在無線通訊系統中為了追求更高傳輸效能的透過結合和超寬頻(UWB)與多天線系統(MIMO)被賦予很高的期待。而改善相關的通訊品質和降低成本更是近幾年無線個人通訊網路中熱烈討論的議題。超寬頻主要是用在室內環境，但環境產生多路徑效應也影響著它的效能。多路徑效應造成的符際干擾(ISI)容易造成系統的錯誤率以及環境的失效率上升。因此，透過使用實數正交設計(ROD)可以有效的改善超寬頻多天線系統。首先，一個基地台可能在服務範圍內會上千移動通訊的使用者，而比較符合成本效益的做法是擴充基地的設備而不是在使用者端增加設計的成本。再來，使用實數正交設計的計算複雜度低也不需要將接收端的信號回授給傳送端。在這篇論文中，模擬環境透過使用射線彈跳追蹤法結合反複利葉轉換可以求出該環境的脈衝響應。因為模擬的頻譜相當大所對應到的時間解析度很高幾乎只有幾奈秒，我們考慮用耙式接收機(RAKE receiver)增加接收信號強度以抑制多路徑效應。再來，我們分析了超寬頻多天線系統使用不同實數正交設計方法的錯誤率效能。值得一提對於屋頂形狀研究相關研究是相對較少。在這篇論文的最後，我們比較了在使用不同維度的實數正交設計在不同模擬環境下的失效率(定義為錯誤率>10-6)。這個環境包含了常見的屋頂形狀包含平坦型、三角型、圓型、金字塔型以及梯形五種並討論了兩種材質。而我們得到在材質為鐵的平坦型屋頂會有最低的失效率，而這是因為在這個環境會有最嚴重的多路徑效應。

Ultra wideband (UWB) combined with multiple input and multiple output (MIMO) is expectable for satisfying high data rates in wireless communication. How to improve quality of communication and cost reduction have become hot research issues in wireless personal network. UWB is mainly applied to indoor environments characterized by multipath effect. Due to this effect, the inter-symbol interference that increases the bit error rate (BER) and outage probability of the UWB systems occurred. The application of real orthogonal design (ROD) in UWB-MIMO is beneficial. First, a base station may serves thousands of mobile end users. It seems more economical to add equipment to base stations rather than the mobile end user. Second, the transmitter does not require any feedback from receiver and its low computation complexity. In this thesis, the ray-tracing techniques and inverse fast Fourier transform are employed to get the impulse response of simulated environments. Based on the large bandwidth, the scale
of time resolution is approximately several nanoseconds. So we take account of the RAKE receiver to increase received signal strength in order to reduce multipath effect. Then, analyzing the BER performance of the UWB-MIMO system when using ROD schemes with RAKE are briefly discussed.Significantly, fewer results are reported for the case of roof shaper. In this thesis intends to compare the outage probability for proposed scheme in different simulated environments. These five roof shapes including the flat shape roof, the triangular shape roof, the arched shape roof, the pyramid shape roof, and the mansard shape roof are constructed by materials of concrete and iron. As the result, we can conclude that the performance of outage probability with iron flat shape roof is better than the other shape roof with high order RAKE finger. Both for concrete and iron cases, it is found that the strong multipath effect for the flat shape roof is the largest.

TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION	1
1.1 Research Background	1
1.1.1 UWB	1
1.1.2 MIMO	2
1.2 Research Motivation	3
1.3 Chapter Outline	4
CHAPTER 2 DESCRIPTION OF SYSTEM	5
2.1 Ray-tracing process	5
2.1.1 Channel impulse response in frequency domain	6
2.1.2 Signal analysis using IFFT and Hermitian processing	9
2.2 Orthogonal designs for UWB system	11
2.3 RAKE receiver	13
CHAPTER 3 PERFORMANCE ANALYSIS OF BER	15

3.1. Encoding, Decoding and Diversity Combining	15
3.1.1 BER formula with ROD	27
3.1.2 BER formula without ROD	28
3.2 Two-ray reflection model	31
3.3 Summary	37
CHAPTER 4 NUMERICAL RESULT	38
4.1 The simulated environments	38
4.2 Simulation Results and Discussions	45
4.2.1 CASE A	46
4.2.2 CASE B	53
4.2.3 CASE C	60
CHAPTER 5 CONCLUSIONS	67
APPENDIX A: TABLE OF MATERIALS	68
REFERENCES	74

LIST OF FIGURES
Figure 1. 1 Benefit of MIMO	2
Figure 2. 1 System block diagram	5
Figure 2. 2 Flow chart of the ray-tracing process	8
Figure 2. 3 Hermitian processing and Inverse fast Fourier transform (IFFT)	10
Figure 2. 4 Principle of the A-rake	14
Figure 2. 5 Principle of the S-rake	14
Figure 2. 6 Principle of the P-rake	14
Figure 3. 1 System block diagram corresponding to the RAKE finger NF	15
Figure 3. 2 The transmitted signal as a train of pulses	17
Figure 3. 3 System block of UWB-MIMO without ROD	28
Figure 3. 4 A sketch of two-ray reflection model	31
Figure 3. 5 Illustrates how the ISI is incurred by the reflection wave.	32
Figure 3. 6 The antenna received signal in case1	33
Figure 3. 7 The antenna received signal in case5	33
Figure 3. 8 The antenna received signal in case9	34
Figure 3. 9 BER performance comparison for NT=2,NR=2 case	34
Figure 3. 10 BER performance comparison for NT=4,NR=4 case	35
Figure 3. 11 BER performance comparison for NT=8,NR=8 case	35
Figure 3. 12 BER performance comparison at middle reflection distance	36
Figure 3. 13 Comparison BER performance with and without the ROD of size 2	36
Figure 4. 1 The simulated environment (top view)	41
Figure 4. 2 The location of transmitting and receiving points in the simulated environment	42
Figure 4. 3 Types of roof shapes	43
Figure 4. 4 (CaseA) Outage comparison for all roof shapes, NF=1	46
Figure 4. 5 (CaseA) Outage comparison for all roof shapes, NF=2	46
Figure 4. 6 (CaseA) Outage comparison for all roof shapes, NF=3	47
Figure 4. 7 (CaseA) Outage comparison for all roof shapes, NF=4	47
Figure 4. 8 (CaseA) Outage comparison for arched roof	48
Figure 4. 9 (CaseA) Distribution area of bad receiving for arched roof when SNR=64dB	48
Figure 4. 10 (CaseA) Outage comparison for flat roof	49
Figure 4. 11 (CaseA) Distribution area of bad receiving for flat roof when SNR=64dB	49
Figure 4. 12 (CaseA) Outage comparison for mansard roof	50
Figure 4. 13 (CaseA) Distribution area of bad receiving for mansard roof when SNR=64dB	50
Figure 4. 14 (CaseA) Outage comparison for pyramid roof	51
Figure 4. 15 (CaseA) Distribution area of bad receiving for pyramid roof when SNR=64dB	51
Figure 4. 16 (CaseA) Outage comparison for triangular roof	52
Figure 4. 17 (CaseA) Distribution area of bad receiving for triangular roof when SNR=64dB	52
Figure 4. 18 (CaseB) Outage comparison for all roof shapes, NF=1	53
Figure 4. 19 (CaseB) Outage comparison for all roof shapes, NF=2	53
Figure 4. 20 (CaseB) Outage comparison for all roof shapes, NF=3	54
Figure 4. 21 (CaseB) Outage comparison for all roof shapes, NF=4	54
Figure 4. 22 (CaseB) Outage comparison for arched roof	55
Figure 4. 23 (CaseB) Distribution area of bad receiving for arched roof when SNR=66dB	55
Figure 4. 24 (CaseB) Outage comparison for flat roof	56
Figure 4. 25 (CaseB) Distribution area of bad receiving for flat roof when SNR=66dB	56
Figure 4. 26 (CaseB) Outage comparison for mansard roof	57
Figure 4. 27 (CaseB) Distribution area of bad receiving for mansard roof when SNR=66dB	57
Figure 4. 28 (CaseB) Outage comparison for pyramid roof	58
Figure 4. 29 (CaseB) Distribution area of bad receiving for pyramid roof when SNR=66dB	58
Figure 4. 30 (CaseB) Outage comparison for triangular roof	59
Figure 4. 31 (CaseB) Distribution area of bad receiving for triangular roof when SNR=66dB	59
Figure 4. 32 (CaseC) Outage comparison for all roof shapes, NF=1	60
Figure 4. 33 (CaseC) Outage comparison for all roof shapes, NF=2	60
Figure 4. 34 (CaseC) Outage comparison for all roof shapes, NF=3	61
Figure 4. 35 (CaseC) Outage comparison for all roof shapes, NF=4	61
Figure 4. 36 (CaseC) Outage comparison for arched roof	62
Figure 4. 37 (CaseC) Distribution area of bad receiving for arched roof when SNR=68dB	62
Figure 4. 38 (CaseC) Outage comparison for flat roof	63
Figure 4. 39 (CaseC) Distribution area of bad receiving for flat roof when SNR=68dB	63
Figure 4. 40 (CaseC) Outage comparison for mansard roof	64
Figure 4. 41 (CaseC) Distribution area of bad receiving for mansard roof when SNR=68dB	64
Figure 4. 42 (CaseC) Outage comparison for pyramid roof	65
Figure 4. 43 (CaseC) Distribution area of bad receiving for pyramid roof when SNR=68dB	65
Figure 4. 44 (CaseC) Outage comparison for triangular roof	66
Figure 4. 45 (CaseC) Distribution area of bad receiving for triangular roof when SNR=68dB	66


LIST OF TABLES
Table 3. 1 The encoding and transmission sequence	16
Table 3. 2 Three positions of antenna array in multi-antenna system	32
Table 4. 1 The power delay profile in all concrete cases	44
Table 4. 2 The power delay profile in all iron cases	44
Table A. 1 Concrete	68
Table A. 2 Cloth Partition	69
Table A. 3 Structure Wood	70
Table A. 4 Iron	71
Table A. 5 Brick	72
Table A. 6 Plywood	73

Alamouti, S. (1998). A simple transmit diversity technique for wireless communications. Selected Areas in Communications, IEEE Journal on, 16(8), 1451-1458. doi:10.1109/49.730453
Alavi, B., Alsindi, N., & Pahlavan, K. (2006). UWB channel measurements for accurate indoor localization. Military Communications Conference, 2006. MILCOM 2006. IEEE, 1-7. doi:10.1109/MILCOM.2006.302143
Asif, H. M., Honary, B., & Ahmed, H. (2012). Multiple-input multiple-output ultra-wide band channel modelling method based on ray tracing. Communications, IET, 6(10), 1195-1204. doi:10.1049/iet-com.2011.0265
Bas, C. U., & Ergen, S. C. (2013). Ultra-wideband channel model for intra-vehicular wireless sensor networks beneath the chassis: From statistical model to simulations. Vehicular Technology, IEEE Transactions on, 62(1), 14-25. doi:10.1109/TVT.2012.2215969
Boche, H., Bourdoux, A., Fonollosa, J. R., Kaiser, T., Molisch, A., & Utschick, W. (2006). Antennas: State of the art. Vehicular Technology Magazine, IEEE, 1(1), 8-17. doi:10.1109/MVT.2006.1663946
Cassioli, D., Win, M. Z., Vatalaro, F., & Molisch, A. F. (2007). Low complexity rake receivers in ultra-wideband channels. Wireless Communications, IEEE Transactions on, 6(4), 1265-1275. doi:10.1109/TWC.2007.348323
Chen, C. H., Liu, C. L., Chiu, C. C., & Hu, T. M. (2006). Ultra-wide band channel calculation by SBR/Image techniques for indoor communication. Journal of Electromagnetic Waves and Applications, 20(1), 41-51. doi:10.1163/156939306775777387
Chen, S. H., & Jeng, S. K. (1997). An SBR/image approach for radio wave propagation in indoor environments with metallic furniture. Antennas and Propagation, IEEE Transactions on, 45(1), 98-106. doi:10.1109/8.554246
Chen, S. H., & Jeng, S. K. (1996). SBR/image approach for radio wave propagation in furnished environments. Antennas and Propagation Society International Symposium, 1996. AP-S. Digest, , 1 453-456 vol.1. doi:10.1109/APS.1996.549635
Chen, S. H., & Jeng, S. K. (1996). SBR image approach for radio wave propagation in tunnels with and without traffic. Vehicular Technology, IEEE Transactions on, 45(3), 570-578. doi:10.1109/25.533772
Coenen, A. J. R. M., & de Vos, A. J. (1992). FFT-based interpolation for multipath detection in GPS/GLONASS receivers. Electronics Letters, 28(19), 1787-1788. doi:10.1049/el:19921139
Demir, U., Bas, C. U., & Coleri Ergen, S. (2013). Engine compartment UWB channel model for intra-vehicular wireless sensor networks doi:10.1109/TVT.2013.2294357
Hamalainen, M., & Iinatti, J. (2005). Analysis of interference on DS-UWB system in AWGN channel. Ultra-Wideband, 2005. ICU 2005. 2005 IEEE International Conference on, 719-723. doi:10.1109/ICU.2005.1570077
Kaiser, T., Feng Zheng, & Dimitrov, E. (2009). An overview of ultra-wide-band systems with MIMO. Proceedings of the IEEE, 97(2), 285-312. doi:10.1109/JPROC.2008.2008784
Kandukuri, S., & Boyd, S. (2002). Optimal power control in interference-limited fading wireless channels with outage-probability specifications. Wireless Communications, IEEE Transactions on, 1(1), 46-55. doi:10.1109/7693.975444
Khaleghi, A., Chávez-Santiago, R., & Balasingham, I. (2011). Ultra-wideband statistical propagation channel model for implant sensors in the human chest. Microwaves, Antennas & Propagation, IET, 5(15), 1805-1812. doi:10.1049/iet-map.2010.0537
Kshetrimayum, R. S. (2009). An introduction to UWB communication systems. Potentials, IEEE, 28(2), 9-13. doi:10.1109/MPOT.2009.931847
Loredo, S., Rodríguez-Alonso, A., & Torres, R. P. (2008). Indoor MIMO channel modeling by rigorous GO/UTD-based ray tracing. Vehicular Technology, IEEE Transactions on, 57(2), 680-692. doi:10.1109/TVT.2007.906362
Mielczarek, B., Wessman, M. -., & Svensson, A. (2003). Performance of coherent UWB rake receivers with channel estimators. Vehicular Technology Conference, 2003. VTC 2003-Fall. 2003 IEEE 58th, , 3 1880-1884 Vol.3. doi:10.1109/VETECF.2003.1285351
Migliore, M. D., Pinchera, D., Massa, A., Azaro, R., Schettino, F., & Lizzi, L. (2008). An investigation on UWB-MIMO communication systems based on an experimental channel characterization. Antennas and Propagation, IEEE Transactions on, 56(9), 3081-3083. doi:10.1109/TAP.2008.928814
Paulraj, A. J., Gore, D. A., Nabar, R. U., & Bolcskei, H. (2004). An overview of MIMO communications - a key to gigabit wireless. Proceedings of the IEEE, 92(2), 198-218. doi:10.1109/JPROC.2003.821915
Priebe, S., Kannicht, M., Jacob, M., & Kurner, T. (2013). Ultra broadband indoor channel measurements and calibrated ray tracing propagation modeling at THz frequencies. Communications and Networks, Journal of, 15(6), 547-558. doi:10.1109/JCN.2013.000103
Rappaport, T. S. (2002). Wireless communications: Principles and practice  (2nd ed.) Prentice Hall.
Sadi, Y., & Ergen, S. C. (2013). Optimal power control, rate adaptation, and scheduling for UWB-based intravehicular wireless sensor networks. Vehicular Technology, IEEE Transactions on, 62(1), 219-234. doi:10.1109/TVT.2012.2217994
Talepour, Z., Ahmadi-Shokouh, J., & Tavakoli, S. (2012). Optimality of transmitter location in a wireless network with RAKE receivers. Communications, IET, 6(18), 3059-3064. doi:10.1049/iet-com.2012.0272
Tarokh, V., Jafarkhani, H., & Calderbank, A. R. (1999). Space-time block codes from orthogonal designs. Information Theory, IEEE Transactions on, 45(5), 1456-1467. doi:10.1109/18.771146
Tian, Z., & Giannakis, G. B. (2005). BER sensitivity to mistiming in ultra-wideband impulse radios - part II: Fading channels. Signal Processing, IEEE Transactions on, 53(5), 1897-1907. doi:10.1109/TSP.2005.845485