正交分頻多工技術(OFDM)是多載波區塊傳輸的一種， 由於它具有抗多路徑傳輸通道及提高頻譜效率的效能，使得它成為現代無線通訊的重要技術之ㄧ。當訊號以區塊方式在通道中傳輸時，訊號會因通道的影響而遭受符碼間干擾(Inter-symbol interference)和區塊間干擾(Inter-block interference)。為了避免信號受到這些干擾的影響，正交分頻多工系統採用保護區間(Guard band)方法來保護所傳輸信號，常見的有循環前置碼(Cyclic prefix)和補零冗餘碼(Zero padding)兩種。

這篇論文探討一種新的冗餘碼; 稱之為虛擬隨機循環後置碼(Pseudo Random Cyclic Postfix)並且採用正交分頻多工調變配合多天線傳輸系統。虛擬隨機循環後置碼的主要特點為利用一組已知的循環碼去做通道估測，並且同時消除符碼區塊干擾。與傳統具循環前置碼的正交分頻多工系統比較，虛擬隨機循環後置碼正交分頻多工系統克服了通道零點(channel null)的問題。

此外，對於補零冗餘碼正交分頻多工系統來說，虛擬隨機循環後置碼正交分頻多工系統利用了補零冗餘碼那段額外的資訊去估測通道。更重要的是，虛擬隨機循環後置碼正交分頻多工系統避免了在通常所使用虛擬隨機後置碼正交分頻多工系統中，進行通道估測時所遭遇的來自訊號的干擾。因此，虛擬隨機循環後置碼正交分頻多工信號雜訊比(SNR)可以提升，我們的方法可以有較好的表現。此外，由於多天線系統可以提供更高的傳輸率和維度增益(diversity gain)，所以我們將虛擬隨機循環後置碼正交分頻多工系統結合時空區塊碼(space-time block code)延伸至多天線傳收的系統中。

另外我們使用了一種名為MSSNR(Maximum Shortening Signal-to-noise Ratio)的盲蔽式通道縮減(Blind Channel Shortening)演算法來減輕在冗餘碼長度小於通道的長度產生的符碼區塊干擾。

在通道方面，我們採用隨機非時變通道(Rayleigh Model)與隨機慢速時變通道(Jake’s Model)情況下來做比較，並且考慮在不同都普勒偏移(Doppler shift)情況下去比較效能。

最後，我們可以由電腦模擬的結果，驗證我們所提出的方法。

Orthogonal frequency division multiplexing (OFDM) due to the robustness to the effect of multipath fading and having high spectral efficiency, it has become a good candidate of wireless communications systems. The block transmission of signal-blocks through the channel will suffer from the inter-block interference (IBI) and inter-symbol interference (ISI). Usually in the transmitter of the OFDM systems, redundancy (or guard interval), such cyclic prefix (CP) or zero padding (ZP), with sufficient length, is inserted in the transmitted block to avoid the IBI. In this thesis, we propose a novel pseudo random cyclic postfix (PRCP-) OFDM system configuration, which adopts the PRCP as redundancy and combines with multiple antennas. In fact, the multiple transmit antenna and multiple receive antenna, which exploits the spatial diversity, can be used to further enhance the channel capacity and achieve high data-rate. The main property of PRCP-OFDM modulation is that it exploits the cyclic-postfix sequences to estimate channel information with a low complexity method. Compared with CP-OFDM, it overcomes the channel null problem. For ZP-OFDM, it uses the additional information to estimate channel which is replaced by zero samples in ZP-OFDM. Moreover, PRCP-OFDM avoids the interference of signals to the desired postfix when we estimate channel impulse response (CIR) and which is different from pseudo random postfix (PRP-) OFDM [8]. Thus, as SNR grows, PRCP-OFDM can have better performance than PRP-OFDM. With the help of [9], [12] and [13], we extend the PRCP-OFDM to the MIMO case with space-time block coding. 
In addition, the so-called MSSNR (Maximum Shortening Signal-to-noise Ratio) algorithm, which is a kind of Blind Channel Shortening method, is employed to alleviate the effect of IBI when the length of PRP or PRCP sequences is shorter than the order of channel impulse response.
To fair compare the system performance among the existing MIMO OFDM methods, we consider the channels which are modeled as the random time-invariant Rayleigh model and the slow random time-varying channel modeled by the Jake’s model.
Via computer simulation, we verify that the performance is improved, in terms of the accuracy of channel estimation and symbol error rate (SER).

Chapter 1 INTERDUCTION 1
Chapter 2 CONVENTIONAL ORTHOGONAL FREQUENCY
DIVISION MULTIPLEXING (OFDM) MODULATION
TECHNIQUE 6
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 CP-OFDM System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Optimal Training Sequnece . . . . . . . . . . . . . . . . . . . . . . 12
2.4 ZP-OFDM System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 NZP-OFDM System . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6 PRP-OFDM System . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Chapter 3 MIMO-OFDM MODULATION TECHNIQUE 32
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Space-Time Block Code (ST-BC) forMultiple Transmit-Antennas 33
3.3 Model Description of Space-Time Block Coded MIMO PRCP-
OFDM System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 Discrete Time MIMO CP-OFDM System with Optimal Train-
ing Pilots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 4 COMPUTER SIMULATIONS 59
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 SER Performance Comparison For Different MIMO OFDM
Systems Under Rayliegh Channel . . . . . . . . . . . . . . . . . . 61
4.3 Symbol Error Rate of Various MIMO OFDM Systems under
Jake’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
III
Chapter 5 COUCLUSIONS 72
Appendix A 73
Appendix B 75
LIST OF FIGURES
Figure 2.1 Block diagram of the discrete CP-OFDM tranceiver. . . . . . . . . . . . . . 9
Figure 2.2 (a)Training over one OFDM symbol. (b)Training over two OFDM
symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Figure 2.3 Block diagram of the discrete ZP-OFDM transceiver. . . . . . . . . . . . . 19
Figure 2.4 Discrete model of NZP-OFDM transceiver. . . . . . . . . . . . . . . . . . . . . . 24
Figure 2.5 Discrete model of PRP-OFDM transceiver. . . . . . . . . . . . . . . . . . . . . . 28
Figure 2.6 Received signal of PRP-OFDM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Figure 3.1 Block diagram of two-branch receiver combing scheme. . . . . . . . . . . . 34
Figure 3.2 Two transmit-antennas with ST-BC encoder and N receive- antennas
combing system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Figure 3.3 Discrete-time model of the ST-BC PRCP-OFDM modulator. . . . . . 38
Figure 3.4 Reversed cyclic shift matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Figure 3.5 Received signal of MIMO PRCP-OFDM. . . . . . . . . . . . . . . . . . . . . . . 44
Figure 3.6 Discrete model of the MIMO CP-OFDM system model. . . . . . . . . . . 52
Figure 4.1 Comparison of NMSE for ST-BC MIMO PRP-OFDM and ST-BC
MIMO PRCP-OFDM with orthogonal cyclic sequence. . . . . . . . . . . . . 63
Figure 4.2 Comparison of SER for ST-BC MIMO PRP-OFDM and ST-BC
MIMO PRCP-OFDM in Rayleigh Model. . . . . . . . . . . . . . . . . . . . . . . . . 63
Figure 4.3 Comparison of SER for PRP-OFDM and PRCP-OFDM with and
without using shortening algorithm in Rayleigh Model Nt = 2,Nr = 1 64
Figure 4.4 Comparison of SER for PRP-OFDM and PRCP-OFDM with and
without using shortening algorithm in Rayleigh Model Nt = 2,Nr = 2 64
Figure 4.5 Comparison of SER for PRP-OFDM , PRCP-OFDM and Optimal
Training-OFDM in Rayleigh Model Nt = 2,Nr = 2 . . . . . . . . . . . . . . . . 65
Figure 4.6 The block diagram of Jake’s Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Figure 4.7 Comparison of SER for ST-BC MIMO PRP-OFDM and ST-BC
MIMO PRCP-OFDM in Jake’s Model v=40km/hr. . . . . . . . . . . . . . . . 69
Figure 4.8 Comparison of SER for PRP-OFDM and PRCP-OFDM with and
without using shortening algorithm in Jake’s Model Nt = 2,Nr = 1
v=40km/hr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Figure 4.9 Comparison of SER for PRP-OFDM and PRCP-OFDM with and
without using shortening algorithm in Jake’s Model Nt = 2,Nr = 2
v=40km/hr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Figure 4.10 Comparison of SER for PRP-OFDM, PRCP-OFDM and Optimal
Training-OFDM in Jake’s Model Nt = 2,Nr = 2 v=40km/hr . . . . . . . 70
Figure 4.11 Comparison of BER for Optimal Training-OFDM in Jake’s Model
Nt = 2,Nr = 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
LIST OF TABLES
Table 3.1 Illustration the cyclic postfix sequences c(i) for D = 8 and x = 3 . . . 41

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