正交分頻多工系統是目前通訊主流技術，為了克服高峰均值比，可以用頻域等化之單載波區塊傳輸系統來解決此問題。考量到最大似然偵測法雖然能獲得最佳解，但高複雜度的缺點使其在現實難以實現；使用一般線性最小均方誤差等化器則是無法獲得最佳解，但在複雜度部分是可以在現實環境中達成。
在本篇論文為了使頻域等化之單載波區塊傳輸系統有更低的錯誤率，我們使用了差分度量結合梯度搜尋，為了使其可以應用在較為高階的傳輸系統，我們重新定義了實係數系統模型。同時，為了使效能更上一層樓並克服高階梯度搜尋的複雜度問題，我們使用跳躍初始序列的機制。
綜合上述的方法，我們在模擬中可以發現錯誤率有下降的趨勢，而複雜度部分也是在接受的範圍內。利用跳躍初始序列的機制配合多次的低階梯度搜尋可取代高階梯度搜尋，也為頻域等化之單載波區塊傳輸系統在實務上的應用有了新的契機。

Orthogonal frequency-division multiplexing (OFDM) systems are the mainstream communication technologies. To overcome the problem of high peak-to-average power ratio (PAPR), we can use single-carrier block transmission system with frequency-domain equalization (SC-FDE). Consider the maximum likelihood (ML) detection, although the optimal solution can be obtained, the disadvantage of high computational complexity makes it difficult to achieve in reality; while the optimal solution cannot be obtained by using the minimum mean square error equalizer (MMSE), but its computational complexity can be achieved in reality.
In this thesis, in order to make the SC-FDE system have a lower bit error rate, we use the differential metric combined with a gradient search algorithm. In order to make it applicable to high-order transmission systems, we redefine the real-valued system model. At the same time, in order to make the performance better and overcome the complexity of high-level search, we use the scheme with jumping initial sequences.
Combining the above methods, in the simulation we show that the bit-error rate can be reduced, and the computational complexity is also within the accepted range.
The high-order search can be replaced by the low order search combined with the scheme with jumping initial sequences. We therefore proposed a new scheme that is practical for the SC-FDE system with high-order modulation.

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