本研究提出應用動態型差異演化策略法（Dynamic Differential Evolution）於天線陣列排列在多輸入多輸出(multiple-input multiple-output )系統中。此最佳化方法有效提升平均的通道容量，這個問題也同樣探討最佳化選擇在發射端天線之間的天線間距。本研究中，亦探討多輸入多輸出窄頻系統通道容量的計算方法。
本研究討論了使用在室內無線通道5千兆赫U-NII ( Unlicensed-National Information Infrastructure bands )頻道的通道容量，且提出在窄頻無線通訊系統中對發射端天線陣列中天線間距的一個最佳化的程序。藉由射線彈跳追蹤法 (Shooting and Bouncing Ray/Image techniques, SBR/Image Techniques )對應不同的頻率響應( frequency responses ) 的發射端與接收端天線陣列中天線間距來計算，並由得到的通道頻率響應，而進一步來計算相應的通道容量 (channel capacity) 。藉由使用動態型差異演化策略法來最佳化天線陣列中的天線間距進而最大化通道容量。   
發射器中天線陣列是在整個室內環境中心與接收器中天線每0.03公尺均勻間距且有150個接收器每0.25公尺間隔平均分怖在整個環境中所有木頭製的桌子上。探討發射器中4種不同的天線陣列排列(線性天線陣列、L型天線陣列、T型天線陣列、方型天線)於直接波與非直接波不同條件的三種不同辦公室環境中：（一）在此環境中有兩個辦公室隔版在發射端的兩側，高度皆為1公尺。（二）在此環境中有兩個辦公室隔版在發射端的兩側，高度皆為2公尺。（三）在此環境中有兩個鐵櫃在發射端的兩側，高度皆為2公尺。在發射端需求尋找更緊密天線陣列的排列及目的達到更高的系統通道容量，思考天線陣列不同的配置排列距離，探討考慮發射端天線陣列中天線非均勻間距二分之一波長距離到一個波長距離與均勻間距二分之一波長距離排列的幾何形狀做為比較。這是值得研究的課題，探討是否改變環境的複雜度與隔板材質和考慮更多的無線電波傳輸的多路徑可以有效地提升平均的通道容量。數值計算結果表明，該方法用於最佳化天線陣列中的天線間距而使平均通道容量增加是有效的。L型天線陣列具有最高的通道容量和方型天線陣列具有最高的改善比率。

The geometrical shape of antenna arrays for maximizing the average channel capacity of the system in a multiple-input multiple-output (MIMO) link is investigated. The optimum element spacing of the transmitting antenna is also included. In this paper, channel capacity of multiple-input multiple-output narrowband system in indoor wireless channels at 5-GHz U-NII (Unlicensed-National Information Infrastructure) bands is calculated. An optimization procedure for the element spacing of the antenna transmitter in narrowband wireless communication system is presented. The frequency responses of different transceiver antenna element spacing are computed by shooting and bouncing ray/image (SBR/Image) techniques, and the channel frequency response is further used to calculate corresponding channel capacity. The transmitter is in the center of the indoor environment and the receivers are uniform intervals distribution, which 150 measurements with 0.25m intervals in the whole wooden table in indoor environment. And the inter-element separation of Receiver antennas (Rx) is 0.03m. Linear shaped array, L shaped array, T shaped array and rectangular shaped array geometries with non-uniform inter-element spacing are investigated for both line-of-sight (LOS) and non-LOS (NLOS) scenarios. The optimal element spacing of antenna for maximizing the channel capacity is searched by dynamic differential evolution (DDE). Numerical results have shown that our proposed method is effective for increasing average channel capacity. It is also found that L shaped array has the highest channel capacity and the improvement ratio for rectangular shaped array is largest.

中文摘要．．．．．．．．．．．．．．．．．．．．．．．．．．III
英文摘要．．．．．．．．．．．．．．．．．．．．．．．．．．V
第一章	概論．．．．．．．．．．．．．．．．．．．．．．．．．1
1.1	研究背景．．．．．．．．．．．．．．．．．．．．．．．1
1.2	研究動機．．．．．．．．．．．．．．．．．．．．．．．9
1.3	研究內容簡介．．．．．．．．．．．．．．．．．．．．．11
第二章	差異型演化法．．．．．．．．．．．．．．．．．．．．．12
2.1	差異型演化法．．．．．．．．．．．．．．．．．．．．．12
2.1.1	介紹差異型演化法法則中的運算方式．．．．．．．．． 13
2.2	動態差異型演化法．．．．．．．．．．．．．．．．．．．20
第三章	系統理論．．．．．．．．．．．．．．．．．．．．．．． 23
3.1	多輸入多輸出窄頻系統表示．．．．．．．．．．．．．．．23
3.2	多輸入多輸出窄頻系統通道容量．．．．．．．．．．．．．27
3.2.1	建立在 CSI-B 狀態下．．．．．．．．．．．．．．． 27
3.2.2	建立在只有 CSI-R 狀態下．．．．．．．．．．．．． 28
3.2.3	中斷容量和統計容量 ．．．．．．．．．．．．．．．30
3.3	影響因素MIMO容量．．．．．．．．．．．．．．．．．．31
3.3.1	空間自由度．．．．．．．．．．．．．．．．．．． 31
3.3.2	特徵矩陣和條件數目．．．．．．．．．．．．．．．． 32
3.3.3	空間關係．．．．．．．．．．．．．．．．．．．． 33
第四章	通道計算模型．．．．．．．．．．．．．．．．．．．．．35
4.1	無線電波傳播通道分析．．．．．．．．．．．．．．．．．35
4.2	通道計算模型分析．．．．．．．．．．．．．．．．．．．37
4.2.1	 利用射線追蹤法計算出頻域響應．．．．．．．．．．38
4.3 射線彈跳追蹤法程式流程分析．．．．．．．．．．．．．．41
第五章	模擬數值結果．．．．．．．．．．．．．．．．．．．．．45
5.1模擬實驗環境及設定．．．．．．．．．．．．．．．．．．45
5.2模擬結果分析．．．．．．．．．．．．．．．．．．．．．58
第六章	結論．．．．．．．．．．．．．．．．．．．．．．．．．79
參考文獻．．．．．．．．．．．．．．．．．．．．．．．．．． 81
附錄 ．．．．．．．．．．．．．．．．．．．．．．．．．．．．86



圖目錄

圖 1.1  SISO, SIMO, MISO和MIMO 示意圖．．．．．．．．．．．2
圖 1.2  802.11a 和HiperLan2 頻帶分配圖 ．．．．．．．．．．．．5
圖 1.3  IEEE 802.11a 頻道分配圖．．．．．．．．．．．．．．．．5
圖 1.4  多輸入多輸出系統通道模型示意圖．．．．．．．．．．．．7
圖 2.1  差異型演化法流程圖．．．．．．．．．．．．．．．．．．13
圖 2.2  差異型進化法中突變方法一的示意圖．．．．．．．．．．．15
圖 2.3  差異型進化法中突變方法二的示意圖．．．．．．．．．． 16
圖 2.4  差異型進化法中突變方法三的示意圖．．．．．．．．．．．17
圖 2.5  差異型進化法中交配向量結構示意圖．．．．．．．．．．．19
圖 2.6  差異型進化法中的交配向量於一個二維目標函數等位線圖描述的示意圖 ．．．．．．．．．．．．．．．．．．．．．．19
圖 2.7  動態差異型型演化策略法流程圖．．．．．．．．．．．．．22
圖 3.1  多輸入多輸出窄頻系統示意圖．．．．．．．．．．．．．．23
圖 3.2  多輸入多輸出窄頻系統矩陣示意圖．．．．．．．．．．．．25
圖 3.3  建立在 CSI-B 狀態下多輸入多輸出窄頻系統一個等效架構． 26
圖 4.1  求得通道頻率響應圖．．．．．．．．．．．．．．．．．．37
圖 4.2  SBR/Image 程式流程圖 ．．．．．．．．．．．．．．．．44
圖 5.1 環境(一)所模擬的辦公室2D立體圖 ．．．．．．．．．．．．46
圖 5.2 環境(二)所模擬的辦公室2D立體圖 ．．．．．．．．．．．．47
圖 5.3 環境(三)所模擬的辦公室2D立體圖 ．．．．．．．．．．．．48
圖 5.4 使用動態差異型演化法於 線性陣列 調整天線間距二分之一波長距離到一個波長的距離示意圖  ．．．．．．．．．．．． 49
圖 5.5 使用動態差異型演化法於 L型陣列 調整天線間距二分之一波長距離到一個波長的距離示意圖   ．．．．．．．．．．．．50
圖 5.6 使用動態差異型演化法於 T型陣列 調整天線間距二分之一波長距離到一個波長的距離示意圖．．．．．．．．．．．．．  51
圖 5.7 使用動態差異型演化法於 方型陣列 調整天線間距二分之一波長距離到一個波長的距離示意圖  ．．．．．．．． ．．．．52
圖 5.8   線性陣列中8根天線間距為二分之一波長與環境中心點示意圖．．．．．．．．．．．．．．．．．．．．．．．．．． 53
圖 5.9   L型陣列中8根天線間距為二分之一波長示意圖．．．．． 54
圖 5.10  T型陣列中8根天線間距為二分之一波長示意圖．．．．． 55
圖 5.11  方型陣列中8根天線間距為二分之一波長與環境中心點示意圖．．．．．．．．．．．．．．．．．．．．．．．．．． 56
圖 5.18 (a)線性陣列、(b) L型陣列、(c) T型陣列、(d)方型陣列 使用動態差異型演化法則最佳化天線陣列間距結果天線位置座標．．．60
圖 5.12 (a)、5.12 (b)、5.12 (c)、5.12 (d) 不同天線陣列使用動態差異型演化法與否其發射端功率對於通道容量比較圖 ．．．．．．．61-62
圖 5.13 (a)、5.13 (b)、5.13 (c)、5.13 (d)不同天線陣列其Number of Function Calls對於使用動態差異型演化法改善率比較圖．．．．． 63-64
圖 5.19 (a)線性陣列、(b) L型陣列、(c) T型陣列、(d)方型陣列 使用動態差異型演化法則最佳化天線陣列間距結果天線位置座標．．．67
圖 5.14 (a)、5.14 (b)、5.14 (c)、5.14 (d) 不同天線陣列使用動態差異型演化法與否其發射端功率對於通道容量比較圖．．．．．．．．68-69          
圖 5.15 (a)、5.15 (b)、5.15 (c)、5.15 (d)不同天線陣列其Number of Function Calls對於使用動態差異型演化法改善率比較圖．．．．．．． 70-71                                      
圖 5.20 (a)線性陣列、(b) L型陣列、(c) T型陣列、(d)方型陣列 使用動態差異型演化法則最佳化天線陣列間距結果天線位置座標．．．74
圖 5.16 (a)、5.16 (b)、5.16 (c)、5.16 (d) 不同天線陣列使用動態差異型演化法與否其發射端功率對於通道容量比較圖．．．．．．．．75-76                       
圖 5.17 (a)、5.17 (b)、5.17 (c)、5.17 (d)不同天線陣列其Number of Function Calls對於使用動態差異型演化法改善率比較圖．．．．．．．77-78                         

表目錄

表 3.1　對應不同系統中空間自由度的數目．．．．．．．．．．．．32
表 5.1　動態差異型演化法則設定參數  ．．．．．．．．．．．．．57
表 B.1	混擬土的材質係數．．．．．．．．．．．．．．．．．．．87
表 B.2	磚頭的材質係數．．．．．．．．．．．．．．．．．．．．88
表 B.3	合成塑膠板的材質係數．．．．．．．．．．．．．．．．．89
表 B.4	鐵的材質係數．．．．．．．．．．．．．．．．．．．．．90
表 B.5	夾板的材質係數．．．．．．．．．．．．．．．．．．．．91
表 B.6	合成纖維板的材質係數．．．．．．．．．．．．．．．．．92
表 B.7	木材的材質係數．．．．．．．．．．．．．．．．．．．．93

[1].	Gergory D. Durgin, Space-Time Wireless Channels. New Jersey: Prentice Hall  PTR,2003.      
[2].	David Tse and Pramod Viswanath, Fundamentals of Wireless Communication. United Kingdom: Cambridge University Press, 2005  .
[3].	Babu Sena Paul, Ratnajit Bhattacharjee,  MIMO Channel Modeling: A Review. IETE  TECHNICAL  Vol  25, ISSUE 6,  NOV-DEC 2008
[4].	Claude Oestges and Bruno Clerckx, MIMO WIRELESS COMMUNICATIONS. 
[5].	Steve Kapp, 802.11a. More bandwidth without the wires. Internet Computing, IEEE  Volume: 6 , Issue: 4 
[6].	暨南大學 電機工程研究所 饒敬國, IEEE 802.11a 技術文件內容簡介
[7].	I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” . Europ. Trans. Telecommun., vol. 10, pp. 585–595, Nov. 1999.     
[8].	G. J. Foschini and M. J. Gans, “On limits of wireless communications  in a fading environment when using multiple antennas,” Wireless Personal Commun., vol. 6, pp. 311–335, Mar.  1998.
[9].	Lang P. Withers, Jr. ” A QUASI-SYMMETRIC MODEL FOR THE TWO-WAY MIMO COMMUNICATION CHANNEL,” Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on Volume: 3 Digital Object Identifier: 10.1109/ICASSP.2007.366511 
[10].	M. A. Mangoud,  “OPTIMIZATION OF CHANNEL  CAPACITY FOR  INDOOR MIMO SYSTEMS USING GENETIC ALGORITHM,” Progress In Electromagnetics Research C, Vol. 7, 137–150, 2009.
[11].	Olgun, U.; Tunc, C.A.; Aktas, D.; Erturk, V.B.; Altintas, “A. OPTIMIZATION OF LINEARWIRE ANTENNA ARRAYS TO INCREASEMIMO CAPACITY USING SWARM INTELLIGENCE,” Antennas and Propagation, 2007. EuCAP 2007. The Second European Conference on Publication Year: 2007 , Page(s): 1 - 6 
[12].	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.
[13].	B. Uguen, E. Plouhinee, Y. Lostanlen, and G. Chassay, “A deterministic ultra-wideband channel modeling,” IEEE Conference on Ultra-Wideband System Technologie, May 2002 s, pp. 1-5
[14].	Y. Zhang, “Ultra-wide bandwidth channel analysis in time domain using 3-D ray tracing,” High Frequency Postgraduate Student Colloquium of IEEE, September 2004, pp. 189-194.
[15].	E. W. Kamen and B. S. Heck, Fundamentals of Signals and Systems Using the Weband Matlab, Prentice-Hall, 2000.
[16].	R. Storn and K. Price, “Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Space,” Journal of Global Optimization, vol. 11, pp. 341-359, 1997.                                    
[17].	A. Qing, “Dynamic differential evolution strategy and applications in electromagnetic inverse scattering problems,” IEEE Transactions on Geoscience and Remote Sensing, vol 44, issue 1, pp.116 - 125, Jan. 2006.                                                          
[18].	T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: John Wiley & Sons, 1991.                                                           
[19].	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.  
[20].	Wei-Ju Chang, Jenn-Hwan Tarng and Szu-Yun Peng, ” Frequency-Space-Polarization on UWB MIMO Performance for Body Area Network Applications,” IEEE Antennas Wirel. Propag. Lett., vol. 7, 2008, pp.577-580. 
[21].	Juan F. Valenzuela-Valdés, Miguel A. García-Fernández, Antonio M. Martínez-González, and David A. Sánchez-Hernández, “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. 
[22].	A. J. Paulraj, R. Nabar and D. Gore, Introduction to Space-Time Wireless Communication. U.K.: Cambridge Univ. Press, 2003. 
[23].	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.  
[24].	Joseph Sahaya Kulandai Raj, Arokiasamy Shyam Prabu, Narayanan Vikram, and Joerg Schoebel, “Spatial Correlation and MIMO Capacity of Uniform Rectangular Dipole Arrays,” IEEE Trans. Antennas Propagat. Lett., vol. 7, 2008, pp97-100. 
[25].	Padam L. Kafle, Apichart Intarapanich, Abu B. Sesay, John McRory,and Robert J. Davies, “Spatial Correlation and Capacity Measurements for Wideband MIMO Channels in Indoor Office Environment,” IEEE Trans. Wirel. Commun., vol. 7, no. 5, MAY 2008, pp.1560-1571.
[26].	Raymond H. Y. Louie, Matthew R. McKay and Iain B. Collings, “Impact of Correlation on the Capacity of Multiple Access and Broadcast Channels with MIMO-MRC,” IEEE Trans. Wirel. Commun., vol. 7, no. 6, June 2008, pp.2397-2407.
[27].	O. Fernandez, M. Domingo, and R. P. Torres, “Empirical analysis of the correlation of MIMO channels in indoor scenarios at 2 GHz,” Inst. Electr. Eng. Proc. Commun., vol. 152, no. 1, Feb. 2005, pp. 82-88. 
[28].	P. Kyritsi, D. C. Cox, R. A. Valenzuela, and P. W. Wolniansky, “Correlation analysis based on MIMO channel measurements in an indoor environment,” IEEE J. Sel. Areas Commun., vol. 21, no.5, Jun. 2003, pp. 713-720. 
[29].	Hamid Reza Bahrami and Tho Le-Ngoc, “MIMO Precoder Designs for Frequency-Selective Fading Channels Using Spatial and Path Correlation,” IEEE Trans. Veh. Technol., vol. 57, no. 6, Nov. 2008, pp. 3441-3452.
[30].	M. Chiani, M. Z. Win, and A. Zanella, “On the capacity of spatially correlated MIMO Rayleigh-fading channels,” IEEE Trans. Inf. Theory, vol. 49, no. 10, Oct. 2003, pp. 2363–2371.
[31].	R. O. LaMaire and M. Zorzi, “Effect of correlation in diversity systems with Rayleigh fading, shadowing, and power capture,” IEEE J. Sel. Areas Commun., vol. 14, no. 3, Apr. 1996, pp. 449–460.
[32].	S. H. Chen and S. K. Jeng ,“An SBR/Image approach for indoor radio propagation in a corridor,” IEICE TRANSACTIONS on Electronics, Vol. E78-C, No.8, August 1995, pp. 1058-1062.
[33].	S. H. Chen and S. K. Jeng, “SBR/Image approach for radio wave propagation in tunnels with and without traffic,” IEEE Transactions on Vehicular Technology, Vol. 45, No.3, August 1996, pp. 570-578.
[34].	C. L. Liu, C. H. Huang and C. C. Chiu, “Channel capacity for various materials of partitions in indoor ultra wideband communication system with multiple input multiple output,” Third IEEE UZ Regional Chapter International Conference in Central Asia on Internet, Tashkent, Uzbekistan, Sep. 2007.