隨著現代通訊技術的持續進步，我們對於通訊傳輸量的需求越來越大，並且對於現在持續發展中的行動通訊技術5G來說對於延遲的要求也隨之提高，而相較於4G主要使用的正交頻分多址(Orthogonal Frequency Division Multiple Access)來說，非正交多重存取(Non-Orthogonal Multiple Access)除了擁有較好的頻譜效率\cite{improves spectrum efficiency}能夠增加傳輸量之外同時又擁有較低傳輸延遲，而這篇報告中所要介紹的便是非正交多重存取(NOMA)中的其中一種，稀疏碼多重存取(Sparse Code Multiple Access)。
本篇論文中主要介紹一種能夠在不論是較少使用者以及較少載波的情況又或者是大量使用者以及大量載波的清況下都能以相對較低的複雜度快速建構出在峰值平均功率比(PAPR)和 標準化的最小乘積距離(normalized minimum product distance)等指標方面甚至是錯誤率方面表現都不錯的碼本建構方式。在我們的建構方式中，無論整體的系統規模大小如何，我們都能照著一樣的步驟快速建構出我們的碼本，而在優化的過程中我們也優先去將各種表現指標優化，最後便能得出一個維持低複雜度且快速地被建構又能維持峰值平均功率比(PAPR)，標準化的最小乘積距離(normalized minimum product distance)等各種指標方面的表現，甚至是錯誤率方面表現都相當不錯的碼本。而基於我們的碼本建構方式所建構出的碼本，在下行鏈路SCMA-OFDM系統中，還可以套用我們本篇論文所提及的降低時域訊號PAPR的方法，藉此達成比PTS(Partial Transmit Sequence)還要更好的PAPR降低幅度。

As the growth of mobile communication techniques, the demand of throughput is became more and more, and the demand of the latency is became stricter for the developing mobile communication technique 5G. In addition, relative to the OFDMA(Orthogonal Frequency Division Multiple Access) which is used in 4G, NOMA(Non-Orthogonal Multiple Access) is suitable for the 5G system by having a better spectrum efficiency\cite{improves spectrum efficiency} which can improve the throughput and a lower transmission latency. And, what we are going to introduce in this paper is SCMA(Sparse Code Multiple Access) which is also belonged to NOMA(Non-Orthogonal Multiple Access).
In this thesis, we mainly introduce a low complexity and quick codebook design method that can have a good performance at user codebook's PAPR(Peak-to-Average Power Ratio), normalized minimum product distance, and even the bit error rate no matter the system has a small number of users and resources or huge number of users and resources. Regardless of the overall system size, our codebook design procedure would be the same and simple. When we are optimizing our codebooks, the values of the criteria are the most important target, so we will have an SCMA codebook that not only can be constructed quickly and has a good performance at each user's codebook PAPR, normalized minimum Euclidean distance, and even at the bit error rate. Besides, the codebooks that constructed in our method can apply our proposed PAPR reduction method which can reduce the PAPR of the time domain signal of the SCMA-OFDM system more than PTS(Partial Transmit Sequence).

1 簡介 .... 1
2 知識背景 .... 3
2.1 正交多重存取(Orthogonal Multiple Access, OMA) .... 3
2.1.1 分頻多重存取(FDMA)系統 .... 4
2.1.2 分時多重存取(TDMA)系統 .... 5
2.1.3 分碼多重存取(CDMA)系統 .... 6
2.2 非正交多重存取(Non-orthogonal Multiple Access, NOMA) .... 7
2.2.1 低密度簽記(Low density signature, LDS) .... 7
2.2.2 稀疏碼多重存取(Sparse code multiple access, SCMA) .... 8
3 SCMA碼本表現指標介紹 .... 10
3.1 回顧SCMA演算法 .... 10
3.2 各使用者碼本的最小乘積距離 .... 11
3.3 單一資源視角的最小歐式距離 .... 12
3.4 單一資源視角的PAPR .... 13
3.5 常見的碼本建構方式 .... 14
3.5.1 基於脈波震幅調變(Pulse-amplitude modulation, PAM)建構 .... 14
3.5.2 基於黃金角度調變(Golden angle modulation, GAM)建構 .... 16
3.5.3 基於星型正交振幅調變(Star Quadrature Amplitude Modulation, Star-QAM)建構 .... 17
3.5.4 非基於特定母群集類型建構 .... 18
4 SCMA碼本設計 .... 20
4.1 SCMA母群集設計 .... 20
4.2 SCMA單一使用者碼本設計 .... 20
4.3 SCMA子群集角度設計 .... 21
4.4 上行瑞利衰落通道模擬結果 .... 24
4.5 下行瑞利衰落頻道模擬結果 .... 30
4.6 較大型系統的模擬結果 .... 36
5 SCMA-OFDM系統的PAPR .... 38
5.1 SCMA-OFDM系統與其PAPR的介紹 .... 38
5.2 SCMA-OFDM系統的PAPR改善方式 .... 40
5.3 模擬結果 .... 48
6 結論 .... 53

[1]S. Zhang, X. Xu, L. Lu, Y. Wu, G. He and Y. Chen, "Sparse code multiple access: An energy efficient uplink approach for 5G wireless systems," Proc 2014 IEEE Global Communications Conference, Austin, TX, 2014, pp. 4782-4787.

[2]IMT-2020 (5G) Promotion Group, 5G vision and requirements, May 2014.

[3]G. D. Forney and L. -. Wei, "Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations," in Proc IEEE Journal on Selected Areas in Communications, vol. 7, no. 6, pp. 877-892, Aug. 1989.

[4]
G. D. Forney, "Multidimensional constellations. II. Voronoi constellations," in Proc IEEE Journal on Selected Areas in Communications, vol. 7, no. 6, pp. 941-958, Aug. 1989.

[5]
M. Taherzadeh, H. Nikopour, A. Bayesteh and H. Baligh, "SCMA Codebook Design," Proc 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall), Vancouver, BC, 2014, pp. 1-5.

[6]
J. van de Beek and B. M. Popovic, “Multiple access with low-density signatures,” in Proc. IEEE GLOBECOM, Hawaii, USA, Dec. 2009, pp.1-6.

[7]
H. Nikopour and H. Baligh, “Sparse code multiple access,” in Proc. IEEE 24th Int. Symp. Pers. Indoor Mobile Radio Commun., 2013, pp. 332–336.

[8]
A. Bayesteh, H. Nikopour, M. Taherzadeh, H. Baligh and J. Ma, "Low Complexity Techniques for SCMA Detection," Proc 2015 IEEE Globecom Workshops (GC Wkshps), San Diego, CA, 2015, pp. 1-6.

[9]
Z. Mheich, L. Wen, P. Xiao and A. Maaref, "Design of SCMA Codebooks Based on Golden Angle Modulation," in Proc IEEE Transactions on Vehicular Technology, vol. 68, no. 2, pp. 1501-1509, Feb. 2019.

[10]
L. Yu, X. Lei, P. Fan and D. Chen, "An optimized design of SCMA codebook based on star-QAM signaling constellations," Proc 2015 International Conference on Wireless Communications \& Signal Processing (WCSP), Nanjing, 2015, pp. 1-5.

[11]
D. Cai, P. Fan, X. Lei, Y. Liu and D. Chen, "Multi-Dimensional SCMA Codebook Design Based on Constellation Rotation and Interleaving," Proc 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring), Nanjing, 2016, pp. 1-5.

[12]
Yen-Ming Chen and Jian-Wei Chen, “On the design of near-optimal sparse code multiple access codebooks,” submitted to IEEE Transactions on Communications

[13]
L. Yang, X. Lin, X. Ma and S. Li, "Iterative Clipping Noise Elimination of Clipped and Filtered SCMA-OFDM System," in IEEE Access, vol. 6, pp. 54427-54434, 2018.

[14]
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, pp. 1616-1626, April 2008.