正交時頻空調變 (OTFS)，為克服高移動性通訊帶來的高都卜勒頻移，而提出之調變技術。於正交分頻多工 (OFDM) 中，因為都卜勒頻率偏移使子載波之間喪失正交性導致效能減損；OTFS 藉由將信號放置在與時間頻率獨立的二維通道上，此二維平面為延遲都卜勒域，傳送信號在此領域中被變化緩慢的通道增益影響，在一個傳送框架中我們可以視其為常數的通道增益，利用這特性 OTFS 得以解決克服高移動性通訊帶來的載波間干擾問題 (ICI)，在快速變化通道下有著優秀性能表現。然而當面臨實際通訊場景通道中分數督卜勒現象時，一分數都卜勒來源的通道增益擴散至整個都卜勒軸中，而非一整數都卜勒偏移上，這項變化使通道預測愈加困難，並在訊號偵測中，因督卜勒軸的能量擴散使通道矩陣稀疏性銳減，使通道等化複雜化。
通道矩陣中，影響接收信號的傳送數量在時延遲域比延遲都卜勒域較少，最大比合併利用這樣性質，將 OTFS 接收端訊號於時延遲域進行估計值計算後轉換到延遲督卜勒域進行判決，如此減少計算複雜度，並提升錯誤率效能。於此本文利用時延遲域干擾量較少特性，將訊號傳送於時延遲域之單載波系統，通道矩陣的下三角特性，使用球狀解碼算法偵測最大概似解之不必進行 QR 分解額外運算之需求。將球狀解碼演算法運用在等化後的時域訊號增強線性等化後錯誤率表現，相較於最大概似偵測於龐大分支的樹中一一拜訪葉，球狀解碼利用搜尋半徑過濾大部分的枝和葉，減少搜尋範圍，能以較低的複雜度趨近最大概似解錯誤率。
在本篇論文中，對於零填充傳輸框架和通道矩陣交互作用於時延遲域信號，利用其特性對於球狀解碼搜尋方式，進行歸零優化對於錯誤率方面的改善。隨著星座圖規模增大招致複雜度需求增加，對搜尋範圍優化減少了搜尋點數和其相關複雜度。模擬結果展示經改良後球狀解碼可有效地降低錯誤率，在錯誤率表現與複雜度的交易中達成平衡，比較於使用於 OTFS 中的最大比合併算法，能以較少的複雜度達到較低的錯誤率。

Orthogonal Time Frequency Space (OTFS) is proposed to overcome the high Doppler shift under high mobility communications. Compared with Orthogonal Frequency Division Multiplexing(OFDM), OTFS demonstrates significant error performance advantages in fast fading channel. However, when encountering fractional Doppler effect in practical scenarios, the sparsity of the channel decreases, making channel equalization more complicated. Number of transmitted signals affecting the received signal is lower in the delay-time domain. This thesis adopted Single-Carrier Block Transmission system (SCBT) with mapping symbols delay-time domain. SCBT with zero padding reduces the computational complexity of sphere decoding(SD). The SD method filters the search area by search radius rather than maximum likelihood detection(ML) exhaustive search. The SD method, based on the zero-padding, improves error rates through Return Zero(RZ) optimization. Furthermore, making search area optimization reduces the increase in visited nodes and relevant complexity from the larger scale of constellation size in high QAM modulation. Simulation results demonstrate that the improved spherical decoding effectively reduces the error rate. It achieves a balance between error rate performance and complexity trade-off, outperforming the maximum ratio combining algorithm in OTFS with lower complexity while achieving lower error rates.

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