Dual Relay Selection for Cooperative NOMA with Distributed Space Time Coding

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1 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access Date of pubication xxxx,, date of current version xxxx,. Digita Object Identifier.9/ACCESS.7.DOI Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding JING ZHAO, ZHIGUO DING, Senior Member, IEEE, PINGZHI FAN, Feow, IEEE, ZHENG YANG 3, AND GEORGE K. KARAGIANNIDIS 4, Feow, IEEE Institute of Mobie Communications, Southwest Jiaotong University, Chengdu, 6756, China emai: ettyzj@63.com, p.fan@ieee.org Schoo of Computing and Communications, Lancaster University, LA 4WA, U.K. e-mai: z.ding@ancaster.ac.u 3 Fujian Provincia Engineering Technoogy Research Center of Photoeectric Sensing Appication, Fujian Norma University, Fuzhou 357, China emai: zyfjnu@63.com 4 Eectrica and Computer Engineering Department, Aristote University of Thessaonii, GR-544 Thessaonii, Greece e-mai: geoarag@auth.gr Corresponding author: Jing Zhao e-mai: ettyzj@63.com. This wor of J. Zhao and P. Fan was supported by the Nationa Natura Science Foundation of China NSFC, No. 6737, and the Project No The wor of Z. Ding was supported by the UK EPSRC under grant number EP/L57/ and by H-MSCA-RISE-5 under grant number The wor of Z. Yang was supported by Nationa Natura Science Foundation of China under Grant 678 and Nationa Natura Science Foundation of China under Grant ABSTRACT We consider a two-user muti-reay cooperative non-orthogona mutipe access NOMA networ with distributed space time coding DSTC. Two dua reay seection strategies are proposed for cooperative NOMA, namey, two-stage dua reay seection with fixed power aocation DRS-FPA and two-stage dua reay seection with dynamic power aocation DRS-DPA. Furthermore, ower and upper bounds on the outage probabiity for the DRS-FPA scheme and the exact outage probabiity for the DRS-DPA scheme are obtained in cosed-form, respectivey. Numerica resuts show that the proposed twostage DRS schemes not ony yied better outage performance than the existing singe reay seection SRS schemes without sacrificing spectra efficiency, but can aso achieve fu diversity gain. INDEX TERMS Cooperative non-orthogona mutipe access, reay seection, space time coding, outage performance. I. INTRODUCTION Non-orthogona mutipe access NOMA has recenty received enormous interest as a promising candidate to significanty boost the spectra efficiency of the fifth generation 5G wireess networs [] [4]. On the other hand, cooperative diversity can combat fading, extend service coverage, improve system capacity and achieve spatia degrees of freedom even if the nodes are equipped with a singe antenna [5], [6]. Then, cooperative NOMA is an emerging and important topic, where users or dedicated reays cooperate in order to improve the transmission reiabiity. The idea of user cooperation for NOMA was firsty proposed in [7], where successive interference canceation SIC is impemented at the user with good channe conditions, in order to decode the signas for the users with poor channe conditions, and then the strong user acts as a reay to assist the wea user. In [8], a dedicated reay has been used for a two-user NOMA system to enhance the performance of the user. Unie the existing wor, in [9] and [], users are not ordered by using their channe conditions, but categorized through their quaity of service QoS requirements. A twostage singe reay seection with fixed power aocation SRS- FPA was introduced for cooperative NOMA [9]. In this wor, the provided simuations and anaytica resuts show that the outage performance of this scheme outperforms that of the conventiona max-min strategy and can aso yied a significant performance gain over orthogona mutipe access OMA. In order to further improve the outage performance, a two-stage singe-reay-seection with haf-dynamic power aocation SRS-haf-DPA [] was proposed, i.e., during the first stage a reay subset is seected, which can successfuy decode a the users messages, as we as the user with a ower data rate can be stricty satisfied, whie maximizing its partner s rate in the second stage. Athough mutipe reay seection MRS schemes [], [] can achieve a better outage performance than the SRS scheme, their spectra efficiencies are imited, due to the VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

2 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding FIGURE. System Mode. orthogonaity between mutipe reays to avoid inter-reay interference IRI. In addition, the compexity exponentiay increases with the avaiabe number of reays. Therefore, dua reaying seection DRS is good choice. In order to dea with the oss of spectra efficiency induced by DRS, distributed space time coding DSTC can be used at reays, that is, DRS for cooperative NOMA with DSTC coud offer a good tradeoff between outage performance and spectra efficiency. Two DRS schemes with different STCs in the two-way ampifyand-forward AF reay channe, was anayzed in [3] and [4], respectivey. However, these wors do not consider the NOMA approach. To the best of the authors nowedge, in the open iterature, there are few MRS schemes, proposed for cooperative NOMA and empoying space time coding. Reca that diversity gains can be achieved by space-time coding at the transmitter side, which requires ony simpe inear processing at the receiver side for decoding [5]. Using the Aamouti code by the two seected reays for DRS scheme, IRI does not exist anymore, which is attributed to compex orthogonaity of the transmitted signas. A cooperative decode-and-forward DF reaying scheme based on Aamouti space time boc coded NOMA, was proposed in [6]. In this wor, it has been pointed out that the cooperative reaying system CRS using STC-NOMA can attain a significant performance gain compared to conventiona CRS- NOMA and the traditiona DF reaying schemes. Two DRS schemes for cooperative NOMA with DSTC are investigated in this paper to extend the CRS-STC-NOMA into genera networs with mutipe reays and mutipe users, which can further improve the system performance and achieve higher diversity gain. The main contributions of this paper can be summarized as foow: A nove two-stage DF dua reay seection with fixed power aocation DRS-FPA and space time coding for two-user cooperative NOMA is proposed, where a reay set can successfuy decode both signas for U and U at stage, whie choosing the two best avaiabe reays according to the max-min criterion, at the second stage. Furthermore, exact cosed-form expressions for the ower and upper bounds of the outage probabiity for the two-stage DRS-FPA scheme, are derived. Numerica resuts show that the outage performance of the proposed scheme is superior to that of the SRS-FPA strategy [9], without oss of spectra efficiency. In order to further improve the system performance, the two-stage DF singe and dua reay seection schemes, with dynamic power aocation SRS-DPA and DRS- DPA, are presented, where DPA is used for both hops instead for the second hop ony, as in []. Furthermore, we obtain exact expressions for the outage probabiity of the two schemes. It is noted that the proposed SRS-DPA and DRS-DPA schemes significanty outperform the SRS-haf-DPA scheme []. 3 The anaytica resuts and simuations demonstrate that a the proposed schemes, such as DRS-FPA, SRS-DPA and DRS-DPA, can achieve maximum diversity gain. In addition, the outage performance gap between the DRS and SRS schemes becomes arger with a decrease in the difference of the user s and user s target data rates or with an increase in the number of the reays. The rest of this paper is organized as foows. Section II introduces the system mode of cooperative NOMA with space time coding and the proposed reay seection schemes. The outage probabiities for the DRS-FPA, SRS-DPA and DRS- DPA schemes are deveoped in Section III. Numerica resuts are presented in Section IV to iustrate the performance of the proposed schemes. Finay, the concusion of this paper is drawn in Section V. II. SYSTEM MODEL Consider a two-user cooperative NOMA networ consisting of a source S, e.g., a base station BS, N haf-dupex reays R, and two users U and U, as depicted in Fig.. Assume that the BS, reays and users are a equipped with a singe antenna. It is assumed that no direct in between the BS and users exists, due to obstaces or heavy shadowing, and the reays assist the users to communicate with the BS. We further assume that the channe of each in is modeed as identicay and independent distributed i.i.d Rayeigh fading. Simiar to [9] and [], we assume that the users are ordered according to their QoS requirements rather than their channe conditions. Particuary, we assume that user has a higher priority than user to be served, i.e., user prefers quic connection with a ow data rate, such as Internet of Things IoT sensors, whie user woud ie a high resoution for onine game or downoading a movie. The detaied mode and reay seection schemes for the cooperative NOMA networ wi be presented in the foowing two subsections, respectivey. A. COOPERATIVE NOMA WITH DSTC In order to impement space-time coding in the cooperative NOMA networ, two reays are seected in the proposed VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

3 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding scheme, and perfect synchronization between reays is assumed. The detais for the reay seection wi be discussed in Section II-B. The transmission for the proposed cooperative NOMA networ with DSTC consists of two phases: during Phase I, the BS broadcasts the superimposed mixture x and x at two successive time sot t and t to N reays, respectivey, as foows: TABLE. DSTC for DF cooperative NOMA R N R N t 3 : z α s + α s z α s + α s t 4 : z α s α s z α s + α s t : x α s + α s, t : x α s + α s, where s ij i, j, } is the signa for U j at time sot t i and α i denotes the power aocation coefficient. Note that α +α and α α according to the NOMA principe, i.e., more power is assigned to the user with a worse channe condition or a ower data rate QoS requirement [7] [9]. It is noted that the symbos s, s and s, s are transferred to user and via the reaying ins, respectivey. It means that athough two time sots are used for the source-to-reay S-R ins, in the mean time, two different information signas can aso be transmitted to user and user, respectivey, which is equivaent to the one time sot scheme used in [9], where ony one symbo is transmitted to users. Therefore, the signas received by the reay R n, n,, N}, are: t : y n g n x + n Rn, 3 t : y n g n x + n Rn, 4 where g n CN, σg n denotes the channe coefficient between the BS and reay n, and the noise n Rn is the additive white Gaussian noise with zero mean and variance of N. Assume that SIC can be successfuy preformed at reays. Therefore, the achievabe rates for reay n to decode the signas of user and user are given by R R DF og α + g n α g n, 5 + / R DF R og + α g n, 6 where denotes the transmit signa-to-noise ratio SNR, and Ri R DF denotes the instantaneous data rate for user i achieved at reay n. During Phase II, the reay nodes R N and R N are seected according to the DRS criterion in Section II-B. For the DF reaying, we assume that the two seected reays can decode both the signas for U and U correcty and then retransmit the encoded NOMA signas to user and user by using the Aamouti code, as shown in Tabe. The received signas at user i, i, } can be derived as: t 3 : r i h Ni z + h N i z + n Di, 7 t 4 : r i h Ni z + h N i z + n Di, 8 It is aso interesting to investigate specia codes in order to achieve the fu asynchronous cooperative diversity order as in [7] and the references therein. However, this is out of the scope of this paper. where h ni CN, σh ni denotes the channe gain from reay n to user i, and the noise n Di is the additive white Gaussian noise with zero mean and variance of N. Then the decoding symbos at user i are given by s i h Ni r i + h N i ri, 9 s i h N i r i h Ni ri. Furthermore, 9 and can be written as: s i h Ni + h N i α s + α s + h Ni n D i + h N i n D i, s i h Ni + h N i α s + α s + h Ni n D i h N i n D i. Then the achievabe instantaneous data rates for user and user at users can be expressed as: R DF og R DF og α hn + h N + α hn + h N, + / 3 α hn + h N + α hn + h N, + / 4 R DF og + α hn + h N, 5 where Ri DF is the achievabe data rate for user i to detect its own signa, SIC is carried out at user to remove the signa for user, and R DF is the instantaneous rate for user to detect the signa for user. For the singe reay seection case, the corresponding instantaneous data rates at users can be written as: R DF og R DF og + + α h N α h N + / α h N α h N + /, 6, 7 R DF og + α h N. 8 It is obvious that the data rates in 3, 4 and 5 are aways higher than those in 6, 7 and 8. This ceary demonstrates that the proposed DRS schemes have better performance than the existing SRS schemes. VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

4 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding Agorithm Two-stage DSR-FPA Scheme : if S r then : System in outage 3: ese if S r then 4: Ony one reay is avaiabe 5: if R DF R and R DF R and R DF R then 6: Success transmission 7: ese 8: System in outage 9: end if : ese : Sort min h n, h n, n S r, choose the st and nd best reay. : if R DF R and R DF R and R DF R then 3: Success transmission 4: ese 5: System in outage 6: end if 7: end if B. RELAY SELECTION SCHEMES In this section, we mainy focus on two DRS schemes, which can significanty enhance the outage performance at the cost of a itte overhead. Two-stage DF DRS-FPA strategy is firsty considered. In the proposed scheme, the first and second best reays wi be chosen simutaneousy instead of seecting the best reay, as in [9]. Furthermore, two-stage DF SRS-DPA and DRS-DPA schemes are presented to improve the performance, where dynamic power aocation is used for both S-R and reay-to-destination R-D ins rather than ony in the R-D in in []. Two-stage DRS-FPA Scheme In order to reaize the Amouti code in the dua reay seection strategy, the two seected reays need to successfuy decode the messages for user and user simutaneousy, i.e., the instantaneous data rates for U and U are arger or equa to their target data rates R and R, respectivey. Therefore, for the two-stage scheme, the first stage is to buid a successfu decoding subset S r depending on the decoding status of the reays, which is different from the scheme in [9] that ony ensure the user with ower data rate stricty, i.e. user, at the first stage. Assuming that SIC is performed at the reays, then the subset of the reays which satisfy the user s and user s target data rates can be defined as foows: S r n : n N, og + α g n R, og + α g n α g n + / R }. 9 In the second stage the reay is seected according to the size of S r, denoted as S r. The detaied agorithm is shown in Agorithm. Two-stage SRS/DRS-DPA Scheme In order to further improve the performance, dynamic power aocation is used in this scheme. Different from the DRS- FPA scheme, at the first stage, there are two conditions for the avaiabe reays. One is that the reay can successfuy decode the messages for both users, the other one is the user with ower QoS requirement, i.e. U, can be stricty satisfied, and then try to maximize another user s rate at the second stage. It is we-nown that the conditions for a reay to decode the two signas correcty are given by og α + g n α g n R, + / og + α g n R. Based on, the range of the power aocation factor α can be expressed as: ɛ g n α g n ɛ g n + ɛ, where ɛ i Ri, i,. Note that if we choose the vaue of α according to, we can ensure that the messages for user and user can be decoded correcty at the reay n. Reca that the QoS requirement of user needs to be stricty satisfied in the first stage, which yieds that og + α h n α h n + / R. Using, the maxima power aocation factor α can be written as: } gn ɛ α min g n + ɛ, h n ɛ h n. 3 + ɛ Note that ony if the vaue of α in 3 is ager or equa to ɛ g n, the conditions in and are aways satisfied. As described above, the subset of the active reays can be obtained by S r n : g n a, h n ɛ g n g n a }, 4 where a ɛ + ɛ and a ɛ + ɛ + ɛ. For the SRS-DPA scheme, ony the best reay in S r is seected to serve U at the second stage, and the seection criterion can be defined as n arg max n S r hn }. 5 For the DRS-DPA scheme, the second stage is to choose two best reays among S r which can maximize the data rate for U. Sort h n in an ascending order, which is denoted by h h N h N. The reay nodes R N and R N corresponding to h N and h N wi be seected. Define γ sum h N + h N. In addition, there is a constraint for user 4 VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

5 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding to achieve a high data rate, that is, SIC can be successfuy carried out at user for both SRS-DPA and DRS- DPA schemes, i.e., og + α h n α h R n +/ and + α γsum R, respectivey. For the case og α γsum+/ S r in the DRS-DPA scheme, just using h N instead of γ sum, which is omitted here. Then the maxima power aocation factor α can be updated by } gn ɛ temp min g n + ɛ, h n ɛ h n, + ɛ } α SRS h n ɛ min temp, h n, 6 + ɛ } gn ɛ temp min g N + ɛ, h N ɛ h N, + ɛ } gn ɛ temp min g N + ɛ, h N ɛ h N, + ɛ α DRS min temp, temp, γ sum ɛ γ sum + ɛ }. 7 It is evident from 6 and 7 that the power aocation coefficient α is reated to the target data rate of user and the channe fading gains for the seected S-R and R-D ins. Furthermore, it is remarabe that if the fina vaue of the power aocation factor α < happen, and the impact of this constraint wi be taen into consideration for the evauation of the outage probabiity. ɛ g n, the system outage wi III. OUTAGE PERFORMANCE ANALYSIS In this section, the system outage probabiities of the considered DRS-FPA, SRS-DPA and DRS-DPA schemes are anayzed. The system outage probabiity can be defined as foows: P out P S r + P S r P, 8 where P is the condition outage probabiity when the size of the active reays set equas to. For the DRS-FPA scheme, when, by using the fact that a channes are assumed to be i.i.d Rayeigh fading, the coverage probabiity P can be cacuated as: } P P R DF R, R DF R, R DF Sr R P h N ξ /, h N η/ } e a, 9 ɛ where ξ, ξ α ɛ, η max ξ ɛα α, ξ } and a ξ + η. It is assumed that α > ɛ α, which aways eads to the system in outage, when a wrong choice for the power aocation coefficient is used. When, the reay nodes R and R wi be seected to assist the communication with U and U. Simiar to the case of, the coverage probabiity P can be written as: P P h + h ξ, h + h η }. 3 It is difficut to obtain the exact distribution of the term h i + h i, i, in 3, therefore, the ower and upper bounds are introduced in the foowing. Let γ i min h i, h i }, β i max h i, h i }, i S r, then rearrange γ i, β i, i,, in an ascending order, which is denoted by γ i, β i, such that γ γ γ and β β β. It can be seen from 3 that h i + h i γ + γ, 3 h i + h i β + β. 3 Then, the outage probabiity P can be bounded as foows: P b P b P ub P P ub, where 33 b P P γ b η } η F γb, ub P P γ ub η } η F γub, where γ b β + β and γ ub γ + γ. The foowing emma provides the cosed-form expressions for the cumuative distribution functions CDFs of γ b and γ ub. Lemma. When a the ins experience i.i.d Rayeigh fading, the CDFs of γ b and γ ub can be respectivey given by F γb z!! 3 3 Q + Q + Q, 34! F γub z! + J + J, 35 where Q e z e z e z + e + z Q 3 e z 4 3 e 3 z e z e +3 z, e z z + 4 Q 4 3 e 3 z z + e z e z + 3, J + e +z + e z,! J e z ze z.! Proof: See Appendix A. VOLUME 4, 6 5, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

6 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding The probabiity of the event that a reay is randomy seected from S r can be written as: α P og + g n α g n R, + / og + α g n } R P g n η/ } e η, 36 whie the probabiity to have avaiabe reays in S r is: N P S r e η e η N. 37 Using 9, 33, 34, 35 and 37 into 8, and after some manipuations, the ower and upper bounds of the system outage probabiity for DRS-FPA scheme can be obtained in the foowing theorem. Theorem. The ower and upper bounds on the outage probabiity for the two-stage DRS-FPA scheme can be respectivey expressed as foows: P b out e η N + Ne η + Pout ub + N e η N e a e η e η N Fγb e η N + Ne η N e η e η e η N Fγub, 38 η N e a η. 39 At high SNRs, the ower and upper bounds of the outage probabiity can be approximated as: Pout b η N N + Naη N η N+ N + N+, 4 Pout ub N N N η N + Naη N + η N. 4 Proof: See Appendix B. From 4 and 4, we can concude that the two-stage DRS-FPA scheme can achieve a fu diversity order of N. For the SRS-DPA and DRS-DPA schemes, based on 6 and 7, the condition coverage probabiity for the SRS-DPA scheme of S r and the DRS-DPA scheme of S r and S r can be obtained as foows, respectivey P SRS P DRS P P DRS P og og P og + α h n R Sr }, + α h N R Sr }, + α γ sum R Sr }. 4 Foowing the steps shown in Appendix C, the exact expressions for the system outage probabiities achieved by the two-stage SRS-DPA and DRS-DPA schemes can be presented in the foowing theorem. Theorem. The outage probabiities of the two-stage SRS- DPA and DRS-DPA schemes for cooperative NOMA can be obtained as foows: P SRS out q N + e a P DRS out q N + Nq q N + where q N q q N e a + f, 43 N q q N c + f q c f. 44 e ɛ x a x a e x dx, c e a a Fγsum f f y a y a + + e, ɛ z ɛ a a z a e z a e z e y dzdy, ɛ z ɛ a a z a e z a F γsum ze y dzdy, F γsum z + z + + e z e z ze z. Proof: See Appendix C. In the high SNR region,, and Pout SRS can be approximated as foows: Pout SRS N N b N + b N a + N π N+ sin i ɛ + a, N N s i i 45 where b a + ɛ. Simiary, the ower and upper approximations on Pout DRS can be respectivey expressed as foows: Pb DRS N N b N + Nb N + b N a + N π N+ sin i ɛ + a, N N s i Pub DRS N b N + Nb N + + N+ N π N Proof: See Appendix C. i 46 N b N a sin i ɛ + a, N s i 6 VOLUME 4, 6 i c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

7 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding It can be seen easiy form 45, 46 and 47 that fu diversity gain can be achieved by cooperative NOMA with both two-stage DF SRS-DPA and DRS-DPA schemes. Note that the proposed two-stage DF DRS schemes incuding DRS-FPA and DRS-DPA coud yied better outage performance than the existing SRS-FPA [9] and SRS-haf- DPA [] schemes. Meanwhie, a the schemes can achieve the fu diversity order. In addition, the DRS-DPA strategy outperforms the DRS-FPA strategy due to its abiity to adjust the power aocation factors dynamicay. IV. NUMERICAL AND SIMULATION RESULTS In this section, the outage performance of the proposed twostage DRS-FPA, SRS-DPA and DRS-DPA schemes for cooperative NOMA networ with space time coding is evauated by using computer simuations. FIGURE 3. Outage performance of the two-stage DF DRS-FPA scheme with space time coding for cooperative NOMA, where R bits/s/hz, R bits/s/hz, the power aocation factor α 4 5 under the different reay numbers N. FIGURE. Impact of the reay numbers N on the outage performance of the two-stage DF DRS-FPA scheme with space time coding for cooperative NOMA, where R.5bits/s/Hz, R bits/s/hz, the power aocation factor α 3 4 [9], where b denotes ower bound and ub denotes upper bound. Figs. and 3 show the outage probabiity for the two-stage DF reaying with the DRS-FPA scheme at the target data rates R.5 bits/s/hz, R bits/s/hz, the power aocation factor α 3 4 and R bits/s/hz, R bits/s/hz, α 4 5, respectivey. It can be seen from both figures that the proposed two-stage DF DRS-FPA scheme can remaraby enhance the outage performance compared to the two-stage DF SRS-FPA scheme [9]. Furthermore, by reducing the gap between R and R as we as by increasing the number of the reays, the outage performance gap between the two reay seection schemes becomes significanty arger. In addition, both ower and upper bounds projected in Theorem match the Monte Caro simuations for a the SNR vaues. Furthermore, the upper bound becomes tighter, when there are more reays. In Fig. 4, the outage performance of the two-stage DF SRS-DPA and DRS-DPA schemes with space time coding is compared to the two-stage DF SRS-haf-DPA scheme [] FIGURE 4. Impact of the reay numbers N on the outage performance of the two-stage DF DRS-DPA scheme with space time coding and the two-stage DF SRS-DPA shceme for cooperative NOMA, where R.5bits/s/Hz, R bits/s/hz and for comparison, the power aocation coefficient of SRS-haf-DPA scheme γ 3 4 []. for cooperative NOMA, where the target data rates R.5 bits/s/hz and R bits/s/hz. Note that both SRS-DPA and DRS-DPA schemes significanty outperform the SRShaf-DPA scheme for a the SNR vaues, whie a of them can achieve the same diversity gain. It is worth mentioning that, as the number of reays N increases, the gain achieved by the DRS-DPA scheme is more obvious compared to the SRS-DPA scheme and SRS-haf-DPA scheme, i.e. when the reay number N 8, the gap between DRS-DPA scheme and SRS-DPA scheme is db, whie the DRS-DPA scheme reaizes about 3.5dB gain over the SRS-haf-DPA scheme at P out 3. In addition, one can observe that the simuation resuts perfecty match the anaytica ones, which are based VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

8 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding on Theorem for the SRS/DRS-DPA schemes. This ceary demonstrates the correctness of the deveoped anaysis. In Fig. 5, we compare the outage performance for the twostage DF DRS-FPA and DRS-DPA schemes with space time coding for cooperative NOMA networ. It can be evidenty seen that the DRS-DPA scheme can obtain much better outage performance than DRS-FPA. The main reason for this is that the cooperative NOMA networ is sensitive to the reation between the target data rates and power aocation factors. Therefore, fixed power aocation can aways ead the system in outage, if a wrong choice is used for the power aocation coefficients, whie in the DRS-DPA scheme, one can adjust the vaues of the power aocation factors dynamicay according to the channe gains and the user s target data rates, which is more fexibe. system with more compicated fading channe mode, such as Naagami-m fading channe [8] for both DF and AF reay seection schemes wi be investigated as a future wor.. APPENDIX A PROOF OF LEMMA Since a the ins experience i.i.d Rayeigh fading, without oss of generaity, it is assumed that σ g i σ h ij, and the CDF of h ij i,, N, j, is F x e x. Based on the order statistics in [9], the CDF and PDF of γ i are F γi x e x and f γi x e x, respectivey. The joint PDF of γ andγ foows that for x y! f γ,γ x, y! f γ i xf γi y [F γi x] The CDF of γ ub can be obtain by!! e x e y [ e x]. 48 FIGURE 5. Outage performance comparison between the two-stage DF DRS-FPA and DRS-DPA schemes with space time coding for cooperative NOMA, where R.5bits/s/Hz, R bits/s/hz, the power aocation factor α 3 4 with different reay numbers N. V. CONCLUSIONS In this paper, we have proposed two inds of two-stage DF dua reay seection schemes with distributed space time coding for cooperative NOMA, i.e., the DRS-FPA scheme and DRS-DPA scheme. Cosed-form ower and upper bounds and exact anaytica expressions of the outage probabiities for DRS-FPA and DRS-DPA schemes were derived, respectivey. The deveoped anaytica resuts match those obtained from simuations we and it is pointed out that a the dua reay seection schemes outperform the existing singe reay seection schemes, as we as achieve fu diversity gain. Furthermore, the impact of the reay number and the users target data rates on the performance was discussed, and the gain achieved by the DRS scheme is more obvious with more reays. Besides, the outage performance of the DRS-DPA scheme is superior to that of the DRS-FPA scheme, because in the DRS-DPA scheme, one can adapt the system with more fexibe parameter seection. A cooperative NOMA F γub z F γ +γ z z/ z x x!! z/ f γ,γ x, y dxdy e +x e z e x dx. 49 Simiary, the CDF and PDF of β i are F βi x e x and f βi x e x e x, respectivey. The joint PDF of β andβ foows that for x y! f β,β x, y! f β i xf βi y [F βi x] The CDF of γ b can be obtain by F γb z F β +β z z/ z x z/!! e x e x e y e y [ e x ]. 5 x f β,β x, y dxdy!! e x e x 3 e z x e z x e x + e x dx! z/ 3 3! e z e x e z e x e +3x +e +x dx. 5 8 VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

9 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding After some computations for 49 and 5, the CDFs for the ower and upper bounds can be expressed as F γb z and F γb z in 34 and 35, respectivey. APPENDIX B PROOF OF THEOREM The diversity orders of the ower and upper bounds of the outage probabiity wi be discussed in the foowing part. In order to anayze the probems easiy, 3 and 3 can be written as foows. γ b β + β < β, 5 γ ub γ + γ > γ, 53 Then it is noted that, P γ b < z > P β < z z F γb z > F β, P γ ub < z < P γ < z F γub z < F γ z, where, z F β e z, F γ z e z. At high SNR, approaches infinity, η/ approaches zero. When x, the exponentia function can be approximated by appying the Tayor series as e x x. Therefore, using the fact that F z β z and F z γ z, the CDFs of the ower and upper bounds can be approximated as foows, respectivey. F γb z z, 54 F γub z z, 55 By using 54 and 55 into 38 and 39, respectivey, the diversity gain can be obtained. APPENDIX C PROOF OF THEOREM SRS DRS The probabiities P and P in 4 can be expressed as foows, respectivey P SRS ɛ } Sr P α h n, P DRS P α ɛ } Sr, γ sum By appying 6 and 7, as and T P q P P SRS and P DRS can be written P SRS T q ; P DRS T T q q. 56 h n a, h n g h n, g n a }, h n g g n, g n a }, h n g g n, T P γ sum a, h N gγ sum, g N a }, h N g g N, T P γ sum a, h N gγ sum, g N a }, h N g g N, q P g N a }, h N g g N, q P g N a }, h N g g N, ɛx where gx x a is a decreasing function, due to the i.i.d Rayeigh fading, the terms T T, q q q. Then the parameters above can be further evauated as foows q T T e ɛ y a y e ɛ z a a + a y e ɛ y a y a e ɛ y a y a y a e y dy, 57 z a f γsum ze y dzdy ɛ y f γsum ze y a e y dzdy y a e y dy e a ɛ z a Fγsum ɛ a a z a e z a F γsum ze y dzdy, y a e y dy e a ɛ z a F hn ɛ a a z a e z a F hn ze y dzdy, where F γsum z is the CDF of γ sum, which can be presented as F γsum z + e z e z + e z ze z. 6 and F hn z is the CDF of h n, F hn z e z S r. 6 In the same way, the probabiity P in 4 can be cacuated by P e ɛ y a y a e y dy. 6 The probabiity of the event that S r can be obtained as foows N P S r Pa P a N, 63 VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

10 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding where P a P g n a, h n ɛ g n g n a e ɛ x a x a e x dx. Then Theorem is proved by substituting the corresponding terms into 8. As γ sum h N + h N, it is easiy found that h N < γ sum < h N, then F hn z > F γsum z > F z hn, where F hn z e x. Therefore, the ower and upper bounds on T can be presented as foows: T b T ub e ɛ y a y a y a e y dy e a e a ɛ z ɛ a a z a e z a e z e y dzdy q e a e a f, 64 e ɛ y a y a y a e y dy e a e a ɛ z ɛ a a z a e z a e z e y dzdy q e a e a g. 65 Assume in the foowing part. Let t y a ɛ, and the above q can be expressed as foows: q ɛ a e ɛ a e e a t e ɛ t e a t ɛ t dt dt e a t ɛ t dt, 66 By using e β 4x γx dx β γ K βγ in [], the first term in q can be cacuated as foows e a t ɛ t 4a 4a ɛ dt K ɛ, 67 Simiar to [], the Gauss-Chebyshev integra is appied to approximate the second integra in q, e a t ɛ t π dt sin i e a t ɛ t, 68 N N i where N is the Gauss-Chebyshev integra approximated sum term. Based on the approximation of the Besse function zk z + z n z, z in [], when, q can be approximated as foows: q ɛ a e + a ɛ ɛ n a ɛ + π sin i a N N t + ɛ t i a + ɛ. 69 Let s f y ɛ z a, and then we can obtain the foowing ɛ z ɛ a a z a e z a e z dz a ɛ e e a s ɛ y a e ɛ s +a ds, 7 As, combining with Gauss-Chebyshev integra, the doube integra f in 64 can be further evauated as foows: a a e ɛ a ɛ +a e a π + N e a s e a s sin i N i e ɛ s +a dse y dy e ɛ s +a ds ɛ + a. 7 s i Simiary, the third term g in 65 can be approximated as g a π + + sin i N N i + cos i ɛ + a. 7 s i where s i N []. At high SNR, substituting 69, 7 and 7 into 43 and 44, respectivey, the approximations for the outage probabiities of the SRS-DPA and DRS-DPA schemes are obtained. REFERENCES [] Z. Ding, X. Lei, G. K. Karagiannidis, R. Schober, J. Yuan, and V. K. Bhargava, A survey on non-orthogona mutipe access for 5G networs: Research chaenges and future trends, IEEE J. Se. Areas Commun., vo. 35, no., pp. 8 95, Oct. 7. [] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Naamura, A. Li, and K. Higuchi, Non-orthogona mutipe access NOMA for ceuar future radio access, in Proc. IEEE Veh. Techno. Conf. VTC Spring, Dresden, Jun. 3, pp. 5. [3] M. Shirvanimoghaddam, M. Doher, and S. J. Johnson, Massive nonorthogona mutipe access for ceuar IoT: potentias and imitations, IEEE Commun. Mag., vo. 55, no.9, pp. 55 6, Sep. 7. [4] S. M. R. Isam, N. Avazov, O. A. Dobre, and K. S. Kwa, Power-domain non-orthogona mutipe access NOMA in 5G systems: potentias and chaenges, IEEE Commun. Surveys Tuts., vo. 9, no., pp. 7 74, Oct. 6. [5] A Nosratinia, T. E Hunter, and A Hedayat, Cooperative communication in wireess networs, IEEE Commun. Mag., vo. 4, no., pp. 74 8, Oct. 4. [6] J. N. Laneman, D. N. C. Tse, and G. W. Worne, Cooperative diversity in wireess networs: Efficient protocos and outage behavior, IEEE Trans. Inf. Theory, vo. 5, no., pp , Dec. 4. [7] Z. Ding, M. Peng, and H. V. Poor, Cooperative non-orthogona mutipe access in 5G systems, IEEE Commun. Lett., vo. 9, no. 8, pp , Aug. 5. [8] J. B. Kim and I. H. Lee, Non-orthogona mutipe access in coordinated direct and reay transmission, IEEE Commun. Lett., vo. 9, no., pp. 37 4, Nov. 5. [9] Z. Ding, H. Dai, and H. V. Poor, Reay seection for cooperative NOMA, IEEE Wireess Commun. Lett., vo. 5, no. 4, pp , Aug. 6. [] Z. Yang, Z. Ding, Y. Wu, and P. Fan, Nove reay seection strategies for cooperative NOMA, IEEE Trans. Veh. Tech., vo. 66, no., pp. 4 3, Sep. 7. [] Y. Jing and H. Jafarhani, Singe and mutipe reay seection schemes and their achievabe diversity orders, IEEE Trans. Wireess Commun., vo. 8, no. 3, pp , Mar. 9. VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

11 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding [] S. Zhang and V. K. N. Lau, Muti-reay seection design and anaysis for muti-stream cooperative communications, IEEE Trans. Wireess Commun., vo., no. 4, pp. 8 89, Apr.. [3] L. Wu and X. Hou, Physica ayer networ coding based on dua reay seection in two-way reay channe, In Int. Conf. Wireess Commun. and Signa Process. WCSP, Nov., pp. 6. [4] J. Yang, Z. Ding, and P. Fan, Performance anaysis of dua reay seection scheme in two-way ampify-and-forward reay channe, In IEEE 4th Int. Conf. on Commun. Tech., Nov., pp [5] S. M. Aamouti, A simpe transmitter diversity scheme for wireess communications, IEEE J. Se. Areas Commun., vo. 6, pp , 998. [6] M. F. Kader and S. Y. Shin, Cooperative reaying using space-time boc coded non-orthogona mutipe access, IEEE Trans. Veh. Tech., vo. 66, no. 7, pp , Ju. 7. [7] X. Guo and X. G. Xia, Distributed inear convoutive space-time codes for asynchronous cooperative communication networs, IEEE Trans. Wireess Commun., vo. 7, no. 5, pp , May. 8. [8] T. Zhang, W. Chen, and Z. Cao, Opportunistic DF-AF seection reaying with optima reay seection in naagami-m fading environments. In st IEEE Int. Conf. on Commun. in China ICCC, Aug, pp. 69ĺC64. [9] H. A. David and H. N. Nagaraja, Order Statistics, John Wiey and Sons, Inc., 5. [] I. S. Gradshteyn and I. M. Ryzhi, Tabe of Integras, Series, and Products Sixth Edition, Academic Press,. PINGZHI FAN M 93-SM 99-F 5 received his PhD degree in Eectronic Engineering from the Hu University, UK. He is currenty a professor and director of the institute of mobie communications, Southwest Jiaotong University, China. He is a recipient of the UK ORS Award, the Outstanding Young Scientist Award by NSFC, and the chief scientist of a nationa 973 research project. He served as genera chair or TPC chair of a number of internationa conferences, and is the guest editor-in-chief, guest editor or editoria member of severa internationa journas. He is the founding chair of IEEE VTS BJ Chapter and IEEE ComSoc CD Chapter, the founding chair of IEEE Chengdu Section. He aso served as a board member of IEEE Region, IETIEE Counci and IET Asia-Pacific Region. He has over research papers pubished in various academic Engish journas IEEE/IEE/IEICE, etc, and 8 boos inc. edited, and is the inventor of granted patents. His research interests incude high mobiity wireess communications, 5G technoogies, wireess networs for big data, signa design and coding, etc. He is an IEEE VTS Distinguished Lecturer 5-7, and a feow of IEEE, IET, CIE and CIC. JING ZHAO received her B.S. degree in communication engineering from Southwest Jiaotong U- niversity, Chengdu, in 9, and she is currenty a PhD student at the same university. She was a visiting Ph.D. student with the Department of Eectrica Engineering, University of Aransas, Fayettevie, USA, from 4 to 5. Her research interests incude high mobiity wireess communications, cooperative communications, 5G networs, signa processing etc. ZHIGUO DING S 3-M 5-SM 5 received the B.Eng. degree in eectrica engineering from the Beijing University of Posts and Teecommunications in, and the Ph.D. degree in eectrica engineering from Imperia Coege London in 5. From 5 to 4, he was with Queens University Befast, Imperia Coege London, and Newcaste University. From to 6, he was an academic visitor with Princeton University. S- ince 4, he has been a Chair Professor with Lancaster University. His research interests are 5G networs, game theory, cooperative and energy harvesting networs, and statistica signa processing. He received the Best Paper Award at the IET Communication Conference on Wireess, Mobie and Computing in 9, was an IEEE COMMUNICATIONS LETTERS Exempary Reviewer in, and hed the EU Marie Curie Feowship from to 4. He is serving as an Editor for the IEEE TRANSACTIONS ON COMMUNICATIONS, the IEEE TRANSACTIONS ON VEHICU- LAR TECHNOLOGIES and the Journa of Wireess Communications and Mobie Computing. He was an Editor for the IEEE WIRELESS COM- MUNICATION LETTERS and the IEEE COMMUNICATION LETTERS from 36. He is a Leading Guest Editor for the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS Specia Issue on Non- Orthogona Mutipe Access for 5G and a Guest Editor for the IEEE Wireess Communications Specia Issue on Non-Orthogona Mutipe Access. ZHENG YANG S received the B.S. degree in mathematics from Minnan Norma University, Zhangzhou, in 8, the M.S. degree in mathematics from Fujian Norma University, Fuzhou, China, in, and the Ph.D. degree in information and communications engineering from Southwest Jiaotong University, Chengdu, China, in 6. Dr. Yang was a visiting Ph.D. student with the Schoo of Eectrica and Eectronic Engineering, Newcaste University, Newcaste upon Tyne, U.K., in 4. He is currenty a Lecturer with the Coege of Photonic and Eectronic Engineering, Fujian Norma University. His research interests incude 5G networs, cooperative and energy harvesting networs, and signa design and coding. VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.

12 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content may change prior to fina pubication. Citation information: DOI.9/ACCESS.8.846, IEEE Access J. Zhao et a.: Dua Reay Seection for Cooperative NOMA with Distributed Space Time Coding GEORGE K. KARAGIANNIDIS M 96-SM 3- F 4 was born in Pithagorion, Samos Isand, Greece. He received the University Dipoma 5 years and PhD degree, both in eectrica and computer engineering from the University of Patras, in 987 and 999, respectivey. From to 4, he was a Senior Researcher at the Institute for Space Appications and Remote Sensing, Nationa Observatory of Athens, Greece. In June 4, he joined the facuty of Aristote University of Thessaonii, Greece where he is currenty Professor in the Eectrica & Computer Engineering Dept. and Director of Digita Teecommunications Systems and Networs Laboratory. He is aso Honorary Professor at South West Jiaotong University, Chengdu, China. His research interests are in the broad area of Digita Communications Systems and Signa processing, with emphasis on Wireess Communications, Optica Wireess Communications, Wireess Power Transfer and Appications, Moecuar and Nanoscae Communications, Stochastic Processes in Bioogy and Wireess Security. He is the author or co-author of more than 45 technica papers pubished in scientific journas and presented at internationa conferences. He is aso author of the Gree edition of a boo on Teecommunications Systems and co-author of the boo Advanced Optica Wireess Communications Systems, Cambridge Pubications,. Dr. Karagiannidis has been invoved as Genera Chair, Technica Program Chair and member of Technica Program Committees in severa IEEE and non-ieee conferences. In the past, he was Editor in IEEE Transactions on Communications, Senior Editor of IEEE Communications Letters, Editor of the EURASIP Journa of Wireess Communications & Networs and severa times Guest Editor in IEEE Seected Areas in Communications. From to 5 he was the Editor-in Chief of IEEE Communications Letters. Dr. Karagiannidis is IEEE Feow and one of the highy-cited authors across a areas of Eectrica Engineering, recognized as 5, 6 and 7 Web-of-Science Highy-Cited Researcher. VOLUME 4, c 8 IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information.