無線電波充電相較於其他無線充電方案有範圍較大及不易受障礙物遮蔽的優點。無線電波充電利用發射器(transmitter)與接收器(receiver)的組合進行充電，發射器作為能量來源發射無線電波為裝有接收器之裝置補充電力。配合天線陣列(antenna array)使用波束成形(beamforming)技術，可調整每支天線傳輸功率與相位，將無線電波集中形成波束，增加無線電波傳輸距離並能改變波束方向，使有效充電範圍(effective charging area)能夠涵蓋特定的位置。波束成形在目標方向上產生主辦(main lobe)，也無可避免地在非目標方向上產生旁辦(side lobe)，造成能量無效損耗。本論文提出一個稱為演化波束成形(Evolutionary Beamforming Optimization, EBO)的演化演算法，可最佳化天線陣列每支天線的傳輸功率以抑制旁辦，達到最小化尖峰旁瓣(peak side lobe)及最大化主瓣的效果。EBO假設的天線陣列採用12支全向性天線組成均勻圓陣(Uniform Circular Array, UCA)，陣列半徑(radius of array)為一倍波長，在此條件下之天線陣列所形成之波束圖形(beam pattern)在以不同方向為目標時皆能有均等的表現。本論文並提出EBO-R (EBO-Reseeding)進一步改良EBO。EBO-R的基本概念為使用重複播種(reseeding)在每個世代中產生小量的隨機個體取代表現差的個體。如此可在維持族群大小的條件下，加強探索最佳化設定的能力，因而可以產出較佳結果，並提升收斂速度與穩定度。本論文透過模擬實驗比較EBO、EBO-R及相關的PSOGSA-E演化演算法，結果顯示EBO-R有最好的效能，而EBO的效能較PSOGSA-E與EBO-R差，但是EBO具有最短的執行時間。

Radio Frequency (RF) charging has a larger charging area than other wireless charging solutions, and it’s less susceptible to the shading of obstacles. The combination of transmitters (or chargers) and receivers (or harvesters) is utilized to perform RF charging. A transmitter, as the energy supplier, emits radio waves to charge a receiver Based on an antenna array, the beamforming technique adjust the amplitude and phase of every antenna in the array to form radio wave beams. The direction of beams can be adjusted, and the transmission distance can be extended so that the effective charging area can cover specific positions. Beamforming produces main lobes in the target direction, but produces side lobes in non-target directions, leading to energy waste. This study proposes an evolutionary algorithm, called Evolutionary Beamforming Optimization (EBO), to optimize the transmission amplitude of every antenna in an antenna array for trying to maximize the strength of the main lobe and to minimize the strength of the peak side lobe. EBO assumes an antenna array consisting of 12 omnidirectional antennas forming the uniform circular array (UCA) with a radius of λ. With the UCA, beamforming can produce nearly identical beam patterns for any target directions. This study also proposes EBO-Reseeding (EBO-R) to further improve EBO. The basic concept of EBO-R is reseeding, which randomly generates new individuals to replace the worst ones in the population in every generation. Reseeding does not increase the population size and endows EBO-R has better capability to explore possible individuals to achieve better results, convergence speeds, and stability than EBO. This study performs simulation experiments to compare EBO, EBO-R and one related evolutionary algorithm, namely PSOGSA-E. The simulation results show that EBO-R has the best performance, and EBO is worse than EBO-R and PSOGSA-E. However, EBO has the shortest execution time.

摘要 i
Abstract ii
致謝 iv
目錄 v
圖目錄 vi
表目錄 vii
1. 緒論 1
2. 背景知識 5
2.1. 天線與天線陣列 5
2.2. 波的相位與干涉 5
2.3. 波束 6
2.4. 陣列因子 9
2.5. 天線的座標與相位 9
2.6. 適應值函數 10
2.7. 演化策略 (Evolution Strategy) 11
2.8. PSOGSA-E 11
3. 初步假設與問題定義 12
3.1. 場景假設 12
3.2 天線陣列的排列 12
3.3. 天線發送功率 13
3.4. 問題定義 15
4. 演化策略應用於波束成形最佳化問題 16
4.1.　Evolutionary Beamforming Optimization 16
4.2.　Evolutionary Beamforming Optimization-Reseeding 17
5. 模擬與分析 19
6. 結論與未來方向 24
引用文獻 25
附錄 27

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