本篇論文考慮雙向中繼傳輸系統，其中兩端的使用者僅具備單一天線，而中繼端為多天線節點；在兩端使用者送出各自的來源訊號後，中繼端將接收訊號以不同功率分離後，分別進行無線射頻獵能以及訊號預編碼，接下來，利用獵能所得的能量，將訊號轉傳回兩端使用者。在這篇論文中，我們藉由優化以下三個參數:相位旋轉因子，預編碼及功率分配比例，來達到提高雙向總傳輸率的目標。因為對三組變數同時做最佳化很困難，所以我們分別把三個變數來做優化。優化相位旋轉因子可以盡可能的增加收割功率，我們研發了一個遞迴演算法，此演算法具有低計算複雜度且能快速地收斂。此外，我們發現一個最接近最佳的初始相位值可以被分析計算出來的。對預編碼做最佳化的原因係讓傳輸率提升，我們最後使用了梯度下降法來逼近最佳預編碼值，並提出一個靠近最佳值的初始解以加速收斂。我們還提出了三個方法來尋找功率分配的最佳比例，並且分析了這三種方法的優點與缺點

A system with two single-antenna users that want to exchange their data via a multi-antenna relay has been investigated in this work. After the two users send their data, the relay performs a signal processing so that the sum-rate is maximum. After deriving the SNR equation, we optimize three parameters to achieve the goal: phase rotating factor, precoder, and power splitting ratio. Since the joint optimization over these three variables is difficult, then we optimize them separately. The purpose of optimizing the phase rotating factor is to get the harvested power as high as possible that will be used for data broadcasting by the relay. We develop an iterative algorithm that has a low computational complexity and fast in convergence. Besides, we find a near optimum point that can be calculated analytically. The purpose of optimizing the precoder is to get the rate as high as possible. Since the conventional method finding the first derivation equals to zero cannot be implemented to find an optimum precoder, we finally use the gradient descent method that is developed with an initial point optimization that is close with the actual optimal point. We consider these three methods to find an optimal solution for the power splitting ratio. It has been analyzed that these three methods have their own positive and negative sides.

TABLE OF CONTENTS

Validation Letter ……………………………………………………………………... i
Abstract (Chinese)……………………………………………………………………. ii
Abstract (English) …………………………………………………………………... iii
Table of Contents .………………………………………………………….…..…… iv
List of Figure …………………………………………. ……………………………. vi

Chapter 1 Introduction …………………………………………………………….. 1
Chapter 2 Related Works ………………………………………………………….. 5
2.1. Optimal Distributed Beamforming for Two-Way Relay Networks …………..5
2.2. Joint Power Splitting and Antenna Selection in Energy Harvesting
Relay Channels ……………………………………………………………... 7
Chapter 3 Methodology ………………………………………………………… ...11
3.1. System Model ………………………………………………………………. 11
3.2. Problem Formulation ……………………………………………………….. 14
3.3. Phase Rotation Optimization ……………………………………………….. 15
3.4. Precoder Optimization ………………………………………………….. 20
3.4.1. Zeroing the First Derivation of the objective ………………………….. 22
3.4.2. The Gradient Descent Method with Constraint ……………………….. 23
3.5. Power Splitting Ratio Optimization ………………………………………... 25
3.5.1. Multidimensional Bisection …………………………………………… 27
3.5.2. The Gradient Descent with Constraint ………………………………… 28
3.5.3. The Supply-Demand Power Balancing Method ………………………. 30
3.6. Combining The Three Optimization Together ……………………………... 33
Chapter 4 Simulation Result ……………………………………………………... 35
4.1. Simulation Result of the Overall Optimization …………………………….. 35
4.2. Simulation Result of the Phase Rotating Factor Optimization …………….. 39
4.3. Simulation Result of the Precoder Optimization …………………………… 40
4.4. Simulation Result of the Power Splitting Optimization ……………………. 42
Chapter 5 Conclusion ……………………………………………………………... 45
References …………………………………………………………………………. 47

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