雖然能夠從傳統上所使用的瞬時(instant)或統計(statistic)型的通道模 型找出傳送和接收波束形成權重向量，然而如此的通道模型並無法提供有意義的 通道資訊。本研究將正交分頻多工的概念導入半相關度通道模型中，提出一種新 的空間特徵結構通道模型，將通道在時間和空間上的因子分離成數個路徑群組的 等效路徑增益、等效傳送角度、組合簽名向量和路徑延遲時間。如此的資訊量不 只能夠用於找出位於傳送和接收端的波束形成權重向量，更能藉此說明波束形成 技術和空間通道之間的關聯性，進而能夠針對不同的通道特性找出相對應的最佳 策略和演算法。
從前面章節的理論推導和模擬分析中，證明了所提出的空間特徵結構通道模 型確實能夠合理解釋通道對於各種波束形成演算法在效能表現上所造成的影 響。當然本篇論文也提出了一套有效的演算法去估測出如此的空間特徵結構通道 矩陣，從模擬分析中也證實了所提出的估測方法相當準確。
從通道的空間特徵結構可以得到一些重要的結論。對於當通道為非時變性 時，將空間特徵結構通道矩陣轉換成通道狀態資訊(CSI)矩陣，使用最大比例傳 輸最大比例接收(MRT，MRC)聯合估測傳送和接收權重向量的方式，可以使整個系 統得到最佳的系統容量。然而在半相關度的時變通道環境下，使用空間特徵結構 分別針對傳送和接收端獨立設計出最佳的波束形成器反而是最有效的策略。
基本上就通道的空間特性而言，當傳輸路徑具有很好的方向性時，以路徑角 度為設計基礎的波束形成器會有較佳的效能；當傳輸路徑呈現高度的角度擴展特 性時，利用信號雜訊的特徵結構反而是較好的設計策略。然而就通道的時間特性 而言，當通道為非時變性時，利用瞬時通道的資訊能夠得到最佳化的波束形成權 重向量；而當通道為時變性時，使用統計性質的通道矩陣所估測出的權重向量會 有較好的效能表現。
本篇論文在波束形成權重向量設計上，主要研究的重點放在全域(global) 的權重向量設計上，也就是在所有子載波上使用相同的波束形成權重向量，然而 如此的設計方式往往無法達到最佳的系統效能。未來研究工作將探討加入子載波 群組化的權重向量設計，也就是相鄰的數個子載波使用相同的傳送和接收權重向 量，然而有兩項技術面的問題待克服，第一個問題為如何在時變通道的環境下維 持一定的效能，第二個需要解決的問題是如何有效處理這些相鄰數個子載波的通 道等化。
從對半相關度通道模型的探討和模擬分析中可以發現，對於位於行動台(MS) 的接收端波束形成器，較佳的設計策略是利用訊號雜訊的特徵結構。然而在快速 衰減(fast fading)通道環境下，如何找出最佳的接收權重向量是相當困難的，
一個針對如此通訊環境而產生的全新演算法是值得做為未來的研究主題。
對於多重用戶傳送波束形成技術，本篇論文也提出一個全新的方式，利用所 提出的通道空間特徵結構設計多重用戶時間槽排程演算法，從模擬的結果中可以 發現確實能夠有效提升整體系統容量。然而在如何設計一個更有效率的排程器方 面，仍然有待未來去研究和探討。最後，希望能將所提出之新式MIMO-OFDM波束 形成技術實際應用於802.16e、802.11n以及第四代行動通訊系統上。
參考文獻
[1] S. Bellofiore, J. Foutz, C. A. Balanis, and A. S. Spanias, “Smart-antenna system for mobile communication networks Part 2: Beamforming and network throughput,” IEEE Antenna’s and Propagation Magazine, Vol. 44, No. 4, Aug.
2002.
[2] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, John Wiley &
Sons, New York, 1981.
[3] H. L. V. Trees, Optimum Array Processing, John Wiley & Sons, New York, 2002.
[4] B. V. Veen and K. Buckley, “Beamforming: A versatile approach to spatial filtering,” IEEE ASSP Magazine, pp. 4-22, Apr. 1988.
[5] A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall, New Jersey, 1989.
[6] J. Litva and T. Lo, Digital Beamforming in Wireless Communications, Artech House Publishers, Massachusetts, 1996.
[7] W.-W. Chang, “Efficient design of beamforming techniques for OFDM systems,”
M.S. thesis, Institute of Electronics, National Chiao Tung University, Hsin-Chu, Taiwan, 2006.
[8] R. V. Nee and R. Prasad, OFDM for Wireless Multimedia Communications, Artech House, Jan. 2000.
[9] Z. Lei and F. P. S. Chin, “Post and pre-FFT beamforming in an OFDM System,”
VTC-2004-Spring. 2004 IEEE 59th.
[10] B. Farhang-Boroujeny, Adaptive Filters Theory and Applications, Wiley, Oct.
2000.
[11] M. Budsabathon, Y. Hara, and S. Hara, “Optimum beamforming for pre-FFT
OFDM adaptive antenna array,” IEEE Transactions on Vehicular Technology, Vol. 53, No. 4, Jul. 2004.
[12] B. Liu, R. Jin, and Y. Fan, “Modified pre-FFT OFDM adaptive antenna array with beam-space channel estimation,” Electronics Letters, Vol. 40, Issue 5, Mar.
2004.
[13] L. Fan, H. Zhang, and C. He, “Minimum bit error rate beamforming for pre-FFT OFDM adaptive antenna array,” VTC-2005-Fall. 2005 IEEE 62th.
[14] Z. Lei and F. P. S. Chin, “Post and pre-FFT beamforming in an OFDM System,”
VTC-2004-Spring. 2004 IEEE 59th.
[15] Y. Sun and H. Matsuoka, “A novel adaptive antenna architecture - subcarrier clustering for high-speed OFDM systems in presence of rich co-channel interference,” VTC-2002-Spring. IEEE 55th.
[16] B. Mondal and R.W. Heath, “An upper bound on SNR for limited feedback MIMO beamforming systems,” IEEE ITW 2004, San Antonio, Texas, Oct. 2004.
[17] D. J. Love, R. W. Heath, and T. Strohmer, “Grassmannian beamforming for multiple-input multiple-output wireless systems,” IEEE Transactions on Information Theory, Vol. 49, No. 10, Oct. 2003.
[18] P. Xia and G.. B. Giannakis, “Design and analysis of transmit-beamforming based on limited-rate feedback,” IEEE Transactions on Signal Processing, Vol.
54, No. 5, MAY 2006.
[19] J. C. Roh and B. D. Rao, “Transmit beamforming in multiple-antenna systems with finite rate feedback: A VQ-based approach,” IEEE Transactions on Information Theory, Vol. 52, No. 3, Mar. 2006.
[20] V. Raghavan, A. M. Sayeed, and N. Boston, “Near-optimal codebook constructions for limited feedback beamforming in correlated MIMO channels with few antennas,” IEEE ISIT 2006, Seattle, USA, Jul. 2006.
[21] A. Barg and D. Y. Nogin, “Bounds on packings of spheres in the Grassmann manifold,” IEEE Transactions on Information Theory, Vol. 48, pp. 2450-2454, Sept. 2002.
[22] J. H. Conway, R. H. Hardin, and N. J. A. Sloane, “Packing lines, planes, etc.:
Packing in Grassmannian spaces,” Experimental Mathematics, Vol. 5, pp.
139-159, 1995.
[23] D. Gerlach and A. Paulraj, “Adaptive transmitting antenna methods for multipath environments,” Global Telecommunications Conference, 1994.
[24] A. Tarighat, M. Sadek, and A. H. Sayed, “A multi user beamforming scheme for downlink MIMO channels based on maximizing signal-to-leakage ratios,” IEEE Transactions on Signal Processing, Vol. 3, pp. 18-23, Mar. 2005.
[25] N. D. Sidiropoulos, T. D. Davidson, and T. Luo, “Transmit beamforming for physical-layer multicasting,” IEEE Transactions on Signal Processing, Vol. 54, No. 6, Jun. 2006.
[26] Y. R. Zheng and C. Xiao, “Simulation models with correct statistical properties for Rayleigh fading channels,” IEEE Transactions on Communications, Vol. 51, No. 6, pp. 920-928, Jun. 2003.
[27] W. C. Jakes, Microwave Mobile Communications. Piscataway, NJ: IEEE Press, 1994.
[28] C.-J. Tsai, “Design of channel estimation and data detection for OFDM systems in time-varying and multipath fading channels,” M.S. thesis, Institute of Electronics, National Chiao Tung University, Hsin-Chu, Taiwan, Jul. 2006.
[29] D. Gesbert, H. Bolcskei, D. A. Gore, and A. J. Paulraj, “Outdoor MIMO wireless channels: Models and performance prediction,” IEEE Transactions on Communications, Vol. 50, No. 12, Dec. 2002.
[30] M. T. Ivrlac, T. P. Kurpjuhn, C. Brunner, and W. Utschick, “Efficient use of
fading correlations in MIMO systems,” VTC-2001-Fall. 2001 IEEE 54th.
[31] “3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 6),” 3GPP TR 25.996 V6.1.0 (2003-09) Technical Report.
[32] D. Bartolome and A. I. Perez-Neira, “Spatial scheduling in multiuser wireless systems: From power allocation to admission control,” IEEE Transactions on Wireless Communications, Vol. 5, Issue 8, Aug. 2006.
[33] M. H. Er, “Linear antenna array pattern synthesis with prescribed broad nulls,”
IEEE Transactions on Antenna and Propagation, Vol. 38, NO. 9, Sept. 1990.
[34] B. Widrow and J. Mccool, “A comparison of adaptive algorithms based on the methods of steepest descent and random search,” IEEE Transactions on Antenna and Propagation, Vol. AP-24, pp. 615-637, Sept. 1976.
[35] Y. Zhao and A. Huang, “A novel channel estimation method for OFDM mobile communication systems based on pilot signals and transform-domain processing,”
Proceedings of Vehicular Technology Conference, 1997 IEEE 47th, vol. 3, pp.
2089-2094, 1997.
[36] B. Yang, K. B. Letaief, R. S. Cheng, and Z. Cao, “Windowed DFT based pilot-symbol-aided channel estimation for OFDM systems in multipath fading channels,” Proceedings of Vehicular Technology Conference, 2000. VTC 2000-Spring Tokyo. 2000 IEEE 51st, vol. 2, pp. 1480-1484, 2000.
自傳
李飛群，1974 年出生於台北縣。2005 年自國立高雄大學電機工程學系畢業，
隨即進入國立交通大學電子工程研究所攻讀碩士學位，致力於無線通訊系統研 究。論文題目是應用於行動通訊中以空間特徵結構為設計基礎之 MIMO-OFDM 波束 形成技術。