投機式波束(Opportunistic beamforming)是一個在同一個時間服務很多使用者，但這個方法有個很重要的點是所傳送的波束必須要盡可能的減少干擾。在傳統的方法中使用有限的回傳位元來回傳使用者的通道資訊，使用的方法是在兩邊都有一樣的編碼本，在這些編碼本(Codebook)中，選擇一組最適合這個系統的波束矩陣，使用者只要回傳引用索瑪給傳送端就可以了。但是一旦使用者改變了，我們就需要找尋新的編碼，如此一來就需要額外的複雜度，在先前的研究中，有人提出了使用一個固定的波束矩陣，雖然可以少回傳位元，但是這個方法的波束矩陣是指向每個群集的中心點，不是指向要傳送的使用者，所以他的效能會下降。
本論文中，我們提出一個在投機式波束之固定矩陣中(Opportunistic beamforming with single beamforming matrix )加入連續迭代的旋轉矩陣。加入旋轉矩陣後可以得到更好的波束矩陣，我們運用的這個方法，會增加一些回傳位元，來傳送旋轉矩陣的角度，而且計算複雜度由於用Divide-and-Conquer 的方法，把大問題切成小問題所以計算複雜度也有所降低，加入這個方法後可以讓我們的系統效能上升。最後再運用能量分配可以讓我們系統更加的上升。

Opportunistic beamforming support multiple users at a time, it is important to form multiple beams with as little interference as possible. In the conventional approach with limited feedback of channel, the method used is the users and base station have the same codebook, and user select a beamforming matrix of the most suitable for this system , the user have only feedback index to base station. But once the user has changed, we need to find new beamforming matrix, this way the need for additional complexity, in a previous study, it was proposed the use of a fixed beam matrix, although this method can reduce feedback but the beamforming matrix is a single beamforming matrix is used, the performance can be degraded.
In this thesis, we propose an Opportunistic beamforming with single beamforming matrix adding successive iterations of the rotation matrix. we use this method, it will be increase feedback on angles, and then we can get rotation matrix, not only computational complexity can use divide-and-conquer type of approach, It works by recursively breaking down a problem into two or more sub-problems of the same type, so it can complexity decreased, but also can improved system performance. we calculate the energy distribution, and then system can improved performance.

[論文審定書+I]
[致謝+II]
[中文摘要+III]
[Abstract+IV]
[圖次+VII]
[第一章 導論+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 集中式天線和分散式天線的差異+4]
[2.2集中式天線和分散式天線的系統架構+6]
[第三章 投機式波束矩陣+8]
[3.1投機式波束+8]
[3.2傳統投機式波束+8]
[3.3投機式波束之固定波束矩陣+10]
[第四章 投機式波束旋轉之能量分配+14]
[4.1 投機式波束加入旋轉矩陣+14]
[4.2投機式波束加入旋轉矩陣下結合Cross-Entropy的能量分配+20]
[第五章 模擬結果+23]
[5.1投機式波束加入旋轉矩陣下的效能比較+24]
[5.2投機式波束加入旋轉矩陣下的在不同SNR下效能比較+26]
[5.3投機式波束加入旋轉矩陣下的加入能量分配+28]
[第六章 結論+30]
[參考文獻+31]
[中英對照表+34]
[縮寫對照表+38]

[1] J.Choi, “Opportunistic beamforming with single beamforming matrix for virtual antenna arrays,” IEEE Trans. Veh Technol., vol. 60, no. 3, Mar. 2011.
[2] R.de Francisco, and D. T. M. Slock,“An optimized unitary beamforming technique for MIMO broadcast channels.”IEEE Trans. Wireless Commun., vol. 9, no. 3, pp. 84 － 90 , Mar. 2010.
[3] R. Zakhour and D. Gesbert, “Coordination on the MISO interference channel using the virtual SINR framework," in Proc. ITG/IEEE Workshop Smart Antennas, Feb. 2009.
[4] H. Kwon, W. Jang, and John M. Cioffi, “Predetermined power allocation for opportunistic beamforming with limited feedback,” IEEE Trans. Wireless Commun., vol. 10, no. 1, Jan. 2009.
[5] B. L. Ng, J. S. Evans, S. V. Hanly, and D. Aktas, “Distributed downlink beamforming with cooperative base stations,” IEEE Trans. Inf. Theory, vol. 54, pp. 5491－5499, Dec. 2008.
[6] A.V. Knyazev, and M.E. Argentati, “Principal angles between subspaces in an a-based scalar product: algorithms and perturbation estimates.” Society for industrial and Applied Mathematics., vol. 23, no. 6, pp. 2009–2041.

[7] J. Choi, “Performance limitation of closed-loop transmit antenna diversity over fast Rayleigh fading channels,” IEEE Trans. Veh. Techno., vol. 51, no. 4, pp. 771–775, Jul. 2002.
[8] T. Yoo, N. Jindal, and A. Goldsmith, “Multi-antenna downlink channels with limited feedback and user selection,” IEEE J. Sel. Areas Commun., vol. 25, no. 7, pp. 1478–1491, Sep. 2007
[9] V. Raghavan, R. W. Heath, and A. M. Sayeed, “Systematic codebook designs for quantized beamforming in correlated MIMO channels,” IEEE J. Sel. Areas Commun., vol. 25, no. 7, pp. 1298–1310, Sep. 2007.
[10] D. J. Love, R. W. Heath, and T. Strohmer, “Grassmannian beamforming for multiple-input multiple-output wireless systems,” IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2735–2747, Oct. 2003.
[11] M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channels with partial side information,” IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 506–522, Feb. 2005.
[12] F. Boccardi and H. Huang, “Optimum power allocation for the MIMO BC zero-forcing precoder with per-antenna power constraints," in Proc. 40th Annual Conf. Inf. Sciences Syst., Mar. 2006.

[13] Z. Ding, W. H. Chin, and K. K. Leung, “Distributed beamformingand power allocation for cooperative networks,”IEEE Trans. Wireless Commun., vol. 6, no. 5, pp. 1817－1822, May 2008.
[14] M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channels with partial side information,” IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 506–522, Feb. 2005.
[15] E. Visotsky and U. Madhow, “Optimum beamforming using transmit antenna arrays,” in Proc. IEEE Veh. Technol, May 1999, pp. 851–856.
[16] M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channelwith partial side information,” IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 506–522, Feb. 2005.
[17] V. Sharma and S. Lambotharan, “Multiuser downlink MIMO beamforming using an iterative optimization approach," in Proc. IEEE Veh. Technol. Conf., Sep. 2006.