在此論文中我們基於雙向放大轉送多輸出多輸入中繼系統下設計低複雜度的中繼預編碼器。最近被提出的特徵模選擇法（eigenmode-selection）用較低的計算複雜度即可達到接近最佳的效能，在這個方法中，作者基於對應的中繼系統下有效多輸出多輸入通道（effective multiple input multiple output channel）的特徵空間（eigenspace）先建構出一個中繼預編碼器的集合，其中集合中可能的中繼預編碼器數是有限的；再根據不同需求的目標函數來找到最好的那一個當作所要使用的中繼預編碼器，也就是選到使得目標函數最好的特徵模。此外，為了更進一步降低目標函數的計算量，分別為最大化通道容量（channel capacity）或是最小化均方誤差（mean-squared error），作者發展基於條件數（condition number）底下的特徵模選擇法，其定義為一矩正之最大與最小特徵值的比例。
然而，隨著系統的自由度（degrees of freedom）越高，中繼預編碼器集合的數目變得很多，也就是計算次數相當高；為了改善這個問題，首先我們利用條件數的特性並請找到條件數跟奇異值（singular value）的關聯，接下來，我們提出針對兩種目標函數分別提出兩種降低集合數的方法，一是最大化條件數和，二是最小化條件數和。從模擬的結果顯示我們提出的方法可以達到跟原本的特徵模選擇法相近的效能，但我們減少搜尋複雜度K(K-1)之一倍。

Recently, an eigenmode-selection approach was suggested for relay precoding in a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, where a finite set of relay precoders are constructed based on the eigenspaces of the effective MIMO channels and one of them with appropriate eigenmodes is selected to meet a specific design criterion. To design a relay precoder subject to the minimization/maximization of the sum of the condition numbers of the effective MIMO channels, this method needs to search for the solution in a relay procoding set of size 2K!, where the condition number is defined as the ratio of the largest to the smallest singular value of a MIMO channel and K denotes the degrees of freedom of the system. Although the eigenmode-selection precoding scheme can achieve close-to-optimal performance, the required search complexity would become prohibitively high when K is large. In this thesis, we propose some low-complexity relay precoder designs based on eigenmode selection for a two-way AF MIMO relay system. We first exploit properties of the condition numbers of the effective MIMO channels, and then present two set-reduction methods based on these properties to reduce the search complexity in selecting appropriate eigenmodes for the minimization/maximization of the sum of the condition numbers. As compared to the original eigenmode-selection precoding scheme, the proposed approaches reach similar performance but reduce the search complexity by a factor of K(K-1).

目 錄
摘 要
誌 謝
目 錄
第一章 簡介
第二章 系統模型
第三章 相關技術
第四章 提出之演算法
第五章 模擬結果及比較
第六章 複雜度比較
第七章 結論
附 錄 論文英文本

Abstract i
Content ii
List of Figures iv
List of Tables vi
I. Introduction 1
II. System Model and Problem Formulation 4
A. System Model 4
B. Problem Formulation 6
III. Related Works 8
A. Iterative Precoding Design 8
B. Relay Precoder Design 9
C. Eigenmode-Selection Precoding 10
1) Analysis of the MSE Matrices 11
2) Developing the Relay Precoding Set 12
3) Eigenmode-Selection Precoding 14
4) Condition Number 15
IV. Proposed Methods 17
A. Motivation 17
B. Set Reduction for Maximizing the Sum of
the Condition Numbers 17
C. Set Reduction for Minimizing the Sum of
the Condition Numbers 19
V. Simulation Results 22
VI. Complexity Comparison 28
VII. Conclusion 30
Reference 31

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