合作式通訊（cooperative communications）是近來被高度關注的主題，而在4G LTE標準為了滿足高傳輸速率與品質的要求，異質網路（heterogeneous network）的部屬已是勢在必行，其中一種重要的低功率節點便是中繼節點，而隨著中繼技術的普及實用化，我們認為此技術是有價值且值得深入研究的，在中繼技術中，除了傳統的單向式傳輸中繼（one-way relay）系統，雙向式傳輸中繼（two-way relay）系統是近幾年被提出並廣泛討論的中繼傳輸方式。它的優點在於可大幅提高通道的使用效率，其立足點是基於每個節點皆知道所有通道完整的訊息，並利用此假設前提來達到雙向式中繼傳輸系統可行的關鍵‘消除自干擾’。
本篇論文之討論與設計係建立於雙向式放大轉送多輸入多輸出中繼系統，該系統設定兩節點透過一中繼節點來交換訊息，並於每個節點上配置多天線。本論文欲改善現有採用最小化相加均方誤差方法在此系統架構下所提出之具高效能編解碼器，皆須以聯合迭代演算法的方式實現，因此衍生的高計算量問題。藉由分析在最小化均方誤差中中繼預編碼器在高訊雜比下運作之主要行為係與條件數（condition number）之關係，並以此分析結果運用格拉姆施密特（Gram-Schmidt）正交化設計一 效能接近於迭代演算法的中繼預編碼器，且該預編碼器具備了對於系統中存在通道估測誤差時的穩健性。

Abstract
In this thesis, we propose a relay precoder design for two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay systems. By exploring the asymptotic behavior of the sum of mean-squared errors (sum-MSE) of the received signals at the two source nodes, we find that it is dominated by the smallest singular values (or the smallest eigenvalues) of the effective MIMO channels of the relay system. This implies that the sum-MSE performance strongly depends on the sum of condition numbers of the effective MIMO channels, where the condition number of a MIMO channel is defined as the ratio of the largest to the smallest singular value. With this observation, unlike the conventional precoder designs that are obtained in an iterative manner based on minimizing the sum-MSE, the proposed one is derived by using the Gram-Schmidt process based on minimizing the sum of condition numbers of the effective MIMO channels. Specifically, the relay precoder is designed to rotate each eigenspace of the effective MIMO channels such that the corresponding eigenvalues are as equal as possible. As compared to the conventional iterative methods, the proposed approach achieves close performance with much lower computational complexity for both perfect and imperfect channel estimations.

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