在採用單一字元之單載波(unique-word based single carrier (UW-SC)) 系統中，我們可以像正交分頻多工 (OFDM) 系統一樣使用低複雜度且有效的頻域等化技術來消除非時變環境中多重路徑干擾 (multipath interference)所造成的符距間干擾 (ISI)，使得此系統對於頻率選擇衰減 (frequency selective fading)非常強健。但是都卜勒效應同時也造成了時間選擇衰減 (time selective fading)，這破壞了原本通道在頻域上的正交特性，使得原先的單閥門等化器不再能夠有效的使用。因此必須再提出其他的方法來抵制時變環境中的符距間干擾。
線性最小均方誤差 (linear minimum mean square error) 法則提供了一個有效的解決方案卻需耗費相當高的複雜度。在這篇論文中，我們利用通道在時域上的稀疏特性提出了一個低複雜度的區塊最小均方誤差 (block MMSE) 等化器降低線性最小均方誤差方法的複雜度。利用先前提出的等化器在時變通道的影響下所獲得的時間分集 (time diversity)，我們可以使用平均法改善最小均方誤差等化器的效能。在前面兩個方法的基礎下，同時考慮此系統所提供的單一字元資訊，最後可以提出一個適應性決策回授等化器 (adaptive decision feedback equalizer) 的架構，再進一步消除前一級等化器所殘留下來的符距間干擾並有效地降低位元誤差率 ( bit error rate)。
最後，從電腦模擬結果以及表格分析，我們可以看出此論文提出的方法不僅有效地消除符距間干擾，擁有相當於線性最小均方誤差的位元錯誤率而且相較於線性最小均方誤差以及其他現存的消除法，此等化器還大幅度降低了複雜度。可以說是一個非常實用的設計。

Unique word based single carrier (UW-SC) systems have been proposed as an alternative to orthogonal frequency division multiplexing (OFDM) systems. UW-SC not only avoids the peak-to-average power ratio problem that plagues OFDM but also supplies the known information of unique words for additional purposes. Although UW-SC is very robust to frequency selective fading in a multipath environment, it is sensitive to the time selective in wireless channel that corrupts the orthogonality of the channel matrix in the frequency domain.
In this thesis, we first derive a low-complexity time-domain block minimum mean-squared error (MMSE) solution as a feedforward filter for UW-SC systems in the presence of inter-symbol interference (ISI) caused by doubly selective channel. For residual ISI reduction, we also present a decision feedback filter after the feedforward filter to form a new decision feedback equalizer adapted by unique word. Simulation results and complexity comparisons are given to show that the proposed method has considerably satisfactory performance and lower complexity than linear MMSE and iterative MMSE.

[1] D. Falconer, S. L. Ariyavisitakul, A. B. Seeyar, and B. Edison, “Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems”, IEEE Commun. Mag., vol. 6, no. 4, pp.58-66, Apr.2002.

[2] IEEE Std 802.16e-2005, “IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems”, February 2006.

[3] H. Sari, G. Karam, and I. Jeanclaude, “Transmission techniques for digital terrestrial TV broadcasting”, IEEE Commun. Mag., vol. 33, no. 2, pp. 100-109, Feb. 1995.

[4] L. H. Lee, and S. M. Phoong, “Performance Study of OFDM and SC-CP Systems in Nonideal Transmission Environment”, Institute of Communication Engineering National Taiwan University.

[5] H. Witschnig, T. Mayer, M. Petit, H. Hutzelmann, A. Springer, R. Weigel, “The Advantages of A Unique Word for Synchronisation and Channel Estimation in a SC/FDE System”, IEE

[6] L. Deneire, B. Gyselinckx, and M. Engels, “Training Sequence versus Cyclic Prefix-A New Look on Single Carrier Communication”, IEEE Commun Lett. Vol. 5, no. 7, July 2001

[7] H. Witschnig, T. Mayer, A. Koppler, L. Maurer, M. Huemer, and R. Weigel, “A Different Look on Cyclic Prefix for SC/FDE”, IEEE conf., 2002

[8] Theodore S. Rappaport, “Wireless Communications Principles and Practice”, Prentice Hall, 1996

[9] Philip Schniter, “Low-Complexity Equalization of OFDM in Doubly Selective Channels”, IEEE Trans. Signal Processing, vol. 52, no. 4, April 2004

[10] Peter M. Clarkson, “ Optimal and Adaptive Signal Processing”, CRC Press, 1993

[11] P. Schniter and H. Liu, “Iterative Equalization for Single-Carrier Cyclic Prefix in Doubly –Dispersive Channels”, in Proc. Asilomar Conf. Signals, Systems, Computers, vol. 1, Nov. 2003, pp. 502-506.

[12] B. K. Ng, and D. Falconer, “A Novel Frequency Domain Equalization Method for Single-Carrier Wireless Transmissions over Doubly-Selective Fading Channels”, IEEE GLOBECOM ’04, vol. 1, pp. 237-241, Dec 2004.

[13] A. Ahmed, M. Sellathurai, S. Lambotharan, and J. A. Chambers, “ Low-Complexity Iterative Method of Equalization for Single Carrier With Cyclic Prefix in Doublly Selective Channels, IEEE Lett. Signal Processing, vol. 13, no. 1, pp. 5-8, Jan. 2006.

[14] C. Tepedelenlioglu, and G. B. Giannakis, “Transmitter Redundancy for Blind Estimation and Equalization of Time- and Frequency-Selective Channels”, IEEE Trans. on Signal Processing, vol. 48, no. 7, pp. 2029-2043, July 2000.

[15] A. Tang, and G. Leus, “A Receiver Architecture for Maximum Diversity Transmissions over Doubly-Selective Channels”, IEEE 6th workshop on signal Processing Advances, pp. 171-175, 2005.

[16] M. K. Tsatsanis, and G. B. Giannakis, “ Modeling and Equalization of Rapidly Fading Channels”, International Journal of Adaptive Control and signal Processing, vol. 10, pps. 159-176, 1996.

[17] G. B. Giannakis, and C. Tepedelenlioglu, “Basis Expansion Models and Diversity Techniques for Blind Identification and Equalization of Time-Varying Channels”, IEEE Proceedings, vol. 86, no. 10, Oct. 1998.

[18] H. Liu, and G. B. Giannakis, “Deterministic Approaches for Blind Equalization of Time-Varying Channels with Antenna Arrays”, IEEE Trans. Signal Processing, vol. 46, pp. 3003-3013, Nov. 1998.

[19] N. al-Dhahir, and J. M. Cioffi, “MMSE Decision-Feedback Equalizaers: Finite-Length Results”, IEEE Trans. on Information Theory, vol. 41, no. 4, pp. 961-975, Jul. 1995.

[20] D. K. Kim, and P. Park, “Adaptive Self-Orthogonalizing Per-Tone Decision Feedback Equalizer for Single Carrier Modulations”, IEEE Lett. Signal Processing, vol. 13, no. 1, pp. 21-24, Jan. 2006.

[21] A. A. (Louis) Beex, R. E. Goshorn, and J. R. Zeidler, “Improved Look-Direction Interference Suppression in NLMS Generalized Sidelobe Canceler using Dynamic Weight Behavior”, 9th IASTED International Conference on Signal and Image Processing, 2003.

[22] Gordon L. Stuber, “Principles of Mobile Communication 2nd edition”, Kluwer Academic Publishers, 2001.