本論文主要由射線彈跳法去模擬研究四種不同屋頂和兩種不同環境材質，求得超寬頻多輸入多輸出系統的頻率響應，並計算和比較超寬頻通訊的通道容量，其中多輸出多輸入系統其通道容量與天線數量呈現線性成長，帶來高傳輸率以及高傳輸品質，藉此能提升系統傳輸率。
　　本論文研究使用的四種不同屋頂分別為：1.平面屋頂　2.三角形屋頂　3.栱形屋頂　4.金字塔形屋頂。兩種不同環境材質分別為：1.混凝土2.鐵皮屋。其次，使用2x2MIMO天線，以及4x4 MIMO天線對於此系統通道容量的影響，並發現到不論在何種環境之中，天線數量與通道容量呈現性關係，這些模擬的情形，在金字塔型屋頂有較高的通道容量且性能明顯的好於其他屋頂形狀。

This paper focuses on the research of channel capacity of Multiple-Input Multiple-Output (MIMO) system for four different geometrical shapes of roof in the materials of concrete and iron in the same environments are investigated. These four roofs include the flat shape roof, the triangle shape roof, the arched shape roof, and the pyramid shape roof. 
A ray-tracing technique is developed to calculate channel frequency responses in four different geometrical shape roofs, and the channel frequency response is further used to calculate corresponding channel capacity.
The channel capacities are calculated based on the realistic environment in this thesis. First, channel capacities of MIMO-UWB System with 2x2 MIMO antennas. Next, the of MIMO-UWB System with 4x4 MIMO antennas are calculated. The channel capacity of narrowband or wideband systems combining with MIMO have been shown that increases approximately linearly with the number of transmitting and receiving antennas.

第一章 概論	                                       1
1.1 研究背景	                                      1
1.2 研究動機	                                      5
1.3 研究內容簡介                                    	8
第二章 通道計算模型                              	9
2.1 無線電波傳播通道分析	                             9
2.2 通道計算模型分析	                            10
2.3 射線彈跳追蹤法程式流程分析	                   13
第三章  系統介紹	                                      17
3.1 多輸入多輸出窄頻系統	                            17
3.2 多輸入多輸出窄頻系統通道容量	                   21
3.2.1 建立在 CSI-B 狀態下	                             21
3.2.2 建立在只有 CSI-R 狀態下	                   22
3.3 影響MIMO容量因素	                             24
3.3.1 空間自由度（Spatial degree of freedom）	          24
3.3.2 特徵矩陣（Eigenmatrix）和條件數目（Condition number 26
3.4 MIMO-UWB系統之通道容量	                             27
第四章 模擬數值結果                              	28
4.1 模擬實驗的環境                               	28
4.2 模擬結果分析與比較	                            34
第五章 結論	                                      45
參考文獻	                                               46


圖目錄

圖1.1 SISO, SIMO, MISO和MIMO 示意圖	2
圖2.1求得通道頻率響應	10
圖2.2 SBR/Image 程式流程圖	16
圖3.1多輸入多輸出窄頻系統矩陣示意圖	17
圖3.2多輸入多輸出窄頻系統示意圖	19
圖3.3建立在 CSI-B 狀態下多輸入多輸出窄頻系統的等效架構圖	20
圖4.1平面屋頂之3D立體圖	30
圖4.2三角形屋頂之3D立體圖	31
圖4.3金字塔形屋頂之3D立體圖	32
圖4.4拱形屋頂之3D立體圖	33
圖4.5平面屋頂時不同材質屋頂與不同天線數量之通道容量比較圖	37
圖4.6三角屋頂時不同材質屋頂與不同天線數量之通道容量比較圖	38
圖4.7金字塔屋頂時不同材質屋頂與不同天線數量之通道容量比較圖		39
圖4.8拱形屋頂時不同材質屋頂與不同天線數量之通道容量比較圖	40
圖4.9 2x2MIMO在混凝土材質各種屋頂形狀之通道容量比較圖	41
圖4.10 3x3MIMO在混凝土材質各種屋頂形狀之通道容量比較圖	42
圖4.11 4x4MIMO在鐵皮材質各種屋頂形狀之通道容量比較圖	43
圖4.12 2x2MIMO在鐵皮材質各種屋頂形狀之通道容量比較圖	44
圖4.12 3x3MIMO在鐵皮材質各種屋頂形狀之通道容量比較圖	45
圖4.12 4x4MIMO在鐵皮材質各種屋頂形狀之通道容量比較圖	46

表目錄
表2.1 對應不同系統中空間自由度的數目	25

[1].Federal Communications Commission, “Revision of Part 15 of the Commission`s
Rules Regarding Ultra–Wideband Transmission System, First Peport and Order,” ET
Docket 98–153, FCC 02–48, Feb. 14, 2002, pp. 1–118.
[2]. Hovinen, V., Hamalainen, M. and Patsi, T.; “Ultra Wideband Indoor Radio Channel Models: Preliminary Results,” IEEE conference on Ultra Wideband Systems and Technologies, May 2002.
[3]. I. Oppermann, M. Hamalainen and J. Iinatti, UWB Theory and Applications, John
Wiley & Sons, 2004.
[4]. H. Jeffrey and Reed, An Introduction to Ultra Wideband Communication Systems,
Prentice Hall PTR, 2005.
[5] D. Tse and P. Viswanath, Fundamentals of Wireless Communication, United
Kingdom,” Cambridge University Press, 2005.
[6].J. G Prokis and M. Salehi, Digital Communications, McGraw-Hill, 2008
[7]. S.Haykin and M Moher, Modern Wireless Communications, Pearson Prentice Hall, 2005.
[8]. N. Costa and S. Haykin, Multiple-Input Multiple-Output Channel Models, Wiley, 2010.
[9]. B. S. Paul and R. Bhattacharjee, ‘MIMO Channel Modeling：A Review,” IETE
Technical, vol. 25, issue 6, Nov–Dec. 2008.
[10]. J.G. Andrews et al , Fundamentals of  WiMAX , Prentice-Hall, 2007 
[11] Gergory D. Durgin, Space-Time Wireless Channels. New Jersey: Prentice Hall PTR,
2003.
[12] Zhemin Xu, Sana Sfar and Rick S. Blum, “Analysis of MIMO Systems With Receive
Antenna Selection in Spatially Correlated Rayleigh Fading Channels,” IEEE Trans.
Veh. Technol., vol.58, no.1, Jan. 2009, pp. 251-262.
[13] Cheng-shan Xiao, and Yahong Rosa Zheng, “On the Ergodic Capacity of MIMO
Triply Selective Rayleigh Fading Channels,” IEEE Trans. Wireless Commun., vol.7,
no.61, June 2008, pp. 2272-2279.
[14] Maria-Gabriella Di Benedetto and Guerion Giancola, Understanding Ultra Wide Band
Radio Fundamentals. New Jersey: Prentice Hall PTR, 2004.
[15] B. Sklar, Digital Communications：Fundamentals and Applications 2/e, Prentice Hall
    PTR, 2004 
[16] Huseyin Arslan, Zhi-Ning Chen and Maria-Gabriella Di Benedetto, ULTRA
WIDEBAND WIRELESS COMMUNICATION. New Jersey: John Wiley & Sons, Inc.,
2006.
[17].	R. C. Qiu, “A study of the ultra-wideband wireless propagation channel and optimum UWB receiver design,” IEEE Journal on Selected Areas in Communications , Vol. 20, No.9, December 2002, pp. 1628-1637.
[18].	B. Uguen, E. Plouhinee, Y. Lostanlen, and G. Chassay, “A deterministic ultra-wideband channel modeling,” IEEE Conference on Ultra-Wideband System Technologies, May 2002, pp. 1-5.
[19].	Y. Zhang, “Ultra-wide bandwidth channel analysis in time domain using 3-D ray tracing,” High Frequency Postgraduate Student Colloquium of IEEE, Sept. 2004, pp. 189-194.    
[20] E. W. Kamen and B. S. Heck, Fundamentals of Signals and Systems Using the Weband Matlab, Prentice-Hall, 2000.  
[21]. B. S. Paul and R. Bhattacharjee, ‘MIMO Channel Modeling：A Review,” IETE
Technical, vol. 25, issue 6, Nov–Dec. 2008.
[22]. C. Oestges and B. Clerckx, “MIMO Wireless Cimmunications,” Elsevier Ltd., Mar.
2007.
[23]. H. Ling, R. Chou and S. Lee, “Shooting and Bouncing Rays：Calculating the RCS of
an Arbitrarily Shaped Cavity,” IEEE Trans. Antennas Propagate, vol. 37, Feb. 1989,
pp. 194–205.
[24]. G. Liang and H. L. Bertoni, “A New Approach to 3–D Ray Tracing for Propagation
Prediction in cities,” IEEE Trans. Antennas Propagate, vol. 46, June 1998, pp.
853–863.
[25]. S. Y. Seidel and T. S. Rappaport, “Site–Specific Propagation Prediction for Wireless
in–Building Personal Communication System Design,” IEEE Trans. on Vehicular
Technol., vol. 43, Nov. 1994, pp. 879–891.
[26]. M. F. Iskander and Z. Yun, “Propagation Prediction Models for Wireless
Communication Systems,” IEEE Trans. on Microwave Theory and Techniques., vol.
50, issue 3, Mar. 2002, pp. 662–673.
[27]. Z. Genc, W. V. Thillo, A. Bourdoux and E. Onur, “60 GHz PHY Performance
Evaluation with 3D Ray Tracing under Human Shadowing,” Wireless
Communications Letters, IEEE Journals & Magazines, vol. 1, issue 2, 2012. pp.
117–120.
[28]. D. E. Goldberg, Genetic Algorithm in Search Optimization and Machine Learning,
Addison Wesley, 1989.
[29]. J. M. Johnson and Y. R. Samii, “Genetic Algorithms in Engineering
Electromagnetics,” IEEE Antennas and Propagation Magazine, vol. 39, issue4, Aug.
1997, pp.7–21.
[30]. R. Storn and K. Price, “Differential Evolution–A Simple and Efficient Heuristic for
Global Optimization over Continuous Space,” Journal of Global Optimization, vol. 11,1997, pp. 341–359.
[31]. S. H. Chen and S. K. Jeng ,“An SBR/Image approach for indoor radio propagation in a corridor,” IEICE Trans. Electron., Vol. E78-C, pp. 1058-1062, Aug. 1995.
[32]. S. H. Chen and S. K. Jeng ,“SBR/Image approach for radio wave propagation in tunnels with and without traffic,” IEICE Trans. Veh. Technol., Vol. 45, pp. 570-578, Aug. 1996.
[33]. C. H. Chen, C. L. Liu, C. C. Chiu and T. M. Hu, “Ultra-Wide Band Channel Calculation by SBR/Image Techniques for Indoor Communication,” Journal of Electromagnetic Waves and Applications Vol. 20, No. 1, pp. 2169-2179, 2006.
[34]. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: John Wiley & Sons, 1991.                                                           
[35]. Z. Xu, S. Sfar and R. S. Blum, “Analysis of MIMO Systems With Receive Antenna Selection in Spatially Correlated Rayleigh Fading Channels,” IEEE Transactions on Vehicular Technology, vol. 58, no. 1, Jan. 2009, pp. 251-262.  
[36]. W. J. Chang, J. H. Tarng and S. Y. Peng, “Frequency-Space-Polarization on UWB MIMO Performance for Body Area Network Applications,” IEEE Antennas and Wireless Propagation Letters, vol. 7, 2008, pp.577-580. 
[37]. J. F. Valenzuela-Valdes, M. A. Garcia-Fernandez, A. M. Martinez-Gonzalez, and D. A. Sanchez-Hernandez, “The Influence of Efficiency on Receive Diversity and MIMO Capacity for Rayleigh-Fading Channels,” IEEE Trans. Antennas Propagat., vol. 56, no. 5, May 2008, pp. 1444-1450. 
[38]. J. B. Andersen, “Array gain and capacity for known random channels with multiple element arrays at both ends,” IEEE J. Sel. Areas Commun., vol. 18, no. 11, Nov. 2000, pp. 2172–2178.  
[39]. A. J. Paulraj, R. Nabar and D. Gore, Introduction to Space-Time Wireless Communication. U.K.: Cambridge Univ. Press, 2003.