目前通訊主流技術是正交分頻多工系統（OFDM），但其有著高峰值功率比(PAPR)的缺點，我們可以使用頻域等化之單載波區塊傳輸系統來解決此問題。理想情況下，我們可以使用最大似然檢測法(ML)來獲得最佳解，但ML卻有著極高的複雜度，所以我們轉而使用考量到一般線性最小均方誤差(MMSE)等化器取代，雖然無法像ML獲得最佳解，但其複雜度相較於ML已大幅的下降。這篇論文中我們結合了差分度量和梯度搜尋，應用在頻域等化之單載波區塊傳輸系統，使其擁有更低的錯誤率，並使用了跳躍初始序列的機制，降低高階梯度搜尋的複雜度。隨著梯度搜尋的階數變高，錯誤率隨之下降，但複雜度也隨之大幅上升，為了在控制住複雜度的情況下降低錯誤率，我們提出了改善的搜尋方法。在模擬結果中我們發現錯誤率相較原本有所下降，複雜度也在可接受範圍。

At present, the mainstream communication technology is Orthogonal Frequency Division Multiplexing (OFDM), but it has the shortcoming of high peak-to average power ratio (PAPR). We can use a single-carrier block transmission system of equalization in frequency domain to solve this problem. Ideally, we can use Maximum Likelihood Detection (ML) to get the optimal solution, but the ML detection has extremely high complexity. We can also use the linear minimum mean square error (MMSE) equalizer, whose complexity has been greatly reduced compared to the ML method. However, by this method we cannot obtain the optimal solution as the ML detection. In this work, we combine the differential metric and gradient search, which are applied to the single-carrier block transmission system of frequency-domain equalization, such that we can obtain lower error rate. We also use the mechanism of jumping initial sequence scheme to reduce the complexity of high-level search. As the order of gradient search becomes higher, the error rate decreases, but the complexity also increases significantly. In order to reduce the error rate while controlling the complexity, we propose an improved search method. In the simulation results, we show that the error rate can be decreased compared, and the complexity is within an acceptable range.

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