (cid:16) t BS , UE1 (cid:17) < R ULUE1 (cid:27) , (22) P UE1 , ULout , t =Pr (cid:26) | h BS , UE1 | ≥| h BS , UE2 | , 13 log (cid:16) t BS , UE1 (cid:17) < R ULUE1 (cid:27) + Pr (cid:26) | h BS , UE1 | < | h BS , UE2 | , 13 log (cid:16) t BS , UE2 (cid:17) < R ULUE2 (cid:27) + Pr (cid:26) | h BS , UE1 | < | h BS , UE2 | , 13 log (cid:16) t BS , UE2 (cid:17) ≥ R ULUE2 , 13 log (cid:16) t BS , UE1 (cid:17) < R ULUE1 (cid:27) , (23) P UE2 , ULout =Pr (cid:26) | h BS , UE2 | ≥| h BS , UE1 | , 13 log (cid:16) t BS , UE2 (cid:17) < R ULUE2 (cid:27) + Pr (cid:26) | h BS , UE2 | < | h BS , UE1 | , 13 log (cid:16) t BS , UE1 (cid:17) < R ULUE1 (cid:27) + Pr (cid:26) | h BS , UE2 | < | h BS , UE1 | , 13 log (cid:16) t BS , UE1 (cid:17) ≥ R ULUE1 , 13 log (cid:16) t BS , UE2 (cid:17) < R ULUE2 (cid:27) . (24) P UE2 , DLout = Pr (cid:26) 13 log (cid:16) t UE1 , UE2 (cid:17) < R DLUE2 (cid:27)| {z } Q Pr (cid:26) 13 log (cid:16) t UE2 , UE2 (cid:17) < R DLUE2 (cid:27)| {z } Q +Pr (cid:26) 13 log (cid:16) t UE1 , UE2 (cid:17) ≥ R DLUE2 (cid:27)| {z } − Q Pr (cid:26) 13 log (cid:16) t , t UE2 , UE2 (cid:17) < R DLUE2 (cid:27)| {z } Q . (26) P UE2 , DLout = (cid:18) − exp (cid:18) − φ β BS , UE1 ρ (cid:19)(cid:19) (cid:18) − exp (cid:18) − φ β BS , UE2 ρ (cid:19)(cid:19) − exp (cid:18) − φ β BS , UE1 ρ (cid:19) · ( − exp − φ β UE1 , UE2 (cid:0) α t UE2 − α t BS φ (cid:1) ρ ! − α t UE2 φ β UE1 , UE2 ρ n X i =1 πn (cid:12)(cid:12)(cid:12)(cid:12) sin (cid:18) i − n π (cid:19)(cid:12)(cid:12)(cid:12)(cid:12) g ( l i ) ) . (37)users. As a compromise solution, we focus on high data rateapplications, e.g. R ULUE1 > bit/s/Hz and R ULUE2 > bit/s/Hz.The closed-form outage probability of UE 1 for uplink NOMAtransmission is derived in (39) at the top of next page, wherein γ ULUE2 = 2 R ULUE2 − . Note that ( a ) in (39) holds when R ULUE1 > bit/s/Hz and R ULUE2 > bit/s/Hz. Similarly, theoutage probability of the uplink transmission of UE 2 can begiven by (40) at the top of next page.Now, we analyze the diversity order for each link for ourproposed scheme to obtain more insights into the systemoutage performance. The diversity order is defined as d =lim ρ →∞ − log P out log ρ [24] and the results are summarized in thefollowing lemma. Lemma 1: By using the high SNR approximation, i.e., − exp( − xρ ) ≈ xρ [14], we obtain the diversity order for eachcommunication link as: d UE1 , DLout = 1 , d UE2 , DLout = 2 , d UE1 , ULout , t = 1 , (41) d UE1 , ULout , t = 0 , and d UE2 , ULout = 0 . (42) The diversity order for the downlink transmission of UE 1 isone. Besides, the diversity order for the downlink transmissionof UE 2 is two since there are two independent observationsof the downlink messages of UE 2 in our proposed scheme.On the other hand, we obtain an uplink transmission for UE 1with a diversity order of one via the superposition transmissionduring the cooperative phase. Interestingly, the diversity orderfor uplink NOMA transmission is zero, which implies thatthere is an error floor for the outage probability at high transmitSNR ρ . This is due to the lack of adaptive power control foruplink NOMA transmission leading to a significant IUI in thehigh transmit SNR regime .On the other hand, as all the nodes transmit their informa-tion at their fixed target data rates and the system throughputis determined by the outage probability. Therefore, to evaluatethe spectral efficiency of our proposed scheme, we define thesystem outage throughput in (43) at the top of this page. We note that the error floor inherently exists in the uplink of cooperativeNOMA schemes with fixed power allocation [22], [25]. UE1 , ULout , t = Pr n | h BS , UE1 | ≥ | h BS , UE2 | , | h BS , UE1 | −| h BS , UE2 | γ ULUE1 < γ ULUE1 /ρ o +Pr n | h BS , UE1 | < | h BS , UE2 | , | h BS , UE2 | −| h BS , UE1 | γ ULUE2 < γ ULUE2 /ρ o +Pr n | h BS , UE1 | < | h BS , UE2 | , | h BS , UE2 | −| h BS , UE1 | γ ULUE2 ≥ γ ULUE2 /ρ, | h BS , UE1 | < γ ULUE1 /ρ o ( a ) = 1 − Pr n | h BS , UE1 | −| h BS , UE2 | γ ULUE1 ≥ γ ULUE1 /ρ o − Pr n | h BS , UE2 | −| h BS , UE1 | γ ULUE2 ≥ γ ULUE2 /ρ, | h BS , UE1 | <γ ULUE1 /ρ o =1 − Z + ∞ γ ULUE1 /ρ Z x − γ ULUE1 /ργ ULUE1 f | h BS , UE2 | ( y ) f | h BS , UE1 | ( x ) dy dx − Z + ∞ γ ULUE2+ γ ULUE2 γ ULUE1 ρ Z x − γ ULUE2 /ργ ULUE2 γ ULUE1 /ρ f | h BS , UE1 | ( y ) f | h BS , UE2 | ( x ) dy dx =1 − β BS , UE1 exp( − γ ULUE1 β BS , UE1 ρ ) γ ULUE1 β BS , UE2 + β BS , UE1 − β BS , UE2 γ ULUE2 β BS , UE1 + β BS , UE2 exp (cid:16) − (cid:18) γ ULUE1 β BS , UE1 ρ + γ ULUE2 + γ ULUE2 γ ULUE1 β BS , UE2 ρ (cid:19) (cid:17) , (39) P UE2 , ULout , t =1 − β BS , UE2 exp (cid:16) − γ ULUE2 β BS , UE2 ρ (cid:17) γ ULUE2 β BS , UE1 + β BS , UE2 − β BS , UE1 γ ULUE1 β BS , UE2 + β BS , UE1 exp (cid:16) − (cid:18) γ ULUE2 β BS , UE2 ρ + γ ULUE1 + γ ULUE1 γ ULUE2 β BS , UE1 ρ (cid:19) (cid:17) . (40) R = (cid:16) − P UE1 , DLout (cid:17) R DLUE1 + (cid:16) − P UE2 , DLout (cid:17) R DLUE2 + (cid:16) − P UE1 , ULout , t (cid:17) R ULUE1 + (cid:16) − P UE1 , ULout , t (cid:17) R ULUE1 + (cid:16) − P UE2 , ULout (cid:17) R ULUE2 . (43) Transmit SNR ρ (dB) O u t age p r obab ili t y -5 -4 -3 -2 -1 P UE2 , downoutSimulation resultsAnalytical resultsP UE1 , downout : CNOMA, HDU-CNOMAP UE2 , downout : HDU-CNOMAP UE1 , upout , t : HDU-CNOMAP UE1 , upout , t : HDU-CNOMAP UE2 , upout : HDU-CNOMAP UE2 , downout : CNOMAP UE1 , upout , t : CNOMAP UE2 , upout : CNOMA Error floor Fig. 3. Outage probability for the proposed HDU-CNOMA scheme and aconventional CNOMA scheme. IV. S IMULATION R ESULTS In this section, the performances of our proposed scheme areevaluated through simulations. Without loss of generality, weassume that the variances of channel coefficient are β BS , UE1 =1 , β BS , UE2 = 0 . , and β UE1 , UE2 = 0 . . The target datarates are R DLUE1 = R DLUE2 = R ULUE1 = R ULUE2 = 1 bit/s/Hz andthe power allocation factors are α t UE1 = 0 . , α t UE2 = 0 . , α t BS = 0 . , and α t UE2 = 0 . . The approximation parameterfor Gauss-Chebyshev integration is set as n = 100 .Figure 3 illustrates the simulation results and analyticalresults for the outage probability of conventional CNOMAscheme and our proposed HDU-CNOMA scheme. Note thatthe outage probability for P UE1 , DLout is the same for bothCNOMA and HDU-CNOMA schemes. It can be observedthat our analytical results closely match with the simulation Transmit SNR ρ (dB) O u t age t h r oughpu t ( b i t/ s / H z ) HDU-NOMA schemeCNOMA schemeNon-cooperative NOMA scheme Performance gain ofHDU-NOMA over CNOMAPerformance gain ofHDU-NOMA overnon-cooperative NOMA Fig. 4. Outage throughput (bits/s/Hz) for HDU-CNOMA scheme, conven-tional CNOMA scheme[14], and non-cooperative NOMA scheme. results, especially for the high SNR regime. Compared to theCNOMA scheme, P UE2 , DLout of our proposed scheme is slightlyhigher due to the power loss in the cooperative phase. Thegap on P UE2 , DLout between CNOMA and HDU-CNOMA canbe further reduced by allocating a higher transmit power forUE 2 than that of the BS during the cooperative phase tomaintain the signal reception reliability at UE 2. On the otherhand, although only a small faction of power is allocated foruplink transmission during t in HDU-CNOMA scheme, ithas a lower outage probability than that of uplink NOMAtransmissions in t , especially for high SNR regime. This isdue to the fact that the side information s assists the BS tocancel the interference in the superimposed signal transmittedduring the cooperative phase. For R ULUE1 = R ULUE2 > bit/s/Hz,we can observe the error floor of P UE1 , ULout , t and P UE2 , ULout foroth CNOMA and HDU-NOMA schemes, which validates ourderivations in (42). Also, it can be observed that our proposedscheme results in a lower error floor than that of the CNOMAscheme. This is because our proposed scheme exploit two timeslots, t and t , for UE 1 to transmit the target data rate R ULUE1 while CNOMA only transmits in t .Figure 4 depicts the outage throughput for all the schemesshown in Figure 2. It can be observed that our proposedscheme achieve the largest outage throughput. In particular, theproposed scheme offers substantial performance gains over thetwo baseline schemes in the moderate to high SNR regime. Al-though the superimposed transmission of the proposed schemeduring cooperative phase slightly degrades the received signalquality at UE 2, the performance gain brought by the extrainterference-free uplink transmission of UE 1 outweighs theperformance loss at UE 2 which increases the overall systemoutage throughput. In contrast, the CNOMA scheme has alowest outage throughput due to the following two reasons.First, compared to the proposed HDU-CNOMA scheme, theCNOMA scheme does not fully exploit the degrees of free-dom in the system for uplink and downlink communications.Second, compared to the non-cooperative NOMA scheme, theperformance of the CNOMA scheme relies on the existenceof short range communication between the strong user andthe weak user [14] which does not always exist in practicalsystems. V. C ONCLUSION In this paper, a novel HDU-CNOMA scheme was proposedto increase the spectral efficiency and to achieve a better trade-off between signal reception reliability and spectral efficiencyfor cooperative NOMA systems. Particularly, the cooperativetransmission and uplink transmission were integrated duringthe cooperative phase, and the side information at the BSwas utilized to obtain an additional interference-free uplinktransmission. 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