Non-orthogonal multiple access (NOMA) and cooperative spectrum sharing (CSS) are integrated into this work to enhance both spectrum eciency and utilization. An overlay spectrum sharing is proposed by exploiting NOMA in coordinated direct and relay transmission (CDRT) (termed as CSS-NOMA-CDRT). In CSS-NOMA-CDRT, a primary strong NOMA user is directly served by primary transmitter (PT), whereas a pri- mary NOMA weak user needs the assistance of a relay to communicate with PT. Instead of using a dedicated relay, a secondary transmitter (ST) acts as a relay to forward the primary symbol to NOMA weak user and ST transmits own symbol to its receiver at the same time. The performance of the proposed CSS-NOMA-CDRT is evaluated along with closed-form so- lutions, in terms of ergodic sum capacity and outage probability. Through the analytical and Monte Carlo simulation results, it is demonstrated that CSS-NOMA-CDRT can obtain remarkable capacity gain as compared to the conventional NOMA-based CDRT. Keywords Coordinated direct and relay transmission, ergodic sum capacity, non-orthogonal multiple access, outage probability, cooperative spectrum shar- ing. 1 Introduction In order to deal with the various requirements of the next generation wireless networks, several candidate technologies are identi ed [1]. However, it may not be possible for a single technology to satisfy the performance requirements of 5G and beyond. Therefore, multiple technologies are required to be integrated [2]. Among the various candidate technologies of 5G and beyond, cognitive radio (CR) spectrum sharing and non-orthogonal multiple access (NOMA) are the two Manuscript received XXX, XX, 2018; revised XXX, XX, 2018. yMd. Fazlul Kader is with the Department of Electrical and Electronic Engineering, Uni- versity of Chittagong, Chittagong-4331, Bangladesh (email: f.kader@cu.ac.bd). 1 key techniques. The principal idea of NOMA is to exploit multiplexing in power domain to share same code/frequency/time, in attempts to signi cantly improve system capacity and serve massive numbers of users [3, 4]. Moreover, exploiting cooperative diversity with NOMA can further enhance system capacity and reliability [5, 6, 7]. The exponential growth of mobile trac, quick proliferation of internet of things and high-rate data communication services may result in spectrum scarcity problem. However, this arti cial scarcity of the spectrum is not because of any physical shortage of spectrum. Instead, it is largely due to inecient xed frequency allocations. CR is a promising and exciting technology which can tackle, or at least partially address this spectrum scarcity problem in the next generation wireless networks [8, 9]. In CR spectrum sharing, secondary or unlicensed users share the same spectrum band with primary or licensed users to enhance spectral utilization. Furthermore, integration of NOMA with spectrum sharing can enhance both spectrum eciency and utilization [10-20], which is the main focus of this paper. In [12], it was rst identi ed that NOMA can be thought as a special case of a cognitive radio network (CRN), where a user experiencing better channel condition, reckoned as a secondary user (SU), may coexist at the same frequency band with a user experiencing poor channel condition, reckoned as a primary user (PU). The application of NOMA in cooperative spectrum sharing (CSS) can be broadly classi ed as NOMA-based underlay CSS [13-16], NOMA-based overlay CSS [17-19], and NOMA-based hybrid CSS [20]. A NOMA scheme to large-scale underlay CRNs with randomly deployed users was studied in [13]. The outage probability (OP) of the proposed protocol was assessed by stochastic geometry tools. An underlay CR network was inves- tigated in [14], where NOMA transmission protocol was followed by two users in the secondary network (SN). It was shown that better sum rate and outage performance achieved by [14] as compared to [13] and orthogonal multiple ac- cess scheme. In [15], a power-domain NOMA inspired cooperative CRN was studied, where a decode-and-forward (DF) relay was employed to assist the si- multaneous communication between a secondary transmitter (ST) and two SUs. Moreover, transmit power assigned by ST for each SU is inversely proportional to the channel gain of the corresponding link. In an underlay CRN scenario, [16] studied a cooperative NOMA scheme, where a SU having strong channel con- dition acted as a relay to help another SU having poor channel condition in the presence of a primary network (PN). However, the interference from PUs and bad transmission performance of SUs because of the strict power constraints imposed on secondary users are the major problem in underlay approaches. An overlay CSS protocol using NOMA with space-time block coding can outperform the conventional superposition coding based protocol in terms of ergodic capacity (EC) and OP [17]. Basically, NOMA transmission policy was applied in phase-2, where ST (acting as a relay for PN) assigned less power to SU experiencing better channel condition and more power to PU experienc- ing worse channel condition. By exploiting NOMA signaling in phase-2, a CSS scheme was proposed in [18] to evaluate the performance for PN and SN in 2 terms of system throughput and OP. By considering the relative position from the transmitter, either PU or SU can perform successive interference cancella- tion (SIC) in NOMA-based spectrum sharing protocol [19, 20]. In [19], a CSS scheme was investigated, where a ST was employed to assist the primary trans- mission. In exchange of cooperation, ST was able to transmit simultaneously with PU at the same frequency band by exploiting NOMA transmission policy. The performance improvement of a hybrid CSS protocol as compared to the traditional overlay/underlay models was demonstrated in [20], in terms of OP and ergodic sum capacity (ESC). The hybrid model jointly considered NOMA- based overlay and underlay models, under a multi-constraint and multi-relay scenario. Exploiting NOMA in coordinated direct and relay transmission (CDRT) can be another crucial strategy for future wireless networks to enhance spectral eciency [21]. The performance of [21] is evaluated in terms of ESC and OP under perfect SIC (pSIC). It was shown that NOMA in CDRT (NOMA-CDRT) can achieve notable capacity gain than NOMA in non-CDRT. However, [21] did not consider any spectrum sharing scenario. Therefore, a NOMA-based overlay spectrum sharing protocol for downlink transmission (termed as CSS-NOMA- CDRT) is proposed in this paper to further enhance system capacity and better spectrum utilization, where NOMA and spectrum sharing are integrated for CDRT. The primary contributions of this work are summarized as follows. 1. A two-phase CSS protocol is proposed by taking into account NOMA transmission policy in both phases over independent Rayleigh fading chan- nels. 2. The analytical derivations of ESC and OP are provided under both pSIC and imperfect SIC (ipSIC), whereas [21]considered only pSIC. 3. The performance improvement of the proposed CSS-NOMA-CDRT over [21] is authenticated through simulation and analysis. Moreover, the correct- ness of analytical resutls are validated by Monte Carlo simulation. 4. We have considered a more general scenario as compared to [21]. The performance of the proposed CSS-NOMA-CDRT is evaluated for two dif- ferent cases such as i) case-1 (C1)- successful decoding at relay and ii) case-2 (C2)- unsuccessful decoding at relay. Contrarily, [21] considered only C1. The rest of this paper is organized as follows. The detailed description of the proposed CSS-NOMA-CDRT is provided in Section II along with signal- to-noise-plus-interference ratio (SNIR) formulation. The performance of CSS- NOMA-CDRT is investigated in terms of ESC and OP in Section III and V, respectively. In Section V, analytical resutls are presented via two-dimensional plots. Simulation resutls are also presented in this section to validate analytical results. At last, Section VI concludes this paper with future suggestions. 3 UE 1UE 2 PT STPhase -1 Phase -1 Phase -2 Phase -2hs,rhp,1 SRFigure 1: Proposed system model. 2 Network Model and Protocol Description 2.1 System Model A CR spectrum sharing scenario is considered as shown in Fig. 1, wherein a SN coexist with a PN. The PN consists of a primary transmitter (PT) called as pri- mary base station (BS) and two users UE 1and UE 2, whereas the SN consists of a ST and a secondary receiver (SR). It is assumed that UE 1(strong/near user) is able to communicate directly with PT, whereas the direct link between PT and UE 2(far/weak user) does not exist or very weak due to deep fading or physical obstacles between them. Therefore, a third node called as relay is required for assisting PT to communicate with UE 2. Instead of using dedicated relay as in [21], we consider that a ST acts as a DF relay to assist primary com- munication. In exchange of cooperation, ST is able to simultaneously transmit own signal to SR by exploiting NOMA. Throughout the manuscript, subscripts p,s, 1, 2, andrare used to represent PT or PN, ST or SN, UE 1, UE 2, and SR, respectively. 2.2 Channel Model The channel between any two nodes iandjis subjected to Rayleigh fading plus additive white Gaussian noise with complex channel coecient hi;j CN(0;!i;j), wherei;j2fPT, UE 1, UE 2, ST, SRgandi6=j. So, the link gain or channel gain i;j=jhi;jj2is exponentially distributed random variable with a mean value or scale parameter !i;j. The data transmission policy along with SNIR formulation is demonstrated in the following section. 2.3 Data Transmission Policy and SNIR Model A complete transmission in the proposed CSS-NOMA-CDRT is divided into two cooperative phases. Thus, a complete transmission requires two transmission slotst1andt2. 4 2.3.1 Phase-1 Duringt1, PT transmits a composite signal Zp=P2 i=1p iPpxifollowing downlink NOMA principle, where xiand iare the data symbol and power allocation coecient, respectively related to UE i. The transmit power of PT is expressed by Pp. Note thatP2 i=1 i= 1 and 1< 2. By taking into account the statistical channel state information (CSI), it is assumed that the channels are sorted as p;1> p;s[7, 22]. Therefore, UE 1performs SIC to decode x1. The received SNIR at UE 1related to symbol x1is given by t1 p;1= 1p p;1 2p^ p;1+ 1; (1) wherep,Pp 2, ^ p;1=j^hp;1j2,^hp;1CN(0;1!p;1), and2denotes noise variance. The symbol 1(011) is a residual interference parameter con- sidering ipSIC; 1= 0 and1= 1 indicate pSIC and without SIC, respectively as a special case. Moreover, the required SNIR at UE 1to decodex2before decodingx1, during SIC process, is given by t1 p;s!p;1= 2p p;1 1p p;1+ 1: (2) On the other hand, ST decodes symbol x2assumingx1as noise. The received SNIR at ST is therefore given by t1 p;s= 2p p;s 1p p;s+ 1: (3) 2.3.2 Phase-2 There are two di erent cases such as C1 and C2 can happen in this phase. The detailed transmission policy in each case is provided below. C1-Successful Decoding at ST After successful decoding of x2at ST, ST transmits a composite signal Zs=p 2Psx2+p rPsxsfollowing downlink NOMA principle, and PT transmits a new data symbol  x1to UE 1with power t2 1Ppsimultaneously with ST. The transmit power of ST is denoted by Ps and t2 1represents power allocation coecient. Considering statistical CSI, it is assumed that s;2< s;r[7,22]. Hence, SR performs SIC to decode own symbolxs, whereas UE 2decodes own symbol x2assumingxsas noise. Note that 2+ r=1 and 2> r; ris the power allocation coecient related to xs. Because of the simultaneous transmission by PT and ST during t2, UE 1 faces interference from ST. However, by exploiting the side information x2ob- tained during t1because of SIC procedure, UE 1can cancel the interfering signalp 2Psx2from the composite interfering signal Zs. Therefore, the received SNIR at UE 1is computed by t2 p;1= t2 1p p;1 rs s;1+ 1: (4) 5 wheres,Ps 2. In addition, the received SNIR at UE 2is given by t2 s;2= 2s s;2 rs s;2+ 1: (5) Contrarily, the required SNIR at SR to decode x2before decoding xs, during SIC process, is expressed by t2 s;2!s;r= 2s s;r rs s;r+ 1; (6) Moreover, the received SNIR at SR after SIC is given by t2 s;r= rs s;r 2s^ s;r+ 1; (7) where ^ s;r=j^hs;rj2and^hs;rCN(0;2!s;r). The parameter 2expresses identical behavior to 1. C2-Unsuccessful Decoding at ST If ST is unable to decode x2att1, it will remain silent during t2. As a result, the communication between PT and UE2fails and no secondary transmission also takes place during t2. However, the interference-free communication between PT and UE 1can occur. Therefore, the most crucial nding of this case is that the secondary transmission completely depends on the successful decoding of x2at ST. Then, the SNIR received at UE1in C2 is given by t2;C2 p;1= t2 1p p;1: (8) 3 Capacity Analysis This section investigates EC of each user in primary and secondary systems along with closed-form expressions over independent Rayleigh fading channels. Moreover, ESC of each system and total capacity of the whole spectrum sharing network are also investigated here. 3.1 Primary system capacity The achievable data rate of the primary system is demonstrated in this section. 3.1.1 Capacity of UE 1 Using (1) and (4), the achievable rate of UE 1att1andt2are respectively given by Ct1 1;p=1 2log2(1 + t1 p;1); (9) Ct2 1;p=1 2log2(1 + t2 p;1): (10) 6 LetU= t1 p;1= 1p p;1 2p^ p;1+1andV= t2 p;1= t2 1p p;1 rs s;1+1. The cumulative distri- bution function (CDF) of UandVcan be respectively written as in [eq. (22), 23] FU(u) = 1 1!p;1 1!p;1+ 21!p;1ueu 1p!p;1; (11) FV(v) = 1 t2 1p!p;1 t2 1p!p;1+ rs!s;1vev t2 1p!p;1: (12) LetA= 1!p;1,B= 21!p;1,C= t2 p;1p!p;1, andD= rs!s;1. The exact EC related to UE 1att1andt2are respectively given by Ct1 1;p=1 2 ln 2Z1 0(1 +u)1A A+Bueu Apdu; (13) Ct2 1;p=1 2 ln 2Z1 0(1 +v)1C C+Dvev Cdv; (14) whereR1 0log2(1 +z)fZ(z)dz=1 ln 2R1 01FZ(z) 1+zdzis used. The integral in (13) can be solved as Ct1 1;p=1 2 ln 2A ABZ1 0(1 +u)1Z1 0B A+Bv eu Apdu =1 2 ln 2A AB e1 ApEi(1 Ap) +e1 BpEi(1 Bp) : (15) where Ei() represents exponential integral function [24]. It is noticed that ipSIC (i.e., 0 < 11) is considered to deduce (15). Hence, considering pSIC (i.e.,1= 0),U= t1 p;1= 1p p;1 2p^ p;1+1can be written as U= 1p p;1. The CDF ofUand the exact EC of UE 1att1under pSIC is therefore respectively given by FU(u) = 1eu Ap; (16) Ct1 1;p=1 2 ln 2Z1 0(1 +u)1eu Apdu =1 2 ln 2e1 ApEi(1 Ap): (17) Similar to (15), (14) can be derived as Ct2 1;p=1 2 ln 2C CDZ1 0(1 +v)1Z1 0D C+Dv ev Cdv =1 2 ln 2C CD e1 CEi(1 C) +e1 DEi(1 D) : (18) 7 Moreover, using (8) and following the similar derivation to (17), the exact EC of UE 1in C2 is computed as Ct2 1;C2=1 2 ln 2e1 t2 1p!p;1Ei(1 t2 1p!p;1): (19) Now, using (15), (18) and (19), the total EC of UE 1under ipSIC can be obtained as CipSIC 1;p=( (15) + (18);C1 (15) + (19);C2(20) Conversely, using (17), (18) and (19), the total EC of UE 1under pSIC can be obtained as CpSIC 1;p=( (17) + (18);C1 (17) + (19);C2(21) 3.1.2 Capacity of UE 2 Using (2), (3), (5), and (6), the achievable data rate of UE 2is expressed by C2;p=1 2log2(1 + min( t1 p;s; t1 p;s!p;1; t2 s;2; t2 s;2!s;r)) =1 2log2 1 + min 2p p;s 1p p;s+ 1; 2p p;1 1p p;1+ 1; 2s s;2 rs s;2+ 1; 2s s;r rs s;r+ 1 : (22) Using [eq. (33), 7], (22) can be written as C2;p=1 2log2(1 + ): (23) where  =min( 2p p;s; 2p p;1; 2s s;2; 2s s;r) min( 1p p;s; 1p p;1; rs s;2; rs s;r)+1. Since it is assumed that Pp=Psand same power allocation factor 2related tox2in both phases for consistency, it can be chosen that r= 1. Thus, (23) is written as C2;p=1 2log2 1 +min(p p;s;p p;1;s s;2;s s;r)(1 1) min(p p;s;p p;1;s s;2;s s;r) 1+ 1 =1 2log2 1 +min(p p;s;p p;1;s s;2;s s;r) min(p p;s;p p;1;s s;2;s s;r) 1+ 1 min(p p;s;p p;1;s s;2;s s;r) 1 min(p p;s;p p;1;s s;2;s s;r) 1+ 1 =1 2log2min(p p;s;p p;1;s s;2;s s;r) + 1 min(p p;s;p p;1;s s;2;s s;r) 1+ 1 ; (24) 8 where 2= 1 1is used. Now, using loga(x=y) = logaxlogay, (24) can be expanded as C2;p=1 2log2(1 + min(p p;s;p p;1;s s;2;s s;r)) 1 2log2(1 + min(p p;s;p p;1;s s;2;s s;r) 1): (25) LetW= min(p p;s;p p;1;s s;2;s s;r) andX= min(p p;s;p p;1;s s;2;s s;r) 1. Using the CDF of the minimum of two exponential distributed RVs, the CDFs ofWandXare given by FW(w) = 1ew(1 p!p;s+1 p!p;1+1 s!s;2+1 s!s;r); (26) FX(x) = 1ex(1 1p!p;s+1 1p!p;1+1 1s!s;2+1 1s!s;r): (27) Now, using (26) and (27), the exact EC of UE 2is obtained by C2;p=1 2 ln 2Z1 0(1 +w)1ew dw 1 2 ln 2Z1 0(1 +x)1exdx =1 2 ln 2 e Ei( ) +eEi() ; (28) where =1 p!p;s+1 p!p;1+1 s!s;2+1 s!s;r,=1 1p!p;s+1 1p!p;1+1 1s!s;2+ 1 1s!s;r, andR1 0log2(1 +z)fZ(z)dz=1 ln 2R1 01FZ(z) 1+zdzis used. 3.1.3 Sum capacity of PN Using (20) and (28), the total EC of PN under ipSIC is obtained as CipSIC PN =( (15) + (18) + (28) ;C1 (15) + (19); C2(29) Conversely, using (21), and (28), the total EC of PN under pSIC is obtained as CpSIC PN =( (17) + (18) + (28) ;C1 (17) + (19); C2(30) 3.2 Capacity of SN Using (7), the achievable data rate of SN is written by CSN=1 2log2(1 + t2 s;r): (31) 9 LetY= t2s;r= rs s;r 2s^ s;r+1= 1s s;r 2s^ s;r+1. Similar to (11), The CDF of Yis written by FY(y) = 1E E+Fyey Es; (32) whereE= 1!s;randF= 22!s;r. The exact EC of SN is therefore given by CSN=1 2 ln 2Z1 0(1 +y)1E E+Fyey Esdy: (33) Similar to (15), (33) can be derived as CSN=1 2 ln 2E EFZ1 0(1 +y)1Z1 0F E+Fy ey Esdy =1 2 ln 2E EF e1 EsEi(1 Es) +e1 FsEi(1 Fs) : (34) It is observed that ipSIC (i.e., 0 <  21) is thought to deduce (34). Hence, considering pSIC (i.e., 2= 0),Y= t2s;r= 1s s;r 2s^ s;r+1can be written as Y= 1s s;r. The exact EC of SN under pSIC is therefore given by CSN=1 2 ln 2e1 EsEi(1 Es): (35) 3.3 Total system capacity Using (29) and (34), the ESC of the proposed spectrum sharing network under ipSIC is obtained as CipSIC CSS =( (15) + (18) + (28) + (34) ;C1 (15) + (19); C2(36) Conversely, using (30), and (35), the ESC of the proposed spectrum sharing network under pSIC is obtained as CpSIC CSS =( (17) + (18) + (28) + (35) ;C1 (17) + (19); C2(37) 4 Outage probability analysis Analytical expression of OP for each user in PN and SN is provided over inde- pendent Rayleigh fading channels, in this section. Let Rp1,Rp2, andRsare the prede ned target rate threshold of UE 1, UE 2, and SU respectively, according to the required quality of service. 10 4.1 Outage probability of PN 4.1.1 Outage probability of UE 1 The OP of UE 1att1under ipSIC is given by Pt1;ipSIC 1;p = 1Prf( t1 p;1>Rth p1)\( t1 p;s!p;1>Rth p2)g = 1Pr( t1 p;1>Rth p1)Pr( t1 p;s!p;1>Rth p2) = 1 1!p;1 1!p;1+ 21!p;1Rthp1eRth p1 1p!p;1Rth p1 !p;1p( 2 1Rthp1); (38) whereRth p1= 22Rp11,Rth p2= 22Rp21 andRth p2 Rthp2+1< 2<1. On the other hand, the OP of UE 1att1under pSIC (i.e., 1= 0) is expressed as Pt1;pSIC 1;p = 1eRth p1 1p!p;1Rth p1 !p;1p( 2 1Rthp1); (39) Moreover, the OP of UE 1att2in C1 and C2 is respectively given by Pt2;C1 1;p= 1Pr( t2 p;1>Rth p1) = 1 t2 1p!p;1 t2 1p!p;1+ 1s!s;1Rthp1eRth p1 t2 1p!p;1; (40) Pt2;C2 1;p= 1Pr( t2;C2 p;1>Rth p1) = 1eRth p1 t2 1p!p;1: (41) 4.1.2 Outage probability of UE 2 The OP of UE 2is given by P2;p= 1Pr( t1 p;s>Rth p2)Pr( t2 s;2>Rth p2) = 1eRth p2 !p;sp( 2 1Rthp2)Rth p2 !s;2s( 2 1Rthp2): (42) 4.2 Outage probability of SN It should be mentioned that the secondary transmission wholly depends on the successful decoding of x2at ST during t1. If ST is unable to decode x2, then SN will be in outage. Hence, the OP of SN is given by Ps= 1Pr( t2 s;r>Rth s)Pr( t1 p;s>Rth p2)Pr( t2 s;2!s;r>Rth p2) = 1 1!s;r 1!s;r+ 22!s;rRths eRth s 1s!s;rRth p2 !p;sp( 2 1Rthp2)Rth p2 !s;rs( 2 1Rthp2); (43) 11 0 5 10 15 20 25 30 35 40 45 50 Transmit SNR [dB]024681012141618Ergodic sum capacity (bps/Hz)ProposedLines: analytical results Markers: simulation results pSIC ipSICt21=1 t21=0.1C1 proposed, NOMA-CDRT (C2) NOMA-CDRT [21]Figure 2: ESC comparison between CSS-NOMA-CDRT and CDRT-NOMA [21] w.r.t transmit SNR showing the impact of varying t2 1. 1=0.1, 2=0.9, !p;1=!s;r=1,!p;s=!s;2=0.5,!s;1=0.1, and= 0:042. whereRth s= 22Rs1. On the other hand, the OP of SN under pSIC (i.e., 2=0) is expressed by Ps= 1eRth s 1s!s;rRth p2 !p;sp( 2 1Rthp2)Rth p2 !s;rs( 2 1Rthp2): (44) 5 Numerical results The analytical (Anl.) and simulation (Sim.) results are presented in this sec- tion to evaluate performance of the proposed CSS-NOMA-CDRT, in terms of ESC/EC and OP. The simulation results for NOMA-CDRT [21] are also plot- ted for comparison purpose. Throughout the simulation, it is considered that Rp1=Rp2=Rs=Rt, 1=0.1, 2=0.9, t2 1=1,!p;1=!s;r=1,!p;s=!s;2=0.5, !s;1=0.1,p=s=, and1=2=, unless otherwise de ned. It should be mentioned that xed power allocation method as in [21] is assumed for a fair comparison. Moreover, it is shown that in each case analytical result is well veri ed with the simulation, which establishes the legitimacy of our analysis. 5.1 Ergodic capacity Figs. 2 and 3 demonstrate ESC comparison between CSS-NOMA-CDRT and CDRT-NOMA [21] with respect to (w.r.t) transmit SNR , wherevaries from 0 to 50 dB. Fig. 2 depicts ESC presenting the impact of varying t2 1, whereas Fig. 3 demonstrates ESC showing the impact of varying and!s;1. From both gures, it is clearly observed that CSS-NOMA-CDRT shows outstanding capacity gain than CDRT-NOMA under pSIC, whereas under ipSIC, the level of 12 0 5 10 15 20 25 30 35 40 45 50 Transmit SNR [dB]024681012141618Ergodic sum capacity (bps/Hz)ProposedpSIC ipSIC (=0.042)ipSIC (=0.022)s, 1=0.1s, 1=0.5Lines: analytical results Markers: simulation results NOMA-CDRT [21]Figure 3: ESC comparison between proposed and CDRT-NOMA [21] w.r.t transmit SNR showing the impact of varying and!s;1. 1=0.1, 2=0.9, t2 1=1,!p;1=!s;r=1, and!p;s=!s;2=0.5. residual interference has a signi cant impact on the capacity gain, particularly at high. This capacity gain is because of spectrum sharing nature of CSS- NOMA-CDRT. Moreover, ESC in C1 shows better performance than ESC in C2. Although, [21] did not consider C2, we have shown here that both protocols show similar performance in C2. This means that when ST or relay is unable to decode symbol during phase-1, it will keep silent throughout phase-2, although BS or PT can still transmit new symbol to UE 1. As a consequence, there is no transmission between BS to UE 2in [21] as well as PT to UE 2and ST to SR in CSS-NOMA-CDRT, resulting capacity decrease in both approaches. From Fig. 2, it is clear that if PT assigns its full power to transmit symbol in phase-2, better capacity can be achieved than the transmitting symbol with partial power allocation. From Fig. 3, it is pointed out that ESC with = 0:022outperforms ESC with= 0:042. This is due to the fact that the lower value of indicates better interference cancellation and vice versa. It is also observed that if UE 1 faces less interference from ST, higher system capacity can be obtained in CSS- NOMA-CDRT. Lastly, ESC improves with an increase in , as anticipated. Note that all the gures except Figs. 2 and 6 are plotted by considering only C1. Fig. 4 and 5 plot EC comparison between PN and SN w.r.t transmit SNR and power allocation coecient 1, respectively. From both gures, it is re- marked that PN achieves signi cantly better capacity than SN. This is because of the fact that primary transmission is possible in both phases, whereas sec- ondary transmission is allowed only in phase-2. It is pointed out from Fig. 4 that EC with pSIC outperforms EC with ipSIC. From Fig. 5, it is seen that SN shows identical performance to UE 1att1; this is because of similar param- eters consideration in both protocols. Finally, it is shown that power allocation factors have a substantial impact on the performance of PN and SN. 13 0 5 10 15 20 25 30 35 40 45 50 Transmit SNR [dB]024681012Ergodic capacity (bps/Hz)Primary network Secondary networkpSICLines: analytical results Markers: simulation results ipSICFigure 4: EC comparison between PN and SN w.r.t transmit SNR . 1=0.1, 2=0.9, t2 1=1,!p;1=!s;r=1,!p;s=!s;2=0.5,!s;1=0.1, and= 0:032. 5.2 Outage probability Outage behavior of the users in CSS-NOMA-CDRT is investigated in Figs. 6 and 7 w.r.t transmit SNR , wherevaries from 0 to 45 dB. Fig. 6 shows OP of each user under pSIC, whereas Fig. 7 shows OP of UE 1att1and SN to show the impact of both pSIC and ipSIC. Note that SIC is performed at UE1duringt1and at SR during t2. It is observed from Fig. 6 that UE 1att2 in C2 outperforms others, with the system parameters assumed here. This is because of the fact that in C2, UE 1can receive PT's signal without facing any interference from ST. However, system capacity degrades signi cantly in C2 as shown in Figs. 2 and 3. On the other hand, OP of UE 1att2in C1 decreases linearly up to a certain , after that it shows a constant behavior because of facing higher interference from ST at high . It is also found that UE 2shows better performance than UE 1att1and SN. A further key observation from Fig. 6 and 7 is that SN shows slightly higher OP than UE 1att1in C1, although similar parameters are considered for both of them. The main reason is that the secondary transmission also depends on the successful decoding of primary symbol at ST during t1. Furthermore, two cases of RtwhereRt=0.5 bps/Hz andRt=1 bps/Hz as well as two cases of , where= 0:0:22and= 0:042, are considered for Fig. 7. It is found that OP with pSIC outperforms OP with ipSIC for any cases of andRt. It is also seen that OP with = 0:022shows better performance than OP with = 0:042. Lastly, it is noticed that OP degrades with an increasing value of Rt, as expected. 14 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Power allocation coefficient 1012345678Ergodic (sum) capacity (bps/Hz)UE1 at t1 UE1 at t2 UE2 SN Sum capacity of PN System sum capacityFigure 5: EC comparison between PN and SN w.r.t power allocation coecient 1under pSIC. t2 1=1,!p;1=!s;r=1,!p;s=!s;2=0.5,!s;1=0.1, and= 20 dB. 6 Conclusion and future works An overlay spectrum sharing is proposed and investigated by exploiting NOMA in CDRT. The performance of the proposed CSS-NOMA-CDRT is assessed, in terms of ESC/EC and OP. The closed-form solutions of ESC/EC and OP are also provided and veri ed with Monte Carlo simulation. It is observed that CSS-NOMA-CDRT can obtain a notable capacity gain as compared to its counterpart, conventional NOMA-CDRT. On the performance of CSS-NOMA- CDRT and NOMA-CDRT, the impact of di erent system parameters are also studied. To the best of author's knowledge, this is the basic work related to CSS in NOMA-based CDRT. Therefore, this work can be extended further to be applied in multiple-input multiple-output scenario, which is subjected to future works.