本論文探討多輸入多輸出（MIMO）雙向放大轉送中繼系統之預編碼器設計，其中訊源節點採用連續干擾消除（SIC）技術來解出訊號。我們提出一個新的聯合訊源與中繼預編碼器設計方法，以三角化各訊源至目標的等效通道，並發展一SIC解碼器來還原所要的訊號。所設計的預編碼器可將MIMO雙向中繼通道轉換為兩組平行的純量通道(一個方向一組)，以便可直接使用現有的純量通道編碼技術。我們也分別針對無傳送速率限制情況與有傳送速率限制情況探討預編碼器之最佳化設計問題，以最大化兩個訊源的傳送速率總和；每一最佳化的問題可先近似為一個幾何規劃的對偶問題，然後再依據加權算術幾何不等式性質和/或梯度搜尋演算法求解。我們進一步處理節點間和天線間的功率分配問題，並經由解出一個幾何規劃的對偶問題而得到最佳功率分配參數，來最大化傳送速率總和。在無傳送速率限制條件下，我們所提出的預編碼器設計方法較之現有相關的迭代式設計作法，具有明顯較低的運算複雜度，但可達到近似的傳送速率總和；當考量傳送速率限制條件時，所設計之聯合訊源與中繼預編碼器可提供給兩個訊源節點足夠的傳送速率，但相較於無傳送速率限制條件下所設計的預編碼器，具有較低的傳送速率總和。

This thesis investigates precoder designs for multiple-input multiple-output (MIMO) two-way relay systems, where amplify-and-forward is adopted at the relay node and successive interference cancellation (SIC) is used at the source nodes. A new design methodology of joint source and relay precoders is proposed for triangularizing the source-destination effective channels, and an SIC decoder is exploited to recover the desired signals. The resulting joint precoders are able to transform MIMO two-way relay channels into two sets of parallel scalar channels, one for each direction, so that existing channel codes for scalar channels can be directly applied. Optimal precoder designs for sum-rate maximization are also considered for situations without rate constraints as well as for those with rate constraints. Each of the optimization problems is first approximated as a dual problem of geometric programming, and then a solution is derived by applying the property of weighted arithmetic-geometric mean inequality and/or a gradient search algorithm. Power allocation issues among nodes and antennas are further dealt with for the developed precoders to enhance the system performance. The optimal power allocation parameters for sum-rate maximization are determined by solving another dual problem of geometric programming. Without considering rate constraints, the proposed design methodology has much less computational complexity than a related iterative design method in finding joint source and relay precoders to achieve a similar sum rate. When rate constraints are considered, the designed joint source and relay precoders are able to offer enough rates for both source nodes, but have degraded sum-rate performance as compared with those designed under no rate constraints.

CONTENTS
Abstract i
CONTENTS ii
LIST OF FIGURES iv
LIST OF TABLES vii
I. Introduction 1
II. System Models 6
III. Joint GTD Precoder Designs with Equal Power Allocation and Without Rate Constraints 10
A. Joint GTD 10
B. The Proposed Family of Precoding Schemes 14
C. Noise Prediction 21
D. Design Examples 22
E. Complexity Analysis of the Design Examples 25
IV. Optimal Power Allocation for Sum-Rate Maximization of the Precoder Designs 28
A. Power Allocation Problem 29
B. Solution to the Power Allocation Problem 31
V. Joint GTD Precoder Designs for Sum-Rate Maximization with Rate Constraints 39
A. The Case of Equal Power Allocation 39
B. The Case of Optimal Power Allocation 42
VI. Simulation Results 45
A. Simulation Results Without Rate Constraints 45
B. Simulation Results with Rate Constraints 53
VII. Conclusion 66
Appendix A: Investigate the Optimal Choice of Precoder Design with Equal Power Allocation and Without Rate Constraints 67
A. Problem Statement 67
B. Weighted Arithmetic-Geometric Mean Inequality 68
Appendix B: A Lemma 71
Appendix C: An Example for Geometric Programming Problem 72
Appendix D: The Region of a Concave Function 75
References 79

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