Non-Orthogonal Multiple Access in Overloaded Multi

Non-Orthogonal Multiple Access in Overloaded Multi-Carriers Systems Using SCMA

by

Su Pyae Sone

A special study submitted in partial fulfillment of the requirements for the degree of Master of Engineering in Telecommunications

Examination Committee:

Dr. Dr. Dr. Dr.

Attaphongse Taparugssanagorn (Chairperson) Poompat Saengudomlert (Co-chairperson) Teerapat Sanguankotchakorn Matthew Dailey

Nationality: Myanmar Previous Degree: Bachelor of Science in Engineering in Information and Communication Technology Asian Institute of Technology Myanmar Scholarship Donor:

AIT fellowship

Asian Institute of Technology School of Engineering and Technology Thailand September 2017

Acknowledgment Firstly, I would like to thank my advisers, Dr. Poompat Saengudomlert and Dr. Attaphonse Taparugssanagorn for their continuous support for this study. This study would have been impossible without their guidance, patience and steering in the right direction. I am also very grateful to have my committee members, Dr. Teerapat Sanguankotchakorn and Dr. Matthew Dailey and thank for their comments and suggestions. I would also like to thank Mrs. Premma Rao, administrative secretary of telecommunication department in AIT for her great help during this study. Finally, I would like to thank to my family, friends and everyone who help and support throughout the whole study.

ii

Abstract Sparse code multiple access (SCMA) is a code domain non-orthogonal multiple access technique introduced for dense-user network like 5G. This study describes the basics of an SCMA scheme using codebook from (Klimen & Sergien,2017), 150% overloading and minimum-distance criterion for separate detection and joint detection. The number of active users in an SCMA system is controlled by a probability value which can be varied. Discretetime deterministic channel is used in this study. The BER performance of an SCMA system is also compared with a multi-carrier multiple access called OFDMA which is widely used in wireless communication these days. According the results of this study, SCMA can be used as a multi-carrier multiple access in overloaded systems by trading off the BER performance and number of supportable users. The behaviors of users in SCMA system are changing according to the number of active users in the system. Keywords: sparse code multiple access, orthogonal frequency division multiple access, nonorthogonal multiple access, overloaded system, multi-carrier multiplexing, separate detection, joint detection, bit error rate

iii

Table of Contents Chapter

Title

Page

Title Page Acknowledgment Abstract Table of Contents List of Figures List of Tables List of Abbreviations List of Symbols 1

2

Introduction

1

1.1 1.2 1.3 1.4 1.5

1 2 2 3 3

4

5

Background Information Problem Statement Objectives Scope and Limitations Organization of the Report

Literature Review 2.1 2.2 2.3 2.4 2.5 2.6 2.7

3

i ii iii iv v vi vii ix

4

Overview of Multiplexing in Multi-Carrier Communication OFDM and OFDMA MC-CDMA SC-FDMA LDS SCMA Previous works on SCMA

4 4 7 7 8 8 12

Methodology

15

3.1 System Design Overview 3.2 Simulation and Parameters 3.3 Performance Evaluation

15 17 18

Simulation Results and Discussions

20

4.1 4.2 4.3 4.4 4.5

20 21 22 24 25

BER Performance of OFDMA BER Performance of SCMA with Separate Detection BER Performance of SCMA with Joint Detection Special Cases of SCMA with Joint Detection Summary

Conclusions and Recommendations

27

5.1 Conclusion 5.2 Future Work

27 27

References

28 iv

List of Figures Figure 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 3.1 3.2 3.3 4.1 4.2 4.3 4.4 4.5 4.6 4.7

Title

Page

(a) conventional multi-carrier technique and (b) OFDM (Nee & Prasad,2000) OFDMA with IFFT/FFT simulation implementation (a) OFDM and (b) OFDMA adapted from (Asif,2010) MC-CDMA simulation structure based on OFDM SC-FDMA structure based on OFDM Example of an indicator matrix F with 16 users and 12 subcarriers (Hoshyar, Wathan, & Tafazolli,2008) LDS structure based on OFDM Block diagram of SCMA simulation structure Multiplexing of codewords from SCMA codebooks (Au et al.,2014) 11 Two mother constellations by using shuffling method (Taherzadeh, Nikopour, Bayesteh, & Baligh,2014) Example of factor graph with K = 2 and N = 4, circles represent variable nodes and squares represent factor nodes. An example of 4-QAM constellation diagram (Klimen Sergien,2017) Cyclic prefix between data block in channel output (Goldsmith,2005) Discrete-time deterministic channel used in this study The average BERs of individual users and the average BER of all users in OFDMA The average BERs of individual users in SCMA with separate detection The average BERs with different numbers of active users in SCMA with joint detection Difference between joint detection and separate detection The average BERs of User 5 and User 6, and the average BER of all active users The special case of the average BER of all active users with active probability equal to 0.5 The special case of the average BER of User 1 and User 3 in SCMA

v

5 5 6 7 8 9 9 10

12 13 15 16 16 20 21 22 23 24 25 26

List of Tables Table 2.1 3.1 3.2

Title

Page

Previous works using SCMA system System parameters Simulation Scenarios

vi

14 18 19

List of Abbreviations 4G

Fourth generation

5G

Fifth generation

AWGN

Additive white Gaussian noise

BER

Bit error rate

CDMA

Code division multiple access

CIR

Channel impulse response

DFT

Discrete Fourier transform

DS-CDMA

Direct sequence CDMA

DSL

Digital subscriber line

FDM

Frequency division multiplexing

FDMA

Frequency division multiple access

FFT

Fast Fourier transform

IDFT

Inverse discrete Fourier transform

IFFT

Inverse Fast Fourier transform

IoT

Internet of things

ISI

Inter-symbol interference

LDS

Low density signature

MA

Multiple access

MAI

Multiple access interference

MC-CDMA

Multi-carrier CDMA

MPA

Message passing algorithm

MT-CDMA

Multi-tone CDMA

NOMA

Non-orthogonal multiple access

OFDM

Orthogonal frequency division multiplexing

vii

OFDMA

Orthogonal frequency division multiple access

PAPR

Peak-to-average power ratio

PDF

Probability density function

QAM

Quadrature amplitude modulation

SC-FDMA

Single carrier FDMA

SCMA

Sparse code multiple access

SNR

Signal-to-noise ratio

SoDeMA

Software defined multiple acces

TDM

Time division multiplexing

TDMA

Time division multiple access

UDN

Ultra-dense network

viii

List of Symbols λ

Overloading factor

Cj

Constellation set for User j

CBn

Codebook of User j

CP

Length of cyclic prefix

df

Total number of Users contributing to Sub-channels

dfi

Total number of Users contributing to ith Sub-channel

F

Factor graph matrix

fj

Connection indication vector of jth User node

gi

Constellation function

h

Discrete-time deterministic CIR

hj

CIR of jth Sub-channel

J

Number of Users

K

Number of Sub-carriers for each SCMA User

Ln

Set of User nodes connected to function nodes

M

Number of codewords in each codebook

n

AWGN noise vector

N

Number of Sub-carriers

P

Probability value of active Users

S

Number of symbols per Users

Vj

Mapping matrix

xj

Codeword of jth User

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Chapter 1 Introduction 1.1

Background Information

The main problem in wireless communications is radio spectrum limitations. Despite the spectrum limitation more and more users use wireless communication these days with the help of multiplexing and multiple access techniques. Multiplexing plays an important role in communications to combine multiple signals into one signal that can be transmitted through the air. Multiple access techniques allow a large number of users to share the allocated spectrum in the most efficient manner by extending the multiplexing techniques and do not degrade the quality of service by much. As stated in (Sklar,2001), there are three major following multiple access (MA) techniques: frequency division multiple access (FDMA), time division multiple access (TDMA), and code division multiple access (CDMA). Each of the fundamental multiple access techniques has some advantages and disadvantages. Moreover, people try to use different types of MA by mixing these three major MA techniques. According to (Weinstein,2009), orthogonal frequency division multiplexing (OFDM) was created to overcome the difficulties of frequency division multiplexing (FDM) and time division multiplexing (TDM). Later, OFDM is widely used in wideband digital communications, such as digital television and audio broadcasting, digital subscriber line (DSL), Internet access, wireless networks, powerline networks, and the fourth generation (4G) mobile communications. Orthogonal frequency division multiple access (OFDMA) is the multi-user version of OFDM. In OFDMA, one user can be supported by at least one sub-carrier of OFDM all the time. Consequently, a lot of sub-carriers are needed to support large number of users. As a disadvantage, an OFDMA signal has a large peak-to-average power ratio (PAPR) that would make the implementation cost high for many users. Since people nowadays are very much interested in Internet of Things (IoT), the fifth generation (5G) mobile networks with ultra-dense network (UDN) requirement that can support many users are needed. Since not all users in the network will be active all the time, using OFDMA in this kind of network is not efficient. Therefore, many researchers have been trying to find new ways to overload the users in the communication network, which refers to allowing more users than the number of sub-carriers, by modifying the multiple access techniques. Once the overloading is applied, the multiple access is no longer orthogonal. Several researchers prefer to use non-orthogonal multiple access (NOMA) over OFDMA. In (Dai et al.,2015), NOMA is divided into two main groups, i.e., power-domain multiplexing and code-domain multiplexing. Different kinds of NOMA include multiple access with low-density spreading (LDS), sparse code multiple access (SCMA), multi-user shared access and pattern division multiple access that can be a good candidate for IoT in 5G wireless communications. SCMA is popular among the different kinds of NOMA because of its dense user supportability, high reliability, and shaping gain. SCMA can be seen like a combination of multi-carrier CDMA (MC-CDMA), which spreads the quadrature amplitude modulation (QAM) symbols over OFDMA tones by using spreading sequence, and LDS, which is a version of MC-CDMA with low density spreading sequences (Nikopour & Baligh,2013). The distinct feature of SCMA is the procedure of QAM and low density spreading sequences like in LDS are combined together and the bits are directly mapped to 1

codewords of the SCMA codebook set. There are three main following parts in SCMA: codebook design, overloading factor, and detection algorithm. For a codebook set, multidimensional constellation with rotations are created as an optimization problem and shaping gain is achieved from the corresponding codebook design. This is the one main reason of having better improvement in comparison to LDS. The performances of SCMA are different according to different overloading factors that can be seen in (Wu, Zhang, & Chen,2015). However, the detection for SCMA scheme is more complex than others. But using message passing algorithm (MPA) instead of traditional minimum distance detection provides low complexity and near-optimal detection results. From the above facts, SCMA becomes an interesting non-orthogonal multiple access techniques in dense or even ultra-dense communication networks for IoT and 5G wireless networks.

1.2

Problem Statement

SCMA is popular for an overloaded multi-carrier system while OFDMA is popular for having good bit error performance because of its orthogonality in wireless communications. If the system is overloaded, its bit error performance will not be as good as a non-overloaded orthogonal system. However, SCMA has a shaping gain from the codebook design that OFDMA does not have. We can do a trade-off the between number of users that can be supported and the bit error performance. Therefore, SCMA and OFDMA can be compared in average bit error rate, and simulations are needed to find out how much they are different. On the other hand, MPA for detection in SCMA is only needed for a relatively large number of users. For a small number of users, minimum distance decision can still be used. For each user, the difference between separate detection and joint detection will be demonstrated for the basic understanding of detection in SCMA before using MPA.

1.3

Objectives

The main objective of this study is to study the basics of SCMA by comparing it with OFDMA. The sub-objectives of this study can be stated as follows: • To build the simulation program of OFDMA by using MATLAB that plots the average bit error rate of all users; • To build the simulation program of SCMA with separate detection of user data symbols by using MATLAB that plots the average bit error rate of each user; • To build the simulation program of SCMA with joint detection of user data symbols by using MATLAB that plots the average bit error rate of all users; • To compare OFDMA with all users active all the time to SCMA with a random number of active users while joint detection is used; • To compare SCMA with separate user detection and with joint detection of user data symbols.

2

1.4

Scope and Limitations

The scope of this study will cover SCMA which is implemented based on the OFDMA scheme by adding codebook mapping and codeword detection. For OFDMA, the scheme will include cyclic prefix and one tap equalization. The channel model should be a realistic one but it is assumed to be discrete-time deterministic channel model in the case of simplicity. Only MATLAB software is used to do simulation experiments. The number of sub-carriers should be flexible but the one used in this study is exactly four because of the limitation in codebook design from (Klimen & Sergien,2017). In SCMA, at least one user will be active all the time even though the numbers of active user is generated randomly with some specific probability. MPA detector should be used for near-optimal low complexity detection but only minimum distance detection is used instead of MPA since only four sub-carriers are used.

1.5

Organization of the Report

This report is organized as follows. The background information of multiple access and SCMA is described in Chapter 1. Chapter 2 dedicates to the review of multiplexing techniques, OFDM, OFDMA, SC-FDMA, MC-CDMA, SCMA, and the existing relevant literatures. The methodology is explained in Chapter 3. The simulation results are reported and analyzed in Chapter 4. In this chapter, we draw conclusions from these evaluations. Finally, in Chapter 5, we conclude the work and discuss the future work that can be extended from this study.

3

Chapter 2 Literature Review 2.1

Overview of Multiplexing in Multi-Carrier Communication

The main motivation to develop multi-carrier system is to overcome fading or interference which can cause the entire communication link to fail in a single carrier system. Before OFDM, people tried to use parallel data transmissions by using conventional nonoverlapping multi-carrier technique which has an inefficient use of spectrum. When researchers found out how to exploit orthogonality, multi-carrier system, e.g., OFDM results in lower spectrum efficiency and more robustness to severe channels as explained in (Nee & Prasad,2000). Later, MC-CDMA was proposed in (Yee, Linnartz, & Fettweis,1994) for indoor wireless radio environment. MC-CDMA can support more capacity than OFDMA and it is also orthogonal as in OFDMA. However, in mobile communications, using OFDMA and MCCDMA in downlink has no problem since base stations have large power sources, but in uplink, there is a problem with limited power sources of mobile phones. Therefore, the research (Myung, Lim, & Goodman,2006b) showed that single-carrier (SC) FDMA is a promising technique for high data rate uplink communication in a cellular system. Moreover, the authors of (Myung, Lim, & Goodman,2006a) proved that SC-FDMA has lower PAPR than OFDMA and it is widely used in 4th generation mobile network. In orthogonal multiple access, the signal dimension is partitioned and allocated exclusively to users so that there is no multiple access interference (MAI). However, in nonorthogonal multiple access (NOMA), all the users share the entire dimension and there is MAI. To overcome MAI in NOMA researchers tried to create low density signature to reduce MAI effect in NOMA (Mohammed, Imran, Tafazolli, & Chen,2012). For IoT in 5G wireless communications, researchers combined the large capacity supportability of MCCDMA and low MAI effect from LDS to propose non-orthogonal sparse code multiple access (SCMA) in (Nikopour & Baligh,2013).

2.2

OFDM and OFDMA

OFDM is the special case of multi-carrier transmission where a single signal is transmitted by adding lower rate sub-carriers. It can be seen as either a modulation technique or a multiplexing technique. One main advantage of OFDM is its robustness against frequency selective fading or narrowband interference. In addition, it is possible to save bandwidth by overlapping channels without carrier interference because of its orthogonality. Figure 2.1 shows the difference between conventional multi-carrier technique and OFDM. First, researchers created OFDM in continuous time systems and it was very difficult to implement at that time. Later, its implementation in discrete time system is done using discrete time Fourier transform (DFT) and inverse discrete time Fourier transform (IDFT).

4

The N-point DFT of x[n] is defined as 1 N−1 2πni ), 0 ≤ i ≤ N − 1. DFT{x[n]} = X[i] , √ ∑ x[n]exp(− j N N n=0

(2.1)

The sequence x[n] can be recovered from its DFT using IDFT: 2πni 1 N−1 IDFT{X[i]} = x[n] , √ ∑ X[i]exp( j ), 0 ≤ i ≤ N − 1. N N i=0

(2.2)

Figure 2.1: (a) conventional multi-carrier technique and (b) OFDM (Nee & Prasad,2000)

Figure 2.2: OFDMA with IFFT/FFT simulation implementation

5

To reduce the mathematical operations in hardware, the DFT and IDFT can be performed using the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). When data x[n] is transmitted through a linear time-invariant discrete-time channel h[n], the output y[n] is the discrete-time convolution of x[n] and h[n]. It is equivalent to the IDFT of the multiplication of X[i] and H[i]. Due to the periodicity of the signal, the multiplication in the frequency domain equals to circular convolution in the time domain. Since actual channel output is not circular convolution, a special prefix called cyclic prefix can be added to the input to get circular convolution. In continuous time, adding cyclic prefix is equivalent to using a guard band after every block of N symbols to eliminate the inter-symbol interference (ISI) between these data blocks. Then, taking the DFT of channel output in the absence of noise yield Y [i] = DFT{y[n] = x[n] ⊗ h[n]} = X[i]H[i], 0 ≤ i ≤ N − 1.

(2.3)

The sequence X[i] can be recovered from the channel output Y [i] for known H[i] by ˆ = Y [i]/H[i], 0 ≤ i ≤ N − 1. X[i]

(2.4)

This process is called one-tap equalization. The simulation block diagram of OFDM using FFT and IFFT is depicted in Figure 2.2. The input to IFFT are the QAM symbols X[0], ..., X[N − 1] and the output are the OFDM signal x[0], ..., x[N − 1]. All of the theory are explained in (Goldsmith,2005). One main challenge in OFDM is high peak-to-average power ratio (PAPR). A low PAPR lets the transmit power amplifier to operate efficiently, whereas a high PAPR makes the transmit power amplifier to have a large back-off to avoid signal distortion. OFDM is also sensitive to frequency offset and timing offset degrading the orthogonality of the sub-channels. OFDMA is the more advanced form of OFDM. In OFDM, users can be allocated in time domain only. But OFDMA can allocate users in both time and frequency domain. Also it can be seen like an extension of OFDM by providing each user with a fraction of the available number of sub-carriers as explained in (Nee & Prasad,2000). Figure 2.3 shows different user allocations between OFDM and OFDMA.

Figure 2.3: (a) OFDM and (b) OFDMA adapted from (Asif,2010)

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2.3

MC-CDMA

There are many types of multiple access schemes based on CDMA, such as direct sequence CDMA (DS-CDMA), multi-carrier CDMA (MC-CDMA) and multi-tone CDMA (MT-CDMA). Among them, MC-CDMA is widely used because the work in (Hara & Prasad,1997) proved that it has the best BER performance. MC-CDMA is the combination of frequency domain spreading and OFDM. Its transmitter spreads the original data stream over different sub-carriers using a given spreading code in the frequency domain. Most researchers use the Hadamard Walsh codes which is an optimum orthogonal set as described in (Hara & Prasad,1997). Each QAM symbol of each user has to pass through the spreader and the duplicated symbols at each sub-channel are added together before passing through the IFFT block. The rest of the process are based on OFDM. MC-CDMA can support a large capacity and it is mainly used in downlink of mobile radio communication. Figure 2.4 shows the simulation structure of MC-CDMA based on OFDM.

Figure 2.4: MC-CDMA simulation structure based on OFDM

2.4

SC-FDMA

SC-FDMA was proposed to overcome the high PAPR problem in OFDM and is widely used for uplink wireless transmission (Myung et al.,2006b) . In OFDM, the transmitted data is transformed using N-point IFFT and the PAPR is proportional to N. The idea of SC-FDMA is to add M-point FFT block before N-point IFFT of the OFDM system as shown in figure 2.5. Usually, M is chosen to be much smaller than N so that FFT partially cancels the final IFFT, 7

resulting in a single carrier type of signal with a low PAPR (Myung et al.,2006a). In SCFDMA, one extra block called sub-carrier mapping is added to get a connection between Mpoint and N-point computational blocks. There are basically two ways to map the M symbols to N symbols: using M consecutive sub-carriers of N-point IFFT and zero-padding the other ones, which is called localized SC-FDMA, and distributing the sub-carriers evenly and again adding zeros for unused ones, which is called distributed SC-FDMA (Myung,2007).

Figure 2.5: SC-FDMA structure based on OFDM

2.5

LDS

In orthogonal multiple access, ISI or MAI is inevitable due to degradation in orthogonality once the system is overloaded. The performance can be improved in an overloaded system by mitigating the interference. The paper (Hoshyar, Wathan, & Tafazolli,2008) stated that significant effort to reduce ISI or MAI in a non-orthogonal multiple access is spreading strategy. The input symbols of each user are spread out by unique interleaving spreading sequences. This spreading procedure can be represented by an indicator matrix F as shown in Figure 2.6. Rows of F denote the number of users and 1’s in each column of F denote the set of sub-carriers that each user uses. Figure 2.7 shows the simulation structure of LDS.

2.6

SCMA

The new scheme called SCMA was proposed in (Nikopour & Baligh,2013) and is similar to LDS but has a better performance. In SCMA, the incoming bits are directly mapped into multidimensional codewords from a codebook of each user which are created by combining 8

Figure 2.6: Example of an indicator matrix F with 16 users and 12 sub-carriers (Hoshyar,

Wathan, & Tafazolli,2008) QAM mapping block and low density spreading block from LDS. It can be an overloaded as in LDS, and has one main advantage in terms of the multidimensional constellation shaping gain of a codebook set.

Figure 2.7: LDS structure based on OFDM

2.6.1

SCMA System Overview

An SCMA system contains J users indexed by j = 1, ..., J. There are in total N sub-carriers and K non-zero sub-carriers that each user uses. For high level of sparsity, K should be much smaller than N. The constellation function g j generates the constellation set C j with M alphabets where log2 (M) is equal to the number of bits per symbol. The mapping matrix V j maps the K-dimensional constellation points to SCMA codewords to form the codebook set. The received signal from the SCMA transmitter can be expressed as

9

J

y=

∑ diag(h j )x j + n,

j=1

(2.5)

J

=

∑ diag(h j )V j g j (b j ) + n,

j=1

where b j is the bits of user j, x j = (x1 j , ..., xK j )T is the codeword of the user j, h j = (h1 j , ..., hK j )T is the channel vector of user j ,and n ∼ C N (0, N0 I) is the ambient noise. The simulation block diagram of an SCMA system can be seen in Figure 2.8. The overloading factor of an SCMA system can be defined as λ := J/N. The literature (Wu et al.,2015) stated that SCMA can work well in highly overloaded scenarios, and the performance will not much degrade even if it is 300% loaded by using iterative multi-user receivers.

Figure 2.8: Block diagram of SCMA simulation structure

2.6.2

SCMA Codebook Design

The SCMA codebook is the most important part in an SCMA system because it provides different shaping gains according to the different designs. An SCMA encoder is defined as a mapping from log2 (M) bits to a K-dimensional complex codebook of size M. Sparsity of the codebook can manage the complexity of the MPA detector. Figure 2.9 from (Au et al.,2014) shows the multiplexing of different codewords of each user from an SCMA codebook having N = 4, K = 2 and J = 6. There are researchers trying to design the optimal codebook (Cai, Fan, Lei, Liu, & Chen,2016), (Taherzadeh, Nikopour, Bayesteh, & Baligh,2014), (Metkarunchit,2017) and (Zhou, Yu, Meng, & Li,2017). SCMA codebooks are mostly designed based on the principles of lattice constellations. 10

Figure 2.9: Multiplexing of codewords from SCMA codebooks (Au et al.,2014)

Constellation rotation is one simple method to construct a codebook. A reasonable power variation with the same minimum Euclidean distance can be achieved by a unitary rotation. It can also control dimensional dependency of a base constellation which helps the decoder to get the correct data in an easier way even in fading environments. Another method is shuffling of real parts and imaginary parts of two different base constellations. For example, let a symbol contain 4 bits and draw the constellation diagram of first 2 bits and last 2 bits as the two base constellations. Then, real parts of first and imaginary parts of second constellations are shuffled to get a mother constellation. In Figure 2.10, 16-points SCMA constellation by using shuffling method can be seen.

2.6.3

Factor Graph Representation

A factor graph is used to represent the factorization of a probability distribution function (PDF) for computing the corresponding marginal distribution through the message passing algorithm. It has two types of nodes, namely variable nodes representing the number of users and function nodes representing the number of sub-carriers. The total number of users contributing to a sub-channel is determined by J

d f = (d f 1 , ..., d f n )T =

∑ f j,

(2.6)

j=1

where d f i is the number of users contributing to ith sub-channel and d f i = d f in a symmetric factor graph. The factor graph matrix is then written as F = (f1 , ..., f j ), where f j are the binary indicator vectors, and the set of user nodes connected to function nodes is defined as Ln = { j|(F)n j = 1, ∀ j}, ∀n. 11

(2.7)

Figure 2.10: Two mother constellations by using shuffling method (Taherzadeh, Nikopour,

Bayesteh, & Baligh,2014) Based on the factor graph, the received signal from the SCMA transmitter is rewritten as yn =

∑ hn j xn j + nn, ∀n.

(2.8)

j∈Ln

Therefore, the complexity of detection is reduced from M J to M d f by using MPA which calculates the marginal distribution for each unobserved node, conditional on any observed nodes. An example of a factor graph drawn according to the factor graph matrix F is shown in Figure 2.11.

2.7

Previous works on SCMA

According to Table 2.1, SCMA was introduced in Papers 1 and 2. The reasons why SCMA has become popular and the possible usages of SCMA in future 5G wireless networks are summarized in Papers 3, 4, 5, and 6. On the other hand, in Paper 7, SCMA was not used mainly because of its disadvantage, high complexity and limitations on codebook. Therefore, in this special study, we will examine the performance of SCMA by comparing to OFDMA in terms of bit error performance to see whether it is worth replacing OFDMA or not. In Paper 8, SCMA was applied on AWGN channels and Rayleigh channels. In this study, we apply SCMA on a discrete time deterministic channel as a starting point. Maximum likelihood detection is used instead of MPA detection since only four subchannels are considered in this study. To the best of our knowledge, no report that compares separate detection for each user and joint detection for each user in SCMA system is avail12

Figure 2.11: Example of factor graph with K = 2 and N = 4, circles represent variable nodes

and squares represent factor nodes. able. Therefore, this study, investigates the difference between separate and joint detection of data symbols.

13

Table 2.1: Previous works using SCMA system

No. Author

Paper Discussion

1

SCMA is proposed as a new multiple access scheme. (Nikopour & Baligh,2013) System model overview , basic method for codebook design and MPA receiver are described. Compare SCMA and LDS for N=4, J=6.

2

(Taherzadeh et al.,2014)

A systematic approach to design SCMA codebook based on principles of lattice constellations. Rotations and shuffling of constellations are described.

3

(Bockelmann et al.,2016)

To solve massive user problem in 5G, described SCMA as one of the solutions. Discussed bout 150% overloading with N=4.

4

(Chen et al.,2016)

Showed designs and application examples that SCMA can resolve four major issues of current wireless system using N=4, M=8, K=2 and J=6.

5

(Nikopour et al.,2014)

Discussed that an extension of SCMA has better performance than OFDMA and can increase spectral efficiency of downlink in 5G system.

6

(Zhang et al.,2014)

SCMA can be used as an energy efficient approach for uplink in 5G and proposed low complexity MPA decoding implementation.

7

(Dai et al.,2015)

Proposed Software Defined Multiple Access called (SoDeMA) by composing CDMA, TDMA, SCMA, LDS-OFDMA and OFDMA, to get very flexible configurations of MA schemes in 5G network.

8

(Klimen & Sergien,2017)

Calculate the bound for BER in AWGN and Rayleigh Channel. Used specific codebook set with N=4, K=2, M=4 and MPA detection.

14

Chapter 3 Methodology Step-by-step procedures of two main multiple access schemes that are compared in this study are explained in this chapter. Then, the parameters of simulations for both OFDMA and SCMA will be presented. Finally, the simulation scenarios for performance evaluations of this study are described.

3.1 3.1.1

System Design Overview OFDMA

The process of an OFDMA is the same as in Figure 2.2 of (Goldsmith,2005). The incoming bits are modulated using the quadrature amplitude modulation (QAM). In this study, M = 4, i.e., 4-QAM is used to carry 2 bits per symbol to be consistent with SCMA in (Goldsmith,2005) which has a codebook limitation. An example of 4-QAM constellation is shown in Figure 3.1. The cyclic prefix for X[0], ..., X[N − 1] is defined as {x[N − µ], ..., x[N − 1]}, where µ + 1 is the length of discrete-time channel impulse response, h[0], ..., h[µ]. Figure 3.2 from (Goldsmith,2005) demonstrates how cyclic prefixes reduce inter-symbol interference (ISI).

Figure 3.1: An example of 4-QAM constellation diagram (Klimen Sergien,2017)

A channel model is required for performance evaluation of transmission systems. Many researchers use Rayleigh fading and AWGN for channel models , e.g., (Klimen & Sergien,2017). However, in this study, the channel is assumed to be known , i.e., discrete-time deterministic channel with channel impulse response (CIR) h = [0.2424 0.9701 0 0] as shown in Figure 3.3, is used for simplicity. One-tap equalization and minimum distance detection are also used. 15

Figure 3.2: Cyclic prefix between data block in channel output (Goldsmith,2005)

Figure 3.3: Discrete-time deterministic channel used in this study

3.1.2

SCMA

SCMA was initially designed for dense or even ultra-dense scenarios, where users are not always active simultaneously. Since no research provides the statistics of the number of active users at a time, the number of active users of an SCMA in this study is controlled with a probability value, and at least one user is assumed to be active all the time. For example, if the probability of a user being active is 0.5, then about half of the users are active at the same time. The incoming bits from each user are directly mapped into a codeword from the codebook of each user. All the codewords of active users are formed into a single multi-dimensional symbol as shown in Figure 2.9. The rest of the process of an SCMA is the same as the process of the OFDMA. The channel model and the equalizer are also the same as the ones for the OFDMA system. A sub-channel of SCMA is used by more than one user since an SCMA is a non-orthogonal scheme. Therefore, there are some interferences from other users. The symbol detection part 16

becomes more complex in SCMA. However, for a small number of users, minimum-distance detection based on exhaustive search can still be used. Choosing how to detect a symbol of a user, i.e., considering other users as interferences referred to as separate detection or not considering other users as interferences referred to as joint detection, is important for a signal detection performance. In this study, both separate and joint detections are considered. In the separate detection, we focus only on one user called ”check user”. A check user is active all the time and the symbols of all other users are assumed to be interferences. In the joint detection, all symbols from different users are considered as data and detected as a combined or aggregated multi-dimensional symbol.

3.2 3.2.1

Simulation and Parameters MATLAB

MATLAB is a multi-paradigm numerical computing software. It allows matrix calculation, plotting of functions, implementation of algorithms, and designing user interfaces. It is widely used for simulations and has a lot of built-in functions that are convenient for signal processing. This study uses MATLAB for all simulations of OFDMA and SCMA systems and for plotting the bit error performance results.

3.2.2

System Parameters

The simulation parameters are kept the same as the ones reported in (Goldsmith,2005) for an OFDMA and (Klimen & Sergien,2017) for an SCMA. In this study, 150% overloading is used as in (Bockelmann et al.,2016). First, the probability of active users is set to 0.8 , later it can vary to study how the SCMA reacts according to the number of active users. The system parameters are shown in Table 3.1. The codebook set from (Klimen & Sergien,2017) used in this study is as follows:   0 0 0 0    CB1 = −0.1815 − 0.1318 j −0.6351 − 0.4615 j 0.6351 + 0.4615 j 0.1815 + 0.1318 j  0 0 0 0 0.7851 −0.2243 0.2243 −0.7851   0.7851 −0.2243 0.2243 −0.7851     0 0 0 0 CB2 =   −0.1815 − 0.1318 j −0.6351 − 0.4615 j 0.6351 + 0.4615 j 0.1815 + 0.1318 j 0 0 0 0   −0.6351 + 0.4615 j 0.1815 − 0.1318 j −0.1815 + 0.1318 j 0.6351 − 0.4615 j   CB3 =   0.1329 − 0.1759 j 0.4873 − 0.6156 j −0.4873 + 0.6156 j −0.1392 + 0.1759 j 0 0 0 0 0 0 0 0

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Table 3.1: System parameters

Notation

Parameter

Value

N

Number of subcarriers

4

J

Number of users

4 (in OFDMA) 6 (in SCMA)

K

Number of sub-carriers used by each user in SCMA

2

M

Number of codewords in a codebook of SCMA or M-QAM in OFDMA

4

h

Discrete-time deterministic CIR

[0.2424 0.9701 0 0]

CP

Length of cyclic prefix

3 (length of h - 1)

S

Number of symbols per user

2000

P

Probability of active users

0.8

λ

Overloading factor (J/K) in SCMA

1.5 (150%)

CB j

Codebook of user n in SCMA

Described on the next page.





0 0 0 0   0 0 0 0  0.7851 −0.2243 0.2243 −0.7851 −0.0055 − 0.2242 j −0.193 − 0.7848 j 0.193 + 0.7848 j −0.0055 + 0.2242 j   −0.0055 − 0.2242 j −0.193 − 0.7848 j 0.193 + 0.7848 j −0.0055 + 0.2242 j  0 0 0 0 CB5 =    0 0 0 0 −0.6351 + 0.4615 j 0.1815 − 0.1318 j −0.1815 + 0.1318 j 0.6351 − 0.4615 j   0 0 0 0    0.7851 −0.2243 0.2243 −0.7851 CB6 =    0.1329 − 0.1759 j 0.4873 − 0.6156 j −0.4873 + 0.6156 j −0.1392 + 0.1759 j 0 0 0 0  CB4 =  

3.3

Performance Evaluation

The system is evaluated in terms of the bit error rate (BER) performances. There are three simulation scenarios as shown in Table 3.2: first with OFDMA, second with SCMA using 18

Table 3.2: Simulation Scenarios

MA scheme

Resultant graphs Average BER of all users

OFDMA

Average BER of each user SCMA (with separate detection) Average BER of each user SCMA (with joint detection)

Average BER of all users Average BER of each user

separate detection and third one with SCMA using joint detection. The following comparisons are done for the system evaluation: • the average BER of each user and the average BER of all users for the OFDMA scheme, • the average BER of each user for the SCMA scheme using the separate detection, • the average BER with different number of active users, i.e., 4 and 5 users in the SCMA scheme with the joint detection, • The average BER of all users for the OFDMA scheme and the average BER of all users for the SCMA scheme with the joint detection.

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Chapter 4 Simulation Results and Discussions The detailed performance analysis and comparisons are shown in this chapter. Comparisons between the average BERs of each user and the average BER of all users are described. Then, differences between the average BERs of each user in the SCMA scheme with separate detection will be presented. We also explain the differences between the average BERs of individual SCMA users and the average BER of all users in SCMA by varying the number of active users in the SCMA. Finally, the chapter ends with a discussion on the results of this study.

4.1

BER Performance of OFDMA

The average BERs of individual users, the average BER of all users (four users), and the theoretical BER of the OFDMA scheme are shown in Figure 4.1. The average BER of all users is almost the same as the theoretical BER of the OFDMA, indicating the accuracy of the simulation program.

Figure 4.1: The average BERs of individual users and the average BER of all users in OFDMA

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In comparison, User 1 has the best BER and User 3 has the worst BER since the used deterministic discrete-time CIR leads to the highest gain in Sub-channel 1 and the lowest channel gain in Sub-channel 3.

4.2

BER Performance of SCMA with Separate Detection

In Figure 4.2, the investigation can be divided into two groups of users for the probability of being an active user of 0.8, i.e., the former group of users with poor BER results and the latter with better BER results. In this study, each user of the SCMA scheme uses 2 sub-carriers out of 4 as previously explained, and Sub-channel 3 has the lowest channel gain. Therefore, Users 2, 4, and 6 which share Sub-channel 3 are in the first group. The rest of the users who do not share Sub-channel 3 are in the second group. One main limitation, which is observed in the case of all users in the SCMA scheme with the separate detection is that the average BER curves of each user remain high as the SNR increases. This phenomenon is called an ”error floor,” which appears due to the dominance of interferences at high SNRs.

Figure 4.2: The average BERs of individual users in SCMA with separate detection

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4.3 4.3.1

BER Performance of SCMA with Joint Detection Comparison between SCMA with Joint Detection and OFDMA

When the joint detection is applied, the average BER of all users in the SCMA scheme becomes comparable with the OFDMA scheme. With the probability of being an active user of 0.8, mostly 4 or 5 users are active at the same time. The SNR difference for BER of 10−2 varies from 0.5 dB to 1.2 dB. When all users are active at the same time, the SNR difference for BER of 10−2 is around 2.5 dB as shown in figure 4.3. Since not all users are active all the time, the SCMA scheme can be used with the near-OFDMA BER performances. This provides a usability trade-off between the BER performance and the number of supportable users.

Figure 4.3: The average BERs with different numbers of active users in SCMA with joint detection

4.3.2

Comparison between Joint Detection and Separate Detection for SCMA

The difference between the joint detection and the separate detection is the disappearance of the error floor as shown in Figure 4.4. There is no error floor any more in the average 22

BER of all users with the joint detection because the joint detection considers data symbols of all users as a combined multi-dimensional data symbol and perform detection by comparing all possible symbol combinations. This is the reason why the SCMA scheme has high computational complexity for optimal detection.

Figure 4.4: Difference between joint detection and separate detection

4.3.3

Comparison between the Average BERs of Individual Users and of All Users

From the users’ point of view, the average BERs of individual users from the first group are worse than the average BER of all active users. For example, when 3 random users (including User 6) are active, User 6 from the first group needs 8.4 dB of SNR for the BER of 10−2 while the average SNR is around 7.8 dB. On the other hand, the average BERs of individual users from the second group are better than the average BER of all active users. User 5 from the second group can be seen as an example in Figure 4.5. However, the difference can be seen only at low numbers of active users. When all the 6 users are active at the same time, the average BERs of individual users become almost equal to the average BER of all users. The reason can be the increasing amount of interferences since the SCMA scheme is a non-orthogonal.

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Figure 4.5: The average BERs of User 5 and User 6, and the average BER of all active users

4.4

Special Cases of SCMA with Joint Detection

One possible case with active probability equal to 0.5 is that all of 3 active users are from the first group which has poor BER results. Then, the average BER of all active users becomes worse than average BER of 3 random active users. On the other hand, if all 3 active users are from the second group, the average BER of all active users is better significantly than the average BER of total 3 random active users. For random active users with active probability equal to 0.5, the BER performance can vary according to the group of active users, but does not vary as much in these special cases. Another special case of the SCMA scheme can be seen when only one user is active most of the time in the system. When the probability of being an active user is less than 0.2, there is only one user in the system. If one active user is from the second group of the SCMA users, the average BER of that one user is much better than the average BER of that user in the OFDMA scheme. The example in the case of Users 1 and 3 can be seen in Figure 4.7.

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Figure 4.6: The special case of the average BER of all active users with active probability

equal to 0.5 4.5

Summary

The overall system performance analysis can be summarized as follows. • For the users’ point of view, if each user uses just one sub-carrier, the OFDMA scheme cannot control the channel gain. However, by designing a codebook to take advantage of shaping gain, the SCMA scheme can better control the channel gain of individual users. • SCMA can be used for a dense or even ultra-dense user scenarios where users are not active all the time with near-OFDMA performances. We can say that it is worth trading off between the BER performance and the number of supportable users. • The separate detection in SCMA is easy to do but does not give good BER performances due to the BER error floor. • The joint detection is required but can lead to high computational complexity for a large number of users.

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Figure 4.7: The special case of the average BER of User 1 and User 3 in SCMA

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Chapter 5 Conclusions and Recommendations 5.1

Conclusion

In this study, the impertinences of multi-carrier multiple access and the evolution of sparse code multiple access (SCMA) can be learned. The difference between an orthogonal multiple access and a non-orthogonal multiple access is demonstrated by overloading the system. Orthogonal frequency division multiple access (OFDMA) is studied as a basic of multicarrier multiple access. The average BERs of individual users and average BER of all users in the system are plotted to see how individual users behave according to the channel gain. The SCMA scheme is built on the top of the OFDMA scheme with 150% overloading. An SCMA codebook set from (Klimen & Sergien,2017) is used and studied how incoming bits are mapped into codewords of a codebook. In this study, the number of active users is controlled by a probability value. We can see how an SCMA system reacts according to the number of active users by varying probability value. We can see the difference between the separate detection and the joint detection in the SCMA scheme. As a summary, We can see the SCMA scheme gives the same average BER of all active users as in the OFDMA scheme when only half of the users in the SCMA scheme are active. Even all users in the SCMA scheme are active, the difference is around 2.5 dB with the OFDMA scheme so that the SCMA scheme can be used by trading off the BER performance with the number of supportable users. If there is no multiple access interference for the SCMA users, the SCMA scheme performs better than the OFDMA scheme because of its shaping gain of the codebook set. Individual user performances in the SCMA scheme is better in low number of active users. The SCMA scheme is sensitive to interferences and the channel gain since it is a non-orthogonal multiple access. To eliminate the interference between users, the joint detection can be used.

5.2

Future Work

The following topics can be studied as an extension of this study. • To increase the codebook size of a user in SCMA for higher number of sub-carriers and bit rate. • Overloading more users with the help of advance detection methods such as MPA detection. • Using more realistic channel for real world systems.

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