本論文旨在探討多輸入多輸出（multi-input multi-output, MIMO）正交分頻多工（orthogonal frequency division multiplexing, OFDM）上行鏈路（uplink）系統中，基地台使用迫零（zero-forcing, ZF）偵測器來解調各使用者於每個子載波所傳送的資料符元，在本論文中，我們以各子載波所屬之通道係數矩陣之奇異值分解（singular value decomposition, SVD）來求得迫零偵測器。為了降低計算複雜度，我們使用冪疊代法（power iterative method），由隨機產生之初始向量，逐步收斂至通道矩陣之奇異向量（singular vector）；此外，若通道脈衝響應的延遲擴展（delay spread）不是很長時，相鄰子載波間通道係數相當接近，亦即，相鄰子載波之通道係數矩陣，其奇異值分解也會相當接近，因此，我們可以將前一子載波經由疊代收斂求得的奇異向量，依序去取代下一子載波的初始值，加速冪疊代法求得下一個子載波通道矩陣的奇異向量，經由電腦模擬可知，利用此相鄰子載波之通道相似性，可降低40%~70%達成收斂所需之遞迴次數，大幅降低在寬頻OFDM系統中的計算複雜度。

Consider the uplink of multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. When the number of antennas is sufficiently large, the zero-forcing (ZF) detection performed at the Base station (BS) is near optimum to demodulate data symbols transmitted by users over each subcarrier. Nevertheless, it requires matrix inversion to perform the ZF detection especially when the number of users and subcarriers are large. In this thesis, we adopt singular value decomposition (SVD) based ZF detection and employ power iterative method to reduce computational complexity of SVD. Furthermore, we exploit the fact that the channel matrices of adjacent subcarriers are similar to reduce the required number of iterations in the power iterative method. Specifically, the initial vectors in the power iteration are substituted by the singular vectors obtained for the channel matrix corresponding to the previous subcarrier, rather than the randomly generated vector. It shows through computer simulations that the proposed method reduces the number of iterations by 40%~70%, which significantly reduces the computational complexity in broadband OFDM systems.

論文審定書﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒ i
致謝﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒ ii
摘要﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒ iii
Abstract﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒ iv
目錄﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒ v
圖次﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒vi
第一章 導論﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒1
第二章 相關文獻﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒4
2.1　正交分頻多工技術的基本概念﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒　4
2.2　多輸入多輸出系統架構﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒　9
第三章 系統模型﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒10
3.1　多輸入多輸出正交分頻多工系統﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒10
第四章 通道估測與迫零偵測器﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒13
4.1　通道估測﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒13
4.2　單載波的迫零偵測器﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒15
4.3　多載波的迫零偵測器﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒18
4.4　利用子載波間通道係數相似性以降低疊代次數﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒19
第五章 模擬分析﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒23
5.1　用最小平方估測法的通道估測表現﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒24
5.2　冪疊代法之收斂次數比較﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒26
5.3　不同收斂誤差下的錯誤率比較﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒30
第六章 結論﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒33
參考文獻﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒34

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