在具有前置循環的通訊系中，如正交分頻多工系統或單載波前置循環調變系統，當循環字首的長度大於通道脈衝響應的長度時，循環字首除了可以避免訊號的符元間干擾外，也將傳送訊號與通道之間的關係由線性摺積轉換為循環摺積。這也使得低複雜度的一階頻域通道估測及補償變為可行。然而循環字首也同時降低了通訊系統的頻寬及功率的使用效益。因此，如何減少循環字首的長度是相當重要的議題。在循環字首長度小於通道長度的情況下，我們將在本篇論文中探討接收端如何利用等化器的特殊設計，使等效通道的長度縮短。本篇論文以矩陣方式描述信號模型。我們利用矩陣描述通道如何經等化器處理轉換為等效通道，並在不同限定條件下利用矩陣特徵向量推導等化器的係數。我們進一步提出一種新的縮短通道等化器使縮短訊號能量干擾比最大。並說明所提出的演算法在減小符元間干擾效能上與傳統方式相同，而所需要的浮點運算次數更比傳統演算法低。

Considering the communication systems with cyclic prefix (CP), such as orthogonal frequency-division multiplexing (OFDM) modulation and single-carrier cyclic prefixed (SCCP) modulation, when the length of CP is longer than the channel length, the use of cyclic prefix (CP) does not only eliminate the inter-block interference, but also convert linear convolution of the transmitted signal with the channel into circular convolution. Unfortunately, the use of CP significantly decreases the bandwidth utilization. Therefore, to reduce the length of CP is a critical issue. The thesis investigates that how to design a channel-shortening equalizer (CSE) at receiver which forces the length of the effective channel response as short as the CP length. The thesis describes the signal model as a matrix form. The effect channel response after CSE is investigated and then the coefficient of channel shortening filter is obtained using singular value decomposition method under various criterions. We further propose a novel CSE maximizing the shortening signal-to-interference ratio. In addition, it is demonstrated that the proposed CSE has the same performance as the conventional scheme but a lower computation complexity.

第一章 導論…………………………………………………………………………1
1.1 研究動機……………………………………………………………….2
2.1 論文架構……………………………………………………………….2
第二章 具有前置循環的通訊系統…………………………………………………3
2.1 正交分頻多工系統…………………………………………………….3
2.2 單載波前置循環系統………………………………………………….6
第三章 縮短通道等化器的設計……………………………………………………8
3.1 縮短通道等化器架構………………………………………………….8
3.2 最佳化縮短通道等化器架構………………………………………...11
3.2.1最佳化縮短通道等化器架構(I)………………….…………….11
3.2.2最佳化縮短通道等化器架構(II)………………………………12
3.2.3 效能分析………………………………………………………13
3.3 簡化的縮短通道等化器架構………………………………………...15
3.4 提出的縮短通道等化器架構………………………………………...17
第四章 演算法複雜度分析………………………………………………………..20
4.1 浮點運算單位………………………………………………………...20
4.2 Cholesky分解複雜度…………………………………………………21
4.3 Gauss-Jordan法求反矩陣複雜度……………………………………..23
4.4 運用解線性方程式法求反矩陣複雜度……………………………...27
4.5 求得反矩陣的演算法複雜度比較…………………………………...29
4.6 最佳化縮短通道等化器演算法的複雜度分析……………………...30
第五章 模擬結果與討論…………………………………………………………..34
5.1 最佳化縮短通道等化器效能分析…………………………………...34
5.2 等化器長度對縮短訊號能量干擾比的影響………………………...37
5.3 MAXSSIR與MINRRES減小符元間干擾效能差異…………….…..41
5.4 MAXSSIR(II)與MAXSSIR(III)的矩陣運算複雜度…………………41
第六章 結論………………………………………………………………………..46
中英對照表…………………………………………………………………………..47
英文縮寫對照表……………………………………………………………………..49
參考文獻……………………………………………………………………………..51

[1] R. D. J. van Nee, G. A. Awater, M. Morikura, H. Takanashi, M. A.Webster, and K. W. Halford, “New high-rate wireless LAN standards,” IEEE Commun Mag., vol. 37, no. 12, pp. 82-88, Dec. 1999.
[2] Air Interface For Fixed Broadband Wireless Access Systems, MAC and Additional PHY Specifications For 2–11 GHz, IEEE Std. 802.16a, 2003.
[3] Digital Video Broadcast. (DVB); Framing Structure, Channel Codingand Modulation For Digital Terrestrial Telev., ETSI EN 300 744 V1.4.1, The European Telecomm. Standards Inst., 2001.
[4] Radio Broadcast. System, Digital Audio Broadcast. (DAB) to Mobile, Portible, and Fixed Receivers, ETSI 300 401, The European Telecomm. Standards Inst., 1995-1997.
[5] D. H. Layer, “Digital radio takes to the road,” IEEE Spectrum, vol. 38, no. 7, pp. 40-46, Jul. 2001.
[6] D. D. Falconer, S. L. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., vol. 40, no. 4, pp. 58–66, Apr. 2002.
[7] H. Sari, G. Karam, and I. Jeanclaude, “Frequency-domain equalization of mobile radio and terrestrial broadcast channels,” in Proc. IEEE Global Commun. Conf. (IEEE GLOBECOM)’94, San Fransisco, CA, Nov. 1994, pp. 1-5.
[8] 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.
[9] N. Al-Dhahir and J. M. Cioffi, “Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach,” IEEE Trans. Inform. Theory, vol. 42, pp. 903-915, May 1996.
[10] D. Daly, C. Heneghan, and A. D. Fagan, “A minimum mean-squared error interpretation of residual ISI channel shortening for discrete multitone transceivers,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 4, 2001, pp. 2065-2068.
[11] P. J.W. Melsa, R. C. Younce, and C. E. Rohrs, “Impulse response shortening for discrete multitone transceivers,” IEEE Trans. Commun., vol. 44, pp. 1662-1672, Dec. 1996.
[12] R. K. Martin, C. R. Johnson Jr., M. Ding, and B. L. Evans, “Exploiting symmetry in channel shortening equalizers,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2003, vol. 5, pp. 97-100.
[13] N. Al-Dhahir and J. M. Cioffi, “Optimum finite-length equalization for multicarrier transceivers,” IEEE Trans. Commun., vol. 44, pp. 56-64, Jan. 1996.
[14] N. Lashkarian and S. Kiaei, “Optimum equalization of multicarrier systems: a unified geometric approach,” IEEE Trans. Commun., vol. 49, pp. 1762-1769, Oct. 2001.
[15] R. Schur and J. Speidel, “An efficient equalization method to minimize delay spread in OFDM/DMT systems,” in Proc. IEEE Int. Conf. Commun., Jun. 2001, vol. 5, pp. 1481-1485.
[16] X. Ma, L. Song, and J. Kleider, "Channel shortening equalization for differential OFDM systems," Proc. IEEE Workshop on Signal Processing Advances in Wireless Commun., Jun. 2005, pp. 860-864.
[17] J. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “Equalizer training algorithms for multicarrier modulation systems,” in Proc. IEEE Int. Conf. Commun., Geneva, Switzerland, May 1993, pp. 761-765.
[18] M. Nafie and A. Gatherer, “Time-domain equalizer training for ADSL,” in Proc. IEEE Int. Conf. Commun., Montreal, QC, Canada, Jun. 1997, vol. 2, pp. 1085-1089.
[19] N. Al-Dhahir, “FIR channel shortening equalizers for MIMO ISI channels,” IEEE Trans. Commun., vol. 49, no. 2, pp. 213-218, Feb. 2001.
[20] R.K. Martin, G. Ysebaert, and K. Vanbleu, “Bit error rate minimizing channel shortening equalizers for cyclic prefixed systems”, IEEE Trans. Signal Process., vol. 55, no. 6, pp. 2605-2616, Jun. 2007.
[21] G. Ysebaert, K. Van Acker, M. Moonen, and B. De Moor, “Constraints in channel shortening equalizer design for DMT- based systems,” Signal Process., vol. 83, no. 3, pp. 641-648, Mar. 2003.
[22] J. Balakrishnan, R. K. Martin, and C. R. Johnson Jr., “Blind, adaptive channel shortening by sum-squared auto-correlation minimization (SAM),” IEEE Trans. Signal Process., vol. 51, no. 12, pp. 3086-3093, Dec. 2003.
[23] R. K. Martin, J. Balakrishnan, W. A. Sethares, and C. R. Johnson Jr., “A blind, adaptive TEQ for multicarrier systems,” IEEE Signal Process. Lett., vol. 9, no. 11, pp. 341-343, Nov. 2002.
[24] Teruyuki Miyajima and Zhi Ding, “Second-order statistical approaches to channel shortening in multicarrier systems,” IEEE Trans. Signal Process., vol. 52, no. 11, pp. 3253-3264, Nov. 2004.
[25] J. R. W. Heath and G. B. Giannakis, “Exploiting input cyclostationarity for blind channel identification in OFDM systems,” IEEE Trans. Signal Process., vol. 47, pp. 848-856, Mar. 1999.
[26] X. Zhuang, Z. Ding, and A. L. Swindlehurst, “A statistical subspace method for blind channel identification in OFDM communications,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 5, 2000, pp. 2493-2496.
[27] X. Cai and A. N. Akansu, “A subspace method for blind channel identification in OFDM systems,” in Proc. IEEE Int. Conf. Commun., 2000, pp. 929-933.
[28] R. van Nee and R. Prasad, OFDM for Wireless Multimedia Communications, Boston: Artech House, 2000.
[29] A.V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2nd ed. New Jersey: Prentice-Hall, 1999.
[30] 謝哲光、陳嘉文。線性代數與動態系統〈第二版〉。全華圖書公司，2002。
[31] G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1989.