在此研究裡，我們考慮一個異質網路(heterogeneous network)，其中包含一個宏單位基地站(macrocell)和數個毫微單位基地站(femtocell)。在每個毫微單位基地站中，基地台個別只服務一個使用者，而此接收者具有分配功率(Power splitting)之獵能(Energy harvesting)功能。與此同時所有毫微單位基地台也對宏單位基地站裡的使用者造成干擾。在假設部份通道資訊(channel state information)─不完整通道資訊(imperfect CSI)和通道之統計特性(channel distribution information)情況下，我們致力於系統能源效率(energy efficiency)最大化，並且共同將波束成型向量和功率分配參數最佳化。在不完整通道資訊的假設中，我們在考慮毫微單位裡的使用者服務品質(quality of service)和獵能功率限制下，針對整體的最糟糕的能源效率最大化設計強健波束成型(robust beamforming)。而在通道之統計特性的假設中，我們在考慮中斷傳送機率限制下針對整體的能源效率最大化。此共同優化間涉及複雜且非凸特性的限制下，我們提出一個集中式連續凸化近似演算法去得到高精準度的近似解。我們模擬結果顯示在這兩個不同的通道資訊下均能達到不錯的表現。在不完整通道資訊的假設中，我們的演算法比強制歸零(zero-forcing)方法和以功率最小化的波束成型設計相比，分別提高了23.1%和267.6%的表現。而在通道之統計特性的假設下，我們的演算法比強制歸零方法和以速率最大化的波束成型設計相比，分別提高116.7%和21.1%的表現。這也代表在以能源效率為主的波束成型設計在下世代的無線通訊系統中是很重要的。

In this work, we consider a heterogeneous cellular network (HCN) with a macrocell and multiple femtocells. In each femtocell, the femto base station (FBS) serves a femto user (FU), which is capable of simultaneous wireless information and power transfer (SWIPT) energy harvesting (EH) in a power splitting manner. All FBSs suppress their interference to macro users (MUs) via a interference power constraint. In such a HCN, we aim to maximize the energy efficiency (EE) of all femtocells via the joint design of beamforming and power splitting ratios under partial channel state information (CSI) - imperfect CSI and channel distribution information (CDI) at FBSs. For the imperfect CSI case, we consider the robust beamforming design that maximizes the worst-case EE for all femtocells under the quality-of-service (QoS) constraints and EH constraints. For the CDI case, we consider the problem of maximizing EE under rate outage constraints. The non-convex objective functions and constraints make the problem difficult to solve. To resolve this issue, We proposed successive convex approximation (SCA) algorithms (EE-SCA-1 for the imperfect CSI case and EE-SCA-2 for the CDI case) that provide high-quality approximate solutions. Simulations demonstrated that our proposed EE-SCA-1 and EE-SCA-2 achieve near-optimal performance for both the imperfect CSI and CDI cases. Furthermore, for the imperfect CSI case, our EE-SCA-1 improved EE by as much as 23.1% and 267.6% over the zero-forcing (ZF) scheme and a power minimization scheme. For the CDI case, our EE-SCA-2 improved EE by as much as 116.7% and 21.1% over the ZF scheme and a rate maximization scheme. It indicates that careful design of energy efficient beamforming scheme is essential for the next-generation wireless communication systems.

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract in Chinese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 System Model and Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Energy Efficiency Maximization under Imperfect CSI at Transmitters 9
3.1 Worst-Case Robust Beamforming and Power Splitter Design . . . . . . . . . . . . . . 10
3.2 Convex Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Successive Convex Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Convergence analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Energy Efficiency Maximization under CDI at Transmitters 24
4.1 Convex Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Successive Convex Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 Simulation Results 33
5.1 Performance for the imperfect CSI case . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2 Performance for the CDI case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
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