正交分頻多工是當今通訊科技的其中一項主流技術，舉例而言它是構成第四代行動通訊的基礎技術，然而由於多重子載波等因素也使得正交分頻多工系統具有高峰均值功率比的問題。透過適當的線性預編碼我們可將之轉變為單載波區塊傳輸系統，即可免除峰均值功率比的問題。
接收端接收到的單載波區塊傳輸訊號可以被轉換到頻域來進行等化，隨後再進行時域的偵測。雖然頻域等化已可讓單載波區塊傳輸系統相較正交分頻多工系統有較低的錯誤率，尤其是在高訊雜比的情況下，但等化後之時域訊號的偵測仍能再進一步地改善。最大概似偵測是改善錯誤率的最佳方法，但因巨大的複雜度致使無法實際執行，而其他一些基於判決反饋的方法也相繼被提出作為替代方案。
在本篇論文中，我們將梯度搜尋演算法運用在等化後的時域訊號上來降低錯誤率。梯度搜訊演算法是以差分度量為基礎，最初提出時是為了改善多天線系統的偵測，現在我們將其再次運用並提出一些能使單載波區塊傳輸系統達到較低錯誤率的搜尋程序。模擬結果顯示，梯度搜尋演算法可有效地改善單載波區塊傳輸訊號偵測的錯誤率，同時此方法也可在錯誤率表現與複雜度之間達成平衡。

The Orthogonal Frequency Division Multiplexing (OFDM) is one of the main technology in modern communications. It is the basic technique underlying the fourth-generation (4G) communication for example. However, the OFDM system has the problem of high peak to-average power ratio (PAPR) due to the multiple sub-carriers. With the appropriate linear precoding in the OFDM system, we can obtain the Single-Carrier Block Transmission system (SCBT), which does not have the problem of PAPR.
The received SCBT signal can be transformed into frequency domain (FD) for equalization, followed by the time-domain (TD) detection. Although the FD equalization (FDE) can already result in lower error rates for SCBT than OFDM systems, especially at high signal-to-noise ratios (SNR), the detection of the equalized TD signal can, however, be further improved. The maximum-likelihood (ML) detection is the optimal method to improve the performance but is impractical to realize due to its enormous complexity. Some methods based on decision feedback have also been proposed to serve as an alternative.
In this thesis, we apply the gradient search algorithm (GSA) in the equalized TD signal to reduce the error rates. The GSA is based on differential metrics (DM), and it was first proposed for the detection of the multiple-antenna system. Now we apply the GSA and pro pose several searching procedures that can achieve lower error rates for the SCBT system. The simulation shows that the GSA can efficiently improve the performance of error rates for the detection of SCBT signals. The proposed method also achieves a trade-off between error performance and complexity.

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