正交分頻多工 (OFDM) 系統是一個具有高速傳輸，節省頻寬及良好抵制干擾能力的通訊系統，近年來已經被廣泛地使用在許多高速傳輸的無線通訊系統之中。如IEEE 802.11a/g高速無線區域網路， HIPERLAN2高速固定式無線網路、 IEEE 802.16都會型區域網路無線通訊及歐洲數位廣播及數位電影的規範等。 當信號在通過具有分散性之通道時會造成區塊間干擾(IBI)，為了處理這個問題，在傳輸端會引入冗餘資料量 (Redundancy)來解決區塊間干擾。 雖然， 插入足夠長度之冗餘資料量可以避免所傳輸之區塊信號受到區塊間干擾， 通訊系統仍然需要獲得正確的通道資訊來做等化之用，以便將所傳輸之區塊信號能被正確復原。 尤其是在時變通道環境下，通道參數隨著時間改變如果無法有效估測通道參數，將會使得符間干擾(ISI)更加嚴重， 因而降低系統品質。
在傳統所謂偽隨機後置編碼(PRP)正交分頻多工系統中，利用接收信號的一階統計特性，可以使用偽隨機後置編碼來做半盲蔽式的非時變通道估測。但在時變通道環境下，將無法利用此統計特性來做通道估測，在現有文獻中也不曾看過有人探討此一問題。 因此，在本篇論文中，我們將提出改良偽隨機後置編碼(PRP)正交分頻多工系統， 加入局部輔助性的訓練區塊序列， 結合卡馬濾波器(Kalman Filter)與最小均方誤差等化器方法，在時域上來實現時變通道的估測及等化。對於時變通道的估測問題，我們首先以一個動態系統模型來描述。接著我們利用卡門濾波器來解出時變通道系數，但在動態系統模型中模型參數通常是隨機且無法確實得知的。而我們從卡門濾波器的演算法中得知，若能獲得模型參數的統計特性，就能利用卡門濾波器來做時變通道估測。在此，我們也提出一些有用的估測方法，在訓練區塊序列的輔助下，對模型參數的統計特性做估測，進而使用在卡門濾波器之中。在得到了通道的資訊之後，使用最小均方誤差等化器(MMSE equalizer)來消除符碼間干擾(ISI)，並可以將其等化後的信號重新調變，再次使用卡馬濾波器對通道系數做進一步的更新以獲取更精確的估測，使得等化器的效能再次改善。在電腦模擬的部分，我們將使用位元錯誤率(Bit Error Rate)來做系統效能的分析，並且與使用頻域通道估測與等化的循環式字首正交分頻多工系統(CP-OFDM)做比較。

Orthogonal Frequency Division Multiplexing (OFDM) techniques have been used in many wireless communication systems to improve the system capacity and achieve high
data-rate. It possesses good spectral efficiency and robustness against interferences. The OFDM system has been adopted in many communication standards, such as the 802.11a/g standards for the high-speed WLAN, HIPERLAN2, and IEEE 802.16 standard, and meanwhile, it is also employed in the European DAB and DVB systems. To avoid the inter-block interference (IBI), usually, in the transmitter of OFDM systems the redundancy with sufficient length is introduced, it allows us to overcome the IBI problem, due to highly dispersive channel. Many redundancy insertion methods have been proposed in the literatures, there are cyclic prefix (CP), zero padding (ZP) and the pseudorandom postfix (PRP). Under such system we have still to know the correct channel state information for equalizing the noisy block signal. Especially, in time-varying channel, the incorrect channel state information may introduce serious inter-symbol interference (ISI), if the channel estimation could not perform correctly.
In this thesis, the PRP-OFDM system is considered. According to the PRP-OFDM scheme, the redundancy with pseudorandom postfix (PRP) approach is employed to make semi-blind channel estimation with order-one statistics of the received signal. But these statistic characteristics may not be available under time-varying channel. Hence, in this thesis, we propose a modified PRP-OFDM system with assistant training sequences, which is equipped with minimum mean-square-error equalizer and utilize Kalman filter algorithm to implement time-varying channel estimation. To do so, we first model time-varying channel estimation problem with a dynamic system, and adopt the Kalman filter algorithm to estimate the true channel coefficients. Unfortunately, since most parameters in dynamic system are random and could not to be known in advance. We need to apply effective estimation schemes to estimate the statistics of true parameters for implementing the Kalman filter algorithm. When the channel state information is known, MMSE equalizer follows to suppress the inter-symbol interference (ISI). Moreover, after making decision the binary data can be used to re-modulate PRP-OFDM symbol and to be re-used in Kalman filter to obtain more accurate CSI to improve the effectiveness of the equalizer. Via computer simulations, we verify that desired performance in terms of bit error rate (BER), can be achieved compared with the CP-OFDM systems.

誌 謝………………….i
Abstract .......................... .ii
Contents ................................. iv
List of Figures and Tables ............................ vi
Chapter 1 Introduction..........................1
Chapter 2 OFDM Systems with Precoder .................4
2.1 Introduction .................................4
2.2 Model Description of OFDM Systems...................5
2.3 OFDM systems with Precoder ...................9
2.4 Pseudo Random Postfix (PRP)-OFDM ..............15
Chapter 3 Modified PRP-OFDM With Kalman Filter For
Time-Varying Channels .........20
3.1 Introduction .............20
3.2 Estimation of Parameters for Kalman Filter ....22
3.2.1 Estimating State Transition Matrix ....................24
3.2.2 Estimating Noise Covariance Matrices ..............25
3.3 Channel Tracking with Kalman Filter and Equalization ...........28
3.3.1 Kalman Filter Time-Domain Channel Tracking .......28
3.3.2 MMSE Equalizer of Modified PRP-OFDM systems.......32
Chapter 4 Computer Simulation .................34
4.1 Introduction .......................34
4.2 Simulation of Estimating Parameters ................................35
4.2.1 Simulation of A .......................35
4.2.2 Simulation of V ........................37
4.2.3 Simulation of W ..........................39
4.3 Simulation of modified PRP-OFDM ..............39
Chapter 5 Conclusions ..........46
References ..............................48
Appendix A ...............................49
Appendix B ..............................50

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