在 本 論 文 中， 針對多用戶(multiuser) 多輸入單輸出(multiple-input single-output, MISO)下行(downlink)無線通訊系統，我們考慮各種不同的傳輸 最佳化問題，此系統包括多根天線的傳輸端(transmitter)服務多個單天線接收 端(receiver)，而且它們共享相同的時間與頻譜資源。在傳輸端可以完美地獲得 接收端的通道狀態訊息(channel state information, CSI)前提下之傳輸設計已 經在文獻中被廣泛地研究。然而，在實際上，由於有限的訓練資源(training resource)或是反饋頻寬(feedback bandwidth)，傳輸端的通道狀態訊息誤差是無法避免的。如果將不完美的通道狀態訊息視為完美的通道狀態訊息，如此設計傳輸端，用戶端之間的干擾將無法被適當地消除，將導致用戶端的服務品質(quality of service, QoS)中斷(outage)或是系統性能大幅地下降。近年來，強健性(robust)傳輸設計以對抗通道狀態訊息誤差已經被視為重要的尖端研究挑戰，而且在過去幾年已經受到廣泛的關注。

在本論文中，在傳輸端只有不完美的通道狀態訊息(亦即，獲得的通道狀態訊息中存在估計誤差)下，我們用最小化傳輸功率或是最大化系統效用(system utility)(例如，加權的傳輸速率和(weighted sum rate))設計傳輸方案，同時用戶端或是系統的效能要求必須滿足。通道狀態訊息誤差模型包括被廣泛使用的複數高斯(Gaussian)隨機向量，或是假設落於一個有界的集合中(稱為不確定集合(uncertainty set))。在第二章到第四章，我們專注於複數高斯通道狀態訊息誤差模型，並且研究在用戶端的服務品質中斷機率限制在指定的數值以下的強健性傳輸設計。此中斷限制的最佳化問題一般非常難解，主要是因為其所牽涉的機率函數不是凸函數(convex function)且沒有閉式表示式。因此，我們可能必須求助近似方法。在第二章和第四章，我們分別針對在單細胞(single-cell)以及兩層異質性網路(two-tier heterogeneous network)的系統開發了幾個新穎易處理的約束方法(restriction approaches)用於解決中斷限制下的傳輸功率最小化問題。此外，我們對所提出方法的效能，複雜度以及可行性(feasibility)之條件也進行嚴謹的分析。雖然各式各樣的子問題所開發的演算法中，若能有閉式解是最好的，但是它們通常僅存在一些特殊的場景。在第三章，我們特別地考慮單用戶(single-user)的場景，假設接收端可藉由所接收到的訓練訊號獲得即時的通道向量(亦即，通道狀態訊息在接收端是不完美的)。我們提出了以最大化中斷傳輸速率(outage rate)(亦即，在滿足給定的中斷機率下之最大可達速率(achievable rate))可得到最佳的訓練功率與資料傳輸策略之閉式解。

相對地，在第五章，我們考慮有界的通道狀態訊息誤差模型，即假設通道狀
態訊息誤差是落在某個球型區域中。傳輸設計方法是最大化在所有可能的通道狀
態訊息誤差中最差的(亦即，最小的)系統效用。此最佳化問題是NP難解的
(NP-hard)，因此任何可以找到最佳解的演算法都可能會遭受到非常高複雜度的
困境。有鑑於此，對於原本的非凸優化問題，我們進一步提出一個低複雜度的演
算法可獲得有效率又精確的次佳解(suboptimal solution)，以及證明此演算法的收斂性與所獲得的解是Parato最佳解。

在第二章到第五章的每一個章節中，我們也提供一些模擬的結果用以驗證所
提出的演算法之效能，及其與現存最先進的演算法做效能的比較。最後，第六章
做一些結論以及討論未來研究方向。

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