在5G 無線通訊系統中，要求更高的頻譜效率、更高的能源效率、更低的延遲時間以
及更大量的連結數目。循環前綴正交分頻多工(CP-OFDM) 不適用於5G 無線通訊系統，
因為有高次頻帶外發射(out-of-subband emission) 與高峰均功率比(peak-to-average power ratio)，另外插入循環前綴（CP）以減輕多重路徑干擾效應會導致額外的浪費並降低頻譜效率。

為了提高頻譜效率，許多新的波形被提出。那些波形屬於無循環前綴的離散傅立葉轉
換擴展正交分頻多工系統(Cyclic Prefix Free DFT-s-OFDM Based System)。他們使用可調整的保護間隔來提高頻譜效率，但是其中許多不能有效緩解次頻帶外發射(out-of-subband emission)，有些其中甚至降低了傳輸可靠性。即使有人提出降低次頻帶外發射的方法，但此仍有許多改善空間。因此，本論文的目的是設計一個合適的頻譜預編碼器以降低次頻帶外發射在無循環前綴的離散傅立葉轉換擴展正交分頻多工系統中。

在本文中，我們提出了一種頻譜預編碼器以降低次頻帶外發射，並提出一種尾部預編
碼器以降低多重路徑干擾效應，提高傳輸可靠性。由於尾部預編碼器的設計與頻譜預編碼器，我們提出了聯合最佳化演算法(joint optimization algorithm) 去設計最佳的預編碼架構。

模擬結果顯示該方法與其他無循環前綴的離散傅立葉轉換擴展正交分頻多工系統想比
具有較低的次頻帶外發射和更低的錯誤率。因此，我們認為設計的頻譜預編碼器非常適用於無循環前綴的離散傅立葉轉換擴展正交分頻多工系統。

The fifth generation (5G) wireless communication system, also called New Radio (NR), is regarded as a promising and important technique. The properties of 5G wireless communication system includes higher spectral efficiency, higher energy efficiency, better link reliability and lower latency.

Cyclic Prefix Orthogonal Frequency Division Multiplexing (CP-OFDM)applied in LTE may not suitable for supporting 5G system. The disadvantages of CP-OFDM are known to be large out-of-subband emission (OSBE)and large peak-to-average power ratio (PAPR). In addition, insertion of a cyclic prefix (CP) to mitigate the multipath effect introduces additional overhead and lowers spectral efficiency which is one of the most important requirements in 5G wireless communication system.

To improve spectral efficiency, many new waveforms are proposed. Those methods belong to cyclic prefix free DFT-s-OFDM based systems. They use flexible guard interval to increase spectral efficiency, but many of them do not effectively mitigate OSBE and some of them even degenerate detection reliability. Even if some methods are proposed to lower the OSBE, but there are still a room for this method to mitigate OSBE more. Therefore, the purpose of this paper is to design a proper spectral precoder to lower the OSBE of cyclic prefix free DFT-s-OFDM based systems.

In this paper we propose a spectral precoder to lower OSBE and a tail precoder to mitigate ISI and improve detection reliability. The design of tail precoder is related to the spectral precoder, so an optimization algorithm considering the tail precoder and the spectral precoder is designed.

The simulation results also indicate that the proposed method has lower OSBE and better error performance than other cyclic prefix free DFT-s-OFDM based systems. Therefore, we believe that the proposed spectral precoder will be one of the best candidates to lower OSBE for cyclic prefix free DFT-s-OFDM based systems.

摘要i
Abstract ii
Contents iv
1 INTRODUCTION 1
1.1 Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.2 Windowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.3 Cancellation techniques . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.4 Precoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.5 Cyclic prefix free DFT-s-OFDM based systems . . . . . . . . . . . . 5
1.4 Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Contribution and Achievement . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 BACKGROUNDS 8
2.1 Orthogonal Frequency Division Multiple Access . . . . . . . . . . . . . . . . 8
2.2 Single Carrier Frequency Division Multiple Access . . . . . . . . . . . . . . . 11
2.3 Generalized DFT-s-OFDM without CP . . . . . . . . . . . . . . . . . . . . . 12
2.4 Improved Unique Word DFT-s-OFDM . . . . . . . . . . . . . . . . . . . . . 15
2.5 Generalized Unique Word DFT-s-OFDM . . . . . . . . . . . . . . . . . . . . 16
3 Precoder design for cyclic prefix free DFT-s-OFDM 18
3.1 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Precoder design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Tail Precoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.2 Spectral Precoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2.1 Singular value decomposition precoding . . . . . . . . . . . 23
3.2.2.2 Orthogonal projection precoding . . . . . . . . . . . . . . . 28
3.2.2.3 Two-stage precoder design . . . . . . . . . . . . . . . . . . 31
3.3 Joint precoder optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 SIMULATION RESULTS 39
4.1 Simulation parameters and evaluation requirement . . . . . . . . . . . . . . 39
4.2 Setting of Existing Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Out-of-subband emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.4 BER Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5 PAPR performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.6 Spectral Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 CONCLUSIONS 49
Bibliography 51

List of Figures
1.1 Transmitter structure of OFDM-based waveform for 5G NR propsoed in [1]. 3
2.1 Cyclic prefix in OFDM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Resource allocation of OFDM. . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Resource allocation of OFDMA. . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 System model of the SC-FDMA system. . . . . . . . . . . . . . . . . . . . . 12
2.5 System model of the G-DFT-s-OFDM system. . . . . . . . . . . . . . . . . . 13
2.6 The frame structure of G-DFT-s-OFDM . . . . . . . . . . . . . . . . . . . . 14
2.7 System model of Improved Unique Word DFT-s-OFDM . . . . . . . . . . . 15
3.1 Transceiver system model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Sprctral precoder block diagram . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Discrete frequency region of CF and Cop . . . . . . . . . . . . . . . . . . . . 33
3.4 Discrete frequency region of CG . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 SEM [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 Out-of-subband emission power of different combinations of parameters . . . 41
4.2 OSBE performance of different combinations of parameters . . . . . . . . . . 42
4.3 OSBE performance comparison of different systems . . . . . . . . . . . . . . 43
4.4 BER performance comparison of different systems . . . . . . . . . . . . . . . 44
4.5 PAPR performance comparison of different systems . . . . . . . . . . . . . . 46
4.6 SE performance comparison of different systems . . . . . . . . . . . . . . . . 47
List of Tables
4.1 The simulation parameters for waveform evaluation. . . . . . . . . . . . . . . 40
4.2 The parameter and simulation results related to SE . . . . . . . . . . . . . . 48

[1] S. Lien, S. Shieh, Y. Huang, B. Su, Y. Hsu, and H. Wei, “5G New Radio: Waveform, Frame Structure, Multiple Access, and Initial Access,” IEEE Communications Magazine, vol. 55, pp. 64–71, June 2017.
[2] 3GPP, “User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone,” Technical Specification (TS)38.101, V15.2.0, Sec. 6.5.2, Jul. 2018.
[3] J. Abdoli, M. Jia, and J. Ma, “Filtered OFDM: A new waveform for future wireless systems,” in 2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), pp. 66–70, June 2015.
[4] X. Zhang, M. Jia, L. Chen, J. Ma, and J. Qiu, “Filtered-OFDM - Enabler for Flexible Waveform in the 5th Generation Cellular Networks,” in 2015 IEEE Global Communications Conference (GLOBECOM), pp. 1–6, Dec 2015.
[5] F. Schaich, T. Wild, and Y. Chen, “Waveform Contenders for 5G - Suitability for Short Packet and Low Latency Transmissions,” in 2014 IEEE 79th Vehicular Technology Conference (VTC Spring), pp. 1–5, May 2014.
[6] T. Wild, F. Schaich, and Y. Chen, “5G air interface design based on Universal Filtered (UF-)OFDM,” in 2014 19th International Conference on Digital Signal Processing, pp. 699–704, Aug 2014.
[7] A. Vahlin and N. Holte, “Optimal finite duration pulses for ofdm,” IEEE Transactions on Communications, vol. 44, no. 1, pp. 10–14, 1996.
[8] R. Zayani, Y. Medjahdi, H. Shaiek, and D. Roviras, “WOLA-OFDM: A Potential Candidate
for Asynchronous 5G,” in 2016 IEEE Globecom Workshops (GC Wkshps), pp. 1–5, Dec 2016.
[9] Y. Medjahdi, R. Zayani, H. Shaïek, and D. Roviras, “WOLA processing: A useful tool for windowed waveforms in 5G with relaxed synchronicity,” in 2017 IEEE International Conference on Communications Workshops (ICC Workshops), pp. 393–398, May 2017.
[10] S. Brandes, I. Cosovic, and M. Schnell, “Reduction of out-of-band radiation in ofdm systems by insertion of cancellation carriers,” IEEE Communications Letters, vol. 10, no. 6, pp. 420–422, 2006.
[11] H. Yamaguchi, “Active interference cancellation technique for mb-ofdm cognitive radio,” in 34th European Microwave Conference, 2004., vol. 2, pp. 1105–1108, 2004.
[12] D. Qu, Z. Wang, and T. Jiang, “Extended active interference cancellation for sidelobe suppression in cognitive radio ofdm systems with cyclic prefix,” IEEE Transactions on Vehicular Technology, vol. 59, no. 4, pp. 1689–1695, 2010.
[13] Yuan-Pei Lin and S. . Phoong, “Window designs for dft-based multicarrier systems,” IEEE Transactions on Signal Processing, vol. 53, no. 3, pp. 1015–1024, 2005.
[14] C. . Chung, “Spectrally precoded ofdm with cyclic prefix,” in 2007 IEEE International Conference on Communications, pp. 5428–5432, 2007.
[15] H. Chen and C. Chung, “Adaptive spectrally precoded ofdm with cyclic prefix,” in The 19th Annual Wireless and Optical Communications Conference (WOCC 2010), pp. 1–5, 2010.
[16] J. van de Beek and F. Berggren, “N-continuous ofdm,” IEEE Communications Letters, vol. 13, no. 1, pp. 1–3, 2009.
[17] R. Xu and M. Chen, “A precoding scheme for dft-based ofdm to suppress sidelobes,” IEEE Communications Letters, vol. 13, no. 10, pp. 776–778, 2009.
[18] M. Ma, X. Huang, B. Jiao, and Y. J. Guo, “Optimal Orthogonal Precoding for Power Leakage Suppression in DFT-Based Systems,” IEEE Transactions on Communications, vol. 59, pp. 844–853, March 2011.
[19] J. A. Zhang, X. Huang, A. Cantoni, and Y. J. Guo, “Sidelobe suppression with orthogonal projection for multicarrier systems,” IEEE Transactions on Communications, vol. 60, no. 2, pp. 589–599, 2012.
[20] G. Berardinelli, “Generalized DFT-s-OFDM Waveforms Without Cyclic Prefix,” IEEE Access, vol. 6, pp. 4677–4689, Dec. 2018.
[21] G. Berardinelli, “Zero-tail DFT-spread-OFDM signals,” IEEE Globecom Workshops (GC Wkshps), pp. 229–234, Dec. 2013.
[22] A. Sahin, R. Yang, M. Ghosh, and R. L. Olesen, “An Improved Unique Word DFTSpread OFDM Scheme for 5G Systems,” in 2015 IEEE Globecom Workshops (GC Wkshps), pp. 1–6, Dec 2015.
[23] S. Wei and J. Wu, “Multiple objective optimization of osbe and isi for cyclic prefix free dft-s-ofdm systems,” in 2020 IEEE 91st Vehicular Technology Conference (VTC2020- Spring), pp. 1–5, May 2020.
[24] L. Hogben, “Handbook of Linear Algebra,” Chapman Hall/CRC Press, 2007.
[25] G. H. Golub and C. F. V. Loan, “Matrix Computations,” The Johns Hopkins University Press, 1996.
[26] P. H. Schoenemann, “A Solution of the Orthogonal Procrustes Problem With Applications to Orthogonal and Oblique Rotation,” University of Illinois at Urbana-Champaign, 1964.
[27] A. Tom, A. Sahin, and H. Arslan, “Mask compliant precoder for ofdm spectrum shaping,” IEEE Communications Letters, vol. 17, pp. 447–450, March 2013.
[28] J. Tong, Q. Guo, S. Tong, J. Xi, and Y. Yu, “Condition number-constrained matrix approximation with applications to signal estimation in communication systems,” IEEE Signal Processing Letters, vol. 21, pp. 990–993, Aug 2014.