在本論文中將研究以正交分頻多工以基礎，利用預先編碼技術去增加頻率多
樣性，我們將利用各種不同符合正交特性的預先編碼矩陣，配合使用通道編碼和
沒有使用通道編碼的差異性，而通道編碼是採用接近Shannon 極限且很受歡迎的
渦輪碼。由於渦輪碼裡的解碼器利用重覆性觀念，是近來年研究的主要方向之
一，雖然重覆性的過程是次佳解，但事實上，它的結果我們是可以接受的，重覆
性架構還提供另一個好處是複雜低，容易實現在硬體上。
通道環境是使用雷利衰減通道，並且接收端是己知通道的情況下，接收端是
以渦輪碼的概念來建構次佳解的重覆式接收器，而接收器的偵測與解碼是利用軟
資訊來互相交換資訊，以達到最大事後機率的目標。但最大事後機率必需要計算
每個位元，其複雜度也頗高，為了要降低接收器的複雜度，我們另外使用球型解
碼來當作偵測器，我們稱為列表式球型解碼，而列表式球型解碼與最佳偵測之
間，是一個Tradeoff 問題。
在各種預先編碼之中，我們證明以離散傅立葉轉換的預先編碼矩陣最能匹配
我們的系統，其多樣性增益將隨著維度越高而越大，而如果再配合多維度信號集
合的設計，更可改善在低維度的多樣性增益。

In this thesis, precoding techniques are used to increase frequency diversity in orthogonal frequency division multiplexing (OFDM) systems. Several orthogonal precoding matrices have been employed, and simulation results are shown for uncoded and coded systems (including block, convolutional and turbo codes). In recent years turbo codes have been an important research topic since they can achieve a performance very close to the Shannon limit, and exploit the concept of iteration. Although the iteration process is a suboptimal solution, it provides an acceptable
performance. Another advantage of the iteration process is its low complexity, which allows hardware implementation.
The channel model used in this research is a Rayleigh Fading channel. It has
been assumed that the channel parameters are known to the receiver. The iterative receiver is based on the concept of turbo codes. The receiver’s estimator and decoder exploit and exchange soft information in order to achieve the maximum-a-posteriori (MAP) probability. However, since obtaining the MAP probability implies including every bit in the computations, complexity is increased considerably. In order to reduce the receiver’s complexity, sphere decoding is used for estimation. In this thesis, this
estimator is named list sphere decoder (LSD). Using LSD or optimal estimation becomes a tradeoff issue.
Amongst the several precoding techniques, the discrete Fourier transform (DFT) precoding matrix is the most effective in OFDM systems. The DFT precoding matrix provides a diversity gain which increases with the number of (signal?) dimensions. If a set of multidimensional signals is included in the system design, the DFT precoding matrix can also improve performance when low dimensions are used.

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