RIePDMA and BPIDDIC detection
 Jie Zeng^{1, 2}Email author,
 Dan Kong^{3},
 Bei Liu^{3},
 Xin Su^{2} and
 Tiejun Lv^{1}
https://doi.org/10.1186/s1363801608013
© The Author(s) 2017
Received: 18 September 2016
Accepted: 19 December 2016
Published: 10 January 2017
Abstract
Pattern division multiple access (PDMA) is a nonorthogonal multiple access (NOMA) scheme which is proposed to meet the demand of massive connection in the future 5G communications. In this paper, we build a random interleaver (RI) enhanced PDMA (RIePDMA) system by bringing the random interleaver into a PDMA system to further improve the overload of PDMA. Furthermore, we analyze several integrated detection and decoding algorithms with interference cancellation (IC) and propose the iterative detection and decoding based on belief propagation and interference cancellation (BPIDDIC). Simulation results show that the proposed RIePDMA system can achieve better block error rate (BLER) performance without increasing the complexity of the receiver. Compared with several other integrated detection and decoding algorithms, the proposed BPIDDIC algorithm can get better BLER performance with an acceptable complexity.
Keywords
1 Introduction
Multiple access (MA) technology is important for wireless communication systems. It creates a connection between users and networks and allows multiple users to access and share resources simultaneously [1]. From 1G to 4G, MA techniques vary accompanying the evolution of wireless communication systems, including frequency division multiple access (FDMA), time division multiple access (TDMA), code division multiple access (CDMA), and orthogonal frequency division multiple access (OFDMA). In orthogonal multiple access (OMA) schemes, the radio resources allocated for different users are orthogonal either in time, frequency, or code domain to avoid or alleviate interuser interference. However, orthogonal resource allocation mechanisms limit the maximum number of supported users with the finite resources.
It is expected that the explosion of data traffic will happen in 5G era. Besides, 5G needs to support massive connectivity of users, due to the emergence of new traffic types and data services [2]. To satisfy these demands, some potential candidates have been proposed to address challenges of 5G, such as ultra dense network (UDN), massive multiple input multiple output (MIMO), device to device (D2D), NOMA, and so on. The major application scenarios for NOMA schemes in 5G systems included enhanced mobile broadband (eMBB), ultrareliable and lowlatency communications (URLLC), and massive machine type communication (mMTC) [3].
This paper focuses on the NOMA technology, which can improve the spectrum efficiency and accommodate massive connectivity. Different from the conventional OMA, NOMA allows multiple users to share time and frequency resources in the same spatial layer via nonorthogonal resource allocation [4]. Recently, more than 10 NOMA schemes are proposed for new radio (NR) in the contribution of the 3rd generation partnership project (3GPP) RAN1 #85 meeting [5], such as power domain nonorthogonal multiple access (PDNOMA), sparse code multiple access (SCMA), multiuser shared access (MUSA), PDMA, and so on. In PDNOMA, users’ signals are superimposed in power domain and transmitted in the same time/frequency resources [6]. Advanced receivers (e.g., successive interference cancellation (SIC) receivers) are used to separate users’ signals. Utilizing power domain superposition and advanced receivers, PDNOMA approaches the channel capacity bound of multiuser systems in both uplink and downlink channel. The PDNOMA can be used in conjunction with MIMO technology to further enhance the system spectral efficiency [7]. SCMA is a novel NOMA technology based on sparse codebooks [8]. The core ideas of SCMA are to accommodate more users with identical resources and increase the throughput of networks without affecting user experience, via nonorthogonal spreading and superposition. The authors in [9] proposed a unified framework for the joint design of multiuser codebooks based on multistage suboptimal approach. MUSA is based on the enhanced multicarrier CDMA scheme [10]. At the transmitter, modulated data symbols of each user are firstly spread by a specially designed sequence to facilitate certain SIC processing at the receiver. The design of spreading sequence is crucial to MUSA [11].
PDMA, evolving from SIC amenable multiple access (SAMA) [12], is based on the joint design of the transmitter and receiver to support massive connection [13]. It can achieve multiplexing and diversity gain by designing multiuser diversity pattern matrix. By utilizing multidomain sufficiently, PDMA enables wider application range, more flexible coding and decoding scheme, and lower processing complexity, compared with other NOMA technologies.
This paper will elaborate on our proposed RIePDMA system and BPIDDIC algorithm. The rest of the paper is organized as follows. In Section 2, we introduce the fundamental principle of PDMA and introduce the system model of the RIePDMA uplink system. Different detection algorithms, including maximum likelihood with IC (MLIC), minimum mean square error with IC (MMSEIC), iterative detection and decoding based on belief propagation (BPIDD), and our proposed BPIDDIC are illustrated in Section 3. Section 4 shows simulation results, together with the complexities analysis of those abovementioned algorithms. In Section 5, we discuss the possible future research directions in PDMA briefly. Finally, Section 6 concludes this paper.
2 System model
2.1 PDMA principle
PDMA is based on the joint design of the transmitter and the receiver. At the transmitter side, the nonorthogonal characteristic pattern based on the multiple signal domains (including time, frequency, and space domain) is used to distinguish the users. At the receiver side, the advanced multiuser detection algorithm is used to separate the multiuser signals [14].
In order to illustrate the concept of PDMA preferably, the characteristic pattern and PDMA pattern matrix are explained first. The characteristic pattern is a column vector containing binary elements 0 and 1. It shows the mapping method of users in resource blocks (RBs), where the element 1 denotes signals of the user are transmitted in the corresponding RB, while the element 0 means the opposite. The number of 1s in the characteristic pattern is defined as the transmission diversity order [15]. Assuming N RBs are available, therefore, there are 2^{ N }−1 different characteristic patterns (except the case that users are not transmitted in those RBs) to be chosen. Assuming K (the number of users multiplexing in these N RBs) is the column number determined by the overloading factor α, α=K/N. We can choose different K characteristic patterns out from the 2^{ N }−1 candidates to construct the PDMA pattern matrix H _{ P D M A }. The PDMA pattern matrix determines the user’s mapping method on RBs. It has a crucial impact on the performance of the PDMA system and the complexity of the detection algorithm. A good PDMA pattern matrix can reach better tradeoff among multiplexed users, diversity order, and detection complexity.
From the PDMA pattern matrix, the signal of user 1 is transmitted in all four RBs, the signals of user 2 and user 3 are transmitted in 3 RBs (the signal of user 2 is transmitted in RB 1, RB 2, and RB 3, the signal of user 3 is transmitted in RB 2, RB 3, and RB 4), and so on.

PDMA can get higher multiuser multiplexing and diversity gain via the nonorthogonal signals superposition transmission in time/frequency/ space/power domain.

PDMA can adopt lowcomplexity multiuser detection algorithms to realize high BLER performance because PDMA pattern matrix is relatively sparse.

PDMA can get coding gain and constellation shaping gain at the same time, by joint optimization design with modulation and channel coding.
2.2 System model of RIePDMA
In order to further improve the overload ability of PDMA, we propose bringing the RI into the PDMA system to form the RIePDMA system. Different from the uplink system of original PDMA, each user in a RIePDMA system is assigned to a unique interleaver after the channel encoder at the transmitter side. And the corresponding deinterleaver is used before the channel decoder at the receiver.
where H _{PDMA}(n,k) denotes the element at the nth line and the kth column of H _{PDMA}, h _{ n m,k } denotes the channel between the kth user and BS at the mth receiving antenna, and n _{nm} denotes the additive white Guassian noise in the nth RB at the mth receiving antenna. \(\hat {\{d\}}_{k}\) denotes the decoded information bits of user acquired by detector and decoder. In the following, we will introduce several integrated detection and decoding algorithms.
3 Integated detection and decoding
Compared with the traditional OMA technologies, PDMA provides more access points for users to support massive connections. However, it also brings crucial interuser interference problem. Therefore, we choose the advanced receiver for multiuser detection to solve it. Herein, we first analyze several integrated detection and decoding algorithms and then propose an iterative detection and decoding algorithm, called BPIDDIC.
3.1 MLIC and MMSEIC
3.2 BPIDD
BP detection algorithm
BP detection 

Step 1: Initialize the posterior probability values 
\(v_{ji}(s)=1/\sqrt {M}\) 
Step 2: Iterative message passing along edges 
a) The messages passed from the i ^{ t h } FN to the j ^{ t h } VN 
\(a_{ij}(s)= \frac {1}{\sigma _{ij}\sqrt {2\pi }}\exp {(\frac {(y_{i}u_{ij}h_{ij}s)^{2}}{2\sigma _{ij}^{2}})}\) 
b)The message passed from the j ^{ t h } VN to the i ^{ t h } FN 
\(v_{ji}(s)=\prod _{l=1,l\neq i}^{N} a_{lj}(s)\) 
where u _{ ij } and σ _{ ij } denote the mean and variance of the interference, 
respectively. 
Step 3 LLR output of the j ^{ t h } VN after the iteration 
\(LLR_{j}=\log (P_{x_{j}}(s)/P_{x_{j}}(s_{0}))\) 
where \(P_{x_{j}}(s)\) denotes the probability of the symbol s, s _{0} means the 
symbol corresponding to 0. 
In the BP algorithm, all possible transmitted symbols are considered to be equal possibility, i.e., there is no prior information. If BP detector can get the prior information before the iterations, the BLER performance of BP algorithm can be improved. For BPIDD, the prior information of the BP detector is provided by the channel decoder. The block diagram of BPIDD is shown in Fig. 3 b. In our case, we choose turbo code for channel encoding. The turbo decoder outputs bit level soft information. The soft information is transmitted to BP detector as the prior information by turbo recoding at probability domain. By iterating the prior information between BP detector and turbo decoder, the BLER of BP detector will be reduced.
3.3 BPIDDIC
To reduce the complexity and improve the BLER performance of BPIDD, we implement IC technique and CRC module into BPIDD and bring out selfadaptive BPIDDIC.
Since some of the PDMA patterns are sparse, the complexity of BP is reduced and the convergence of iteration is guaranteed. Moreover, with the implementation of CRC module, our receiver scheme becomes selfadaptive. The number of iterations can be reduced, especially in high signaltonoise ratio (SNR) region, and will not affect the BLER performance of the receiver. With the implementation of IC technology, the correctly decoded information can be canceled, and the interuser interference will be reduced. Therefore, the BLER performance can be improved.
4 Simulation results and analysis
4.1 Performance analysis
Simulation parameters
Parameter  Value 

Carrier frequency  2 GHz 
Length of information bits  432 bits 
System bandwidth  10MHz 
Modulation coding rate  QPSK; 1/2 Turbo 
Carrier modulation  OFDM 
Antenna configuration  1Tx;2Rx 
Channel model  Uma 
Channel estimation  Ideal 
Overloading factor  150%; 200%; 300% 
Number of BP iterations  4 
4.2 Complexity analysis
Time consumption of several integrated detection and decoding algorithms (unit: s)
SNR(dB)  −2  0  2  4  6  8 

MLIC  97,875  97,991  99,837  97,755  97,717  96,947 
MMSEIC  2386  2394  2400  2422  2425  2425 
BPIDD  28,508  27,471  27,838  27,577  29,760  28,278 
BPIDDIC  31,055  29,642  20,911  12,919  9091  8145 
5 Future research
Based on our current exploration and consideration, the further research can be conducted from the following possible directions.
5.1 Power domain pattern design
In the current studies, the PDMA pattern only consists 0 or 1 elements, which leaves out the effect of the amplitude and the phase. The joint design of the amplitude and the phase, called the power domain pattern design, will be studied in future research.
5.2 Space domain pattern design
The space domain pattern design can be explained as the combination of PDMA and MIMO. Specially, the quasiorthogonal spacetime block code (QOSTBC) in space domain can be adopted when designing the PDMA pattern. And the ordered successive interference cancellation (OSIC) can be used at the receiver side to improve the overall performance of system. And the pattern design with joint QOSTBC scheme in space domain and power allocation in power domain will be studied in the future work.
6 Conclusions
PDMA technology is of vital importance as a candidate multiple access technology in future 5G wireless communication system. In this paper, RIePDMA is firstly proposed in PDMA uplink system to further improve the overload ability and the BLER performance of PDMA. We evaluate the BLER performance of the proposed RIePDMA and BPIDDIC with the linklevel simulation. The simulation results show that the proposed RIePDMA scheme can obviously improve the BLER performance without increasing the complexity of the receiver remarkably. The higher the overload is, the greater BLER performance gains RIePDMA can get. At the same time the proposed BPIDDIC can get better BLER performance with an acceptable complexity increment of the receiver.
Declarations
Acknowledgements
This work was supported by the China’s 973 project (No. 2012CB31600), the China’s 863 Project (No. 2015AA01A709), the National S&T Major Project (No. 2016ZX03001017), Science and Technology Program of Beijing (No. D151100000115003), S&T Cooperation Projects (No. 2015DFT10160B), and by State Key Laboratory of Wireless Mobile Communications, China Academy of Telecommunications Technology (CATT), and by BUPTSICE Excellent Graduate Students Innovation Fund.
Authors’ contributions
The work presented in this paper corresponds to a collaborative development by all authors. JZ defined the research line, guided and organized the study, and wrote the paper. DK and BL detailed some parts of the paper. XS and TL gave many modification suggestion about the paper. All authors have read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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