基於頻率不變與恆定模量約束下抑制峰值旁瓣之寬頻波束成形設計

Abstract

波束成形 (beamforming) 技術非常重要，尤其是針對像衛星通訊這樣的長距離通訊中。在現今的通訊系統中，寬頻傳輸變得越來越重要，為了要達到更高的傳輸率並提升通道容量。本論文中將聚焦寬頻均勻線性陣列 (uniform linear array) 波束成形之設計。為了確保在所有頻率下訊號皆具有一致的發射方向，頻率不變 (frequency-invariant) 約束將被採用。此外，考慮動態範圍比 (dynamic range ratio) 約束，將盡可能地避免傳輸訊號的失真藉由減少輸入功率後退。而滿足恆定模量限制 (constant modulus constraint) 將最大化功率放大器 (power amplifier) 的效率。此外，旁瓣 (peak sidelobe level) 抑制將減少功率洩漏至不希望的方向。據作者所知，在寬頻波束成形的設計中，並沒有論文同時涉及旁瓣的抑制及恆定模量的約束。該問題將會被轉換成一個秩為一的非凸優化問題，並且將透過基於Dattorro迭帶演算法所提出的演算法來解決該問題。數值結果顯示，與先前的研究相比，在此篇論文中所構建的問題與所提出的方法將會在旁瓣抑制達到更好的效果，並且，波束成形係數將會滿足恆定模量的限制，而且此約束並沒有被達成在前人的偉業中。

Beamforming is essential to compensate path loss between the transmitter and the receiver, particularly in long-range communications, such as satellite communications (SatComs). Wideband transmission is increasingly necessary in contemporary communication systems to enhance channel capacity and support high data rate transmissions. In this thesis, wideband uniform linear array (ULA) beamforming coefficients design was studied. The frequency-invariant constraint is employed to maintain a consistent direction of departure (DoD) for transmitted signals across all frequencies and to ensure a constant beamwidth. Also, dynamic range ratio (DRR) constraints are considered to keep transmitted signals from distortion to the fullest extent possible by reducing the input power backoff. Constant modulus constraints (CMCs) are met to maximize the efficiency of power amplifiers (PAs). Moreover, peak sidelobe level (PSL) is suppressed to reduce power leakage to undesired direction. The optimization problem will be transferred into a problem with rank-one constraint, which is nonconvex. Then the problem will be solved through the proposed algorithm based on Dattorro iterative algorithm. The numerical results show that the proposed method can obtain a lower PSL compared with the previous work. Additionally, beamforming coefficients satisfy CMCs which has not been achieved in the previous works. To the best of the author’s knowledge, this is the first work that addresses both PSL suppression and CMCs in wideband beamforming coefficients design.