使用交替方向乘子法的動態範圍比約束下之寬頻波束成形

Abstract

波束成形（Beamforming）是一種訊號處理技術，透過調整多個來源訊號的相位，使訊號能量集中於特定方向，從而在目標角度實現建設性的組合。隨著對支援更多使用者及實現更高資料速率的需求不斷上升，對寬頻無線通訊的需求也迅速增加。本論文提出一種基於交替方向乘子法（alternating direction method of multipliers, ADMM）架構的設計方法，用於在時延線（time-delay line, TDL）結構下設計寬頻波束成形係數。為了在保持主波束於期望方向幅度不失真的同時，降低旁瓣區域的干擾，設計中引入了在無失真約束下的最大旁瓣抑制（peak sidelobe level, PSL）。此外，為確保主波束在不同頻率下能始終指向相似方向，本研究進一步加入空間響應變異（spatial response variation, SRV）抑制，以最小化發射方向（direction of departure, DoD）的變化。再者，為了提升各個 TDL 分支上功率放大器（power amplifier, PA）的功率效率，本方法亦考慮動態範圍比（dynamic range ratio, DRR）限制所形成的優化問題為非凸問題。此論文提出的方法利用 ADMM 的可分解特性，藉由引入輔助變數，將問題分解為數個可處理的子問題，同時不會大幅增加空間複雜度。這與先前工作中所採用的半正定鬆弛（semidefinite relaxation, SDR）方法不同，後者需付出較高的計算成本。因此，本方法能大幅縮短運算時間，並支援更大規模模型的實現。模擬結果顯示，與先前方法在相同設定下相比，所提出的方法在旁瓣抑制效果與運算時間方面均有更佳表現。此外，本論文亦進行擴大模型規模的模擬，驗證所提方法的可擴展性。

Beamforming is a signal processing technique that combines signals from multiple sources by adjusting their phases to direct signal energy toward a specific direction, allowing constructive combination at the intended angle. The demand for wideband wireless communication is rapidly increasing due to the growing need to support more users and achieve higher data rates. In this thesis, a method is proposed based on the framework of alternating direction method of multipliers (ADMM) to design the wideband beamforming coefficients under a structure based on time-delay lines. To reduce interference in the sidelobe region while maintaining the mainlobe＇s amplitude in the desired direction, peak sidelobe level (PSL) suppression is incorporated under the distortionless constraint. Additionally, to ensure that the main beam consistently points in a similar direction across different frequencies, spatial response variation (SRV) suppression is employed to minimize variations in the direction of departure (DoD). Furthermore, a dynamic range ratio (DRR) constraint is applied to improve the power efficiency of the power amplifiers (PAs) on each TDL branch. The resulting optimization problem is nonconvex. The proposed method leverages the decomposability of ADMM to break the problem into several tractable subproblems using auxiliary variables, without significantly increasing the space complexity. This contrasts with the semidefinite relaxation (SDR)-based method used in the previous work, which incurs higher computational cost. As a result, the proposed approach significantly reduces runtime and enables implementation on larger models compared to the previous method. The simulation outcomes indicate that that the proposed method achieves better PSL suppression and lower runtime under the same settings as in the previous work. In addition, simulations involving enlarged models are also presented to verify the scalability of the method.