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On the performance of an enhanced transmission scheme for cooperative relay networks with NOMA
EURASIP Journal on Wireless Communications and Networking volume 2018, Article number: 165 (2018)
Abstract
In this paper, an enhanced transmission scheme for cooperative relaying networks with nonorthogonal multiple access (ECRNNOMA) is proposed. In the proposed scheme, two different kinds of transmission schemes are investigated which are the single signal transmission and the enhanced superposition transmission schemes. Particularly, for the single transmission scheme, a successive interference cancellation (SIC) is utilized to decode the received signal, sent by the relay, at the destination. On the other hand, for the enhanced superposition coded signal transmission scheme, a maximum ratio combining (MRC) is utilized at the destination to improve the ergodic sumrate (SR) of the proposed system. Specifically, two power allocation (PA) strategies are comprehensively discussed to characterize the performance of our proposed scheme. The achievable average SR of the proposed systems are analyzed for independent Rayleigh fading channels, and also their asymptotic expressions are also provided. Qualitative numerical results corroborating our theoretical analysis show that the enhanced superposition coded signal transmission scheme applied to the proposed ECRNNOMA improves the SR performance significantly in comparison to the others.
Introduction
A nonorthogonal multiple access (NOMA) technique has been widely considered as a promising multiple access (MA) potential candidate for future wireless networks due to its superior spectral efficiency [1, 2]. Different from the traditional orthogonal multiple access (OMA) techniques [3, 4] such as frequencydivision multiple access (FDMA) and timedivision multiple access (TDMA), NOMA explores the nonorthogonal resource allocation. The key idea of NOMA is to explore the power domain for realizing MA, where different users are served at different power levels [5]. In NOMA, signals of multiple users are superimposed in the power domain at the transmitter while the successive interference cancellation (SIC) is conducted on the received superimposed signal at the receiver, respectively. As composing a superimposed signal for transmission, an uneven power allocation can be used in general so that a receiver with a lower channel gain is assigned with a higher power and a receiver with a higher channel gain with a lower power. Furthermore, the authors in [6] provided an overview of the latest NOMA research and innovations as well as their applications. Since multiple users can be served simultaneously, it is also shown that NOMA networks also reduce the delay since users are no longer forced to wait until an orthogonal resource block becomes available. A comprehensive overview of the present and emerging powerdomain SCbased NOMA research into 5G is studied in [7], where it also offers a general view of some implementation issues, including computational complexity, error propagation, deployment environments, and standardization status. In addition, a resource allocation for downlink nonorthogonal multiple access systems is proposed in [8], in which, the former pairs the users to obtain the high capacity gain, while the latter allocates power to users to balance system throughput and user fairness. Furthermore, the authors in [9] investigated a dualhop cooperative relaying scheme using NOMA, where two sources communicate with their corresponding destinations via a common relay.
Conventionally, due to the compatibility of the NOMA technology with other communication technologies, it can be integrated in existing and future wireless systems. In [10–13], the secrecy issue of NOMA has been considered, which improves the security capability, the reliability and the transmission rate in the physical layer communication. In [14], the authors have proposed a complete resource allocationbased user selection scheme which has a low computational complexity with excellent performance for both perfect and imperfect channel state information (CSI) scenarios. Moreover, a bestnear bestfar user selection scheme is proposed in [15]. The application of cooperative simultaneous wireless information and power transfer (SWIPT) to NOMA networks are investigated in [15–18], where the NOMAstrong users are considered as energy harvesting relays to help the NOMAweak users. It is worth noting that, on top of their spectral efficiency and outage performance, the fairness is also an important issue in NOMA systems [19, 20], since there is a tradeoff between the total throughput and the user fairness. In addition, since index modulation (IM) [21–26] technology has the superiorities for the energy efficiency and low complexity, the authors investigated NOMAbased IM to mitigate interuser interference, while maintaining high spectral efficiency [27, 28].
Moreover, multipleinput multipleoutput (MIMO) [29–31] systems have been widely considered as a candidate for the fifth generation (5G) wireless communication due to their transmission reliability. The authors in [32] proposed cooperative NOMA systems in MIMO channels, which maximizes the achievable rate from the base station to the celledge user under transmit power constraints and achievable rate constraint from the base station to the central user. Considering the imperfect channel state information (CSI), a robust beamforming design is investigated for NOMA systems in MIMO channels [33]. Specifically, the joint power allocation and relay beamforming design for a NOMA amplifyandforward (AF) relay network is studied in [34], where an alternating optimizationbased algorithm is proposed to maximize the achievable rate of the destination.
Recently, the cooperative relay networks (CRNs) are drawing much attention because the relaying transmission is a promising technique which can be applied to increase the system capacity. Currently, the CRNNOMA systems are widely studied [1, 15, 16, 18, 35–41]. In [35], a NOMAbased cooperative relaying system over Rician fading channels is studied and an analytical framework is developed to evaluate its performance. In [36], an accurate closed form approximation is obtained for the exact outage probability of a CRNNOMA with an amplifyandforward (AF) relay. Specifically, in [37], the resource allocation problem is studied for a NOMA wireless network with a oneway orthogonal frequency division multiplexing (OFDM) AF relay in order to optimize subchannel assignment and power allocation. In addition, the work of the NOMAbased cooperative AF relaying strategy over Nakagamim fading channels is introduced, and the authors show that the cooperative NOMA outperforms conventional OMA systems [38]. A cooperative NOMA transmission technique using MRC is studied in [1]. This technique exploits prior information in NOMA systems. Moreover, the work of NOMA in the coordinated direct and relay transmission (CDRT) with the decodeandforward (DF) protocol has been introduced in [39], it includes exact and asymptotic expressions for achievable rates of the system driven in independent Rayleigh fading channels. Since the performance of the achievable rate is limited by a poor channel, a novel receiver design for the CRNbased NOMA by using MRC is proposed in [40], which has advantages in the view point of ergodic SR and outage probability. Unfortunately, the proposed scheme in [40] requires a symbol allocated with a lower power to be decoded first, which degrades the outage performance. In order to further improve the outage performance, a twostage power allocation CRS using NOMA is proposed in [41], in which the relay nodes forward a new superpositioncoded symbol with a different power allocation.
Consider a superpositioncoded signal is transmitted to the relays. In our proposed system, there are three kinds of transmissions, namely, CTRSNOMA superposition case, CTRSNOMA single case I, and CTRSNOMA single case II, respectively. For the CTRSNOMA superposition case, both of two relay nodes forward the superposition coded signal x_{R} to the destination. Without loss of generality, for the CTRSNOMA single case, we discussed two kinds of the power allocation schemes, i.e., for relay nodes i, the transmitted symbol x_{i} is allocated with a higher PA factor for case I, while a lower PA factor for case II. Therefore, in this manner, the proposed CTRSNOMA single case contains all the possible transmission strategies, which is necessary to employ two relays to support that of the strategies. In addition, the proposed scheme is possible to provide the mentality to study the multirelaying systems and applicable in the future cooperative NOMA networks. These motivate us to investigate an enhanced transmission scheme with two relays. The implementations and contributions of this paper are summarized in the following:

In order to further improve the ergodic SR, we comprehensively investigate an enhanced 2stage superposed transmission scheme for CRNNOMA with two relays is considered, where, unlike existing works, not only the source but also the relays are allowed to transmit superpositioncoded signals, which is more general and challenging.

Without loss of the generality, in the proposed system, two different kinds of transmission schemes are proposed. Specifically, the first scheme is named CTRSNOMA single case, which is similar to the single relay scenario. Upon a reception from the source, each relay decodesandforwards a single corresponding symbol to the destination. Assuming that the CSI is perfectly known at the destination, the received signals can be decoded by utilizing SIC. In addition, two kinds of PA methods are analyzed. Specifically, the signal with more power at the source is allocated with a lesser power at the relay, while the other signal with lesser power at the source is allocated with a more power at the relay. Otherwise, an opposite PA scheme is considered. On the other hand, the second scheme is named CTRSNOMA superposition case; unlike the existing works, not only source but also all relay nodes are allowed to forward superpositioncoded signals to the destination. Upon a signal reception, MRC is utilized to maximize the system performance.

Closedform solutions of the ergodic SR for all the transmission schemes at high transmit signaltonoise ratio (SNR) are derived with a negligible performance loss. It is worth noting that, there is few works that focus on the 2stage superposed transmission for multiple relay networks, since it is hard to obtain the exact expression of the ergodic SR. Furthermore, the theoretical results are shown to highly agree with the simulation results, especially in the high SNR region.

Through the numerical results, both analytically and numerically, we compare the proposed NOMA schemes with the TDMA scheme in terms of ergodic SR. It is shown that, the proposed CTRSNOMA superposition case outperforms the TDMA and other two NOMA schemes significantly.
The rest of the paper is organized as follows. Section 2 describes a system model of the CTRSNOMA and two proposed transmission schemes. In Section 3, the performance of two proposed systems in terms of achievable ergodic SRs are analyzed, and the numerical results are presented in order to corroborate the performance of two schemes of our CTRSNOMA system in Section 4. Finally, Section 5 concludes this paper.
System model
Consider a simple CTRS consisting of one source, two relays, and one destination, and assume all nodes operate in a halfduplex mode, where the decodeandforward (DF) scheme is considered, as shown in Fig. 1. The channels from the source to the relay node i∈{1,2} and from the relay node i to the destination are denoted as \(\phantom {\dot {i}\!}h_{{SR}_{i}}\) and \(\phantom {\dot {i}\!}h_{R_{i}D}\), respectively, and they are assumed to be independent complex Gaussian random variables with variances \(\alpha _{S_{i}R}\), and \(\alpha _{R_{i}D}\), respectively. In our proposed scheme, each transmission involves two time slots. Note that according to the NOMA principle, the power allocation factors a_{1} and a_{2} are with a_{1}>a_{2} and a_{1}+a_{2}=1, which are related to the quality of the channel coefficients. At the first time slot, assuming the adoption of the superposition code, the superposed signal
is transmitted from the source to the relay node i, where x_{i} denotes the broadcasted symbol at the source, and P_{t} stands for the total transmit power.
The received signal at the relay node i is given by
where \(n_{R_{i}}\sim {\mathcal {CN}(0,\sigma ^{2})}\) denotes the additive white Gaussian noise (AWGN) with zero mean and variance \(\sigma _{R_{i}}^{2}\).
Consider that the NOMA decoding principle requires the symbol with more allocated power to be decoded first. In order to successfully and simultaneously decode x_{1} and x_{2} at the relay i, the SIC technique is utilized. Obtaining the transmitted signals in this manner, the reception SNRs for x_{1} and x_{2} at the relay i can be respectively expressed as
where \(\rho =\frac {P_{t}}{\sigma ^{2}_{R_{i}}}\) is the transmission SNR.
Proposed CTRSNOMA superposition case
At the second time slot of the proposed CTRSNOMA superposition case, both of two relay nodes forward the superpositioncoded signal x_{R} to the destination
where b_{i}, with b_{1}+b_{2}=0.5 and b_{1}>b_{2}, is the new power allocation coefficient, where the similar PA assumption of a_{i} is considered. By utilizing a MRC reception at the destination, the corresponding received SNR for x_{1} and x_{2} are given as
and
Therefore, the achievable SR for the proposed CRSNOMA can be obtained from
Proposed CTRSNOMA single case
In this case, we further investigate a relay transmission method considered in [39] for our proposed CTRSNOMA system as a benchmark. After a signal reception from the source, two relay nodes simultaneously DF the signals to the destination node during the second time slot. In this scenario, we assume that the relay node i forwards the signal x_{i} to the destination. The received signal at destination can be expressed as
where \(n_{D}\sim {\mathcal {CN}(0,\sigma ^{2})}\) denotes AWGN with zero mean and variance \(\sigma _{R_{D}}^{2}\) and c_{i} is the new PA factor with c_{1}+c_{2}=1 and c_{1}>c_{2}.
Case 1: If x_{1} is allocated with PA factor c_{1}, the corresponding received SNR for x_{1} and x_{2} are given as
with the achievable SR for the proposed CTRSNOMA single case I can be obtained from
Case 2: Without loss of the generality, if x_{2} is allocated with PA factor c_{1}, the corresponding received SNR for x_{1} and x_{2} are given as
with the achievable SR for the proposed CTRSNOMA single case II as
Achievable ergodic SR analysis
In this section, the achievable ergodic SR of our proposed CTRSNOMA system is analyzed in detail; the closedform expressions are obtained for the achievable ergodic SRs assuming that each independent channel undergoes Rayleigh fading.
Achievable SR for the proposed CTRSNOMA single case I
Further denoting \(\left h_{{SR}_{i}}\right ^{2}=\beta _{{SR}_{i}}\) and \(\left h_{R_{i}D}\right ^{2}=\beta _{R_{i}D}\), we have
Letting \(X=\text {min}\left \{\gamma _{R_{1}}^{(x_{1})},\gamma _{R_{2}}^{(x_{1})},\gamma _{I}^{(x_{1})}\right \}\), the complementary cumulative distribution function (CCDF) of X can be obtained as
Noting that the CCDF of \(\beta _{\delta }=e^{\frac {x}{\alpha _{\delta }}}\), for δ∈{SR_{i},R_{i}D}, when \(x<\frac {a_{1}}{a_{2}}\), (13) can be equivalently represented as
where E[·] stands for the statistical expectation. For the case \(x>\frac {a_{1}}{a_{2}}\), \(\overline {F}_{X}(x)=0\) always holds due to
Since the derivatives of (14) with respect to \(\frac {1}{1+x}\) is quite involved, we try to find an approximation result by considering the high transmission SNR, i.e., ρ≫0, as follows
With (16) and using the equality
for the high SNR case, the achievable ergodic rate for x_{1} can be obtained as follows
where the second term in (18) is simplified by using
[42, Eq. (3.352.1)], and Ei(·) denotes the exponential integral function.
Correspondingly, letting \(Y=\text {min}\left \{\gamma _{R_{1}}^{(x_{2})},\gamma _{R_{2}}^{(x_{2})},\gamma _{I}^{(x_{2})}\right \}\), CCDF of Y can be obtained as
By taking derivative of (20), the PDF of Y can be obtained as
From (20) and (21), the achievable ergodic rate for x_{2} can be calculated as
where the integral result
[42, Eq. (3.352.4)] is used. Combing (18) and (22), the achievable SR can be finally expressed as
Achievable SR for the proposed CTRSNOMA single case 2
Denoting \(\mathcal {J}=\text {min}\left \{\gamma _{R_{1}}^{(x_{1})},\gamma _{R_{2}}^{(x_{1})},\gamma _{II}^{\left (x_{1}\right)}\right \}\), the CCDF of \(\mathcal {J}\) can be obtained as
Considering a high SNR case, the closedform expression of \(\mathcal {J}\) is given as
with the corresponding ergodic rate as
where where \(\int _{0}^{u}\frac {e^{\mu x}dx}{x+\beta }=e^{\mu \beta }\left [\text {Ei}\left (\mu u\mu \beta \right)\text {Ei}\left (\mu \beta \right)\right ]\) [42, Eq. (3.352.1)] is used.
On the other hand, for \(\mathcal {T}=\text {min}\left \{\gamma _{R_{1}}^{(x_{2})},\gamma _{R_{2}}^{(x_{2})},\gamma _{II}^{\left (x_{2}\right)}\right \}\), the CCDF of \(\mathcal {T}\) can be obtained as follows
and the corresponding closedform expression for the ergodic rate of x_{2} can be written as follows
where \(\mathcal {K}_{1}=\frac {1}{a_{2}\rho }\left (\frac {1}{\alpha _{{SR}_{1}}}+\frac {1}{\alpha _{{SR}_{2}}}\right)+\frac {1}{c_{1}\rho \alpha _{R_{2}D}}\). Synthesizing (27) and (29), the achievable SR can be expressed as
Achievable SR for the proposed CTRSNOMA superposition case
For our proposed CRSNOMA scheme, the corresponding SNRs for x_{1} are given as
Assuming \(\mathcal {V}=\text {min}\left \{\gamma _{R_{1}}^{(x_{1})},\gamma _{R_{2}}^{(x_{1})},\gamma _{D}^{\left (x_{1}\right)}\right \}\), the CCDF of \(\mathcal {V}\) can be obtained from
It is clear that the derivative of (31) is quite involved. We turn to an approximation of it for the higher SNRs. With the approximations
for ρ≫1, we have
Otherwise \(C_{D}^{(x_{1})}=0\), \(\frac {\beta _{{SR}_{1}}a_{1}\rho }{\beta _{{SR}_{1}}a_{2}\rho +1}<\frac {a_{1}}{a_{2}}\), \(\frac {\beta _{{SR}_{2}}a_{1}\rho }{\beta _{{SR}_{2}}a_{2}\rho +1}<\frac {a_{1}}{a_{2}}\), and \(\frac {b_{1}\beta _{R_{1}D}\rho }{b_{2}\beta _{R_{1}D}\rho +1}+\frac {b_{1}\beta _{R_{2}D}\rho }{b_{2}\beta _{R_{2}D}\rho +1}<\frac {2b_{1}}{b_{2}}\) always hold.
On the other hand, for x_{2}, letting
the CCDF of \(\mathcal {G}\) can be obtained from
Therefore, letting \(\mathcal {D}_{1}=\frac {1}{b_{2}\rho \alpha _{R_{1}D}}\frac {1}{a_{2}\rho \alpha _{{SR}_{1}}} \frac {1}{a_{2}\rho \alpha _{{SR}_{2}}}\) and \(\mathcal {D}_{2}=\frac {1}{a_{2}\rho \alpha _{{SR}_{1}}} \frac {1}{a_{2}\rho \alpha _{{SR}_{2}}}\frac {1}{b_{2}\rho \alpha _{R_{2}D}}\), substituting (35) back into (17), the closed form of ergodic rate for x_{2} is given as
where \(\int _{0}^{\infty }\frac {e^{\mu x}dx}{x+\beta }=e^{\mu \beta }\text {Ei}\left (\mu \beta \right)\) [42, Eq. (3.352.4)] is used in the second term. Finally, the closedform expression of SR for the conventional NOMA can be denoted as
Discussion: Figure 2 displays two extended system models. One is the multipair scenario with two relay nodes and K pairs of source nodes while the other is Z relay nodes scenario with two source nodes, where Z is an even integer with Z≥2.
In Fig. 4a, each pair of source and destination (SD) want to communicate with each other via two relay nodes, which can be seen as a group. The received signals at each relay can be given as
where \(h_{S_{k}R_{i}}\) denotes the channels from the source node k to the relay node i for k∈{1,...,K}, and i = 1,2. a_{1,k} and a_{2,k} are the power allocation factors employed at source k with a_{1,k}>a_{2,k} and a_{1,k}+a_{2,k}=1. Without loss of generality, according to the NOMA principle, the symbol allocated with more transmit power will be decoded first. Similar to the proposed CTRSNOMA superposition case, the relay will forward decoded signals with new superposition coding to the destination
where b_{i,j} is the new PA factor at relay i with \(\sum _{j=1}^{K}\left (b_{i,2j1}+b_{i,2j}\right)=K\). Finally, each destination will decode their desired signal by using SIC.
In Fig. 1b, a cooperative networks consisting of one source, one destination and L (even number) relay nodes is considered. It is easy to see that each two relays can be seen as a group, and the received signal for each relay is given as
where a_{m} is the PA factor at the source for m∈{1,...,M} with M≤L (decodable condition) and i=1,2. In this system model, each relay is feasible to follow the proposed three transmission strategies. It is worth noting that the total relay power constraint should be P_{t}. In addition, for the CTRSNOMA superposition case, there are total (T+1)M PA factors, while for the CTRSNOMA single case, it is T+M.
Since that the finite power allocation factors and superposed transmission symbols should be considered which is quite involved to derive the closedform expressions of the SR and PA factors, our future work will focus on finding an approximate way to solve the problems.
Numerical results
In this section, we examine the performance of our proposed CTRSNOMA schemes in terms of the ergodic SR. All results are averaged over 80,000 channel realizations. In the following figures, we use “simulation” and “analysis” to denote the simulation and analytical results, respectively. Figures 3 and 4 depict the ergodic SR performance of our proposed CTRSNOMA single case I, CTRSNOMA single case II, CTRSNOMA superposition case, and the TDMA schemes versus the transmission SNR. We have set fixed \(\phantom {\dot {i}\!}\alpha _{{SR}_{1}}=5\), \(\phantom {\dot {i}\!}\alpha _{{SR}_{2}}=1\), \(\phantom {\dot {i}\!}\alpha _{R_{1}D}=2\), \(\phantom {\dot {i}\!}\alpha _{R_{2}D}=20\), b_{1}=0.4, and a_{1}=c_{1}={0.6,0.8} in Fig. 3, while a_{1}=c_{1}=0.7, b_{1}=0.3, \(\phantom {\dot {i}\!}\alpha _{{SR}_{1}}=\alpha _{{SR}_{2}}=10\), \(\phantom {\dot {i}\!}\alpha _{R_{1}D}=2\), and \(\phantom {\dot {i}\!}\alpha _{R_{2}D}=\{10,40\}\) in Fig. 2. It is clear that the CTRSNOMA superposition case shows a better performance compared with other three schemes, and there is a good match between the simulation results and the analysis results, especially at the high SNR region, which supports the practical utility of our design. Remarkably, in Fig. 4, with increased PA factor a_{1} and c_{1}, the ergodic SR performance of CTRSNOMA single case I and CTRSNOMA superposition case are also improved, but decreased for the CTRSNOMA single case II. Particularly, the improvement ergodic SR of the CTRSNOMA superposition case is small. This is because, for high SNR case, i.e., ρ≫1, the ergodic rate of x_{1} is given as \(C_{D}^{(x_{1})}\sim \frac {1}{2}\text {log}_{2}\left (1+\min \left \{\frac {a_{1}}{a_{2}}, \frac {2b_{1}}{b_{2}}\right \}\right)=\frac {1}{2}\text {log}_{2}\left (1+\frac {a_{1}}{a_{2}}\right)\), for a_{1}={0.6,0.8} and b_{1}=0.4. Onthe other hand, in Fig. 4, the ergodic SR performance of CTRSNOMA single case II and CTRSNOMA superposition case have improved along with the increased \(\alpha _{R_{2}D}\) while no meaningful change can be observed for the for the CTRSNOMA single case I.
Figures 5, 6, and 7 depict the ergodic SR performance with respect to power allocation factors a_{1} and b_{2} for the CTRSNOMA superposition case, CTRSNOMA single case I, and CTRSNOMA single case II, respectively. For both figures, We have set fixed \(\phantom {\dot {i}\!}\alpha _{{SR}_{1}}=\alpha _{{SR}_{2}}=10\), \(\phantom {\dot {i}\!}\alpha _{R_{1}D}=\alpha _{R_{2}D}=2\). In Fig. 5, comparisons are made with fixed b_{1}=0.35 and c_{1}=0.7 for different transmit SNRs as ρ={25,35}dB. As seen from the figure, there exists an optimal value of a_{1} that maximizes the ergodic SR for the CTRSNOMA superposition case and CTRSNOMA single case I, which always outperforms the maximum value of the CTRSNOMA single case II. In addition, with the increase of the SNR, the corresponding a_{1} for the optimal ergodic SR will be close to 1. Particularly, in Figs. 6 and 7, to simplify the analysis, we further assume that c_{2}=2∗b_{2}. From the Figs. 6 and 7, we observe that the optimal SR exists when b_{2} is close to 0.5 for the CTRSNOMA superposition case; and b_{2} is close to 0 for the other two cases. Furthermore, for an increased a_{1}, the corresponding ergodic SR will be also increased for these three cases.
Figures 8, 9, and 10 compare the ergodic SR performance of the proposed CTRSNOMA schemes versus power allocation factors with fixed \(\phantom {\dot {i}\!}\alpha _{{SR}_{1}}=1\), \(\phantom {\dot {i}\!}\alpha _{{SR}_{2}}=10\), \(\phantom {\dot {i}\!}\alpha _{R_{1}D}=1\), \(\phantom {\dot {i}\!}\alpha _{R_{2}D}=2\), and ρ=25 dB. The maximum results of the ergodic SR are 3.9059 bps/Hz, 3.2252 bps/Hz, and 3.3605 bps/Hz, respectively, for Figs. 6, 7, and 8. In sum, the ergodic SR of CTRSNOMA superposition case has an outstanding advantage over the other two CTRSNOMA schemes.
Conclusions
In this paper, considering the CTRSNOMA system, two cases named CTRSNOMA superposition case and CTRSNOMA single case have been studied. Specifically, for the CTRSNOMA single case, two PA strategies have been investigated. Also, for each one of three PA schemes, the closedform expression for the achievable ergodic SR is derived. Numerical results have been presented to corroborate the theoretical analyses, and the results have shown us that the performance of the ergodic SR for the CTRSNOMA superposition case gains a significant improvement and also outperforms the CTRSNOMA single case. It remains a future work to investigate the design rule for the time slot length and the efficient slot assignment method for users with different QoS requirements.
Abbreviations
 AF:

Amplifyandforward
 AWGN:

Additive white Gaussian noise CDRT: Coordinated direct and relay transmission
 CRN:

Cooperative relay networks
 CSI:

Channel state information
 DF:

Decodeandforward
 FDMA:

Frequencydivision multiple access
 MRC:

Maximum ratio combining
 NOMA:

Nonorthogonal multiple access
 OFDM:

Orthogonal frequency division multiplexing
 OMA:

Orthogonal multiple access: SIC: Successive interference cancellation
 SR:

Sumrate
 PA:

Power allocation
 SWIPT:

Simultaneous wireless information and power transfer
 TDMA:

Timedivision multiple access
References
 1
Z Ding, M Peng, HV Poor, Cooperative nonorthogonal multiple access in 5G systems. IEEE Commun. Lett. 19(8), 1462–1465 (2015).
 2
Y Zhang, H Wang, T Zheng, Q Yang, Energyefficient transmission in nonorthogonal multiple access. IEEE Tans. Veh. Technol. 66(3), 2852–2857 (2017).
 3
Y Wang, W Feng, L Xiao, Y Zhao, S Zhou, Coordinated multicell transmission for distributed antenna systems with partial CSIT. IEEE Commun. Lett. 16(7), 1044–1047 (2012).
 4
W Feng, Y Wang, N Ge, J Lu, J Zhang, Virtual MIMO in multicell distributed antenna systems: coordinated transmissions with largescale CSIT. IEEE J. Sel. Areas Commun. 31(10), 2067–2081 (2013).
 5
Z Ding, F Adachi, HV Poor, The application of MIMO to nonorthogonal multiple access. IEEE Trans. Wirel. Commun. 15(1), 537–552 (2016).
 6
Z Ding, X Lei, GK Karagiannidis, R Schober, J Yuan, VK Bhargava, A survey on nonorthogonal multiple access for 5G networks: research challenges and future trends. IEEE J. Sel. Areas Commun. 35(10), 2181–2195 (2017).
 7
SM Riazul Islam, N Avazov, OA Dobre, K Kwak, Powerdomain nonorthogonal multiple access (NOMA) in 5G systems: Potentials and Challenges. IEEE Commun. Surv. Tutor. 19(2), 721–742 (2016).
 8
SM Riazul Islam, M Zeng, OA Dobre, K Kwak, Resource allocation for downlink NOMA systems: Key techniques and open issues. IEEE Wirel. Commun. Mag. 25(2), 40–47 (2018).
 9
F Md. Kader, MB Shahab, SY Shin, Exploiting nonorthogonal multiple access in cooperative relay sharing. IEEE Commun. Lett. 21(5), 1159–1162 (2017).
 10
B He, A Liu, N Yang, VKN Lau, On the design of secure nonorthogonal multiple access systems. IEEE J. Sel. Areas Commun. 35(10), 2196–2206 (2017).
 11
Y Liu, Z Qin, M Elkashlan, Y Gao, L Hanzo, Enhancing the physical layer security of nonorthogonal multiple access in largescale networks. IEEE Trans. Wirel. Commun. 16(3), 1656–1672 (2017).
 12
Q Yang, HM Wang, D Kwan Ng, M Lee, NOMA in downlink SDMA with limited feedback: performance analysis and optimization. IEEE J. Sel. Areas Commun. 35(10), 2281–2294 (2017).
 13
Y Zhang, HM Wang, Q Yang, Z Ding, Secrecy sum rate maximization in nonorthogonal multiple access. IEEE Commun. Lett. 20(5), 930–933 (2016).
 14
C Chen, W Cai, X Cheng, L Yang, Y Jin, Low complexity beamforming and user selection schemes for 5G MIMONOMA systems. IEEE J. Sel. Areas Commun. 35(12), 2708–2722 (2017).
 15
NT Do, D Costa, TQ Duong, B An, A BNBF user selection scheme for NOMAbased cooperative relaying systems with SWIPT. IEEE Commun. Lett. 21(3), 664–667 (2017).
 16
Z Yang, Z Ding, P Fan, N AlDhahir, The impact of power allocation on cooperative nonorthogonal multiple access networks with SWIPT. IEEE Trans. Wirel. Commun.16(7), 4332–4343 (2017).
 17
Y Xu, C Shen, Z Ding, X Sun, S Yan, G Zhu, Z Zhong, Joint beamforming and powersplitting control in downlink cooperative SWIPT NOMA systems. IEEE Trans. Signal Process. 65(18), 4874–4886 (2017).
 18
Y Liu, Z Ding, M Elkashlan, HV Poor, Cooperative nonorthogonal multiple access with simultaneous wireless information and power transfer. IEEE J. Sel. Areas Commun. 34(4), 938–953 (2016).
 19
J Choi, Power allocation for maxsum rate and maxmin rate proportional fairness in NOMA. IEEE Commun. Lett. 20(10), 2055–2058 (2016).
 20
M Hojeij, CA Nour, J Farah, C Douillard, Waterfillingbased proportional fairness scheduler for downlink nonorthogonal multiple access. IEEE Commun. Lett. 6(2), 230–233 (2017).
 21
M Wen, E Basar, Q Li, B Zheng, M Zhang, Multiplemode orthogonal frequency division multiplexing with index modulation. IEEE Trans. Commun. 65(9), 3892–3906 (2017).
 22
M Wen, B Ye, E Basar, Q Li, F Ji, Enhanced orthogonal frequency division multiplexing with index modulation. IEEE Trans. Wirel. Commun. 16(7), 4786–4801 (2017).
 23
J Li, X Jiang, Y Yan, W Yu, S Song, MH Lee, Low complexity detection for quadrature spatial modulation systems. Wirel Pers. Commun. 95(4), 4171–4183 (2017).
 24
M Wen, X Cheng, M Ma, B Jiao, HV Poor, On the achievable rate of OFDM with index modulation. IEEE Trans. Signal Process. 64(8), 1919–1932 (2016).
 25
J Li, M Wen, X Jiang, W Duan, Spacetime multiplemode orthogonal frequency division multiplexing with index modulation. IEEE Access.5:, 23212–23222 (2017).
 26
J Li, M Wen, X Cheng, Y Yan, S Song, MH Lee, Generalised precoding aided quadrature spatial modulation. IEEE Trans. Veh. Technol. 66(2), 1881–1886 (2016).
 27
X Zhu, Z Wang, J Cao, NOMAbased spatial modulation. IEEE Access.5:, 3790–3800 (2017).
 28
Y Chen, L Wang, Y Ai, B Jiao, L Hanzo, Performance analysis of NOMASM in vehicletovehicle massive MIMO channels. IEEE J. Sel. Areas Commun. 35(12), 2653–2666 (2017).
 29
H Lin, F Gao, S Jin, G Ye Li, A new view of multiuser hybrid massive MIMO: Nonorthogonal angle division multiple access. IEEE J. Sel. Areas Commun. 35(10), 2268–2280 (2017).
 30
H Xie, F Gao, S Jin, An overview of lowrank channel estimation for massive MIMO systems. IEEE Access. 4(99), 7313–7321 (2016).
 31
H Xie, F Gao, S Zhang, S Jin, A united transmission strategy for TDD/FDD massive MIMO systems with spatial basis expansion Model. IEEE Trans. Veh. Technol. 66(4), 3170–3184 (2017).
 32
Y Li, M Jiang, Q Zhang, Q Li, J Qin, Cooperative nonorthogonal multiple access in multipleinputmultipleoutput channels. IEEE Trans. Wirel. Commun. 17(3), 2068–2079 (2018). http://ieeexplore.ieee.org/document/8247238/.
 33
Q Zhang, Q Li, J Qin, Robust beamforming for nonorthogonal multiple access systems in MISO channels. IEEE Trans. Veh. Technol. 65(2), 10231–10236 (2016).
 34
C Xue, Q Zhang, Q Li, J Qin, Joint power allocation and relay beamforming in nonorthogonal multiple access amplifyandforward relay networks. IEEE Trans. Veh. Technol. 66(8), 7558–7562 (2017).
 35
R Jiao, L Dai, J Zhang, R MacKenzie, M Hao, On the performance of NOMAbased cooperative relaying systems over Rician fading channels. IEEE Trans. Veh. Technol. 66(12), 11409–11413 (2017).
 36
X Liang, Y Wu, DW Ng, Y Zuo, S Jin, H Zhu, Outage performance for cooperative NOMA transmission with an AF relay. IEEE Commun. Lett. 21(11), 2428–2431 (2017).
 37
S Zhang, B Di, L Song, Y Li, Subchannel and power allocation for nonorthogonal multiple access relay networks with amplifyandforward protocol. IEEE Trans. Wirel. Commun. 16(4), 2249–2261 (2017).
 38
J Men, J Ge, Nonorthogonal multiple access for multiple antenna relaying networks. IEEE Commun. Lett. 19(10), 1686–1689 (2015).
 39
JB Kim, IH Lee, Capacity analysis of cooperative relaying systems using nonorthogonal multiple access. IEEE Commun. Lett. 19(11), 1949–1952 (2015).
 40
M Xu, M Wen, F Ji, W Duan, Novel receiver design for the cooperative relaying system with nonorthogonal multiple access. IEEE Commun. Lett. 20(8), 1679–1682 (2016).
 41
W Duan, M Wen, Z Xiong, M Lee, Twostage power allocation for dualhop relaying systems with nonorthogonal multiple access. IEEE Access.5:, 2254–2261 (2017).
 42
IS Gradshteyn, IM Ryzhik, Table of integrals, series, and products, 7th ed (Academic Press, Manhattan, 2007).
Acknowledgements
The authors would gratefully acknowledge the grants from the National Natural Science Foundation of China (61371113, 61401241, 61501264, 61571315 and 61631004), and the Nantong UniversityNantong Joint Research Center for Intelligent Information Technology (KFKT2017B01).
Finally, we would like to thank the Editor and Reviewer for their constructive remarks and careful reading of our paper, which were essential in improving the overall presentation of the paper.
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WD, JH, and GZ conceived and designed the study. WD, YJ, and QS performed the simulations. WD and JH wrote the paper. JH, GZ, JC, YJ, and QS reviewed and edited the manuscript. All authors read and approved the manuscript.
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Duan, W., Zhang, G., Sun, Q. et al. On the performance of an enhanced transmission scheme for cooperative relay networks with NOMA. J Wireless Com Network 2018, 165 (2018). https://doi.org/10.1186/s1363801811755
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Keywords
 Nonorthogonal multiple access
 Ergodic sumrate
 Maximum ratio combining power
 Allocation