摘要i Abstract iii Acknowledgements v Table of Contents vii List of Figures ix List of Tables xv Abbreviations xvii Symbols xix Dedication xxi 1 Introduction 1 2 Complete Complementary Code under Different Channel Gains 3 2.1 Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Complete Complementary Code Correlation under Different Channel Gains . 8 2.2.1 Auto Correlation under Different Channel Gains . . . . . . . . . . . 14 2.2.2 Cross Correlation under Different Channel Gains . . . . . . . . . . . 17 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Performance Analysis of Single User Complementary Code MIMO-CDMA System with Multiapth Fading Channel 23 3.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.1 Channel Gain Estimation . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.2 Transmitting Desired Data . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Bit Error Rate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4 Numerical Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . 45 4 Performance Analysis of Multi-User Complementary Code MIMO-CDMA System with Multiapth Fading Channel 51 4.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.2 System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.1 Channel Gain Estimation . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.2 Transmitting Desired Data . . . . . . . . . . . . . . . . . . . . . . . 60 4.3 Bit Error Rate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.4 Numerical Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . 74 5 Conclusion 85 5.1 Contributions of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2 Difficulties in implementation . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.3 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Bibliography 89 A Multi-path Channel Model 91 B Periodic Correlation Function and Aperiodic Correlation Function 97 B.1 Auto Correlation with Periodic and Aperiodic . . . . . . . . . . . . . . . . . 97 B.2 Cross Correlation with Periodic and Aperiodic . . . . . . . . . . . . . . . . . 99 C Perfect Estimation Results 103 C.1 Transmitting Desired Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 C.2 Bit Error Rate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 D Complete Complementary Code Used in Matlab 111 D.1 Number of subcarrier M=2, chip’s length N=4, number of users K=2 . . . . . 111 D.2 Number of subcarrier M=4, chip’s length N=16, number of users K=4 . . . . 112 D.3 Number of subcarrier M=8, chip’s length N=64, number of users K=8 . . . . 112 2.1 The auto correlation for different shift when the length of spreading code for single carrier is four. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The cross correlation between the different complete complementary code for different shift when the length of spreading code for single carrier is four. 5 2.3 The auto correlation for different shift when the length of spreading code for two different carriers is four. . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 The cross correlation for different shift when the length of spreading code for two different carriers is four. . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1 In 4G standard for highway, when the speed of movement reachs 120 km/h, the bit duration is about Tb = 10 ns and the coherence time is Tc = 0.3 ms[4] [8]. System can transmit n = 3  109 bits in one coherence time, and use one bit to do estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 The transmitter of MIMO multi-carrier CDMA system. . . . . . . . . . . . . 26 3.3 The receiver of MIMO multi-carrier CDMA system. . . . . . . . . . . . . . 27 3.4 The channel impulse response relationship between transmitters and receivers under the MIMO system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.5 The block diagram of the baseband equivalent system model. . . . . . . . . . 28 3.6 The block diagram of the signals passed through the nRth on the mth subcarrier’s antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.7 The block diagram of the channel gain estimation, which use know value of estimation code C0 to divide signal dmk ;nR and the output is inverse of channel gain g(m) k;nR (t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.8 Probability density function of non zero mean Gaussian distribution and the decision threshold of system is zero, where the shaded side is the area of error. 42 3.9 The bit error probability with parameters shown in Table 3.1 where code C0 estimate channel in 40 dB. Number of users K = 1 and number of antennas NT = NR = 2 are fixed but varied with different number of sub-carriers M = [2; 4; 8]. We put those parameters into two different systems respectively. The red one is basic Complementary MIMO-CDMA system proposed by [3] and the blue one is proposed by this thesis. We can see that the performance of our system is better than [3] when they are in the same case, both of them can get advantage of multi-carrier. Although the channel gains are canceled, the diversity gain can be achieved by codes. . . . . . . . . . . . . . 46 3.10 The bit error probability with parameters shown in Table 3.1 where code C0 estimate channel in 40 dB. This time, the number of sub-carriers M = 4 and number of users K = 1 are fixed. The different is the number of antennas NT = NR = [1; 2; 3]. We can that the more antennas system have, the more obvious difference between MI-free and with MI will be obtained. In addition, both of them can get better performance with multiple antennas, where the transmitting diversity can be achieved by codes. . . . . . . . . . . 47 3.11 The bit error probability with parameters shown in Table 3.1 where code C0 estimate channel in 40 dB. The number of sub-carriers M = 4, number of users K = 1 and number of antennas NT = NR = 2 are all fixed. The method proposed by [2] uses Hybrid-BPSK-QPSK architecture, the resource needs to share with the other channel. Thus number of sub-carrier which system can support will be halved toM = 2 and the length of chip also need double numbers. From Chapter 2, we know that when multi-path delay is multiple of M, the orthogonality depends on time domain and the system will not affected by the frequency-selective fading channel. In other words, if multi-path delay is multiple ofM, the multi-path interference will be zero. From this figure, both our system which represented the lowest in the green legend and multi-path delay is multiple of M in [3] which are MI-free and their BER are extremely close. Compare with MI-free, IQCCC and odd delay time, we can find that MI-free system performs better apparently. . . . 48 3.12 The bit error probability with parameters shown in Table 3.1 where code C0 estimate channel in 10 dB. Number of users K = 1 and number of antennas NT = NR = 2 are fixed but varied with different sub-carriers number M = [2; 4; 8]. This figure is similar to Figure 3.9, but we can find that this system is sensitive to noise. If we can not guarantee SNR in estimation step, the performance will become worse, hence estimation method like minimum mean square error is needed. In this way, the more accurate channel gains estimation can be achieved. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.13 The bit error probability with parameters shown in Table 3.1 where code C0 estimate channel in 20 dB. Number of users K = 1 and number of antennas NT = NR = 2 are fixed but varied with different sub-carriers number M = [2; 4; 8]. This figure is similar to Figure 3.9, but we can find that this system is sensitive to noise. If we can not guarantee SNR in estimation step, the performance will become worse. Comparing with Figure 3.12, higher SNR gives system more stable BER. Therefore, estimation method like minimum mean square error is needed. In this way, the more accurate channel gains estimation can be achieved. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1 In 4G standard for highway, when the speed of movement reach 120 km/h, the bit duration is about Tb = 10 ns and the coherence time is Tc = 0.3 ms[4] [8]. System can transmit n = 3  109 bits in one coherence time, and use k bits to do estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.2 The transmitter of MIMO multi-carrier CDMA system. . . . . . . . . . . . . 54 4.3 The receiver of MIMO multi-carrier CDMA system. . . . . . . . . . . . . . 55 4.4 The channel impulse response relationship between transmitters and receivers under the MIMO system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.5 The block diagram of the baseband equivalent system model. . . . . . . . . . 56 4.6 The block diagram of the signals passed through the nRth on the mth subcarrier’s antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.7 The block diagram of the channel gain estimation, which use know value of estimation code C0 to divide signal dmk ;nR and the output is inverse of channel gain g(m) k;nR (t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.8 The bit error probability with parameters shown in Table 4.1 where code C0 estimate channel in 40 dB. Number of users K = 2 and number of antennas NT = NR = 2 are fixed but varied with different number of sub-carriers M = [4; 8]. We put those parameters into two different systems respectively. The red one is basic Complementary MIMO-CDMA system proposed by [3] and the blue one is proposed by this thesis. We can see that the performance of our system is better than [3] when they are in the same case, both of them can get advantage of multi-carrier. Although the channel gains are canceled, the diversity gain can be achieved by codes. In addition, comparing with Figure 3.9, the difference of performance between our system and [3] is increased due to appearance of MAI. . . . . . . . . . . . . . . . . . . . . . 75 4.9 The bit error probability with parameters shown in Table 4.1 where code C0 estimate channel in 40 dB. This time, the number of sub-carriers M = 4 and number of users K = 2 are fixed. The different is the number of antennas NT = NR = [1; 2]. We can that the more antennas system have, the more obvious difference between MI-free and with MI will be obtained. In addition, both of them can get better performance with multiple antennas, where the transmitting diversity can be achieved by codes. In addition, comparing with Figure 3.10, the difference of performance between our system and [3] is increased due to appearance of MAI. . . . . . . . . . . . . . . . . . . . . . 76 4.10 The bit error probability with parameters shown in Table 4.1 where code C0 estimate channel in 40 dB. The number of sub-carriers M = 4, number of users K = 2 and number of antennas NT = NR = 2 are all fixed. The method proposed by [2] uses Hybrid-BPSK-QPSK architecture, the resource needs to share with the other channel. Thus number of sub-carrier which system can support will be halved toM = 2 and the length of chip also need double numbers. From Chapter 2, we know that when multi-path delay is multiple of M, the orthogonality depends on time domain and the system will not affected by the frequency-selective fading channel. In other words, if multi-path delay is multiple ofM, the multi-path interference will be zero. From this figure, both our system which represented the lowest in the green legend and multi-path delay is multiple of M in [3] which are MI-free and their BER are extremely close. Compare with MI-free, IQCCC and odd delay time, we can find that MI-free system performs better apparently. . . . 77 4.11 The bit error probability with parameters shown in Table 4.1 where code C0 estimate channel in 40 dB. Number of sub-carriers M = 4 is fixed and number of antennas and users are changed, NT = NR = [1; 2], K = [1; 2]. Compare with the curve of k = 1 and k = 2, MAI actually is not the main problem of system but it still has some influence so that the BER of different users are slightly different. From this figure, Figure 4.8 and Figure 4.9, we can conclude that the influence of MI is bigger than MAI. . . . . . . . . . . . 78 4.12 The bit error probability with parameters shown in Table 4.1 where code C0 estimate channel in 40 dB. Number of sub-carriers M = 8 and number of antennas NT = NR = 1 are fixed and number of users are changed, K = [4; 8]. When we increase user’s number, number of sub-carrier should follow the restraint of complete complementary code which M  K. It shows the same result with Figure 4.11 where MAI is not the main problem for CC-based system and when sub-carrier are increased, performance will be better. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.13 The bit error probability of systems which are located in worse channel compared with Figure 4.8. The variance of each path in this channel are [0:67; 0:86; 1:02] whose frequency-selective fading is more serious. This figure shows that both systems are suffered form frequency-selective fading, system in [3] especially. Therefore, the difference of performance between our system and system in [3] becomes larger apparently. . . . . . . . . . . . 80 4.14 The bit error probability of systems which are located in worse channel compared with Figure 4.9. The variance of each path in this channel are [0:67; 0:86; 1:02] whose frequency-selective fading is more serious. This figure shows that both systems are suffered form frequency-selective fading, system in [3] especially. Therefore, the difference of performance between our system and system in [3] becomes larger apparently. . . . . . . . . . . . 81 4.15 The bit error probability of systems which are located in worse channel compared with Figure 4.12. The variance of each path in this channel are [0:67; 0:86; 1:02] whose frequency-selective fading is more serious. In this case, MAI is more serious following frequency-selective fading. Therefore, the more users in system, the higher BER system obtain. . . . . . . . . . . . 82 4.16 The bit error probability of systems which are located in different delay spread compared with Figure 4.8. This figure shows that delay spread is not the main factor to effect the performance of system. It is because that complementary code is more sensitive to the variance of channel gains. Even the delay spread becomes longer, if the variance of each channel gain dose not change, the performance of system will not change too. Otherwise, even the delay spread becomes shorter, if the variance of each channel gain change dramatically, the performance of system will be suffered too. This result can be concluded with this figure, Figure 4.14 and Figure 4.15. . . . . . . . . . . 83 4.17 The bit error probability with parameters shown in Table 4.1. Number of subcarrier M = 4, number of antennas NT = NR = 2 and number of users K = 4 are fixed but SNR of estimation step are changed in [5; 10; 20; 30; 40; 50] dB. From this figure, higher SNR in estimation step gives system more stable BER performance due to the accuracy of channel gains. Furthermore, SNR of estimation over than 40 dB can not affect the performance anymore, which can be seem as a perfect estimation given in Appendix C. . . . . . . . . . . . 84 A.1 Two examples for polarization of wave transmitted by antenna, which shows the relation between electric field Hx, Hy and magnetic field respectively. . . 91 A.2 The block diagram of the BPSK communication system. h (t) is the channel impulse response and bh (t) is the channel impulse response including the modulation/demodulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 B.1 The auto periodic correlation for different shift when the length of spreading code for two different carriers is four. . . . . . . . . . . . . . . . . . . . . . 98 B.2 The auto aperiodic correlation for different shift when the length of spreading code for two different carriers is four. . . . . . . . . . . . . . . . . . . . . . 99 B.3 The cross periodic correlation for different shift when the length of spreading code for two different carriers is four. . . . . . . . . . . . . . . . . . . . . . 100 B.4 The cross aperiodic correlation for different shift when the length of spreading code for two different carriers is four. . . . . . . . . . . . . . . . . . . . 101