A Near Optimal Power Allocation Scheme for Cooperative Relay Networking with NOMA

Haiyang Yu,Wei Duan＊,Guoan ZhangYancheng JiXiaojun ZhuJaeho Choi

1 The School of Electronics and Information,Nantong University,Nantong 226000,China

2 Division of Electronics and Information Engineering,Chonbuk National University,561-756,Korea

3 Department of ECE,CAIIT,Chonbuk National University,Jeonju,561-756,Korea

Abstract:In this paper,we propose cooperative relay networks with non-orthogonal multiple access in order to design a near-optimal power allocation strategy.Like other next generation wireless technologies,spatially multiplexed transmissions are achieved by relay nodes which enables decode-and-forward relaying of a new superposition code after reception from the source.It is worth noting that,since it is hard to exactly prove the proposed PA scheme,due the fact that it is one kind of the approximate conjectures.Therefore,mathematical and numerical methods have been used to clarify the feasibility of the proposal.Numerical results indicate that it is able to asymptotically achieve the optimal sum rate at the higher signal-to-noise ratio region with the proposed strategy applied instead of negligible performance loss.

Keywords:non-orthogonal multiple access; cooperative multi-relay networks; decode-and-forward; two-stage power allocation

I.INTRODUCTION

With the comparison to the orthogonal multiple access orthogonal multiple access (OMA),non-orthogonal multiple access (NOMA) was came up as a potential technique to satisfy the tradeoff between data demand and system capacity by reason of the significantly superior spectral efficiency and balanced user access [1]-[6].In contrast to the conventional OMA,the preexisting dominant NOMA scheme has been categorized as power domain and code domain multiplexing,where the superposed signal is considered at the transmitter by using superposition coding due to different channel conditions.The successive interference cancellation (SIC) technology has been employed to detect the superposed signal at the receiver,for its higher capability and lower complexity [7].Following NOMA transmit principles,the weak user should be allocated with a higher power while the strong user with a lower one.In [8],the authors have shown that the NOMA outperforms conventional OMA in both mathematical and theoretical methods,regarding the average and optimum sum rates.In addition,the NOMA also provides advantages regarding supporting complex connectivity and meeting different quality-of-service (QoS) requirements [9],[10].Moreover,code-domain multiplexing is one of the technique which asssigns disparate data codes to users on an individual basis in the systems that without additional time frequency required,such as multiple access (MA) with low-density spreading (LDS) [11] and sparse code multiple access (SCMA) [12].Because the NOMA system has attractive features compared with other communications technologies,such as the enhanced user fairness,low latency,and compatibility,it has typically been integrated into existing and next-generation wireless systems [13],[14].In [15] and [16],the challenges of NOMA on security and reliability are dealt with to improve the secrecy rate (or capacity) in the physical layer communication.By controlling the secrecy outage and QoS requirement,an optimal secure NOMA [17] design that enables NOMA to outperform OMA irrespective of the number of users has been investigated in [18].In [19]-[21],simultaneous wireless information and power transfer (SWIPT) with cooperative NOMA [22],[23] have been investigated,where the radio frequency can transfer,with information and energy,and stronger users playing as energy harvest relays have assisted with weaker users [24],[25].When the relay system is considered,the difference between relay based transmission and point-to-point transmission has been traced into [26].In addition,SWIPT is mainly focused on the cooperative relay systems (CRS) [27] with the decode-and-forward (DF) [28] and amplify-and forward (AF) relaying [29],[30].On account of the fact that CRS can considerably improve the NOMA system capacity,a cooperative relay selection via comparison diversity gain and minimal outage probability has been studied in [31].The authors in [32] have shown the significant improvement of QoS by combining NOMA with a cooperative relaying scheme.By regarding a poor channel condition signal as noise,a stronger signal can be decoded from the superposition coded signal by using SIC.The cooperative NOMA provides a better chance for poor channel condition signals to improve the outage performance.The authors in [2] have studied the cooperative relay networks with non-orthogonal multiple access (CRN-NOMA) system,which significantly improves the capacity compared to the OMA.Based on [2],the authors in [33] have proposed a novel receiver design by employing the maximum-ratio-combining (MRC),which results in a further capacity improvement.Unfortunately,the proposed scheme in [33] decodes the symbol with the comparatively lower power even if it results in the degradation of the outage performance.Power allocation in [34] with known channel state information (CSI) [35],[36] is the key idea to the NOMA system,which provides a stable performance [37],though CSI can not reach a perfect value at practical applications [38].In the meanwhile,the channel capacity only related to CSI in the fading channels [39] [40].In NOMA,for users,CSI has mainly been used in user demultiplexing at receiver and power allocation for user at the transmitter.On account of the aforementioned shortcomings,in order to get a better outage performance,for the CRS-NOMA systems,two stage power allocation is proposed in [4],which first allocates the power at transmitter and then forwards the allocated power in the relay node with the new superposed symbol.Considering this relay NOMA scheme,we propose a simpler algorithm and show the comparisons with the scheme in [4].The implementations and contributions are summarized as follows:

· Since the closed-form expressions of the power allocation (PA) factors in [4] are hard to be obtained,in this paper,a near-optimal PA scheme is investigated,which is very close to the optimal one at a high signal-to-noise ratio (SNR) region.The motivation is surely to save the calculation time for more possibilities after the enormous change of the parameter,especially for the changes of the power allocation factor in [4],the range of the parameter has a barrier to prevent us from explore the channel possibilities.

In this paper,we propose cooperative relay networks with non-orthogonal multiple access in order to design a near-optimal power allocation strategy.

· Without loss of the generality,in the proposed system,a simple and near-optimal PA scheme is discussed and the proposed scheme is analyzed in two ways.i.e.,by optimizations and numerical methods.Specifically,the signal with more power at the source is allocated with a less power at the relay while the other signal with less power at the source is allocated with a more power at the relay.

· Through the numerical results,the proposed scheme shows a similar performance compared with the scheme in [4].In high SNR region the performance of the proposed scheme performs very close to that of the optimal one.

The proposed PA scheme is simple and practical without the performance loss compared to the existing work [4],as shown in the numerical results in Section IV.This paper is organized as follows.Section II sums up the system model and the power allocation scheme under investigation is designed.The numerical results are discussed to show the advantage of the proposed system in Section IV.Section V concludes this paper.

II.SYSTEM MODEL and OBJECTIVE PROBLEM

The proposed CRS is composed of one source,one relay,and one destination,all nodes are assumed to operate in a half-duplex mode.In addition,there is no direct link between the source and the destination.hSD,hSRandhRDindicate the channel from the source to the destination,from the source to the relay,and from the relay to the destination,respectively.Meanwhile,αSRandαRDdenote the channel variance,respectively.Like [4],during the first time slot,the relay and the destination receive the signal from the source defined by

respectively,where,fori=1,2,denotes the broadcasted symbol,for i=1,2; the power allocation factorsaiwitha1+a2=1 anda1＜a2;Ptpresents the transmit power; andrepresents the additive white Gaussian noises (AWGNs).As shown in [4],by employing the DF at the relay node,a new superposition coded signalwith new PA factorsa3+a4=1,which is transmitted to the destination.

Finally,by using the linear combination (LM) at the receiver,the corresponding effective SNRs forx1andx2are given by

and

It is clear that,for these two corresponding equations,the PA factora4in Eq.(5) is used to computea2*in Eq.(4),as well as the valuea2in Eq.(4) is used to computea4*Eq.(5).On the other hand,they also involve several parameters,i.e.,the channel coefficients and SNR.With the observation of this biconvex problem,the iterative algorithms should be employed to obtain the exact values ofa2*anda*4to solve this problem.In addition,Table 1 shows the calculation details which has been mentioned in [4].The maximum SR can not be calculated directly as it is related witha2*anda4*simultaneously.In the meanwhile,there are many parameters in (1) includingαSD,αRD,JandJ.Whenever that of the numerical values ofαSDorαRDincrease,the number of the iterations will be increased correspondently,in order to satisfy the constraintsξ,in the following section,we turn to design an easy near-optimal power allocation strategy.

In our proposed scheme a simply and practical strategy is invented.It is worth noting that,compared with the scheme in [4],with two kinds of the methods,i.e.,mathematical and numerical methods,the results clearly showed that our proposed PA strategy is an effective method without the performance loss in the high SNR region.The proposed scheme plays a power allocation factor interchanging between the source and relay nodes.Moreover,with our proposed concept,it is possible to provide a new mentality to solve the PA problems in the cooperative relay NOMA networking for the future work.

III.SIMPLE AND NEAR OPTIMAL PA DESIGN

In this section,a simple and near-optimal PA scheme is discussed.The proposed scheme is analyzed in two ways i.e.,by optimizations and numerical methods.

3.1 Mathematical discussion

Since the achievable SR can be expressed as

Consider the high transmission SNR case,i.e.,ρ＞＞1, it is easy to see that

Table I.Sub-optimal power allocation factors.

which leads to

In addition,Since log(⋅) is a monotonic function,we have

Therefore,with (8) and (9),the optimization problemT2can be approximately rewritten as

In the following subsections,we will analyze the optimization problemT2with different cases ofY.

1) Case 1,forY a=2ρβSR:the objective problemT2can be rewritten as

From (10),it is clear that,for any feasiblea2with 0＜a2＜1,one can always find that,for a smallera2,the result ofCsumwill be greater.In addition,the solution strictly follows the NOMA principle,i.e.,the symbolx1is decoded first in the first phase and thus is given more powers,correspondingly,x2is with small power.Thus,we conclude that if and only ifa2→0,the objective problemT2has the optimal solution.

2) Case 2,for:Proposi-tion 1,the optimization problemT2is able to be written as

Proof:FromT2,withwe have

If A is great enough to approximate to infinity,1+A is approximated as A.Thus,the optimization problem {max Α} can be equivalently written asBy this way,the objective problem (11) can be approximately converted into

Fig.1.The analysis of ergodic sum rate of the proposed optimization(or scheme,algorithm) for power allocation factors a1 and a3,(a) ρ=25dB,(b) ρ=30dB.

Specifically,similar to [41],for slack valuea,optimizing the optimization problem {max A} can be equivalently rewrite as {maxa}s ta..A ≥,for the optimization problem (12),after introducingand the slack valueτ,we have

which completes the proof.

SynthesizingCase 1 and Case 2,one can say that the optimal SR of the proposed system can be obtained with great {a1,a4} and small {a2,a3} in the feasible interval,i.e.,0 ＜ai＜1.

3.2 Numerical discussion

On the other hand,Figure 1 depicts the average SR performance versus power allocation factorsa1anda3with fixedαSD=1，αSR=10 andαRD=2 forρ=25 dB andρ=30 dB,respectively.Forρ=25 dB,Csum=5.3065 bps/Hz witha1=0.980 anda3=0.015 while forρ=30 dB,Csum=6.1838 bps/Hz w i t ha1=0.990 anda3=0.010.From the figures,it is also interesting to see thata1→1 anda3→0 asρrises.Note that similar phenomenons can be also observed from other system configurations.

3.3 Suboptimal closed-form expressions of the power allocation factors

Based on the above mathematical and numerical discussions,we may simply requirea1=a4anda2=a3to solve the optimization problem that is more tractable.This condition providesς2=1.Using the approximations of Ei (-x)=Ec+ln(x) +xa n dex=1 +x,f o r small values ofx,whereEcdenotes the Euler constant,the ergodic SR can be approximated as

From (14),the first-order and the second-order derivatives ofwith respect to the power allocation factora2can be respectively derived as

and

From (16),it is easy to see that as long asit follows thatotherwiseSinceis a decreasingfunction for and meanwhileforthere exists maximumassociated withLettingthe suboptimal power allocation factora2can be obtained as

IV.NUMERICAL RESULTS

In this section,examine the performance of the proposed scheme regarding the ergodic SR with fixedαSD=1.All results are averaged over 20,000 channel realizations.Comparisons are made with the CRS-NOMA [2] and the maximum ratio combining (MRC) case of CRS-NOMA in two considered system setups:(1)αSR=10,αRD=2 andαSR=2,αRD=10.For the MRC case of CRS-NOMA,the destination decodesx2at the second phase by combining the two received signals at two phases,resulting in

Figure 2 shows the ergodic SR performance of the sub-optimal scheme versus the power allocation factora2withαSR=10,andaSD=1,where we seta1=a4anda2=a3.By using the closed-form solutiona2*,we obtain the sub-optimal SR at 5.3739 bps/Hz,6.2000 bps/Hz,and 7.0285 bps/Hz,forρ=25 dB,ρ=30 dB,andρ=35 dB,respectively.The results are close to the optimal solutions as verified in the figure.In addition,when SNR is high,the mismatch betweena2*and the optimal solution becomes negligibly small.

Fig.2.The analysis of ergodic sum rate of the proposed sub-optimization(or scheme,algorithm) for the power allocation factor a2.

Fig.3.The ergodic SRs achieved by our proposed PA scheme,CRS-NOMA [2] and the optimal in [4] versus the high transmit SNR.

Figure 3 compares the SR performance achieved by the proposed scheme with that of MRC [2] and the optimal scheme [4],where to reach the optimal ergodic SR requires the exhaustive search whereas to come to the sub-optimal SR needs the sub-optimal power allocation such as Eq.(17).In figure 3,it is easy to see that at the higher SNR,the proposed suboptimal result get similar performance with the optimal one,which supports the practical utility of our design.Remarkably,the performance of this manuscript and CRS-NOMA [2] gets very close at high SNR region.This observation is consistent with (17) and [2,Eq.(15)],where these equations approachlog2ρas SNR increases.In addition,the advantage enlarges for the case

V.CONCLUSION

In this paper,a near optimal PA strategy has been investigated for CRN-NOMA,which is simple and practical.We have tried to clarify the feasibility of the proposed scheme by two different methods:one is the mathematical tactic for the optimization problem,and the other one is the numerical tactic for the association between the PA factors.The numerical results have showed that the corresponding achievable SR performance of our proposed PA scheme is very close to that of the optimal scheme.

ACKNOWLEDGEMENTS

This work has been partly supported by the research funds of the National Natural Science Foundation of China (NO.61371113,61401241),the research funds of Chonbuk National University in 2017,BK-21 of Korea and the Nantong University-Nantong Joint Research Center for Intelligent Information Technology (KFKT2016B04).