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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2017.2789193, IEEE Access IEEE ACCESS, VOL. 6, JAN. 2018

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Two-Stage Superposed Transmission For Cooperative NOMA Systems Wei Duan, Xue-Qin Jiang, Member, IEEE, Miaowen Wen, Member, IEEE, Jue Wang, Member, IEEE, and Guoan Zhang

Abstract—In this paper, a two-stage superposed transmission scheme for cooperative non-orthogonal multiple access (NOMA) systems is proposed. During the first N time slots, the source simultaneously transmits the superposition coded symbols to the relay and destination, both of which, instead of decoding, keep the receptions in reserve. At the last time slot, the relay decodes and forwards a new superposition coded symbol with corresponding power allocation factors to the destination. The destination jointly decodes the received signals during the total N + 1 time slots by employing maximum ratio combining. Assuming Rayleigh fading channels, the ergodic sum-rate (SR), outage probability and outage capacity of the system are investigated considering the high transmit signal-to-noise ratio cases. An approximate expression for the ergodic SR is also derived at the expense of a negligible performance loss. By means of numerical results, it is shown that the transmission rate and ergodic SR of the proposed scheme overwhelm that of the time-division multiple access and conventional NOMA schemes.

Index Terms: Non-orthogonal multiple access (NOMA), power allocation, ergodic sum-rate, decode-and-forward (DF), outage performance. I. I NTRODUCTION Recently, a novel multiple access (MA) technique, named non-orthogonal multiple access (NOMA), has been widely considered as a candidate for the fifth generation (5G) wireless communication due to its superior spectral efficiency, balanced user fairness, intense connections, and low access latency [1]–[8]. In contrast to conventional orthogonal multiple access (OMA) [9], such as frequency-division multiple access (FDMA) and time-division multiple access (TDMA), NOMA explores the non-orthogonal resource allocation. The key idea of NOMA is to explore the power domain for realizing MA, where different users are distinguished with different power levels [10]–[12], while the successive interference cancellation (SIC) is employed to cancel the multi-user interference at the receiver [13], [14], respectively. Furthermore, in NOMA, an uneven power allocation is employed in general, so that a higher power is assigned to the user associated with a worse channel condition. W. Duan, J. Wang and G. Zhang are with School of Electronics and Information, Nantong University, Nantong 226019, China. (e-mail: {sinder, wangjue, gzhang}@ntu.edu.cn) X. Jiang is with School of Information Science and Technology, Donghua University, Shanghai, China. (e-mail: [email protected].) M. Wen is with School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510640, China. (e-mail: [email protected].) This work was supported in part by National Natural Science Foundation of China (61501190, 61671143, 61401240, 61771264, 61371113 and 61401241).

Owing to various advantages it promises and its compatibility with other communication technologies, NOMA has received considerable interest in existing and future wireless communications systems. In [15]–[18], the physical-layer security issue of NOMA has been considered, which imposes the performance in terms of security capability, reliability and outage probability. In particular, the authors aimed at maximizing of the secrecy sum rate (SR) of a single-input single-output (SISO) NOMA system [18], where each user has a predefined quality of service (QoS) [19] requirement. On the other hand, the user, relay and antenna selection based NOMA schemes have been also proposed [20]–[22]. In [21], the outage performance of cooperative relaying in twouser NOMA systems was investigated with a best-near bestfar user selection. The authors of [22] proposed a complete resource allocation based user selection scheme with lower computational complexity and excellent performance for both perfect and imperfect channel state information (CSI) scenarios. The application of cooperative simultaneous wireless information and power transfer (SWIPT) to NOMA networks was investigated in [21], [23]–[26], where the strong users are considered as energy harvesting relays to help the weak users. In particular, the opportunistic scheduling for downlink scenarios in multi-user multi-relay cooperative networks with SWIPT was studied in [23] which optimizes the power-splitting ratio. It is worth noting that, in addition to the capability, the outage performance and the spectral efficiency, the fairness is also an important issue in NOMA systems [3], [27], [28], since there is tradeoff between total user throughput and user fairness. In consideration of imperfect CSIs, the power-efficient resource allocation for multicarrier NOMA systems was investigated in [10] which provides significant transmit power savings and enhanced robustness against channel uncertainty. The cooperative relay networks (CRNs) have been the focus of a great deal of research since it can be applied to increase the system capacity [29]–[32]. The authors of [29] presented an overview of the developments for the cooperative relay communications, where the single antenna mobiles in a multiuser environment are enabled to share their antennas to achieve transmit diversity. In [30], the authors proposed three different TDMA-based cooperative protocols with amplify-andforward (AF) and decode-and-forward (DF) modes of relaying, where the ergodic and outage capacity behaviors are also studied. In addition, an orthogonal DF protocol that employs rotated n-dimensional constellations was investigated in [31]. An uplink transmission technique based on the DF protocol was proposed in [32] which exploits the spatial degrees of

2169-3536 (c) 2017 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


freedom of the virtual multiple-input-multiple-output (MIMO) channel and is also extended in a doubly opportunistic manner by incorporating both multiuser diversity and relay selection diversity. Moreover, the provided cooperative technique is the first technique that exploits both kinds of opportunism. Recently, the CRN-NOMA systems have been widely studied in [33]–[39]. In [33], the performance of a NOMAbased cooperative relaying was investigated, where an efficient approximation method using Gauss-Chebyshev Integration for the achievable rates is also proposed. The outage performance for a downlink cooperative NOMA scenario with the help of an AF relay was studied in [34], which indicates that the cooperative NOMA is obviously superior to the cooperative OMA in coding gain without losing any diversity order. In [35], the authors studied the resource allocation problem for a singlecell NOMA relay network, where an orthogonal frequencydivision multiple (OFDM) AF relay allocates the spectrum and power resources to the source-destination pairs to optimize the sub-channel assignment and the power allocation. The outage behavior of the mobile users was considered for the NOMA based cooperative AF relaying in [36]. Moreover, a cooperative NOMA transmission technique using maximum ratio combining (MRC) was studied in [2], which exploits a priori information in NOMA systems. Analogously, the work of NOMA in the coordinated direct and relay transmission (CDRT) with the DF protocol was introduced in [37], where the exact and asymptotic expressions for the achievable rate of the proposed system are derived. Realizing that the performance of the achievable rate is limited by a poor channel, the authors of [38] proposed a novel receiver design for the CRN based NOMA by using MRC, showing the advantages in terms of ergodic SR and outage probability. Unfortunately, the proposed scheme in [38] required the symbol allocated lower power to be decoded first which deteriorates the outage performance. In order to solve this problem and further improve the outage performance, a two-stage power allocation CRN using NOMA was proposed in [39], in which, the relay forwards a new superposition coded symbol with a different power allocation. On one hand, employing the multiple time slots transmission can effectively increase the spectrum efficiency of the system. To the best of our acknowledge, there is no studies that focus on the multiple time slots CRN-NOMA system. On the other hand, multiple time slots transmission is possible to provide a higher transmission rate. These motivate us to investigate the CRN-NOMA system with multiple time slots transmission. The implementations and contributions of this paper are summarized in the following: • We comprehensively investigate the two-stage superposed transmission scheme for CRN-NOMA with multiple time slots. Unlike existing works, not only the source but also the relay are allowed to transmit superposition coded signals thanks to the multiple time slots transmission, which is more general and challenging. In addition, the superposed strategy used at the relay is efficient and necessary, it improves the transmission rate of the proposed scheme from {1/2, 1} to 2(MM−1) compared with the TDMA and conventional NOMA schemes, where M

2

Fig. 1. The two-stage superposed transmission scheme for the NOMA based CRN.

is an integer number as the total transmission time slots. In order to further improve the ergodic SR, the MRC is employed to jointly decode the received signals during the N + 1 time slots. With the proposed receiver, the relay and destination will not decode the received signals from the source immediately. Instead, they will conserve them until the corresponding time slot comes. • Closed-form solutions of the ergodic SR, outage probability and outage capacity at high transmit signal-tonoise ratio (SNR) are derived. An approximate expression for the ergodic SR is also derived with a negligible performance loss. 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 scheme with the TDMA and conventional NOMA schemes in terms of ergodic SR and transmission rate. It is shown that the proposed scheme outperforms the benchmark schemes significantly. The rest of this paper is organized as follows. Section II describes the system model of the two-stage superposed transmission for CRN-NOMA. In Section III, performance in terms of achievable ergodic SR, outage probability and outage capacity is analyzed. In addition, an approximate expression for the ergodic SR is also derived. Numerical results are presented to show the excellent performance of our proposed scheme in Section IV. Section V concludes this paper. Notations: CN (·) represents a complex Gaussian distribution. Ei (·), Ec and E [·] denote the exponential integral function, the Euler constant and the expectation, respectively. Pr {A|B} denotes the conditional probability of event A on 2 event B. |·| stands for the norm square of a scalar. •

II. S YSTEM MODEL AND PROPOSED SCHEME A simple CRN consisting of one source, one relay, and one destination is considered as shown in Fig. 1, in which



3

all nodes operate in half-duplex mode. It is assumed that each node is equipped with a single antenna and there is a direct link between the source and destination. The channel gains from the source to destination, from the source to relay, and from the relay to destination are denoted by hSD , hSR , and hRD , respectively, which are assumed to be independent complex Gaussian random variables with variances αSD , αSR , and αRD , respectively. Furthermore, the CSI is assumed perfectly known to each receiving node. For NOMA, with the aid of superposition coding (SC) and successive interference cancellation (SIC), each sub-channel can transmit more than one signal with the same frequency, implying that each sub-channel in NOMA can accommodate more users. In our proposed scheme, the transmission involves N + 1 time slots. Specifically, the source transmits its signal by adopting the superposition coding at the t-th time slot, with 1 ≤ t ≤ N , which are given in the form of √ √ st = a2t−1 Pt x2t−1 + a2t Pt x2t , (1) where xi , for i ∈ {2t[− 1, 2t}, ] denotes the broadcast symbol 2 at the source with E |xi | =1, a2t−1 and a2t , with a2t−1 + a2t = 1, are the power allocation factors, and Pt stands for the total transmit power. Moreover, the superposed signal st is simultaneously transmitted from the source to relay and destination nodes. Therefore, the received signals at the source and relay nodes at the t-th time slot can be expressed as (t) yR (t) yD

=

(t) (t) hSR st + nR , (t) (t) hSD st + nD ,

(2)

= (3) { } ( ) (t) (t) respectively, where nR , nD ∼ CN 0, σ 2 represent the additive white Gaussian noises (AWGNs) at the t-th time slot with zero mean and variance σ 2 . At the receiver, SIC is performed at receivers with relatively high signal-to-interference-plus-noise ratio (SINR), and carried out in descending order of SINR. Without loss of generality, according to the NOMA principle, we further assume that x2t−1 is decoded first and allocated with more transmit √ √ power, i.e., a2t−1 > a2t , and then x2t is subsequently decoded. At the relay, the term contributed by x2t in (2) is treated as noise to decode x2t−1 , and then x2t is acquired through SIC. In this manner, the effective SNRs for x2t−1 and x2t at the relay can be respectively expressed as (t) 2 h a2t−1 Pt SR (t) γR,x2t−1 = (4) 2 (t) 2 a P + σ hSR 2t t and (t)

(t) 2 hSR a2t Pt

. (5) σ2 Further assume that, different from the existing studies, to improve the system performance, the relay will not forward the decoded signals to the destination but instead conserve them until the (N + 1)-th time slot comes while the source will not transmit any signal to the receiving nodes, i.e., the relay and destination. In this manner, at the (N + 1)-th time γR,x2t =

slot, relay node forwards a new symbol xR with superposition coding to the destination: N √ ∑ bm Pt x2m , xR =

(6)

m=1

∑N where bm with m=1 bm = 1 is a new power allocation coefficient, and x2m denotes the decoded signal at the relay with lower power. Therefore, the signal received at the destination at the N -th time slot is given by (N )

(N )

yRD = hRD xR + nD ,

(7)

(N ) nD

where is the AWGN at the destination at the second time slot with zero mean and variance σ 2 . It is clear that there are (N + 1) signals received at the destination, which are (1) (N ) (N ) yD , ..., yD , yRD . By employing the MRC at the destination, the corresponding received SNRs for x2t−1 and x2t can be expressed as (t) 2 γD,x2t−1 = hSD a2t−1 ρ, (8) and γD,x2t

(t) 2 2 hSD a2t ρ |hRD | bt ρ , (9) = + 2 ∑ 2 N −1 (t) j=t+1 bj ρ + 1 hSD a2t−1 ρ + 1 |hRD |

respectively, where ρ = σP2t denotes the transmit SNR. In light of (9), the corresponding received SNR at the destination for x2N is given by (N −1) 2 hSD a2N ρ 2 γD,x2N = + |hRD | bN ρ. (10) (N −1) 2 hSD a2N −1 ρ + 1 III. P ERFORMANCE ANALYSIS In this section, in order to characterize the performance of our proposed scheme, we analyze the achievable ergodic SR, the outage probability and the outage capacity over the Rayleigh fading channel. A. Ergodic SR analysis As illustrated in Section II, the achievable rates of symbol (t) x2t−1 and x2t can be obtained from γR,x2t−1 and γD,x2t−1 , respectively, as ( { }) 1 (t) Cx2t−1 = log2 1 + min γR,x2t−1 , γD,x2t−1 , (11) N +1 and ( { }) 1 (t) Cx2t = log2 1 + min γR,x2t , γD,x2t , (12) N +1 where N1+1 results from the N + 1 time slots transmission. Therefore, according to (10), (11) and (12), the achievable SR for the total system can be expressed as Csum

=

N ∑ t=1

Cx2t−1 +

N −1 ∑

Cx2t + Cx2N ,

(13)

t=1



4

( { }) (t) where Cx2N = N1+1 log2 1 + min γR,x2t , γD,x2N . Therefore, after some manipulations, F Y (y) can be finally 2 2 reexpressed as (18) shown at the top of the next page. Since (t) (t) 2 Denoting hSR = βSR , |hRD | = βRD , and hSD = it is hard to obtain the exact expression of F Y (y) directly, we try to find the approximation at high transmit SNR, i.e., βSD , we have { } ρ ≫ 1. In this case, we have βSD a2t ρ ∼ a2t , and { } βSD a2t−1 ρ+1 a2t−1 βSR a2t−1 ρ (t) min γR,x2t−1 , γD,x2t−1 = min βSD a2t−1 ρ, , βSR a2t ρ + 1 βRD bt ρ bt ∼ ∑N −1 , ∑N −1 βRD j=t+1 bj ρ + 1 and j=t+1 bj { } (t) which approximately results in min γR,x2t , γD,x2t { } } { b a t 2t βSD a2t ρ βRD bt ρ + ∑N −1 = min + , βSR a2t ρ . F Y (y) ∼ Pr βSR a2t ρ > y y < a ∑ −1 2t−1 βSD a2t−1 ρ + 1 βRD N b ρ + 1 j=t+1 bj j j=t+1 y b a t 2t − (t) + ∑N −1 = e αSR a2t ρ , for y < . (19) Letting X = min{γR,x2t−1 , γD,x2t−1 }, the complementary a2t−1 j=t+1 bj cumulative distribution function (CCDF) of X can be obtained a2t bt as For the case y > a2t−1 + ∑N −1 , F Y (y) = 0 always holds { } j=t+1 bj βSR a2t−1 ρ as > x . (14) F X (x) = Pr βSD a2t−1 ρ > x, βSR a2t ρ + 1 βSD a2t ρ βRD bt ρ a2t bt + < . + ∑N −1 ∑N −1 β a ρ + 1 a − αx SD 2t−1 2t−1 β b ρ + 1 RD j=t+1 bj j=t+1 j Noting that F βδ (x) = e δ , for δ ∈ {SR, SD}, (14) can be equivalently represented as a2t bt Therefore, letting τ = a2t−1 + ∑N −1 and using ) ) ( ( j=t+1 bj x x ∫ ∞ ∫ ∞ F X (x) = F SR F SD 1 1 − F (x) a2t−1 ρ − a2t xρ a2t−1 ρ dx, (20) log2 (1 + x) fX (x)dx = x x ln2 1+x − −a 0 0 = e (a2t−1 ρ−a2t xρ)αSR 2t−1 ραSD . (15) the corresponding rate of x2t during the t-th time slot can be It is clear that, for x > a2t−1 , F (x) = 0 always holds. On X finally expressed as (21) shown in the next page, where a2t ∫ u −µx the other hand, for the case x < a2t−1 , taking the derivative a2t e dx (22) = eµβ [Ei (−µu − µβ) − Ei (−µβ)] of (15), the probability distribution function (PDF) of F X (x) x+β 0 can be thus obtained as ] [ [40, Eq. (3.352.1)] is used. Specifically, considering the high 1 1 + fX (x) = SNR, for x2N during the N -th time slot, the objective CCDF a2t−1 ραSD (a2t−1 − a2t x) ραSR x x − − a2t−1 of Z is given as { } ×e (a2t−1 −a2t x)ραSR a2t−1 ραSD , for 0 < x < . a2t a2N F Z (z) ∼ Pr + βRD bN ρ > z, βSR a2N ρ > z a2N −1 Thus, the corresponding rate of x2t−1 during the t-th time slot ( ) ( ) can be finally expressed as (16) shown at the top of the next 1 a2N βSR a2t−1 ρ = F SR Pr βRD bN ρ > z − page, where (a) denotes the approximation that βSR a2t ρ+1 ∼ a2N ρ a2N −1 a2t−1 in the high SNR region. a2N z z a2t − a ρα − b ρα +a bN ραRD 2N SR N RD 2N −1 = e , (23) (t) In order to obtain the CCDF of Y (= min{γR,x , γD,x2t }, 2t ) ∑N −1 a2t for t ̸= N , letting bt − j=t+1 bj y − a2t−1 = Ω and with the PDF of z(as ) 1 1 βRD bt ρ ∑ −1 = Φ, we have fZ (z) = + βRD N j=t+1 bj ρ+1 a2N ραSR bN ραRD { } a2N z z − b ρα + − a ρα βSD a2t ρ ×e 2N SR N RD a2N −1 bN ραRD . (24) Pr + Φ > y, βSR a2t ρ > y . (17) βSD a2t−1 ρ + 1 Finally, the corresponding achievable rate, for the x2N , can be From (17), it is clear that there are four cases that should be expressed as discussed as follows: (N −1) R2t a2t ( ) ∫ y − a2t−1 ∞ 1 1 1 , Ω > 0; 1) βRD > = log (1 + z) + ρΩ N +1 2 a2N ραSR bN ραRD 0 a2t a z z 2N y − a2t−1 − b ρα +a − a ρα × e 2N SR N RD 2N −1 bN ραRD dz 2) βRD < , Ω < 0; 1 1 ρΩ ( ) a2N ραSR + a2N −1 bN ραRD e −1 1 a2t y − a2t−1 = − Ei − . 3) βRD > , Ω < 0; (N + 1)ln2 a2N ραSR bN ραRD ρΩ (25) a2t y − a2t−1 4) βRD < , Ω > 0. Putting (16), (21) and (25) together, the corresponding ergodic ρΩ 2169-3536 (c) 2017 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


5

∫ R2t−1

a2t−1 a2t

= 0

∫

1 log (1 + x)fX (x)dx N +1 2 −a

a2t−1 a2t

∫

x 2t−1 ραSD

∼

=

y−

1 αRD

e

a2t−1 a2t

y − a ρα 2t SR

−

y−

a2t a2t−1 ρΩ

−Ω

∫

u 

−

∞

a2t ρ−a

2t−1 ρ

ubt ρ ∑N −1 b ρ+1 j=t+1 j

y−

e

a2t y− a2t−1 ρΩ

 ubt ρ α ∑N −1 SD u b ρ+1 j=t+1 j

y−

−Ω

+

1−e e αRD

( y − a ρα 2t SR

1 − e−

y−

)∫

a2t a2t−1 ρΩ

u 

−

a2t y− a2t−1 ρΩ

−Ω

1−e

−

y−

a2t a2t−1 ρΩ

)∫

y−

a2t a2t−1 ρΩ

u 

−

a2t

( ) − y − y− a2t−1 ρΩ + 1 − e−Ω e a2t ραSR

(2N ) Csum

RD

du −αu

1−

∫

∞

αRD

e

y−

a2t a2t−1 ρΩ

−

1−

1 αRD


a ρ−a  2t 2t−1 ρ y−

1

y−

∫

(16)

−αu

 ubt ρ α ∑N −1 SD u b ρ+1 j=t+1 j

a2t ρ−a  2t−1 ρ y−

e

0

(t) Csum

x

RD

du

0

( y − a ρα 2t SR

R2t

−


y−

+e

)

e a2t−1 ραSD dx log2 (1 + x)e dx + a 2t−1 (N + 1)a2t−1 ραSD (N + 1)a2t−1 ραSD 0 a2t 1 [ ( ) ( )] 1 e a2t−1 ραSD 1 − Ei − Ei − (N + 1) ln 2 a2t−1 a2t ραSD a2t−1 ραSD

(a)

F Y (y) =

( log2 1 +

∞

u 


a ρ−a  2t 2t−1 ρ y−

e

 ubt ρ α ∑N −1 SD u b ρ+1 j=t+1 j

 ubt ρ α ∑N −1 SD u b ρ+1 j=t+1 j

−αu

RD

du

−αu

RD

du.

(18)

τ

1 1 log2 (1 + y) dFY (y) + log (1 + τ ) (1 − FY (τ )) N +1 2 0 N +1 ∫ τ ) y 1 1 1 ( − log2 (1 + τ ) − 1 − e αSR a2t ρ dy = N +1 (N + 1)ln2 0 1 + y y bt ∫ a a2t + ∑N −1 − 2t−1 e αSR a2t ρ b j=t+1 j = dy (N + 1)ln2(1 + y) 0 [ ( )) ( 1 ( )] 1 1 1 e αSR a2t ρ bt Ei − − Ei − , = + ∑N −1 (N + 1)ln2 αSR a2t ρ a2t−1 αSR a2t ρ j=t+1 bj =

1 [ ( ) ( )] e a2t−1 ραSD 1 1 = Ei − − Ei − (N + 1) ln 2 a2t−1 a2t ραSD a2t−1 ραSD ( [ ( )) 1 )] ( αSR a2t ρ e 1 1 bt 1 + Ei − + ∑N −1 − Ei − (N + 1)ln2 αSR a2t ρ a2t−1 αSR a2t ρ j=t+1 bj

[ ( 1 1 1 ) ( )] + e a2N −1 ραSD 1 1 e a2N ραSR a2N −1 bN ραRD = Ei − − Ei − − (N + 1) ln 2 a2N −1 a2N ραSD a2N −1 ραSD (N + 1)ln2 ( ) 1 1 ×Ei − − . a2N ραSR bN ραRD

(21)

(26)

(27)



6

rate of the signal x2t−1 and x2t , for t ̸= N and the special case t = N , can be expressed in the closed-form expressions as (26) and (27), respectively. On the other hand, for (26) and (27), by further assuming the high transmit SNR and applying the approximations of ex ∼ 1 + x and Ei(−x) ∼ Ec + ln(x), for small x, the approximation of the achievable ergodic SR for the total system can be expressed as (28). Based on this, the achievable ergodic SR for the triple time slots case can be expressed as ( ( ) 1 1 b1 Ec esum = C log2 + + log2 ρ − N +1 a1 a2 a4 a2 a4 b2 ln2 ( )) 1 1 − log2 + . (29) a4 αSR b2 αRD B. Outage Probability Analysis Since each user transmits with a predetermined target data rate according to its required QoS, the outage probability is an important performance metric for the proposed system. The closed-form solutions of the outage probability with asymptotic expressions are presented in this subsection. x Assume that RxT2t and RT2t−1 are the predefined target rate thresholds of x2t and x2t−1 at the t-th time slot according to their required QoS. The outage event occurs when Rx2t x and Rx2t−1 are smaller than RxT2t and RT2t−1 , respectively, where Rxm denotes the achievable rate for date xm , resulting in the exact outage probability for the total N + 1xtime slots 2t−1 as (30). Further assuming that Wt = x2(N +1)RT − 1, x2t 2N Wg = 2(N +1)RT −1 and Wz = 2(N +1)RT −1, respectively. Therefore, the exact expressions for U1 , U2 and U3 can be written as follows: { ( ) } (t) U1 = Pr min γR,x2t−1 , γD,x2t−1 > Wt { } { } (t) = Pr γR,x2t−1 > Wt Pr γD,x2t−1 > Wt { Wt − e a2t−1 ραSD , for Wt < a2t−1 a2t = (31) 0 , for Wt > a2t−1 a2t , U2

= = =

and U3

( { ) } (t) Pr min γR,x2t , γD,x2t > Wg { } (t) Pr γR,x2t > Wg Pr {γD,x2t > Wg }  Wg bt  e− αSR a2t ρ , for Wg < a2t + ∑N −1 a2t−1  0

, for Wg >

j=t+1

a2t a2t−1

+

bt ∑N −1 j=t+1

bj

bj

,

(32)

{ ( ) } (t) = Pr min γR,x2t−1 , γD,x2t−1 > Wz { } { } (t) = Pr γR,x2t−1 > Wz Pr γD,x2t−1 > Wz = e

−a

Wz 2N ραSR

Wz N ραRD

−b

+a

a2N 2N −1 bN ραRD

.

(33)

By substituting (31), (32) and (33) { back into (30), with the } a2t bt ∑N −1 conditions {Wt , Wg } < min a2t−1 , + , a2t a2t−1 b j=t+1

j

the outage probability can be finally obtained in the closed-

form expression as Pout = 1 −

N ∏

e

−a

Wt 2t−1 ραSD

t=1 ∑ − N t=1

= 1−e fz = where W

Wz a2N αSR

+

N −1 ∏

e

−α

t=1 ∑ −1 − N t=1

Wt a2t−1 ραSD

Wz bN αRD

−

Wg SR a2t ρ

e−

fz W ρ

fz Wg W αSR a2t ρ − ρ

,(34)

a2N a2N −1 bN αRD .

C. Outage Capacity Analysis In this subsection, the outage capacity analysis of our proposed finite time slot CRN-NOMA system is introduced. Since obtaining the exact outage capacity for the proposed scheme is considerably tough, the approximate outage capacity at high transmit SNR is derived as shown in the following. Let Pout = ε and employ the approximation ex ∼ 1 + x for small x. In the high transmit SNR region, (34) can be equivalently converted into the following form as ε

=

N ∑ t=1

N −1 ∑ fz Wt Wg W + + . (35) a2t−1 ραSD αSR a2t ρ ρ t=1

Further assuming the predefined target data rate thresholds Wt = Wg = Wz = W, after some algebraic simplifications, Eq. (35) can be finally expressed as ( N N −1 ∑ ∑ 1 1 1 W = + + a ρα α a ρ a ρα 2t−1 SD SR 2t 2N SR t=1 t=1 )−1 ( ) 1 a2N + ε+ ,(36) bN ραRD a2N −1 bN ραRD with the outage capacity as Cout =

1 log2 (1 + W) . N

(37)

IV. N UMERICAL R ESULTS In this section, we examine the performance of our proposed scheme in terms of ergodic SR, outage probability and outage capacity with fixed αSD = 1. All results are averaged over 80, 000 channel realizations. In the following figures, we use “Simulation”, “Analysis”, “Approximation” and “nTS” to denote the simulation, analytical, approximation results, and n transmission time slots, respectively. Figs. 2 and 3 depict the ergodic SR performance with respect to power allocation factors b2 and a1 for the triple time slots transmission scenario, respectively. In Fig. 2, comparisons are made with fixed αSR = 10, αSD = 1, a1 = a3 = 0.7 and a2 = a4 = 0.3 for different transmit SNRs as ρ = {15, 20, 25} dB in two considered system setups: (1) αRD = 10; (2) αRD = 2. As seen from the figure, there exists an optimal value of b2 that maximizes the ergodic SR. In addition, with the increase of the SNR and αRD , the corresponding b2 for the optimal ergodic SR will be close to 0. Particularly, in Fig. 3, to simplify the analysis, we further assume that a1 = a3 with fixed b1 = 0.9, αSD = 1, αRD = 2 and αSR = 10. From the figure, we observe that the optimal SR exists when a1 is close to 1. Furthermore, for the higher transmit SNR, the power allocation factors a1 and



esum C

7

( N ( ) ) ( ) N∑ ) ( −1 ( ∑ bt 1 1 1 1 1 + 1+ + ∑N −1 ∼ 1+ ln ln (N + 1)ln2 t=1 a2t−1 ραSD a2t a2t ραSR a2t−1 t=1 j=t+1 bj ( )( ( )) ) 1 1 1 1 − 1+ + Ec + ln + a2N ραSR a2N −1 bN ραRD a2N ραSR bN ραRD ( N ( ) ( ( )) ) −1 ∑ ( 1 ) N∑ 1 bt 1 1 1 ln + ln + ∑N −1 − Ec + ln ∼ + (N + 1)ln2 t=1 a2t a2t−1 a2N ραSR bN ραRD t=1 j=t+1 bj (N −1 ( ) ) ∏ 1 bt bN αSR αRD log2 ρ 1 Ec ln + + − . (28) = ∑N −1 (N + 1)ln2 a a b α + a α N + 1 (N + 1)ln2 2t 2t−1 N RD 2N SR a2t j=t+1 bj t=1

Pout

[ ] x = 1 − Pr Rx1 > RxT1 , Rx2 > RxT2 , ..., Rx2N −1 > RT2N −1 , Rx2N > RxT2N {( ) ( ) ( )} x2N x1 x2 = 1 − Pr X1 > 22RT − 1 ∩ Y1 > 22RT − 1 ∩ ... ∩ Z > 22RT − 1 = 1−

−1 ( ) N∏ ) ( ) ( x2t−1 x2N x2t Pr Xt > 22RT −1 Pr Yg > 22RT − 1 Pr Z > 22RT − 1 . {z } t=1 | {z }| {z } t=1 | N ∏

U1

U2

4.8 5

4.6 ρ=25 dB ρ=20 dB ρ=15 dB

4.2 4 3.8 α SD =1, α SR =10, α RD=10

3.6 3.4

U3

ρ= 20 dB ρ= 15 dB ρ= 10 dB

4.5

Ergodic Sum Rate [bps/Hz]


4.4

(30)

4

3.5

3

3.2 α SD =1, α SR =10, α RD=2 2.5

3

α SD =1, α RD=2, α SR =10

2.8 0

0.05

0.1

0.15

2 0.7

0.75

0.8

0.85

0.9

0.95

1

a1

b2

Fig. 2. The ergodic SRs achieved by our proposed NOMA schemes versus power allocation factors b2 with fixed a1 = a3 =0.7 for ρ = {15, 20, 25} dB in different cases.

Fig. 3. The optimal ergodic SRs achieved by our proposed scheme versus power allocation factors a1 with fixed b1 =0.9 for ρ = {10, 15, 20} dB in different cases.

b2 corresponding to the achievable ergodic SR are close to 1 and 0, respectively. For comparison, the TDMA and conventional NOMA [37] are considered as two benchmark schemes, where the transmission protocol is similar to that of the one in [37]. The details is shown as follows: • The source transmits the data symbols to the relay and destination during one time slot. Then, the relay and destination will decode the receptions. • The relay forwards the decoded signal to the destination

while the destination will decode the transmitted signal from the relay. It is clear that, assuming M (even integer) time slots transmission, for both two benchmark schemes, to complete one data transmission requires two time slots. By this way, the achievable average rates of the TDMA and conventional NOMA with M time slots can be finally expressed as CT DM A =

M/2 1 ∑ log2 (1 + GT ) , M i=2



22

8

7

TDMA Conventional NOMA Proposed NOMA

20

6.5

Proposed 2TS Proposed 4TS Proposed 6TS C-NOMA TDMA

18 6


Transmission Rate

16 14 12 10 8

5.5

5

4.5

6

4

4 3.5 2 0 2

4

6

8

10

3 15

12

20

Transmission Time Slots

Illustration of the transmission rate for our proposed NOMA Fig. 4. scheme compared with the TDMA and conventional NOMA cases versus the transmission time slots.

7

SR (x ~x ): Simmulation 1

M/2

4

SR (x ~x ): Analysis 1

4

SR (x ,x ): Simmulation 1

6

2

SR (x ,x ): Analysis 1

2

SR (x ,x ): Simulation 3

4

SR (x ,x ): Analysis 3


Fig. 4 illustrates the transmission rate versus the transmission time slots, where the comparison is made considering three schemes, namely the proposed and conventional NOMA schemes, and the TDMA scheme as a benchmark. One can see that our proposed NOMA scheme shows its advantage for each number of the transmission time slots. In general, more transmission time slots lead to a higher transmission rate of the proposed NOMA scheme. For two benchmark schemes, each transmission involves two time slots, where single data symbol is transmitted for the TDMA scheme while a superposed data symbol transmission is considered for the conventional NOMA scheme, respectively. Therefore, the transmission rate of 1/2 and 1 can be achieved for the TDMA and the conventional NOMA schemes, respectively. Note that for our proposed NOMA scheme, each transmission can be efficiently completed within the transmission rate as 2(MM−1) . For cases with larger M , the transmission rate is close to 2 which outperforms the other 2 benchmark schemes. Fig. 5 illustrates the comparison ergodic SRs of our proposed NOMA scheme and the TDMA and conventional NO (t) 2 MA ones versus the transmit SNR, where we let hδ = βδ ,

30

The ergodic SRs achieved by our proposed, the TDMA and Fig. 5. conventional NOMA schemes with 2, 4, 6 time slots versus the transmission SNR with a1 = a3 = b1 .

and M/2 1 ∑ 1 ∑ CCN = log2 (1 + GC,1 ) + log2 (1 + GC,2 ) , M i=2 M i=2 { } (2i−1) 2 (2i) 2 hSR ρ (2i−1) 2 hRD ρ where GT = min , hSD ρ + , 2 2 } { (2i−1) 2 hSR a1 ρ (2i−1) 2 and GC,2 = GC,1 = min hSD a1 ρ, (2i−1) 2 a2 ρ+1 hSR { } (2i−1) 2 (2i) 2 min hSR a2 ρ, hRD ρ .

25

SNR [dB]

4

Approximation

5 Dash Line: α RD=30, α SD =1, α SR =3 Solid Line: α RD=3, α SD =1, α SR =30 4

3

2

4.3 4.2 4.1

1 15

26.8 20

25

30

27

27.2 35

SNR [dB]

Fig. 6. The ergodic SRs achieved by our proposed scheme, the approximate expression with 3 time slots versus the transmission SNR with a1 = a3 = b1 .

for δ ∈ {SR, RD, SD}. It shows that the ergodic SR of our proposed scheme is higher than that of the TDMA and the conventional NOMA schemes, which supports the practical utility of our design. In addition, the achieved ergodic SR of the TDMA and conventional NOMA schemes will not change with different time slots transmission due to that the transmission rate of the TDMA and conventional NOMA will not change with increasing transmission time slots. Remarkably, the 2TS of the proposed and conventional NOMA



9

schemes have the same SR performance, for the reason that the proposed NOMA scheme can be seen as a special case of the conventional one.


6

SR 3TS: Simmulation SR 4TS: Simmulation SR 5TS: Simmulation SR 3TS: Analysis SR 4TS: Analysis SR 5TS: Analysis

Outage probability

6.5

10 0

Dash Line: α RD=40, α SD =1, α SR =5 Solid Line : α RD=5, α SD =1, α SR =40 5.5

α SD =1, α SR =2, α RD=2, W=0.7

α SD =1, α SR =10, α RD=10, W=0.5 10 -1 α SD =1, α SR =10, α RD=10, W=0.7 3TS: Simulation (Case 1) 3TS: Analysis (Case 1) 3TS: Simulation (Case 2) 3TS: Analysis (Case 2) 3TS: Simulation (Case 3) 3TS: Analysis (Case 3) 3TS: Simulation (Case 4) 3TS: Analysis (Case 4)

5

10 -2 4.5

5

10

α SD =1, α SR =2, α RD=2, W=0.5

15

20

25

30

SNR [dB]

4 15

20

25

30

35

Fig. 8. The outage probability for our proposed scheme with the target rate as 0.5 and 0.7 with respect to the transmission SNR.

SNR [dB]

In Figs. 6 and 7, we show the ergodic SR for different channel gains, with respect to the number of transmission time slots, to show the superiority of our proposed scheme. Fig. 6 shows the ergodic SRs of the total system for our proposed 3TS scheme versus the transmission SNR, wherein the approximate results is obtained by (28). Moreover, two system setups are considered: (1) αRD = 3, αSR = 10; (2) αRD = 30, αSR = 10 with fixed a1 = a3 = b1 = 0.95. Fig. 7 shows the ergodic SR of different channel gains for our proposed scheme with fixed a2t−1 = 0.9 and respect to the number of transmission time slots which are: (1) αSR = 5, αRD = 40; (2) αSR = 40, αRD = 5. The relay power allocation factors are given as {b1 = 0.8, b2 = 0.2}, {b1 = 0.8, b2 = 0.15, b3 = 0.05} and {b1 = 0.7, b2 = 0.15, b3 = 0.1, b4 = 0.05} for 3, 4 and 5 transmission time slots, respectively. It is clear that there is a good match between the analytical results using Eqs. (26) and (27), as well as the approximation expression of the ergodic SR (28) and the simulation results in both Figs. 6 and 7, especially in the high SNR region. Specifically, with the increasing time slots N , the performance of SR will be also improved as shown in Fig. 7. In addition, the achieved ergodic SR with greater αRD is higher since bN αSR SR bN + a2N ααRD in (28) will be greater with a larger αRD , which results in better performance in the ergodic SR. In Fig. 8, we show the outage performance of our proposed scheme in simulation and analytical results with N = 3 transmission time slots, where we set a1 = a3 = b1 = 0.9, a2 = a4 = b2 = 0.1. In addition, there are four groups of data

symbols: (1) W = 0.7 with αRD = 2, αSR = 2; (2) W = 0.5 with αRD = 2, αSR = 2; (3) W = 0.7 with αRD = 10, αSD = 10; (4) W = 0.5 with αRD = 10, αSD = 10. The results reveal that a good match exists between the simulation and analytical results. It is also observed that the performance of the outage probability improves as the channel gains of αSR and αRD increase and the threshold W decreases. 2.5

Outage Capacity: Case 1 Outage Capacity: Case 2

ǫ=0.6 2

Outage Capacity [bps/Hz]

Fig. 7. The ergodic SRs achieved by our proposed scheme with N = 3, 4, 5 time slots versus the transmission SNR with a1 = a3 = b1 .

Case 1: α SD =2, α SR =30, α RD=3 1.5 ǫ=0.1 Case 2: α SD =2, α SR =3, α RD=30 1

ǫ=0.01 0.5

0 0

5

10

15

20

25

30

SNR [dB] Fig. 9. The outage capacity of the proposed NOMA-CRN system for N = 3 with ε = {0.6, 0.1, 0.01} with respect to the transmission SNR.

The outage capacity with respect to the transmission SNR and ε is illustrated in Fig. 9, where ε is set to be {0.6, 0.1, 0.01} with fixed {αSD = 2, αRD = 30, αSR = 3}



and {αSD = 2, αRD = 3, αSR = 30}, respectively. It is pointed out that the outage sum capacity degrades with an decreasing value of ε. Moreover, the performance of the outage sum capacity for the higher αRD case is always better than that of the lower one. V. C ONCLUSIONS In this paper, a two-stage superposed transmission for the CRN with finite time slots in the NOMA system has been proposed. We have employed the MRC and SIC to jointly decode the receptions from the source and relay nodes during multiple time slots, where the transmitted signal at the relay node is also designed as a superposition code. Finally, we have analyzed the performance in terms of ergodic SR, outage probability, outage capacity, and derived the corresponding closed-form expressions. The theoretical derivations have been shown to highly agree with the simulation results. By means of the numerical results, our proposed scheme has been shown to achieve a significantly improved transmission rate and exhibit a better SR behavior than the TDMA and conventional NOMA schemes. Our future concerns will be the optimization problems on the power allocations for the NOMA symbols in the proposed finite time slots NOMA-CRN scenario. R EFERENCES [1] Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett., vol. 21, no. 12, pp. 1501-1505, Dec. 2014. [2] Z. Ding, M. Peng, and H. V. Poor, “Cooperative non-orthogonal multiple access in 5G systems,” IEEE Commun. Lett., vol. 19, no. 8, pp. 14621465, Aug. 2015. [3] N. Otao, Y. Kishiyama, and K. Higuchi, “Performance of non-orthogonal access with SIC in cellular downlink using proportional fair-based resource allocation,” International Symposium on Wireless Commun. Systems (ISWCS), Aug. 2012, pp. 476-480. [4] Y. Zhang, H.-M. Wang, and T. Zheng, “Energy-efficient transmission design in non-orthogonal multiple access,” IEEE Tans. Veh. Technol., vol. 66, no. 3, pp. 2582-2587, Mar. 2016. [5] V. Nguyen, H. Tuan, T. Q. Duong, H. V. Poor, and O. Shin, “ Precoder design for dignal duperposition in MIMO-NOMA multicell networks,” IEEE J. Sel. Areas Commun., to appear 2017. [6] J. Choi, “Non-orthogonal multiple access in downlink coordinated two point systems,” IEEE Commun. Lett., vol. 18, no. 2, pp. 313-316, Feb. 2014. [7] Z. Ding, P. Fan, and H. V. Poor, “Impact of user pairing on 5G nonorthogonal multiple-access downlink transmissions,” IEEE Tans. Veh. Technol., vol. 65, no. 8, pp. 6010-6023, Aug. 2016. [8] N. Zhang, J. Wang, G. Kang, and Y. Liu, “Uplink non-orthogonal multiple access in 5G systems,” IEEE Commun. Lett., vol. 20, no. 3, pp. 458-461, Mar. 2016. [9] K. Tourki, H. Yang, and M. Alouini, “Accurate outage analysis of incremental decode-and-forward opportunistic relaying,” IEEE Trans. Wireless Commun., vol. 10, no. 4, pp. 1021-1025, Apr. 2011. [10] Z. Wei, D. Kwan Ng, J. Yuan, and H.-M. Wang, “Optimal resource allocation for power-efficient MC-NOMA with imperfect channel state information,” IEEE Tans. Commun., to appear 2017. [11] Z. Yang, Z. Ding, P. Fan, and N. Al-Dhahir, “The impact of power allocation on cooperative non-orthogonal multiple access networks with SWIPT,” IEEE Trans. Wireless Commun., vol. 16, no. 7, pp. 4332-4343, Jul. 2017. [12] Z. Ding, F. Adachi, and H. V. Poor, “The application of MIMO to nonorthogonal multiple access,” IEEE Trans. Wireless Commun., vol. 15, no. 1, pp. 537-552, Jan. 2016. [13] J. Wang, Q. Peng, Y. Huang, H.-M. Wang, and X. You, “Convexity of weighted sum rate maximization in NOMA systems,” IEEE Commun. Lett., vol. 24, no. 9, pp. 1323-1326, Sept. 2017.

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[14] Q. Yang, H.-M. Wang, D. Kwan Ng, and M. Lee, “NOMA in downlink SDMA with limited feedback: Performance analysis and optimization,” IEEE J. Sel. Areas Commun., to appear 2017. [15] B. He, A. Liu, N. Yang, and V. K. N. Lau, “On the design of secure non-orthogonal multiple access systems,” IEEE J. Sel. Areas Commun., to appear 2017. [16] Z. Ding, X. Lei, G. K. Karagiannidis, R. Schober, J. Yuan, and V. Bhargava, “A Survey on Non-Orthogonal Multiple Access for 5G Networks: Research Challenges and Future Trends,” IEEE J. Sel. Areas Commun., to appear 2017. [17] Y. Liu, Member, Z. Qin, M. Elkashlan, Y. Gao, and L. Hanzo, “Enhancing the physical layer security of non-orthogonal multiple access in large-scale networks,” IEEE Trans. Wireless Commun., vol. 16, no. 3, pp. 1656-1672, Mar. 2017. [18] Y. Zhang, H.-M. Wang, Q. Yang, and Z. Ding, “Secrecy sum rate maximization in non-orthogonal multiple access,” IEEE Commun. Lett., vol. 20, no. 5, pp. 930-933, May 2016. [19] Z. Yang, Z. Ding, P. Fan, and N. Al-Dhahir, “A general power allocation scheme to guarantee quality of service in downlink and uplink NOMA systems,” IEEE Trans. Wireless Commun., vol. 15, no. 11, pp. 72447257, Nov. 2016. [20] S. Lee, D. da Costa, Q. Vien, T. Q. Duong, and R. Sousa Jr., “Nonorthogonal multiple access schemes with partial relay selection,” IET Commun., vol. 11, no. 6, pp. 846-854, Mar. 2017. [21] N. Do, D. da Costa, T. Q. Duong, and B. An, “A BNBF user selection scheme for NOMA-based cooperative relaying systems with SWIPT,” IEEE Commun. Lett., vol. 21, no. 3, pp. 664-667, Mar. 2017. [22] C. Chen, W. Cai, X. Cheng, L. Yang, and Y. Jin, “Low complexity beamforming and user selection schemes for 5G MIMO-NOMA systems,” IEEE J. Sel. Areas Commun., to appear 2017. [23] N. Do, D. da Costa, T. Q. Duong, V. N. Bao, and B. An, “ Exploiting direct links in multiuser multirelay SWIPT cooperative networks with opportunistic scheduling,” IEEE Tans. Commun.,, vol. 16, no. 8, pp. 5410-5427, Aug. 2017. [24] Z. Yang, Z. Ding, P. Fan, and N. Al-Dhahir, “The impact of power allocation on cooperative non-orthogonal multiple access networks with SWIPT,” IEEE Trans. Wireless Commun., vol. 16, no. 7, pp. 4332-4343, Jul. 2017. [25] Y. Xu, C. Shen, Z. Ding, X. Sun, S. Yan, G. Zhu, and Z. Zhong, “Joint beamforming and power-splitting control in downlink cooperative SWIPT NOMA systems,” IEEE Trans. Signal Process., vol. 65, no. 18, pp. 4874-4886, Sep. 2017. [26] Y. Liu, Z. Ding, M. Elkashlan, and H. V. Poor, “Cooperative nonorthogonal multiple access with simultaneous wireless information and power transfer,” IEEE J. Sel. Areas Commun., vol. 34, no. 4, pp. 938953, Apr. 2016. [27] J. Choi, “Power allocation for max-sum rate and max-min rate proportional fairness in NOMA,” IEEE Commun. Lett., vol. 20, no. 10, pp. 2055-2058, Oct. 2016. [28] M. Hojeij, C. A. Nour, J. Farah, and C. Douillard, “Waterfilling-based proportional fairness scheduler for downlink non-orthogonal multiple access,” IEEE Commun. Lett., vol. 6, no. 2, pp. 230-233, Apr. 2017. [29] A. Nosratinia, T. Hunter, and A. Hedayat, “Cooperative communication in wireless networks,” IEEE Commun. Mag., vol. 42, no. 10, pp. 74-80, Oct. 2004. [30] R. U. Nabar, H. Bolcskei and F. W. Kneubuhler, “Fading relay channels: performance limits and space-time signal design,” IEEE J. Sel. Areas Commun.,, vol. 22, no. 6, pp. 1099-1109, Aug. 2004. [31] K. V. Srinivas, and R. Adve, “An orthogonal relay protocol with improved diversity-multiplexing tradeoff,” IEEE Trans. Wireless Commun., vol. 10, no. 8, pp. 2412-2416, Aug. 2011. [32] C. G. Tsinos, and K. Berberidis, “A Cooperative Uplink Transmission Technique With Improved Diversity-Multiplexing Tradeoff,” IEEE Trans. Veh. Technol., vol. 64, no. 7, pp. 2883-2896, July 2015. [33] R. Jiao, L. Dai, J. Zhang, R. MacKenzie, and M. Hao, “On the performance of NOMA-based cooperative relaying systems over Rician fading channels,” IEEE Trans. Veh. Technol., to appear 2017. [34] X. Liang, Y. Wu, D. W. Ng, Y. Zuo, S. Jin, and H. Zhu, “Outage performance for cooperative NOMA transmission with an AF relay,” IEEE Commun. Lett., to appear 2017. [35] S. Zhang, B. Di, L. Song, and Y. Li, “Sub-channel and power allocation for non-orthogonal multiple access relay networks with amplify-andforward protocol,” IEEE Trans. Wireless Commun., vol. 16, no. 4, pp. 2249-2261, Apr. 2017. [36] J. Men, and J. Ge, “Non-orthogonal multiple access for multiple antenna relaying networks,” IEEE Commun. Lett., vol. 19, no. 10, pp. 1686-1689, Oct. 2015.



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11

Jue Wang (M’14) received the B.S. degree in communications engineering from Nanjing University, Nanjing, China, in 2006, and the M.S. and Ph.D. degrees from the National Communications Research Laboratory, Southeast University, Nanjing, in 2009 and 2014, respectively. From 2014 to 2016, he was a PostDoctoral Research Fellow with the Singapore University of Technology and Design. He is currently a Lecturer with the School of Electronic and Information Engineering, Nantong University, Nantong, China.

Wei Duan received B.S. degree from Cheng Du University of Technology, Chengdu, China, in 2008, and the M.S. degree and Ph.D. degree from Chonbuk National University, Jeonju, South Korea, in 2012 and 2017, respectively. He is currently a lecturer at the Nantong University, Nantong, China. His research interests include cooperative networks and non-orthogonal multiple access techniques.

Xue-Qin Jiang (M’12) received the B.S degree from Nanjing Institute of Technology, Nanjing, Jiangsu, P.R. China, in computer science. He received the M.S and Ph.D. degree from Chonbuk National university, Jeonju, Korea, in electronics engineering. He is now an Associate Professor at School of Information Science and Technology, Donghua University, Shanghai, China. He is the author/coauthor of more than 70 technical papers, several book chapters. His main research interests include LDPC codes, physical-layer security and wireless communications.

Guoan Zhang received the B.S. degree in precision instruments, the M.S. degree in automatic instruments and equipment, and the Ph.D. degree in communication and information systems from Southeast University, Nanjing, China, in 1986, 1989, and 2001, respectively. He is currently a Full Professor with the School of Electronics and Information, Nantong University, Nantong, China. His current research interests include cognitive wireless networks and vehicular ad hoc networks.

Miaowen Wen (M’14) received the B.S. degree from Beijing Jiaotong University, Beijing, China, in 2009, and the Ph.D. degree from Peking University, Beijing, China, in 2014. From 2012 to 2013, he was a Visiting Student Research Collaborator with Princeton University, Princeton, NJ, USA. He is currently an Associate Professor with South China University of Technology, Guangzhou, China. He has authored a book and more than 80 papers in refereed journals and conference proceedings. His research interests include index modulation and nonorthogonal multiple access techniques. Dr. Wen received the Best Paper Award from the IEEE International Conference on Intelligent Transportation Systems Telecommunications in 2012, the IEEE International Conference on Intelligent Transportation Systems in 2014, and the IEEE International Conference on Computing, Networking and Communications in 2016. He received the Excellent Doctoral Dissertation Award from Peking University. He currently serves as an Associate Editor of the IEEE ACCESS, and on the Editorial Board of the EURASIP Journal on Wireless Communications and Networking, and the Physical Communication (Elsevier).
