Doubly Irregular Sparse Code Multiple Access with

Doubly Irregular Sparse Code Multiple Access with EXIT Analysis 1 School

2 School

Iswahyudi Hidayat1,2 , Linda Meylani1,2 , Adit Kurniawan1 , M. Sigit Arifianto1 and Khoirul Anwar2 of Electrical Engineering and Informatics, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung, 40132 Indonesia of Electrical Engineering, Telkom University, Jl. Telekomunikasi No. 1 Terusan Buah Batu, Bandung, 40257 Indonesia Email: {iswahyudihidayat, lindameylani}@telkomuniversity.ac.id, {adit, msarif2a}@stei.itb.ac.id, [email protected]

Abstract—Sparse Code Multiple Access (SCMA) is one of the potential candidates of multiple access technique to support future networks. This paper proposes doubly irregular SCMA (DI-SCMA) to increase the user capacity of massive wireless networks. The idea is coming from the fact that successive interference cancellation (SIC) works better when the degree distributions of the both user and resource nodes are irregular. Since iterative decoding is involved, we use extrinsic information transfer (EXIT) chart to predict the performances. With careful design of the degree distribution, we conduct computer simulations to observe the benefit of irregularity of the system. Our results confirmed that the proposed DI-SCMA can increase the user capacity with overloading factor of 300%. The efficiency of the proposed DI-SCMA is expected to be high as indicated by the small gap between area of capacity and coding rate in EXIT chart. Keywords : SCMA, EXIT Chart, doubly irregular SCMA, overloading factor

I. I NTRODUCTION The fifth Telecommunication generation (5G) focuses on services of (i) enhanced mobile broadband, (ii) ultra reliablelow latency, (iii) massive machine–type communication, where 5G technology must be able to support communication of large amount of user. Sparse code multiple access (SCMA) is a technique of non–orthogonal multiple access (NOMA) proposed to increase the capacity and accessibility of the network. SCMA is developed based on low density signature code division multiple access (LDS–CDMA) [1] with multidimensional constellation (MDC) [2], [3]. In SCMA, incoming bits are directly mapped into multi-dimensional complex codewords. Message passing algorithm (MPA) is exploited in SCMA receiver to eliminate the interference from other users, based on a sparsity codewords, where we represent interference and the intended received signal using degree distribution. Performances of SCMA in uplink and downlink were presented by [4] and [5]. The original SCMA, called as MDC–CDMA, introduced in [2], [3], alocates the same number of resource to every user and sets the same number of user to every resource. This scheme is called as regular SCMA and can achieve overloading factor of 150%. To improve SCMA overloading factor, authors in [6] proposed irregular SCMA (IrSCMA),

where every user or layer in SCMA accesses a different number of resources. However, number of users that access one resource is the same as that of MDC–SCMA. Other similar research to IrSCMA have been conducted by [7] and [8] to deal with different performance requirement for every user. However, [7] and [8] do not consider overloading factor improvement. This paper proposes doubly irregular SCMA (DI–SCMA) to achieve higher users capacity. In this scheme, SCMA is designed with different number of resources allocated to every user. We also allow different number of users to access the same resource. To analyze performance of the proposed technique, we use extrinsic information transfer (EXIT) chart to observe the behavior of the scheme. EXIT chart introduced by Stephan ten Brink [9] was originally used to analyze iteration process in turbo system, however, in this paper we use EXIT chart for analysis of wireless network. Information transfer is illustrated by two nodes that transfer information in the form of a priori mutual information from user nodes to resource nodes. The rest of this paper is organized as follow. System model of doubly irregular SCMA and EXIT chart analysis are presented in Sections II and III, respectively. Discussion relevant to the proposed technique is described in Section IV. Conclusions are made in Section V. II. S YSTEM M ODEL In multiuser system, J users share K resource elements. In orthogonal scenario, J is less or equal to K to ensure that every user is protected from interferences. In the orthogonal scenario, there is no overloading, while in non-orthogonal scenario, J is larger than K resultiing an overloading factor of ⌘ = J/K beyond 1. LDS–CDMA and SCMA system are kinds of non–orthogonal technique of multiple access schemes. In LDS–CDMA and SCMA system, each user access N resources from the total available K resources (N < K). In LDS–CDMA system, every user spread their modulated symbol aj to N resources by using low density spreading signature sj = [s1,j , ..., sK,j ]T to obtain vector after spreading process xj = aj sj . In MDC–SCMA, modulation and spreading process are replaced by multi-dimensional codebook. Therefore, log2 (M ) bits from every user are maped into K dimensional

complex codebook of size M . The K-dimensional complex codewords of codebook are sparse vectors with N < K non zero elements. Codebook design in MDC–SCMA is influenced by three important factors: mapping matrix, constellation points, and operator constellation. Resources used by every user j depend on binary mapping matrix FK⇥J consisting binary indicator vector fj as F = (f1 , f2 , ..., fJ ).

(1)

User node j and resource node k are connected if and only if Fkj = 1. Total number of users contributing to resource k PJ is determined by dkf = (df 1 , df 2 , ..., df k )T = j=1 fj . As an example of a mapping matrix with J = 6 users and K = 4 resources [2] is 0 1 1 1 1 0 0 0 B1 0 0 1 1 0C C Freg = B (2) @0 1 0 1 0 1A . 0 0 1 0 1 1 d1f

d2f

d3f

d4f

In matrix Freg , we get = = = = 3. It means that there are 3 different users using the same resource. SCMA codewords are multiplexing over K orthogonal resources. The complexity of decoding process in SCMA is influenced by sparsity in codewords determined by the mapping matrix. The received signal after synchronous transmission can be expressed as J X y= hj xj + n, (3) j=1

where xj = (x1j , ..., xKj )T is K dimension complex SCMA codewords of user j, hj is channel vector of user j and n ⇠ CN (0, N0 I) is the additive white Gaussian noise. The proposed DI–SCMA is a modified version of MDC–SCMA that have higher overloading factor with irregular structur of mapping matrix. The mapping matrix design in proposed model is different compared to MDC–SCMA and is also different compared to the model in [6]. MDC–SCMA alocates the same number of resources for every user. Each resource was interfered by a same number of users. We also consider [6] that proposed irregular SCMA with overloading factor of 200%, where each user in SCMA uses different number of resources, where number of interfering users in every resource is still the same with MDC–SCMA. Mapping matrix in [6] is also different at even and odd channels uses, where the matrix for the even channel is 0 1 1 1 1 0 0 0 0 0 B 1 0 0 1 1 0 0 0C C Firreg = B (4) @ 0 1 0 1 0 0 1 0A . 0 0 1 0 0 1 0 1 In this paper, we assume perfect channel estimation and perfect synchronization, where the channel is a single path channel model. We also consider a factor graph as shown in Fig. 1, to

User Node

Resource Node

Fig. 1. Factor Graph of the proposed DI-SCMA having matrix Fprop with J = 12 and K = 4.

model a network structure, where several users are transmitting using given a number of resource node. The relationship between factor graph and transmission in a network has been presented, for example, in [10], [11]. Interested reader can also refer to [12] for the case of many to one communication. III. P ROPOSED DI-SCMA AND EXIT C HART OF N ETWORKS In doubly irregular SCMA, every user uses different number of resources. In this paper, we assume a maximal multiuser detection (MUD) capability of Q = 4 as used in [13]. The proposed mapping matrix Fprop with number of users J = 12 and number of resources K = 4 is 0 1 1 1 1 0 0 1 1 0 0 1 1 1 B1 0 0 1 1 0 1 1 1 1 1 0C C Fprop = B @0 1 0 1 0 1 0 1 1 1 0 1A . (5) 0 0 1 0 1 0 0 0 0 0 1 1

The factor graph representation of (5) is shown in Fig. 1 with df = {4, 7, 8}. Number of resources used by each user is also different. In this poposed DI–SCMA scheme, we expect to achieve overloading factor of 300%. Although EXIT chart is originally used to evaluate the behavior of physical channel decoding, in this paper, we use the EXIT chart to evaluate behaviour of a network [14]. EXIT chart describes the exchange of extrinsic mutual information between resource node (RN) and user node (UN), IE,RN and IE,U N , respectively. The area under RN and UN determines network capacity and coding rate in SCMA system, respectively. The procedures to obtain IE,RN and IE,U N are as follow: 1) Determine degree distribution of UN, ⇤(x) and degree distribution of RN ⌦(x) in polynomial representation, X ⇤(x) = ⇤d v x dv , (6) dv

⌦(x) =

X

⌦d f x d f .

(7)

df

where dv and df represents degree in UN and RN, respectively. As an example, let us consider Fprop in (5), where Fprop has dv = {2, 3} and df = {4, 7, 8} to support a total of 12 users. The 9 users use degree 2, while 3 users use degree 3 of transmission. We can then represent the UN degree distribution as ⇤(x) = 9 2 3 3 12 x + 12 x . Similarly, for the RN, two nodes are

utilized by 8 users and a node by 4 and 7 users, therefore, we have degree distribution of ⌦(x) = 14 [x4 +x7 ]+ 24 x8 . 2) Determine degree distribution for UN and RN based on edge perspective, (x) and !(x) as

and

⇤ (x) , ⇤0 (1) 0

!(x) =

⌦ (x) . ⌦0 (1)

0.8

(8)

0.5 0.4

(10)

q = (p),

where p = 1 IA,U N is erasure probability entering UN and IA,U N is apriori mutual information of UN. 4) Extrinsic mutual information for UN is, therefore, q.

k=0

where Q is the multiuser detection (MUD) capability determined by the SCMA codebooks, d is a degree in resource node. In this paper, we consider Q = 4. Note that for regular SCMA, Q = d is always satisfied, while for irregular SCMA, d is varying and may have d Q. 6) IE,RN is expressed as p.

Λ(x) = 34 x2 + 41 x3

0.3 0.2

Matrix Fprop 0.1

RN UN

(11)

5) To obtain IE,RN , we determine erasure probability output of RN first. By following the approach in [14] and [15], erasure probability output of RN can be expressed as ◆ min(Q,d) 1 ✓ X d 1 k p=1 q (1 q)d k 1 , (12) k

IE,RN = 1

Ω(x) = 41 x4 + 14 x7 + 24 x8 0.7 0.6

(9)

3) Determine erasure probability emanating from UN

IE,U N = 1

0.9

IE,RN,IA,UN

0

(x) =

1

(13)

IV. A NALYSIS AND D ISCUSSION In this section, we evaluate EXIT chart for regular Freg , irregular Firreg , and the proposed double irregular Fprop . From (6)–(13) we can evaluate EXIT chart for Freg , Firreg and the proposed Fprop . For Fprop , degree distributions of 9 2 3 3 UN and RN in node perspective are ⇤(x) = 12 x + 12 x and 1 4 2 8 7 ⌦(x) = 4 [x + x ] + 4 x , respectively. The edge perspective can be expressed as 2 1 (x) = x + x2 , (14) 3 3 and 4 3 7 16 !(x) = x + x6 + x7 . (15) 27 27 27 Based on (10) and (12), we can get erasure probability of output UN and RN as 4 1 IE,U N = (IA,U N ) (IA,U N )2 , (16) 3 3 and 4 7 IE,RN = 4 (IA,RN ) + 7 (IA,RN ) 27 27 16 + (17) 8 (IA,RN ), 27

0

0

0.1

0.2

0.3

0.4

0.5 0.6 IA,RN,IE,UN

0.7

0.8

0.9

1

Fig. 2. EXIT Chart of the proposed DI-SCMA with Fprop to achieve overloading factor of 300%.

respectively, where

i (IA,RN ) =

i

follows (12) as

min(K,i) 1 ✓

X

k=0

i k

◆ 1

(1 IA,RN )k (IA,RN )i

Therefore we obtain IE,RN = + + + + +

k 1

.

(18)

4 7 42 + (IA,RN )6 + (1 IA,RN )(IA,RN )5 27 27 27 105 2 (1 IA,RN ) (IA,RN )4 27 140 (1 IA,RN )3 (IA,RN )3 27 16 112 (IA,RN )7 + (1 IA,RN )(IA,RN )6 27 27 336 (1 IA,RN )2 (IA,RN )5 27 560 (1 IA,RN )3 (IA,RN )4 . (19) 27

The curve of IE,RN is shown with circle ”o” representing capacity of SCMA system. The curve IE,U N is shown with asterisk ”*” representing coding rate of SCMA system. Decoding process is successful if the curve of IE,U N is below the curve of IE,RN . From Fig. 2 we can state that our proposed SCMA can be decoded, indicated by an open tunnel between RN and VN curves. For Freg in (2), we have ⇤(x) = x2 and ⌦(x) = x3 . Therefore, we have IE,U N = IA,U N ,

(20)

1

1 3

Ω(x) = x

0.9

0.8

0.8

0.7

0.7

0.6

0.6

IE,RN,IA,UN

IE,RN,IA,UN

0.9

0.5 0.4

Ω(x) = x3

0.5 0.4

Λ(x) = x2 0.3

Λ(x) = 12 x + 12x2

0.3

0.2

0.2 Matrix Freg

0.1 0

Matrix Firreg 0.1

RN UN 0

0.1

0.2

0.3

0.4

0.5 0.6 IA,RN,IE,UN

0.7

0.8

0.9

1

0

RN UN 0

0.1

0.2

0.3

0.4

0.5 0.6 IA,RN,IE,UN

0.7

0.8

0.9

1

Fig. 3. EXIT Chart of the regular SCMA with Freg to achieve overloading factor of 150%.

Fig. 4. EXIT Chart of single irregular SCMA with Firreg to achieve overloading factor of 200%.

IE,RN = (IA,RN )2 + 2(1

satisfied by Freg , by keeping the number of users accessing each resource to be the same, as well as the amount of resource used by each user. In Fregext , each user uses two resources to transmit their data, but number of users accessing each resource is increased from 3 (in Freg ) to 6 . By using (6)– (13), ⇤(x) = x2 , ⌦(x) = x6 , extrinsic mutual information for UN and RN is IE,U N = IA,U N , (25)

IA,RN )2 ,

IA,RN )(IA,RN ) + (1

(21)

= 1.

Fig. 3 shows an EXIT chart for Freg , which is indicating that a successful decoding is achievable. However, Fig. 3 shows that the gap between RN and UN curves is large, describing that the resource is not used optimally. For matrix Firreg , we have ⇤(x) = 12 x + 12 x2 , and ⌦(x) = 3 x . Therefore we have IE,U N and IE,RN as IE,U N = IE,RN = (IA,RN )2 + 2(1

2 IA,U N , 3

(22) IA,RN )2 ,

IA,RN )(IA,RN ) + (1

(23)

= 1.

Fig. 4 shows EXIT chart for Firreg , where smaller gap area is achieved rather than the gap of Freg . However the loss is still big potential with crossing at IA,RN = 0.667. Mapping matrices Freg , Firreg and Fprop have different number of users. Freg only has 6 users, and Firreg has 8 users. If number of users in both mapping matrices are increased match to number of users in Fprop by observing the regularity of Freg , we obtain, for example,

Fregext

0 1 B1 =B @0 0

1 0 1 0

1 0 0 1

0 1 1 0

0 1 0 1

0 0 1 1

1 1 0 0

1 0 1 0

1 0 0 1

0 1 1 0

IE,RN =(IA,RN )5 + 5(1

0 1 0 1

1

0 0C C. 1A 1 (24)

Fregext is a modified mapping matrix from Freg with 12 users. The regularity principle of mapping matrix has been

IA,RN )(IA,RN )4 2

+ 10(1

IA,RN ) (IA,RN )3

+ 10(1

3 IA,RN )3 IA,RN .

(26)

The EXIT chart for Fregext is shown in Fig. 5 resulting in decoding failure. Firregext is from Firreg with 12 users as

Firregext

0

1 B1 =B @0 0

1 0 1 0

1 0 0 1

0 1 1 0

0 1 0 0

0 0 0 1

0 0 1 0

0 0 0 1

1 1 0 0

0 0 1 1

0 1 1 0

1 1 0C C. 0A 1 (27)

4 8 2 By using (6)–(13), ⇤(x) = 12 x+ 12 x and ⌦(x) = x5 . The extrinsic mutual information for UN and RN can be expressed as: 16 IE,U N = IA,U N , (28) 20

IE,RN =(IA,RN )5 + 5(1

IA,RN )(IA,RN )4

+ 10(1

IA,RN )2 (IA,RN )3

+ 10(1

3 IA,RN )3 IA,RN .

(29)

to keep working until a stopping set is found. Based on EXIT analysis, we found that the proposed doubly irregular SCMA has higher user capacity rather than irregular SCMA or MDC–SCMA. The typical example shows that the propose DI–SCMA reaches overloading factor 300%, while the conventional SCMA reaches only 150%. From the results of EXIT chart we also found that the proposed model has better efficiency indicated by small open gap between EXIT curves of resource node and user node.

1 0.9 0.8

Ω(x) = x6

0.7

IE,RN,IA,UN

0.6 0.5

R EFERENCES

0.4

[1] R. Hoshyar, F. P. Wathan, and R. Tafazolli, “Novel low-density signature for synchronous CDMA systems over AWGN channel,” IEEE Transactions on Signal Processing, vol. 56, no. 4, pp. 1616–1626, April 2008. [2] H. Nikopour and H. Baligh, “Sparse code multiple access,” in 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), London, UK, Sept 2013, pp. 332–336. [3] M. Taherzadeh, H. Nikopour, A. Bayesteh, and H. Baligh, “SCMA codebook design,” in 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall), Vancouver, BC, Canada, Sept. 2014, pp. 1–5. [4] K. Au, L. Zhang, H. Nikopour, E. Yi, A. Bayesteh, U. Vilaipornsawai, J. Ma, and P. Zhu, “Uplink contention based SCMA for 5G radio access,” in 2014 IEEE Globecom Workshops (GC Workshops), Austin, TX, USA, Dec. 2014, pp. 900–905. [5] H. Nikopour, E. Yi, A. Bayesteh, K. Au, M. Hawryluck, H. Baligh, and J. Ma, “SCMA for downlink multiple access of 5G wireless networks,” in 2014 IEEE Global Communications Conference, Austin, TX, USA, Dec. 2014, pp. 3940–3945. [6] M. Zhao, S. Zhou, W. Zhou, and J. Zhu, “An improved uplink sparse coded multiple access,” IEEE Communications Letters, vol. 21, no. 1, pp. 176–179, Jan. 2017. [7] S. Zhang, B. Xiao, K. Xiao, Z. Chen, and B. Xia, “Design and analysis of irregular sparse code multiple access,” in 2015 International Conference on Wireless Communications Signal Processing (WCSP), Nanjing, China, Oct. 2015, pp. 1–5. [8] L. Yu, P. Fan, Z. Ma, X. Lei, and D. Chen, “An optimized design of irregular SCMA codebook based on rotated angles and EXIT chart,” in 2016 IEEE 84th Vehicular Technology Conference (VTC-Fall), Montreal, QC, Canada, Sept. 2016, pp. 1–5. [9] S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Transactions on Communications, vol. 49, no. 10, pp. 1727–1737, Oct. 2001. [10] M. N. Hasan and K. Anwar, “Massive uncoordinated multiway relay networks with simultaneous detections,” in 2015 IEEE International Conference on Communication Workshop (ICCW), London, UK, June 2015, pp. 2175–2180. [11] K. Anwar and R. P. Astuti, “Finite-length analysis for wireless superdense networks exploiting coded random access over Rayleigh fading channels,” in 2016 IEEE Asia Pacific Conference on Wireless and Mobile (APWiMob), Sept. 2016. [12] M. Chiani, G. Liva, and E. Paolini, “The marriage between random access and codes on graphs: Coded slotted ALOHA,” in 2012 IEEE First AESS European Conference on Satellite Telecommunications (ESTEL), Oct. 2012, pp. 1–6. [13] A. A. Purwita and K. Anwar, “Massive multiway relay networks applying coded random access,” IEEE Transactions on Communications, vol. 64, no. 10, pp. 4134–4146, Oct. 2016. [14] K. Anwar, “High-dense multiway relay networks exploiting direct links as side information,” in 2016 IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia, May 2016, pp. 1–6. [15] ——, “Graph-based decoding for high-dense vehicular multiway multirelay networks,” in 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring), Nanjing,China, May 2016, pp. 1–5.

0.3

Λ(x) = x2

0.2 Matrix Freg

ext

0.1 0

RN UN 0

0.1

Fig. 5.

0.2

0.3

0.4

0.5 0.6 IA,RN,IE,UN

0.7

0.8

0.9

1

EXIT Chart of the factor graph Fregext .

1 0.9 Ω(x) = x5 0.8 0.7

IE,RN,IA,UN

0.6 0.5 0.4 0.3

Λ(x) = 34 x2 + 14 x

0.2 Matrix Firreg ext 0.1 0

RN UN 0

0.1

Fig. 6.

0.2

0.3

0.4

0.5 0.6 IA,RN,IE,UN

0.7

0.8

0.9

1

EXIT Chart of the factor graph Firregext .

The EXIT chart of Firregext is shown in Fig. 6, where the tunnel is close indicating a decoding failure since the iteration does not start. V. C ONCLUSION We have proposed doubly irregular SCMA for massive wireless networks to increase the numbers of supported users. The double irregularity of degree distribution of user nodes and resource nodes helps the double irregular decoding process