NON-orthogonal multiple access (NOMA) has recently

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1 1 Full-Duplex Device-to-Device Aided Cooperative Non-Orthogonal Multiple Access Zhengquan Zhang Zheng Ma Member IEEE Ming Xiao Senior Member IEEE Zhiguo Ding Senior Member IEEE and Pingzhi Fan Fellow IEEE Abstract This paper presents a full-duplex device-to-device (DD aided cooperative non-orthogonal multiple access (NOMA scheme to improve the outage performance of the NOMA-weak user in a NOMA user pair where the NOMA-weak user is helped b the NOMA-strong user with the capabilit of full-duplex DD communications. The expressions for the outage probabilit are derived to characterize the performance of the proposed scheme. The results show that the proposed cooperative NOMA scheme can achieve superior outage performance compared to the conventional NOMA and orthogonal multiple access (OMA. In order to further improve the outage performance an adaptive multiple access (AMA scheme is also studied which dnamicall switches between the proposed cooperative NOMA conventional NOMA and OMA schemes according to the level of residual self-interference and the qualit of links. The results show that the AMA scheme can achieve the best outage performance. Index Terms Cooperative non-orthogonal multiple access full-duplex device-to-device communications 5G sstems. I. INTRODUCTION NON-orthogonal multiple access (NOMA has recentl attracted significant attention both in academia and industr as a promising candidate technolog in the fifthgeneration (5G wireless networks [1] [] and has alread been introduced to 4G long term evolution-advanced (LTE- Advanced sstems as multiuser superposition transmission (MUST [3] to improve the downlink performance due to its higher spectrum efficienc than traditional orthogonal multiple access (OMA. In order to further improve the performance of NOMA recentl cooperative NOMA (C-NOMA schemes have attracted some attentions. In [4] the authors proposed a half-duplex user-aided N-timeslot cooperative NOMA scheme and the results show that the proposed cooperative NOMA Copright (c 015 IEEE. Personal use of this material is permitted. However permission to use this material for an other purposes must be obtained from the IEEE b sending a request to pubs-permissions@ieee.org. This work was supported in part b the National Natural Science Foundation of China under Grant National Science and Technolog Major Project under Grant 016ZX National High-tech R&D Program of China under Grant 014AA01A707 Fundamental Research Funds for the Central Universities under Grant 68016ZDPY06 Huawei HIRP Project under Grant YB01504 the EU Marie Curie Project QUICK under Grant 6165 and the Big Data Processing in Wireless Networks Sweden STINT initiation grant. The work of Z. Zhang was also supported b the KTH-CSC Programme. Z. Zhang Z. Ma and P. Fan are with the Ke Lab of Information Coding and Transmission Southwest Jiaotong Universit Chengdu China. M. Xiao is with the Communication Theor Lab School of Electrical Engineering and the ACCESS Linnaeus Center Roal Institute of Technolog Sweden. Z. Ding is with the School of Computing and Communications Lancaster Universit LA1 4YW U.K. scheme could improve the outage probabilit due to the achievement of the maximum diversit gain. In [5] a novel cooperative simultaneous wireless information and power transfer (SWIPT NOMA protocol was proposed in which the NOMA-strong users that were close to the source act as energ harvesting relas to help the NOMA-weak users. In [6] the application of NOMA to the coordinated multiple points (CoMP sstems was studied. In [7] a cooperative beamforming NOMA scheme was proposed which emploed intra-beam superposition coding of a multiuser signal at the transmitter and the spatial filtering of inter-beam interference followed b the intra-beam successive interference cancellation (SIC at the terminal receiver. In addition the performance of NOMA for relaing networks was also investigated [8] [9]. Device-to-device (DD communications enable the direct communications between users [10] and DD users can also pla as relas to cooperate data transmission which can improve the sstem performance b sharing with the bandwidth used b cellular base stations (BSs. With the help of full-duplex radio [11] full-duplex DD communications can further improve the sstem performance in heterogeneous networks [1]. In order to further improve the outage performance of the NOMA-weak user 1 in a user pair and reduce cooperative dela in this paper we focus on full-duplex DD-aided cooperative NOMA in which the user pair is predefined and configured and the NOMA-strong user has the capabilit of full-duplex DD communications. With the help of full-duplex operation the NOMA-strong user can receive data from the BS and forward the data to the NOMA-weak user over the same carrier frequenc simultaneousl. Compared to the existed works the contributions of this paper are summarized as follows. We present a full-duplex DD-aided cooperative NOMA scheme to improve the transmission reliabilit of the NOMA-weak user in which the NOMA-weak user is cooperated b the NOMA-strong user with the capabilit of full-duplex DD communications. We analze the outage performance and derive the expressions for the proposed full-duplex DD-aided cooperative NOMA scheme. We also investigate the impact of the full-duplex mode and cooperation on the outage performance and further stud an adaptive multiple access (AMA scheme to 1 Note that for the two users that are served in NOMA the user with a higher signal-to-interference-plus-noise ratio (SINR is considered as the NOMAstrong user while the user with a lower SINR is considered as the NOMAweak user.

2 improve the outage performance which enables the BS to dnamicall choose a proper multiple access mode among the proposed cooperative NOMA conventional NOMA and OMA schemes according to the level of residual self-interference and the qualit of channels. II. SYSTEM MODEL Fig. 1 illustrates the sstem model of full-duplex DDaided cooperative NOMA which consists of one BS one NOMA-strong user having the capabilit of the full-duplex DD communications UE1 and one NOMA-weak user UE. The BS transmits a superposed signal x P 31 x 1 + P 3 x to a pre-defined NOMA user pair based on statistical channel state information (CSI where E[ x i ] 1 i 1 P 31 P 3 and P 3 (1 P 3. It holds that P 31 P 3 and P 3 (1 P 3 where P 3 is the total transmit power at the BS; (0 1 is the power allocation factor. In general in order to ensure the performance of NOMA sstems the NOMA-strong user is allocated less power than the NOMAweak user. Consequentl the power allocation factor can be further limited to ( The NOMA-strong user forwards x to the NOMA-weak user with transmit power P 1. The optimal order for decoding in downlink is the increasing order of channel gain normalized b noise and interference power. Similar to [4] full-duplex DD-aided cooperative NOMA still consists of direct transmission and cooperative phases. Due to the NOMA-strong user working in the full-duplex mode the direct transmission phase and cooperative phase can be performed simultaneousl. In the direct transmission phase UE1 first decodes and cancels UE s signal b SIC before decoding its own data. In the cooperative phase UE1 forwards the decoded data x to UE then UE combines and decodes the signals from the BS and UE1. Since the NOMAstrong user UE1 works in the full-duplex mode it suffers from residual self-interference which is caused b co-channel transmission and imperfect interference cancellation. The involved channels are BS UE1 BS UE UE1 UE1 and UE1 UE whose channel coefficients are denoted as h 1 h h 11 and h 3 3 respectivel. Channels BS UE1 BS UE and UE1 UE are subjected to Raleigh fading while the residual self-interference channel UE1 UE1 is assumed to be free of fading. III. PERFORMANCE ANALYSIS A. Full-Duplex DD-Aided Cooperative NOMA In the k-th time slot k the BS transmits a superposed signal with different powers to two users and is [1] x[k] P 31 x 1 [k] + P 3 x [k]. (1 Self-interference refers to the signals that are transmitted b a full-duplex node and looped back to the receiver simultaneousl. Through multi-stage selfinterference cancellation technologies including antenna cancellation radio frequenc (RF and digital interference cancellation [11] those strong loop signals can be suppressed to a low level. However loop back signals still remain in the receiver due to imperfect interference cancellation and are considered as interference when decoding the desired data. 3 Note that in this paper we focus on the improvement of the performance b virtue of cooperation in NOMA sstems. We assume that sophisticated channel estimation algorithms have been used with sufficient training information to obtain perfect CSI. Base Station High h 1 h 1 1 UE1 h 3 SIC of UE signal h Received SINR UE UE1 signal decoding UE signal decoding Fig. 1. Sstem model of full-duplex DD-aided cooperative NOMA The NOMA-strong user UE1 receives downlink signal from the based station and residual self-interference due to its co-channel transmission thus its received signal is represented as 1 [k] h 1 [k]( P 31 x 1 [k]+ P 3 x [k]+h 11 [k] P 1 s[k]+n 1 [k] ( where s(k is the transmit signal to UE and E[ s(k ] 1; n i CN (0 σi is the additive white Gaussian noise (AWGN at UEi i 1. The NOMA-strong user UE1 first decodes UE s data x then cancels it from the received signal and detects its own data. Therefore the received SINR that UE1 detects UE s data x is given b h 1 P 3 (1 h 1 P 3 1 h 1 P 31 + h 11 P 1 + σ1 h 1 P 3 + h 11 P 1 + σ1. (3 The received SINR at UE1 to detect its own information is h 1 P 31 h 1 P 3 11 h 11 P 1 + σ1 h 11 P 1 + σ1. (4 The NOMA-strong user UE1 decodes and forwards the data x to the NOMA-weak user UE thus a processing dela τ is introduced which is assumed to be one without loss of generalit. The NOMA-weak user UE receives both downlink signal from the BS and signal forwarded b UE1 which is expressed as x 1 Low [k] h [k]( P 31 x 1 [k] + P 3 x [k] + h 3 [k] P 1 x [k τ] + n [k] where P 1 is the transmit power of UE1. We assume that the two signals from the BS and UE1 are full resolvable at UE so that the can be appropriatel co-phased and merged b maximal ratio combining (MRC. Therefore the received SINR at UE to detect information from the BS is expressed as h P 3 h P 31 + (1 h P 3 h P 3 +. (6 The received SINR at UE to detect information forwarded from UE1 is written as 1 h 3 P 1. (7 Therefore the overall SINR received at UE after MRC is M RC + 1 (1 h P 3 h P 3 + σ x (5 + h 3 P 1. (8

3 3 Outage probabilit is an important metric to characterize the sstems which is defined as the probabilit that the data rate supported b the instantaneous channel conditions is below a target rate R th. We first define the following outage events: Ei m j {i m j < } i j 1 and m 1 3 which means that the outage occurs when the i-th user detects the signal of the j-th user or the i-th user detects the signal forwarded b the j-th user under the m-th multiple access scheme where m 1 3 donate the proposed cooperative NOMA conventional NOMA and OMA schemes respectivel. In addition we also define the outage event as E 1 M RC {1 M RC < } { < }. Ēi m j is the complementar set of Ei m j. As defined in [5] the outage event of the NOMA-weak user is {E 1 : (Ē1 1 E1 M RC (E1 1 E1 }. As a result the outage probabilit of the NOMA-weak user is P C NOM A out Pr(E 1 Pr(Ē1 1 E1 M RC + Pr(E1 1 E1 (1 Pr(E1 1 Pr(E1 M RC + Pr(E1 1 Pr(E1. (9 Note that R T 1 is the threshold to detect the signals of UE1 and UE in full-duplex DD-aided cooperative NOMA while T R T 1 is for OMA because two time slots are allocated to the two users. In order to assist the derivation we define random variables (RVs X h 1 P 3 /σ1 Y h P 3 / W h 3 P 1 / and constant A SI h 11 P 1 /σ1. Considering Raleigh fading it holds that X Exp(1/ 1 Y Exp(1/ and W Exp(1/ 3 where 1 ϵ{ h 1 }P 3 /σ1 ϵ{ h }P 3 / 3 ϵ{ h 3 }P 1 / and ϵ{ } denotes expectation. In downlink NOMA the maximum SINR to detect the NOMA-weak user is limited which can be obtained b the (1 X lim operation and is lim X X+A+1 1. For the outage event E1 1 when 1 the probabilit of the event E1 1 is Pr(E1 1 1; when 0 < < 1 we have ( (1 X Pr(E1 1 Pr X + A + 1 < ( A+1 (10 ( 1 e x 1 dx ( S I +1 ( Therefore the probabilit of the event E1 1 can be written as Pr(E1 1 1 T 1 1 ( A+1 ( 1 0 < < 1. (11 Similar to derive the probabilit of the event E1 1 the probabilit of the event E 1 can be solved through replacing A + 1 with 1 in (11 and can be expressed as ( (1 Y Pr(E 1 Pr Y + 1 < 1 T 1 1 ( 0 < < 1. (1 Let V Y +1 then Z M RC V + W. The probabilit of outage event E 1 M RC can be expressed as Pr{E 1 M RC } Pr{V + W < }. When 0 < < 1 the integral domain is D {(v w 0 < v < 0 < (1 Y w < v}. When the integral domain is D {(v w 0 < v < 1 0 < w < v}. As a result the probabilit can be solved as Pr{E 1 M RC } f V (v f W (wdvdw v+w 1 ( 3 1 e e ( I( (1 1 e ( I( < < 1 (13 where I(a b p p 1 e (at+ b t dt. Substituting (11 (1 and (13 into (9 and after simplification the outage probabilit of the NOMA-weak user can be expressed as P C NOM A out e ( 1 +( S I +1 ( 1 e ( e (( 1 +( S I +1 3 ( 1 3 (1 1 I( e ( < < 1. (14 Note that when S I 0 and removing terms related with forwarding link 3 full-duplex DD-aided cooperative NOMA degrades to the conventional NOMA. Thus the outage probabilit of the NOMA-weak user in the conventional NOMA is equal to the probabilit of the event E 1. According to (1 the outage probabilit of the NOMA-weak user in the conventional NOMA can be written as out 1 T 1 1 ( 0 < < 1. (15 P NOM A For OMA the instantaneous SINR received at the NOMAweak user is expressed as OM A h P 3. (16 Thus the outage probabilit of the NOMA-weak user can be solved as P OM A out Pr{E3 } T 0 1 e B. Adaptive Multiple Access Scheme d 1 e T. (17 According to (14 (15 and (17 there is a tradeoff among the proposed cooperative NOMA conventional NOMA and OMA schemes in terms of outage performance. In order to further improve the outage performance we stud an AMA scheme which dnamicall switches to a proper multiple access scheme b the qualit of channels. The resulting outage probabilit of the NOMA-weak user is given b P AM A out Pr(EC NOM A E NOM A E OM A. (18

4 4 Based on E NOM A E C NOM A E (18 can be further simplified as Pout AM A Pr(EOM A E NOM A ((Ē C NOM A 1 M RC (E C NOM A 1 Pr(Ē C NOM A 1 Pr(E OM A M RC + Pr(E C NOM A 1 Pr(E OM A E. (19 For the probabilit Pr(E C NOM A Pr(E OM A E 1 the integral domain of the event E is { < T 1 } while the integral domain of the event E OM A is { < T }. When 1 the probabilit of the event E is equal to one thus Pr(E OM A E Pr(E OM A. Furthermore if T > under the condition < 1 the probabilit of the event E OM A E is Pr(E OM A E Pr(E otherwise its probabilit is Pr(E OM A E Pr(E OM A. To sum up we have Pr(E OM A E Pr(E < 1 and T > Pr(E OM A other s. (0 Next we derive the probabilit of event {E OM A E C NOM A M RC }. When 1 its integral domain is D1 {(x 0 < x < T 0 < < (+ 1x+ x+1 }. When < 1 and T T 1 the integral has the same integral domain D1. When < 1 and T > T 1 its integral domains are D {(x 0 < x < T 1 0 < < (+ 1x+ x+1 }. After solving the integral the probabilit can be written as Pr(E OM A M RC 1 e T / 1 e 3 (T I( 1 1 T + 1 { 1 }or{ < 1 T T 1 } ( 1 3 e 3 (T 1+ 1 I( { < 1 T > }. (1 Substituting (11 (1 (17 (0 and (1 into (19 we obtain the outage probabilit of the NOMA-weak user in the adaptive multiple access scheme as in ( shown at the top of the next page. IV. NUMERICAL RESULTS The numerical results for the outage probabilit of fullduplex DD-aided cooperative NOMA scheme are presented together with Monte Carlo simulations. All parameters referred to Monte Carlo simulations are summarized in Table I including power allocation factor outage threshold R th average SINR threshold for user pairing 4 average SNR of cooperative channel 3 and residual self-interference. In Monte Carlo 4 The average SINR threshold for user pairing refers to the minimum SINR difference between the channels BS U E1 and BS U E which is used to decide whether those two user can form a user pair in downlink NOMA sstems. If the SINR difference between the channels BS U E1 and BS U E is above this threshold UE1 and UE can form a user pair. simulations we first predefine a user pair (UE1 UE and fix a set of parameters: Power allocation factor outage threshold R th average SINR threshold for user pairing average SNR of cooperative channel 3 and residual self-interference then generate random numbers for channels BS UE1 BS UE and UE1 UE with Raleigh fading next decide and collect statistics on the outage event followed b calculating the statistical results. Through changing the parameters and repeating the above steps the simulation results shown in Fig. and Fig. 3 can be obtained. TABLE I MONTE CARLO SIMULATION PARAMETERS Parameter Value Power allocation factor Outage threshold R t h 0.5b/s/Hz 1.0b/s/Hz Average SINR threshold for user pairing 3dB 6dB Average SNR of cooperative channel 3 1dB 1dB Residual self-interference 0dB 3dB 1dB Fig. depicts the outage probabilities of the AMA fullduplex DD-aided cooperative NOMA conventional NOMA and OMA schemes with power allocation factors 0. and dB and the SNR threshold for user pairing 6dB under the threshold for outage R th 0.5b/s/Hz. The results show that the proposed full-duplex DD-aided cooperative NOMA scheme can dramaticall improve the outage performance of the NOMA-weak user with proper power allocation when residual self-interference is below a certain level. With the increasing of residual self-interference and power allocated for the NOMA-strong user the gain from the cooperation is graduall decreased. With more power allocated for the NOMA-strong user the outage performance of NOMA is also graduall decreased. The results also show that the performance curve of the AMA scheme is almost overlapped with that of full-duplex DD-aided cooperative NOMA. This is because the AMA scheme chooses the best multiple access scheme among cooperative NOMA conventional NOMA and OMA schemes dnamicall while the cooperative NOMA is absolutel dominant among these three scheme under the parameters 3 1 db and the SNR threshold for user pairing 6 db. Consequentl the AMA scheme nearl degrades to the cooperative NOMA. Fig. 3 illustrates the outage probabilities of the AMA fullduplex DD-aided cooperative NOMA conventional NOMA and OMA schemes with power allocation factor dB and the SNR threshold for user pairing 3dB under the threshold for outage R th 1.0b/s/Hz. The results show that the AMA scheme can achieve superior outage performance to other multiple access schemes. Furthermore Fig. and Fig. 3 also reveal that the AMA scheme can achieve the best outage performance and an obvious gain when there is no dominant multiple scheme. Conversel it can still achieve the similar outage performance as the dominant multiple scheme but no further gain. V. CONCLUSIONS A full-duplex DD-aided cooperative NOMA scheme is presented to improve the outage performance of the NOMA-weak

5 5 Pout AM A 1 e T / 1 ( 1 e T 1 ( S I +1 ( 1 e 3 ( I( e T 1 e T 1 ( S I +1 ( 1 e 3 ( I( 1 1 T < 1 and T > < 1 and T. ( Outage probabilit of the far user Outage probabilit of the far user AMA Theoretical 10 AMA Simulated C NOMA Theoretical C NOMA Simulated NOMA Theoretical NOMA Simulated 10 3 OMA Theoretical OMA Simulated SI0dB SI3dB SI1dB (a AMA Theoretical AMA Simulated 10 C NOMA Theoretical C NOMA Simulated NOMA Theoretical NOMA Simulated OMA Theoretical OMA Simulated 10 3 SI0dB SI3dB SI1dB (b Fig.. Outage probabilit of the AMA full-duplex DD-aided cooperative NOMA conventional NOMA and OMA schemes under 3 1dB and R t h 0.5b/s/Hz. (a 0.. (b 0.4 Outage probabilit of the far user AMA Theoretical AMA Simulated C NOMA Theoretical C NOMA Simulated NOMA Theoretical NOMA Simulated OMA Theoretical OMA Simulated SI0dB SI3dB SI1dB user in downlink NOMA sstems. Expressions for the outage probabilit are derived in order to evaluate the performance of the proposed cooperative NOMA. Numerical results and simulations are developed to demonstrate the performance gain of the cooperative NOMA scheme. In order to further improve outage performance an AMA scheme is also studied which dnamicall switched to a proper multiple access scheme based on the level of residual self-interference and the qualit of channels. The analtic and numerical results show that the AMA scheme can achieve the best outage performance and obtain an obvious gain when there is no multiple access scheme with absolute advantage. REFERENCES [1] Y. Saito A. Benjebbour Y. Kishiama and T. Nakamura Sstem level performance evaluation of downlink non-orthogonal multiple access (NOMA in Proc. IEEE 4th Int. Smp. Pers. Indoor Mobile Radio Commun. (PIMRC Sep. 013 pp [] Z. Ma Z. Zhang Z. Ding P. Fan and H. Li Ke techniques for 5G wireless communications: Network architecture phsical laer and MAC laer perspectives Sci. China Info. Sci. vol. 58 pp. 1-0 April 015. [3] Stud on Downlink Multiuser Superposition Transmission (MUST for LTE 3GPP TR Dec [4] Z. Ding M. Peng and H. V. Poor Cooperative non-orthogonal multiple access in 5G sstems IEEE Commun. Lett. vol. 19 no. 8 pp Aug [5] 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 April 016. [6] J. Choi Non-orthogonal multiple access in downlink coordinated twopoint sstems IEEE Commun. Lett. vol. 18 no. pp Feb [7] N. Nonaka Y. Kishiama and K. Higuchi Non-orthogonal multiple access using intra-beam superposition coding and SIC in base station cooperative MIMO cellular downlink in Proc. IEEE 80th Veh. Technol. Conf. (VTC Fall Sep. 014 pp [8] J. Kim and I. Lee Capacit analsis of cooperative relaing sstems using non-orthogonal multiple access IEEE Commun. Lett. vol. 19 no. 11 pp Nov [9] J. Men and J. Ge Non-orthogonal multiple access for multiple-antenna relaing networks IEEE Commun. Lett. vol. 19 no. 10 pp Oct [10] M. N. Tehrani M. Usal and H. Yanikomeroglu Device-to-device communication in 5G cellular networks: Challenges solutions and future directions IEEE Commun. Mag. vol. 5 no. 5 pp Ma 014. [11] J. I. Choi M. Jain K. Srinivasan P. Levis and S. Katti Achieving single channel full duplex wireless communication in Proc. ACM Int. Conf. Mobile Comput. Netw. (MobiCom Sep. 010 pp [1] L. Wang F. Tian T. Svensson D. Feng M. Song and S. Li Exploiting full duplex for device-to-device communications in heterogeneous networks IEEE Commun. Mag. vol. 53 no. 5 pp Ma 015. Fig. 3. Outage probabilit of the AMA full-duplex DD-aided cooperative NOMA NOMA and OMA schemes with 0.4 and 3 1dB under R t h 1.0b/s/Hz