Optimisation of convergence‐aware coded PDMA for 5G wireless systems
2018; Institution of Engineering and Technology; Volume: 13; Issue: 2 Linguagem: Inglês
10.1049/iet-com.2018.5429
ISSN1751-8636
AutoresJin Xu, Xueqin Han, Hanqing Ding, Zhigang Li, Zeqi Yu, Xiaoming Dai,
Tópico(s)Wireless Communication Networks Research
ResumoIET CommunicationsVolume 13, Issue 2 p. 243-250 Research ArticleFree Access Optimisation of convergence-aware coded PDMA for 5G wireless systems Jin Xu, Corresponding Author Jin Xu xujin@bupt.edu.cn School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorXueqin Han, Xueqin Han School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorHanqing Ding, Hanqing Ding School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorZhigang Li, Zhigang Li School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorZeqi Yu, Zeqi Yu School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorXiaoming Dai, Xiaoming Dai School of Computer and Communication Engineering, University of Science and Technology Beijing, No. 30, Xueyuan Road, Haidian District, Beijing, People's Republic of ChinaSearch for more papers by this author Jin Xu, Corresponding Author Jin Xu xujin@bupt.edu.cn School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorXueqin Han, Xueqin Han School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorHanqing Ding, Hanqing Ding School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorZhigang Li, Zhigang Li School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorZeqi Yu, Zeqi Yu School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 136, Kexue Road, Gaoxin District, Zhengzhou, People's Republic of ChinaSearch for more papers by this authorXiaoming Dai, Xiaoming Dai School of Computer and Communication Engineering, University of Science and Technology Beijing, No. 30, Xueyuan Road, Haidian District, Beijing, People's Republic of ChinaSearch for more papers by this author First published: 01 January 2019 https://doi.org/10.1049/iet-com.2018.5429Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Orthogonal frequency division multiplexing-based pattern division multiple access (PDMA) is considered as a promising multiple access scheme for future wireless communication systems due to its high spectral efficiency and powerful ability to support massive users. In this study, it is shown that two pattern matrices with unequal diversity gain in the PDMA system have better convergence performance compared with the signature matrices in a traditional low-density signature multiple access system by simulations and extrinsic information transfer (EXIT) chart analysis. For a low-density parity check (LDPC)-coded PDMA system, the EXIT characteristics between the front-end multiple-user detector (MUD) and the LDPC decoder may be mismatch, which usually leads to degraded performance when an iterative detection and decoding algorithm is used. To overcome this problem, a two-stage iterative optimisation algorithm, which is easy to implement is proposed to find an optimal (near optimal) degree distribution pair for the LDPC code. Both EXIT chart analysis and simulation results demonstrate that the proposed algorithm exhibits further performance gain compared with regular (3,6) LDPC-coded systems under both an additive white Gaussian noise channel and a Rayleigh fading channel. 1 Introduction Orthogonal multiple access (OMA) is widely adopted in current wireless communication systems due to the fact that a low complexity detection algorithm can be employed at the receiver. However, the OMA systems are facing the challenges of the rapid increase of mobile data growth and a huge number of access users [1, 2], such as in an internet of things scenario. Non-orthogonal transmission by squeezing more users to a limited number of time-frequency resource can provide both higher spectral efficiency and more user connections over the OMA scheme [3]. In [4], a typical non-orthogonal transmission scheme called multi-carrier code division multiple access (MC-CDMA) had been presented to support overloaded users where non-orthogonal spreading sequences are employed and successive interference cancellation algorithms are used at the receiver. Since all scheduled users collide in each resource element (RE), the optimal detection algorithm, such as the maximum-likelihood algorithm is infeasible when the number of users is large, which leads to a constrained application. To overcome this problem, in [5], an improved scheme called low-density signature multiple access (LDSMA) was proposed which employs a sparse spreading sequence at the transmitter side and a message passing-based detector at the receiver side to achieve a trade-off between complexity and performance. The sparse-spreading sequence can efficiently alleviate the inter-user interference of the non-orthogonal transmission system and decrease the computational complexity significantly over the MC-CDMA system [6]. However, for the LDSMA system, all spreading sequences are of the same number of non-zero elements, which is convenient for design but difficult to optimise for further performance improvement. In [7], we had proposed a convergence-aware non-orthogonal multiple access scheme called successive interference cancellation amenable multiple access, which was renamed pattern division multiple access (PDMA) to overcome this problem. The PDMA employs an irregular spreading sequence (with a different number of non-zeros in each spreading sequence) instead of a regular spreading sequence (with the same number of non-zeros in each spreading sequence) to accelerate the convergence of the message passing-based detector, and the proposed idea had been demonstrated by simulations. In this study, we analyse its convergence characteristic from the viewpoints of diversity order and extrinsic information transfer (EXIT) tool. For low-density parity check (LDPC)-coded PDMA systems [8], generally speaking, iterative detection and decoding (IDD) can improve the receiver performance significantly [9, 10]. However, the EXIT characteristics between the PDMA detector and the LDPC decoder may be mismatch, which leads to degraded performance [9]. In this study, to overcome this problem, we proposed a two-stage optimisation algorithm to optimise the LDPC degree distribution which therefore can match the EXIT charts of the above two components. In this way, the bit-error ratio (BER) performance of the LDPC-coded PDMA system can be further improved. In addition, the proposed optimisation algorithm is easy to implement. This paper is organised as follows: Section 2 gives a review of the PDMA system and analyses the convergence behaviour of the PDMA system with an EXIT chart tool. Section 3 is about the proposed two-stage optimisation algorithm and simulation results. Section 5 is the conclusion. 2 Review of PDMA Consider an uplink-coded PDMA system as shown in Fig. 1, which schedules users on physical REs, where both base stations and all users are equipped with a single antenna for simplicity. The channel-coded bits of each user are first multiplied with their user-specific sparse spreading sequence (named pattern sequence (PS) in the PDMA) and then modulated on REs. Assume that all users take their symbols on the same constellation set and have the same number of data symbols in each frame. As shown as dashed borders in Fig. 2, the PS of the ith user equipment corresponding to the ith column of the pattern matrix (PM). Assume that an user-specific PS has non-zero elements, then is defined as the effective spreading factor of this user. Similarly, denotes the number of symbols collide at a specific RE. We define two types of support sets, one is row support set and the other is column support set . The row support set denotes the subset of users that share the jth RE, and the column support set denotes the subset of the RE where the ith user is spread. Fig. 1Open in figure viewerPowerPoint Block diagram of PDMA system Fig. 2Open in figure viewerPowerPoint PMs for PDMA systems (a) PM , (b) PM At the receiver side, after performing orthogonal frequency division multiplexing demodulation, a baseband signal is delivered to believe propagation-based multiple-user detector (MUD). Furthermore, an IDD algorithm is used at the receiver side, which performs two kinds of iterative operations, one is the inner iterative operations within belief propagation-based MUD and the other is turbo-style processing between MUD and channel decoders. The received signal at the jth RE can be expressed as (1)where denotes the channel fading coefficient from the ith user to the jth RE, is the transmitted symbol of the ith user and , is the additive white Gaussian noise (AWGN) with mean zero and variance . The single user average bit signal-to-noise ratio is define as in [9] (2)where denotes the average symbol energy and each symbol carries m bits, denotes the single side power spectral density, denotes the channel coding rate. 2.1 PMs in PDMA systems For example, we had designed two convergence-aware PMs corresponding to 150 and overloaded cases in [7] for the PDMA systems, which are also shown in Fig. 2 in this paper. The overloading factor defined as the ratio of the number of users to the number of scheduled REs, i.e. [6]. Take PM for example, the first column of denotes the PS of user 1, thus user 1 spread over RE1 and RE2 for transmission. The second and last column of denote the PS of user 2 and user 3, respectively, while user 2 and user 3 spread their symbols and over RE1 and RE2, respectively. In addition, the diversity order (effective processing gain) of user 1, user 2, and user 3 are 2, 1, and 1, respectively. During the iterative detection process, user 1 can converge first and then assist user 2 and user 3 to converge. This is a prominent advantage of the PDMA over the LDSMA or other sparse code multiple access (SCMA) systems employing a regular PS. Generally speaking, the larger means the better diversity gain. However, the average row weight increases with the average column weight , which means stronger interference occurs and higher computational complexity. As a result, we need to trade-off between and computational complexity in practice. 2.2 Symbol-wise belief propagation-based MUD A PDMA system with users and REs can be depicted by a factor graph , where variable node and function node denote the transmitted symbol belongs to the ith user and the received signal on the jth RE, respectively. The connections between the received signals and the corresponding users are represented by edges [11, 12]. Fig. 3a shows the factor graph of PM and Fig. 3b denotes the corresponding tree graph. In this study, all belief information propagated on the graph is expressed in a log-likelihood ratio (LLR) manner. Fig. 3Open in figure viewerPowerPoint Factor graph of and extrinsic information passing processes (a) Factor graph of , (b) Tree graph of , (c) Extrinsic information from function node to variable node , (d) Extrinsic information from variable node to function node The task of the SWBP-based MUD is to calculate the soft output information to the channel decoder based on the channel observations and the a priori LLRs fed back from the channel decoders, where , denotes the constellation mapping. According to the turbo principles [13], to obtain , , in an iterative manner, we need to complete the algorithm as the following five steps: Step 1: For all i and j, if , calculate the extrinsic information from the function node to variable node during the nth iteration, as shown in Fig. 3c, according to (3) Where denotes the jth row of matrix , , , , , denotes the row support set except i, denotes a variable node set with indices belonging to . At the first iteration, i.e. , . Step 2: Similarly, for all i and j, if , calculate the extrinsic information from variable node to function node during the nth iteration as shown in Fig. 3d (4)where , denotes the column support set except j, denotes the variable node set with indices belonging to . Step 3: After performing step 1 and step 2 iteratively for rounds, the soft outputs are calculated at each variable node. For variable node , , , the extrinsic LLR can be written as (5) Step 4: After symbol-to-bit LLR conversion, the extrinsic LLRs of SWBP-based MUD will be sent to the channel decoders. Channel decoders output extrinsic information and feedback to SWBP-based MUD as a priori LLRs. Step 5: After performing the above four steps times, the channel decoders make a hard decision as the final output. 2.3 EXIT chart analysis of the proposed PM An extrinsic information transfer (EXIT) chart is a powerful tool to analyse the convergence behaviour of the IDD systems [14]. To draw the EXIT chart of the coded-PDMA system, the receiver is divided into two parts, one is the SWBP-based MUD, the other is the channel decoder. Let and denote the average mutual information (AMI) at the input of SWBP-MUD and channel decoder, respectively. Let and denote the AMI at the output of SWBP-MUD and channel decoder, respectively. To calculate for each , first, we need to model the a priori LLR whose AMI equal to as the output of an AWGN channel whose input belongs to the BPSK signal. Second, we perform Monte–Carlo simulation to calculate the output extrinsic LLR information, denote as Z. At last, we get the according to the output LLRs Z. As aforementioned, the a priori LLR can be modelled as (6)where and , . It is worth mentioning that the a priori LLRs may not be Gaussian, the reason that we still approximate it as Gaussian is that the output AMI is insensitive to the shape of the input LLRs. Define function as in paper [9], (7)where . The computer implementation of and the inverse function can be found in the Appendix of Paper [9]. So, if is given, we can obtain (8)Combining (8) into (6), we obtain the LLR . Then, by implementing the SWBP-based MUD algorithm conditioned on channel observations and a priori LLR , we can obtain the soft output extrinsic information Z. The AMI between the extrinsic LLRs Z and the transmitted bit X can be expressed as (9)where and denote the probability distribution functions of LLR Z conditioned that and respectively. Finally, we can obtain according to (9). Similarly, we can also obtain the EXIT of as a function of with the above method. In Fig. 4, the solid lines with markers denote the EXIT of the PM while the dashed lines denote the EXIT of in [6], respectively, conditioned on different . The solid line without marker denotes the EXIT chart of rate 0.5 turbo code according to the LTE standard [15]. We have the following conclusions: The EXIT curves of both and increase with . Furthermore, PM shows better performance over at the same all the time. At the right end of the EXIT, the performance of and coincides with each other due to the fact that the input AMI which means no multi-user interference. The EXIT chart of is flat due to that the tanner graph of is cycle-free. SWBP-MUD algorithm shows the same performance as maximum a posteriori algorithm (see Fig. 5). Fig. 4Open in figure viewerPowerPoint EXIT comparison between and , BPSK, AWGN Fig. 5Open in figure viewerPowerPoint Raw BER and BLER performance comparison between and in [6] 3 LDPC code optimisation for PDMA system As mentioned in the introduction, the EXIT mismatch between SWBP-based MUD and LDPC decodes may lead to degraded performance in the IDD system. Therefore, it is interesting to derive a valid algorithm to match these two component EXIT charts, which can, therefore, compensate the performance lose. For simplicity, in this study, we fix the PM and optimise the LDPC code. As we know, the BER performance of the LDPC code is mainly determined by its degree distribution [16]. As a result, the most important issue is to find an optimal or near optimal degree distribution for the LDPC codes. 3.1 Review of degree distribution of LDPC code The degree distribution polynomials of the LDPC code can be denoted as and , where coefficients and denote the fraction of edges in the graph connected to degree-p variable nodes and degree-q check nodes, respectively, and denote the maximum degree of variable nodes and check nodes, respectively. The code rate R can be written as follows [17, p. 79]: (10)where , for all p and q, and . 3.2 Joint factor graph and optimisation problem For an LDPC-coded PDMA system, the IDD receiver can be depicted by a joint factor graph [18]. Take an LDPC-coded PDMA system with PM for example, the corresponding jointfactor graph is shown in Fig. 6a. In this figure, , denotes a function node decoder (FND) ofthe MUD (MUD-FND), where the subscript b denotes thebth subblock and the subscript j denotesthe jth RE in the bth subblock. , denotes a variable node decoder (VND) ofthe MUD (MUD-VND), where the subscript b also denotes thebth subblock, the subscript i denotes theith user in the bth subblock. , denotes a VND of the LDPC code (LDPC-VND), while denotes a check node decoder (CND) of theLDPC codes (LDPC-CND), where . One point to note is that and are indeed the same node, i.e. . We denote them as two kinds of nodes onlyto facilitate the EXIT analysis. The EXIT processes during one outer iterationcan be summarised as follows: Conditioned on the channel observations and a prioriLLRs provided by the neighbouring MUD-VND, each MUD-FND calculatesthe extrinsic information which is then delivered to itsneighbouring MUD-VNDs. The extrinsic LLRs of each MUD-VND are delivered to the correspondingLDPC-VND transparently. Conditioned on the LLRs received from MUD-VND and LDPC-CND, eachLDPC-VND calculates the extrinsic information and delivered to itsneighbouring LDPC-CND. Each LDPC-CND calculates the extrinsic information and feed back toits neighbouring LDPC-VND. Each LDPC-VND calculates a posteriori informationand feed back to its neighbouring MUD-VND as apriori information. Fig. 6Open in figure viewerPowerPoint Joint factor graph and message passing of the receiver ofLDPC-coded PDMA system with PM (a) Joint factor graph of LDPC-codedPDMA with PM,(b) Module A and module B of thejoint factor graph, (c) EXIT of as a function of and , BPSK modulation, i.i.dRayleigh fading channel As aforementioned, the aim of the optimisation problem is to find an optimal (near optimal) degree distribution pair for the LDPC code with which the iterative receiver can converge to the lowest signal-to-noise ratio (SNR) for a prefixed target code rate . For simplicity of analyses, we divide the joint factor graph into two parts as module A and module B as shown in Fig. 6b [19]. The FND of module A in Fig. 6b corresponding to the combination of MUD-FND and MUD-VND in Fig. 6a, the VND and CND of module B in Fig. 6b corresponding to the LDPC-VND and LDPC-CND in Fig. 6a respectively. According to the analysis of Fig. 6a, the effective EXIT of module A with varying variable node degree is (11)where and are defined as in [9]. However, cannot be expressed in the closed form due to the nonlinearity of the SWBP-based MUD, thus we choose to obtain it by performing Monte–Carlo simulations. For example, under an i.i.d Rayleigh fading channel and PM, we obtain the EXIT of as a function of and as shown in Fig. 6c in the way as in Section 2.3. The expression of will be given later. It is shown in Fig. 6c that we draw four EXIT curves with from 0 to 3 dB, i.e. the interval is equal to 1 dB. In practice, we need to decrease the interval to 0.1 dB to improve the performance of the algorithm. In addition, we can obtain these EXIT charts offline, which can reduce the complexity of the optimisation algorithm proposed in the next subsection. Similarly, according to the analysis of Fig. 6a, the effective EXIT of module B with varying check node degree is (12)Moreover, according to Fig. 6a, the effective EXIT is (13)As mentioned before, is considered as a priori AMI for FNDs to get the during the Monte–Carlo simulations. Let and . Define cost function as follows [20]: (14) At a certain , if , the iterative receiver can converge, whereas it cannot converge if . As we know, under a certain code rate, the optimal pair can ensure the convergence, i.e. with the minimal , which is also called threshold SNR [9]. Additionally, it should be noted that the minimised threshold SNR under a certain code rate and the maximised code rate under a certain SNR are equivalent. Therefore, the task of degree distribution optimisation can be converted to solve the following optimisation problem: (15) In principle, at a certain , we can find an optimal distribution pair by solving (15) such that the achievable code rate maximised. However, as we can see, it is seems difficult to solve the optimisation problem (15) directly. To simplify the calculations, we turn to the proposed two-stage optimisation algorithm in the next subsection. 3.3 Proposed two-stage optimisation algorithm By the proposed two-stage iterative optimisation algorithm, (15) can be decomposed into two parts as shown in (16) and (17). The main idea is, we can iteratively optimise the degree distribution of one kind of node with that of the other kind of node being fixed. At a prefixed sufficiently large , at the first stage, we optimise the variable node degree distribution with the check node degree distribution fixed. The optimisation problem of this stage can be expressed as follows: (16)where be the largest variable node degree allowed, in this study, we choose a sufficiently large and reasonable number . In the second stage, we optimise the check node degree distribution conditioned on the updated variable node degree distribution. The optimisation problem of this stage can be expressed as (17)where is the largest check node degree allowed. In this study, we choose a sufficiently large and reasonable number . Linear programming problems (16) and (17) can be solved by Matlab software package [21]. We perform the above two steps rounds iteratively aiming at obtaining a near-optimal degree distribution pair. During the iterative processes, if the code rate R according to a degree distribution pair is larger than the target code rate , then we decrease by 0.1 dB, i.e. , and repeat the above two steps iteratively until . According to our experiment results, usually is sufficient to obtain the final result. 3.4 Some optimisation results and discussion For example, assume that the target code rate , the initial degree distribution pair , , i.e. a regular (3,6) LDPC, dB, and . With the proposed two-stage iterativeoptimisation algorithm, we obtain four degree distribution pairs of theoptimised LDPC codes as follows in different scenarios, and the correspondingEXITs are shown in Fig. 7. Code 1: Code 2: Code 3: Code 4: Fig. 7Open in figure viewerPowerPoint Comparison of EXIT charts between regular (3,6) LDPC-codedPDMAs and optimised LDPC-coded systems (a) EXIT of with regular (3,6) and code 1, respectively, under AWGN, (b) EXIT of with regular (3,6) and code 2, respectively, under AWGN, (c) EXIT of with regular (3,6) and code 3, respectively, under a fading channel,(d) EXIT of with regular (3,6) and code 4, respectively, under a fading channel For a comparison purpose, under the AWGN channel and i.i.d Rayleigh fading channel, the EXIT charts of the regular (3,6) LDPC-coded PDMA systems are also plotted in Fig. 7. In Fig. 7a, the threshold SNR () of the regular (3,6)-LDPC coded PDMA system with PM is 1.2 dB, whereas with an optimised LDPC code (code 1), the threshold SNR decreased to 0.7 dB. In other words, by optimising the degree distribution of the LDPC codes, there is 0.5 dB performance gain. Similarly, in Fig. 7b, for the PDMA system with PM, there is also about 0.5 dB performance gain by replacing the regular (3,6) LDPC with the optimised irregular LDPC code (code 2). Figs. 7c and d corresponding to the i.i.d Rayleigh fading channel, and their 0.6 and 0.8 dB performance gain with code 3 and code 4 compared with the regular (3,6) LDPC-coded system, which are larger than their AWGN counterparts, respectively. The LDPC codes designed for the non-IDD system, e.g. 802.16e, usually exhibit a poor performance in the IDD system due to that it cannot match the EXIT of the font-end detector, which, therefore, leads to the proposed optimisation algorithm. The performance gain shown above comes from the optimisation algorithm, which can efficiently match the EXIT curves of SWBP-based MUD and channel decoders. Table 1 gives the threshold SNRs of all considered cases predicted by the EXIT-based method. Table 1. Threshold SNRs for all cases, dB , AWGN , AWGN , fading fading regular (3,6) 1.2 1.9 3.3 3.5 WiMax-LDPC 0.7 1.7 2.8 3.0 optimised LDPC 0.7 1.4 2.7 2.7 3.5 BER simulation results In this subsection, BER performance is shown in Fig. 8 to verify the effective of the proposed EXIT chart-based two-stage optimisation algorithm. All LDPC codes employed are of rate 0.5 and code length bits. These codes are constructed by IT++ lib [22] and with girth 8. The number of outer iterations between SWBP-based MUD and LDPC decodes is set to in all cases. Furthermore, during each outer iteration, SWBP-based MUD performs iterations while each LDPC decoder performs 30 log-domain belief propagation iterations. In Fig. 8a, under the AWGN channel and BPSK modulation, compared with the regular (3,6) LDPC-coded systems with PM and PM, there are 0.3 dB and 0.4 dB BER performance gains when code 1 and code 2 are employed, respectively. In Fig. 8b, it is shown that for the i.i.d Rayleigh fading channel and BPSK modulation, compared with the regular (3,6) LDPC-coded PDMA system with PM and PM, there are 0.6 and 0.8 dB performance gain when code 3 and code 4 are employed, respectively. The numerical simulation results coincide with the EXIT chart-based analysis approximately, all cases considered achieve promising performance gain. Fig. 8Open in figure viewerPowerPoint BER performance comparison under AWGN channel (a) BER performance comparison under AWGN channel, (b) BER performance comparison under i.i.d Rayleigh fading channel 4 Conclusion PDMA systems with unequal diversity PSs exhibit convergence awareness. In this study, we have analysed the convergence behaviour of the PDMA systems with EXIT tools and numerical simulations. Then, we fixed the PM and optimised the LDPC degree distribution with the proposed two-stage optimisation algorithm. The overall performance is improved significantly. The proposed optimisation algorithm can also be extended to other coded systems, such as the SCMA and massive multiple-input multiple-output system. 5 Acknowledgments The works of Jin Xu and Hanqing Ding are supported by the Henan Province important project in Colleges and Universities (no. 18B510019) and the Henan Province Key Science and Technology Attack Plan Project (182102210610). The work of Xueqin Han was supported by the Henan Province Key Science and Technology Attack Plan Project (142102210080). The work of Zeqi Yu was supported by the National Natural Science Foundation of China (grant no. 61601411). References 1Dai L.L., Wang B.C., Yuan Y.F. et al.: ‘Non-orthogonal multiple access for 5G: solutions, challenges, opportunities, and future research trends’, IEEE Trans. Mag., 2015, 53, (9), pp. 74– 81 2Boccardi F., Heath R.W., Lozano A. et al.: ‘Five disruptive technology directions for 5G’, IEEE Trans. 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