預編碼(Precoded)正交分頻多工(Orthogonal Frequency Division Multiplexing, OFDM)系統是一種高速率的無線傳輸系統，此系統在頻域將預編碼矩陣與調變訊號相乘，使得傳送訊號擁有頻率多樣性(Frequency Diversity)，然而，使用預編碼矩陣會提高運算複雜度；為了降低運算複雜度，在先前的研究中提出將使用Walsh-Hadamard Matrix之預編碼矩陣與快速傅立葉逆轉換(Inverse Fast-Fourier Transform, IFFT)結合成為一個低複雜度轉換矩陣的系統架構，但此系統其運算複雜度改善有限。
在本篇論文我們使用一種實部與虛部都為整數的稀疏高斯整數序列(Sparse Gaussian Integer Sequence, SGIS)建構出轉換矩陣，此轉換矩陣型式為循環矩陣(Circular Matrix)且每一行向量(Column Vector)都由SGIS構成，SGIS中非零元素的個數與序列長度無關，最多非零元素個數為16；使用此SGIS降低複雜度的比例會隨著子載波(Subcarrier)數量增加而加大，峰均值功率比(Peak-to-Average Power Ratio, PAPR)也會較傳統OFDM低；也由於轉換矩陣是循環矩陣，能夠和通道矩陣結合，讓接收端的複雜度降低並且仍然能用一階頻域等化器(One-Tap Frequency Domain Equalizer, 1-Tap FDE)補償回來；除此之外，因為轉換矩陣的傅立葉轉換是么正矩陣(Unitary Matrix)，預編碼OFDM可以視為是多載波分碼多工(Multi-carrier Code Division Multiple Access, MC-CDMA)的一種。
特別值得注意的一點是，我們提出的MC-CDMA系統應用在上行傳輸(Uplink)因為展頻碼正交性失去而產生多重存取干擾(Multiple Access Interference, MAI)的問題時，會較傳統使用Walsh-Hadamard Matrix的MC-CDMA系統為優。

Precoded Orthogonal Frequency Division Multiplexing (OFDM) Systems provide high data rate wireless communications. A precoding matrix multiplying by the modulated symbols in the frequency domain obtains frequency diversity. However, it causes high computational complexity. Due to reduce computational complexity, authors let the Walsh-Hadamard matrix as the precoding matrix and combined with the inverse fast Fourier transform matrix to generate a new transform matrix in previous literature. However, the improvement is limited. In this paper, the sparse Gaussian integer sequence (SGIS), whose real parts and imaginary parts are both integers, is employed to construct the transform matrix, where the transform matrix is a circular matrix and each column consist of a SGIS. The number of nonzero elements of a SGIS is uncorrelated to the sequence length and is 16 at most. Therefore, the percentage of reducing complexity is increased obviously as increasing the number of subcarriers. Moreover, the peak-to-average power ratio of the proposed systems is much lower than traditional OFDM systems. Furthermore, the complexity of receiver is also be decreased since the transform matrix is a circular matrix. The transform matrix can be combined with the channel matrix and be compensated together by the one-tap equalizer in the frequency domain. Besides, since the fast Fourier transform of the proposed transform matrix is a unitary matrix, the proposed precoded OFDM system can be viewed as a multi-carrier code division multiple access (MC-CDMA) system. It is worth noting that the proposed MC-CDMA system in uplink is more robust to the multiple access interference (MAI) than the traditional MC-CDMA system with Walsh-Hadamard matrix, where the MAI is caused by losing the orthogonality among spreading codes.

論文審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
目錄 vi
圖次 viii
表次 x
第一章 概論 1
1.1 研究動機 2
1.2 論文架構 3
第二章 系統模型 4
2.1 正交分頻多工系統之基本架構 4
2.2多載波分碼多重存取與預編碼正交分頻多工 8
第三章 轉換矩陣設計 11
3.1 預編碼矩陣與轉換矩陣之關係 11
3.2 使用完美序列之轉換矩陣產生方法 13
第四章 接收端設計與系統效能 15
4.1預編碼正交分頻多工之傳送訊號與接收機設計 15
4.2 預編碼正交分頻多工之錯誤率分析 17
4.2.1 迫零均衡等化器 18
4.2.2 最小方均根誤差等化器 19
4.3 預編碼正交分頻多工運用在上行傳輸 21
第五章 模擬結果與討論 23
5.1 三種型態的接收機效能 24
5.2 模擬值與理論值 26
5.3 峰均值功率比 28
5.4 錯誤率比較 30
5.5 上行傳輸錯誤率 32
5.6 時變通道效能 34
第六章 結論 36
參考文獻 37
中英對照表 42
縮寫對照表 48

[1] L. J. Cimini, “Analysis and simulation of a mobile radio channel using orthogonal frequency division multiplexing,” IEEE Trans. Commun., vol. 33, no. 7, pp. 665–675, Jul. 1985.
[2] W. Y. Zou and Y. Wu, “COFDM: An overview,” IEEE Trans. Broadcast., vol. 41, no. 1, pp. 1–8, Mar. 1995.
[3] Y. Wu and W. Y. Zou, “Orthogonal frequency division multiplexing: a multi-carrier modulation scheme,” IEEE Trans. Consum. Electron., vol. 41, no. 3, pp. 392–399, Aug. 1995.
[4] H. C. Wu, “Analysis and characterization of intercarrier and interblock interferences for wireless mobile OFDM systems,” IEEE Trans. Broadcast., vol. 52, no. 2, pp. 203–210, Jun. 2006.
[5] IEEE Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: High-Speed Physical Layer in the 5 GHz Band, IEEE Std. 802.11a-1999, Sep. 1999.
[6] IEEE Standard for Local and Metropolitan Area Networks, IEEE Std. 802.16-2004, Oct. 2004.
[7] Radio broadcasting system: Digital audio broadcasting (DAB) to mobile, portable and fixed receivers, ETSI, ETS 300 401, 1.3.2 ed., 2000.
[8] Digital video broadcasting (DVB): Framing structure, channel coding and modulation for digital terrestrial television, ETSI, EN 300 744, 1.3.1 ed., 2000.
[9] S. H. Tsai, Y. P. Lin, and C. C. J. Kuo, “MAI-free MC-CDMA systems based on Hadamard–Walsh codes,” IEEE Trans. Signal Process., vol. 54, no. 8, pp. 3166–3179, Aug. 2006.
[10] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun., vol. 42, no. 10, pp. 2908–2914, Oct. 1994.
[11] H. H. Chen, J. F. Yeh, and N. Suehiro, “A multicarrier CDMA architecture based on orthogonal complementary codes for new generations of wideband wireless communications,” IEEE Commun. Mag., vol. 39, no. 10, pp. 126–135, Oct. 2001.
[12] I. Oppermann, P. Van Rooyen, and B. Vucetic, “Effect of sequence selection on MAI suppression in limited spreading CDMA systems,” Wireless Networks, vol. 4, no. 6, pp. 471–478, Oct. 1998.
[13] W. M. Jang, L. Nguyen, and P. Bidarkar, “MAI and ICI of synchronous downlink MC-CDMA with frequency offset,” IEEE Trans. Wireless Commun., vol. 5, no. 3, pp. 693–703, Mar. 2006.
[14] S. Hara and R. Prasad, “Overview of multicarrier CDMA,” IEEE Commun. Mag., vol. 35, no. 12, pp. 126–133, Dec. 1997.
[15] S. Hara and R. Prasad, “DS-CDMA, MC-CDMA and MT-CDMA for mobile multi-media communications,” in Proc. IEEE Veh. Technol. Conf., Atlanta, USA, Apr. 1996, vol. 2, pp. 1106–1110.
[16] L. L. Yang and L. Hanzo, “Performance of generalized multicarrier DS-CDMA over Nakagami-m fading channels,” IEEE Trans. Commun., vol. 50, no. 6, pp. 956–966, Jun. 2002.
[17] Y. Cao, T. T. Tjhung, and C. C. Ko, “Performance of a new premulticoded multicarrier DS-CDMA system in Nakagami fading,” IEEE Trans. Commun., vol. 55, no. 7, pp. 1363–1373, Jul. 2007.
[18] A. S. Ling and L. B. Milstein, “The effects of spatial diversity and imperfect channel estimation on wideband MC-DS-CDMA and MC-CDMA,” IEEE Trans. Commun., vol. 57, no. 10, pp. 2988–3000, Oct. 2009.
[19] D. K. Kim and S. H. Hwang, “Capacity analysis of an uplink synchronized multicarrier DS-CDMA system,” IEEE Commun. Lett., vol. 6, no. 3, pp. 99–101, Mar. 2002.
[20] G. Manglani and A. K. Chaturvedi, “Multi-tone CDMA design for arbitrary frequency offsets using orthogonal code multiplexing at the transmitter and a tunable receiver,” IET Commun., vol. 5, no. 15, pp. 2157–2166, Oct. 2011.
[21] N. Yee, J. P. M. G. Linnartz, and G. Fettweis, “Multi-carrier CDMA in indoor wireless radio networks,” in Proc. IEEE Int. Symp. Personal Indoor and Mobile Radio Communications (PIMRC), Yokohama, Japan, Sep. 1993, pp. 109–113.
[22] N. Yee, J. P. M. G. Linnartz, and G. Fettweis, "Multi-carrier CDMA in indoor wireless radio networks," IEICE Trans. Commun., vol. E77-B, no. 7, pp. 900–904, Jul. 1994.
[23] W. M. Jang, L. Nguyen, and M. W. Lee, “MAI and ICI of asynchronous uplink MC-CDMA with frequency offset,” IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2164–2179, Jul. 2008.
[24] J. C. Lin, “Low-complexity noncoherent PN code chip timing recovery with resistance to MAI for a bandlimited CDMA Receiver,” IEEE Trans. Veh. Technol., vol. 52, no. 5, pp. 1215–1328, Sep. 2003.
[25] S. Boussakta and A. G. J. Holt, “Fast algorithm for calculation of both Walsh- Hadamard and Fourier transforms (FWFTs),” IEE Election. Lett., vol. 25, no. 20, pp. 1252–1354, Sep. 1989.
[26] S. Wang, S. Zhu, and G. Zhang, “Walsh- Hadamard coded spectral efficient full frequency diversity OFDM system,” IEEE Trans. Commun., vol. 58, no. 1, pp. 28–34, Jan. 2010.
[27] H. Bogucka, “Application of the joint discrete Hadamard-inverse Fourier transform in a MC-CDMA wireless communication system-performance and complexity studies,” IEEE Trans.Wireless Commun., vol. 3, no. 6, pp. 2013–2018, Nov. 2004.
[28] M. S. Ahmed, S. Boussakta, B. S. Sharif, and C. C. Tsimenidis, “OFDM based on low complexity transform to increase multipath resilience and reduce PAPR,” IEEE Trans. Signal Process., vol. 59, no. 12, pp. 5994–6007, Dec. 2011.
[29] C. P. Li, S. H. Wang, and C. L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM Systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
[30] W. W. Hu, S. H. Wang, and C. P. Li, “Gaussian integer sequences with ideal periodic autocorrelation functions,” IEEE Trans. Signal Process., vol. 60, no. 11, pp. 4006–4016, Nov. 2012.
[31] J. G. Proakis and M. Salehi, Digital Communications, 5th ed. New York, 2008: McGraw-Hill.
[32] G. Faria, J. A. Henriksson, E. Stare, and P. Talmola, “DVB-H: digital broadcast services to handheld devices,” Proc. IEEE., vol. 94, no. 1, pp. 194–209, Jan. 2006.
[33] L. Rugini, P. Banelli, and G. Leus, “Simple equalization of time-varying channels for OFDM,” IEEE Commun. Lett., vol. 9, no. 7, pp. 619–621, Jul. 2005.