Performance Analysis of Relay Assisted Cooperative Non-Orthogonal Multiple Access Systems

Transcription

1 Performance Analysis of elay Assisted Cooperative Non-Orogonal Multiple Access ystems Jiayi Zhang, Member, IEEE, Linglong Dai, enior Member, IEEE, uicheng Jiao, Xu Li and Ying Liu Abstract Non-orogonal multiple access NOMA is a promising multiple access technique for e fif generation 5G wireless communications. In order to enhance e performance gains of NOMA systems, a relay assisted cooperative NOMA scheme is designed in is paper. In e proposed scheme, e concept of NOMA is exploited to realize e transmission of e source information in e second time slot. The destination can only receives a single data symbol in conventional cooperative systems, while e destination can reliably acquire two data symbols in two time slots. Therefore, e proposed scheme can achieve higher achievable rate performance an existing schemes. Moreover, e complex power allocation algorim can be avoided to alleviate e complexity of cooperative NOMA systems. For ayleigh fading channels, we derive exact expressions for two important performance metrics of e proposed scheme, i.e., e outage probability and e achievable rate. In addition, asymptotic results are presented in terms of simple elementary functions to provide useful insights to guide e practical implementation. Monte-Carlo simulations are provided to demonstrate e performance of e proposed scheme and e accuracy of e derived analytical results. Index Terms Non-orogonal multiple access, cooperative relay, outage probability, achievable rate. I. INTODUCTION Non-orogonal multiple access NOMA is one of e most promising multiple access techniques to support massive connectivity in future fif generation 5G wireless networks [], []. Compared to conventional orogonal multiple access OMA techniques, NOMA can serve multiple users using e same resources in e time/frequency/code domain but wi different power levels, i.e., multiple users symbols are multiplexed using superposition coding in e power domain []. At e NOMA receiver, we can first decode e symbol wi e best quality, and en apply successive interference cancellation IC [3] to detect e remaining symbols. On e oer hand, cooperative relay transmission has been shown to be able to significantly improve e transmission reliability, network coverage, and achievable rate of cellular This work was supported in part by e International cience & Technology Cooperation Program of China Grant No. 5DFG76, e National Natural cience Foundation of China Grant Nos , 6577 and 66, e Beijing Natural cience Foundation Grant No. 7, and e Fundamental esearch Funds for e Central Universities. J. Zhang, X. Li, and Y. Liu are wi e chool of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, P.. China jiayizhang@bjtu.edu.cn. L. Dai and. Jiao are wi Department of Electronic Engineering as well as Tsinghua National Laboratory for Information cience and Technology TNList, Tsinghua University, Beijing 8, P.. China. daill@tsinghua.edu.cn networks [], [5]. Thus, e integration of NOMA and cooperative relaying has recently attracted increasing interests to improve e roughput of future 5G wireless networks [6], [7]. pecifically, a cooperative NOMA transmission scheme was proposed in [8], where e users wi better channel qualities can be severed as relays to improve e performance of e users wi poor channel qualities. More recently, NOMA wi a dedicated relay was proposed to improve e transmission reliability for a user wi poor channel qualities [9], while e auors in [] presented e outage behavior analysis of NO- MA wi multiple-antenna relays. Furermore, a cooperative relaying systems using NOMA C-NOMA was proposed in [], where only e relay transmits e decoded symbol to e destination in e second time slot. However, most of existing schemes have not considered to send e source symbols in e second time slot, which fails to fully exploit e NOMA principle for furer performance enhancement. In addition, power allocation wi high complexity is required by ese schemes to realize high achievable rates. In is paper, we propose a relay assisted cooperative NO- MA scheme to fully exploit e NOMA principle to enhance e performance gain furer. pecifically, in e first slot, e source transmits e same symbol to e destination and e relay, respectively. In e second time slot, unlike e existing C-NOMA scheme [], e source in e proposed scheme can transmit symbols to e destination, and e destination can use e IC detection strategy to reliably decode e symbols. Therefore, e proposed scheme can achieve higher achievable rates an existing C-NOMA [] and C- OMA [] schemes. Moreover, because each node transmits e data symbol wi its maximum power, e complicated power allocation required by previous works is no longer needed by e proposed scheme. Finally, e exact expression for e outage probability as well as its high-n approximation are derived to show at e diversity order of e proposed scheme is e same as existing C-NOMA schemes. The rest of e paper is organized as follows: ection II introduces e system model of e proposed relay assisted cooperative NOMA. In ection III, we provide a detailed analysis for e outage probability and achievable rate of e proposed scheme. Numerical results are provided in ection IV to validate e eoretical analysis. Finally, ection V concludes is paper by summarizing e key findings. imulation codes are provided to reproduce e results presented in is paper:

2 Fig.. First time slot econd time slot a a First time slot econd time slot a a a C-NOMA. P x P x b Proposed relay assisted cooperative NOMA. Two system models of different relaying protocols. II. YTEM MODEL OF THE POPOED CHEME As illustrated in Fig. b, we consider a simple cooperative network where a source node,, communicates wi a destination node, D, wi e assistance of a fixed decodeand-forward DF [] relay node,, which fully decodes, reencodes, and retransmits e source message to e destination D. Moreover, e source can also directly communicate e destination D. We furer assume e relay works in e half-duplex mode, i.e., e relay cannot transmit and receive a symbol at e same time. The general notation h a, a {, D, D}, is defined to denote e channel coefficients of e link between, and D, respectively. Wiout loss of generality, e fading gains in all involved links are assumed to follow e ayleigh distribution wi e probability density function PDF given by f ha x = exp xωa, a {, D, D}, Ω a where Ω a denotes e average power, and e cumulative distribution function CDF given by F ha x = exp xωa, a {, D, D}. The communication process for cooperative relay systems consists of two consecutive time slots. During e first time slot, e source transmits a symbol x wi e power P to bo e relay and e destination D. Accordingly, e received signals at and D can be expressed as r a,x = P h a x + n, a {, D}, 3 D D where n is e additive white Gaussian noise AWGN wi zero mean and variance σ. We assume at E{ x } = wi E{ } denoting expectation. The received Ns for symbol x at and D are given by γ a,x = P h a σ = ρ h a, a {, D}, where ρ P /σ represents e transmit N. In e second time slot, forwards e decoded symbol x wi e power P to D, and transmits anoer symbol x wi E{ x } = and e power P to D. While in e C-NOMA scheme [], only e relay transmits e decoded symbol to e destination D as in Fig. a. Then, e received signal at D is given by r D = P h D x + P h D x + n. 5 Usually, e fading gain h D of e -D link is smaller an e fading gain h D of e -D link, i.e., E{ h D } < E{ h D }, due to e distance difference. This natural characteristic of e channel difference between different transceivers facilitates us to utilize e NOMA principle at e second time slot. However, C-NOMA in [] employs complex power allocation at e source to distinguish two symbols, i.e., power allocation coefficients a and a. According to e IC-based NOMA scheme, e destination D firstly decodes e symbol x by treating e symbol x as a noise term. Then, x is canceled from r D by using IC to decode x. ince we are interested in e effect of channel gains on e outage performance, we follow e typical assumption [] at e transmit power of and is e same as P = P = P. Therefore, e received Ns for symbols x and x are respectively obtained as γ D,x = ρ h D ρ h D +, 6 γ D,x = ρ h D. 7 ince we utilize e fixed DF scheme at e relay, e end-toend N for e transmitted symbol x wi e aid of can be expressed as γ ee,x = min {γ D,x, γ,x }. 8 III. PEFOMANCE ANALYI In is section, we derive analytical expressions for e outage probability and achievable rate of e proposed relay assisted cooperative NOMA system in ection II. In addition, asymptotic high-n expressions are also presented to provide useful insights into e effects of system and channel parameters on e performance. Finally, our derived result will be compared wi existing results. A. Outage Probability We first illustrate e outage probability of e relay assisted cooperative NOMA system. The outage probability is defined as e probability at e instantaneous received N γ falls below a pre-defined reshold γ. Thus, we can use e CDF

3 3 of e received N to readily evaluate e outage probability as shown in e following Theorem. Theorem. For e relay assisted cooperative NOMA system, e outage probabilities P o,x and P o,x for symbols x and x are respectively given by P o,x P o,x = exp γ Ω De γ ρω D γ Ω D + Ω D + Ω De γ ρ Ω + D Ω + Ω D ρ Ω + D Ω, 9 γ Ω D + Ω D Ω D = exp γ γ. γ Ω D +Ω D ρω D ρω D Proof: Employing e definition of outage probability P o = Pr γ < γ = F γ γ, we can directly derive e outage probability of x in e -D link, P o,x, as P D,x = exp γ. ρω D To derive e outage probability of x, e CDF of γ ee should be obtained at first. Wi e help of, and 6, e CDF of γ D,x is given by [, Eq.] F D,x z = F X z y + f Y y dy z y + = exp y ρω D ρω D Ω D = exp z zω D + Ω D ρω D Ω D dy, 3 where X ρ h D, Y ρ h D, and Z γ D,x. In fixed DF relaying systems, an outage event occurs if eier one of e two-hop links cannot decode x. Using 3, e outage probability can be expressed as P ee,x γ F C,x γ F D,x γ + F D,x γ F D,x γ F D,x γ = Ω De γ Ω + D. γ Ω D + Ω D ρ Ω The selection combining technique is used at e receiver, and e total outage probability of x is given by P o,x = P D,x γ P ee,x γ. 5 ubstituting and into 5 and after some algebraic manipulations, we can attain 9. Moreover, following similar steps in [3], e outage probability of x in e -D link, P o,x, can be obtained as P o,x = P γ D,x > γ, γ D,x > γ. Wi e help of 6 and 7, e proof is finished. To investigate e impact of fading parameters on e outage performance, we present e asymptotic outage probability expressions at e high N regime in Lemma as follow. Lemma. The achievable diversity order of each symbol are e same as one. Proof: In e high-n regime, e outage probabilities of x and x can be approximated as γ Po,x = γ Ω D + Ω D ρ, 6 Po,x γ Ω D γ Ω D + Ω D = + γ Ω D + Ω D ρω D γ Ω D + Ω D, 7 where we have used e approximation of e x x when x [, Eq...]. The proof is concluded by defining log P e diversity order as lim o ρ log ρ =. It is remarkable at e high-n outage probability of x, Po,x, is independent of Ω, while Po,x is an decreasing function of Ω D and Ω D. Note at e outage probability of x is lower bounded by a fixed value of γ Ω D /γ Ω D + Ω D as ρ. The outage performance can be improved by adopting a low reshold γ. Moreover, bo outage probabilities are monotonically decreasing functions of e transmit N ρ. Unlike e legacy DF scheme where e diversity order is two, e diversity order of our proposed fixed DF based scheme is one. This is due to at fixed DF requiring e relay to fully decode e source information limits to e performance of direct transmission between e source and relay []. B. Achievable ate Achievable rate is a key performance metric for wireless communication systems, so we now focus on e achievable rate performance of e proposed relay assisted cooperative NOMA systems. According to e NOMA and fixed DF relay scheme, e total achievable rate of x is given by x = min {log + γ D,x, log + γ,x } }{{} C,x + log + γ D,x }{{} D,x, 8 where C,x denotes e achievable rate of x transmitted rough, and D,x denotes e achievable rate of x transmitted directly from to D. The parameter / is due to using two time slots in relaying systems. By substituting into 8, we can readily derive D,x as D,x = exp x ln + x dx ln ρω D = ln exp ρω D ρω D Ei ρω D, 9 where Ei is e exponential integral function [, Eq. 8..], and we have used e integral identity [, Eq..337.]. The achievable rate of x can be derived as x = D,x by using e same meod to derive x. Moreover, we evaluate C,x by presenting e following Theorem. Theorem. For e relay assisted cooperative NOMA system, e approximated achievable rate of x transmitted rough

4 can be obtained as C,x ln N w k Ω D e x k ρ Ω + D Ω + x k x k Ω D + Ω D, k= where N is e number of integration points, e abscissas x k and e weights w k are defined as [ π k x k = tan cos N π + π ], π sin k N w k = π Ncos [ π cos k N π ]. + π Proof: Please see Appendix. Alough e expression of c,x presented in Theorem is given in terms of sum series, we only need a few terms e.g., N < 6 as verified by extensive Monte-Carlo simulations to get a satisfactory accuracy e.g., smaller an 6 for all considered cases. Combining e aforementioned results 9 and, we derive e total achievable rate of x and x as N w k Ω D e x k ρ Ω + D Ω ln + x k x k Ω D + Ω D k= e ρω D Ei. 3 ρω D Because e exact analytical results above cannot directly provide physical insights, we now focus on e high-n regime and present e Lemma as follows. Lemma. In e high-n regime, e asymptotic achievable rate of 3 is given by = log ρ E c ln + log Ω D + N w k Ω D ln + x k x k Ω D + Ω D. k= Proof: As ρ, we can apply e approximations of Ei x E c + ln x [, Eq. 8..] and e x + x when x [, Eq...] on 3. After some algebraic manipulations, can be obtained to finish e proof. From, it is obvious at, as e transmit N ρ increases, e achievable rate improves. Moreover, a higher value of Ω D /Ω D will decrease e achievable rate, which means at e short distance of e -D link benefits e rate performance of e relay assisted cooperative NOMA system. It is wory to mention at e proposed scheme can achieve e rate scaling of log ρ, while e rate scaling of conventional C-OMA [] and C-NOMA [] is log ρ. This advantage is obtained by exploiting e second time slot and e NOMA principle in e proposed scheme. in e second time slot, e source can send symbol x to e destination D. Thanks to e NOMA principle, e destination D can decode symbols x and x by employing e IC principle. IV. NUMEICAL EULT In is section, we provide numerical results to validate e outage probability and achievable rate results obtained Outage Probability 3 imulation results High-N results Analytical P o,x 9 Analytical P o,x Ω D =, 3, Transmit N ρ db Fig.. Outage probability against e transmit N ρ, where different values of Ω D are considered but Ω is fixed as and γ is fixed as db. Achievable ate bits/hz Prop. imulation Prop. Analytical Prop. High-N C-NOMA C-OMA log ρ Ω D =, 5, Ω D = Transmit N ρ db Fig. 3. Achievable rate against e transmit N ρ, where different values of Ω D are considered but Ω is fixed as. in ection III. We also provide some insights into e system performance. To validate e accuracy of e aforementioned expressions, comparisons wi complementary Monte Carlo-simulated performance results are also presented. More specifically, 6 realizations of ayleigh distribution random variables are generated. The distances of all links can be represented by e average power. Furermore, a typical simulation scenario illustrated in Fig. is considered wi an normalized distance parameter of e D link as Ω D =. The outage probability performance is presented in Fig. against e transmit N ρ when different values of Ω D are considered. We can observe at e simulation results provide a perfect match to e analytical results obtained in ection III. In addition, as e quality of e -D link increases, e outage probability P o,x in 9 for e symbol x also improves. However, e gap between e corresponding curves decreases as Ω D increases from, 3 to 5, which implies at its effect becomes less pronounced. Moreover, it is obvious from Fig. at e high-n approximations are sufficiently

5 5 tight at moderate Ns and become exact at high Ns. Additionally, its accuracy improves for small values of Ω D. Note at P o,x reduces to a constant value related to Ω D as ρ increases, which means e outage probability of x is limited to e average power of e -D link. The diversity orders of x and x are one, which has been accurately predicted in Lemma. Fig. 3 depicts simulation results, analytical result 3, and high-n approximation of e achievable rate against e transmit N ρ for e relay assisted cooperative NOMA system. It can be observed at e analytical curves are consistent wi e simulation ones. In e high-n regime, e asymptotic expression derived in is well matched wi e exact one proving is asymptotic approximation to be accurate enough, and becomes tight as Ω D increases. The proposed scheme is also compared to existing C-NOMA [] and C-OMA [], respectively. From Fig. 3, we can find at e proposed scheme provides outstanding performance gains over C-NOMA and C-OMA. This is because we use IC at e destination, and enable e transmission of x during e second phase. Thanks to e relay node, e fading gain of x is also enhanced by shorting e distance of e -D link e.g., larger values of Ω D. Moreover, it is wor mentioning at e rate scaling of log ρ is achieved by e proposed scheme, while C-NOMA and C-OMA can only achieve e rate scaling of log ρ. In contrast to C-NOMA, e proposed scheme can also achieve a higher achievable rate in e low-n regime. V. CONCLUION In is paper, we have proposed a relay assisted cooperative NOMA scheme. Analytical expressions of outage probability and achievable sum rate were derived. More specifically, e outage probability was given in closed-form, while an efficient numerical expression for e achievable sum rate was also obtained. Furermore, e high-n asymptotic expressions for bo performance metrics were presented to get better insights into e impacts of system parameters on e performance. Our analysis validated at larger average power of e -D link has a beneficial effect on system performance. Finally, e proposed scheme outperforms conventional C- NOMA and C-OMA schemes in terms of achievable sum rate in whole N regime. APPENDIX The achievable rate C,x can be expressed as [5, Eq. ] C,x = ln = ln ubstituting into 5, we have ln + x f C,x x dx F C,x x k dx. 5 + x C,x = Ω D ln + x xω D + Ω D exp x + dx. 6 ρ Ω D Ω Unfortunately, e involving integral is very difficult to be solved in a closed form. However, by changing e variable of e integration in 5 as x = tanθ, C,x can be written as C,x = π F C,x tan θ sec θdθ. 7 ln + tan θ Then, we can use an efficient N-point Gauss-Chebyshev formula [6, Eq ] to numerically derive C,x ln N k= w k F C,x x k + x k, 8 where x k and w k are given by and, respectively. ubstituting into 8, e proof can be concluded. EFEENCE [] L. Dai, B. Wang, Y. Yuan,. Han, I. Chih-Lin, and Z. 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