稀疏陣列波束圖樣之整合旁瓣優化與效能評估

Abstract

近年來，稀疏陣列的設計在雷達和無線通信等各個領域受到廣泛關注。著名的稀疏陣列包括最小冗餘陣列（MRA）、嵌套陣列（NA）和互質陣列（CA），僅舉幾例。相比於擁有相同感測器數量的均勻線性陣列（ULAs），稀疏陣列能提供更大的孔徑和更高的自由度（DOF）。它們通過其結構化的差分共陣列，能實現更好的來向角（DOA）估計。然而，由於其不均勻的感測器放置，MRAs、NAs和CAs的傳統波束圖樣存在某些限制。與ULA相比，它們可能會顯示出更高的旁瓣水平或不規則的主瓣形狀。它們可能缺乏明確的零點，這使得主瓣與旁瓣區域之間的區分變得困難。此外，大多數現有的波束圖樣合成方法也未充分考慮這些稀疏陣列。 在本論文中，我們提出一種基於最小化整合旁瓣水平（ISLL）的波束成形權重設計演算法。該方法透過放置第一個零點來定義主瓣和旁瓣區域。該算法採用自適應動量估計（Adam）來迭代性地解決問題。我們的演算法不受特定陣列配置的限制。它允許靈活地放置第一個零點，以明確定義主瓣和旁瓣區域，實現更好的旁瓣抑制或更集中的主瓣能量。 模擬結果證明了所提出的演算法在不同陣列配置中的性能。對於ULAs，我們的方法在相同主瓣寬度下可達到比現有設計更低的ISLL和平均旁瓣水平（MSLL）。我們將所提出的方法應用於嵌套陣列（NA）與互質陣列（CA），並在不同的參數設定與感測器數量下評估其波束圖樣。結果顯示，旁瓣抑制效果與主瓣形狀的品質與第一零點的位置及正則化參數的選擇密切相關。此外，我們通過重建信號實驗展示了所提出的波束成形權重在不同干擾情境下的有效性。我們亦展示了所提出方法在波束碼本設計上的潛在應用。

In recent years, the design of sparse arrays has received widespread attention in various fields such as radar and wireless communications. The well-known sparse arrays include the Minimum Redundancy Array (MRA), Nested Array (NA), and Coprime Array (CA), to name just a few. Compared to uniform linear arrays (ULAs) with the same number of sensors, sparse arrays provide a larger aperture and higher degrees of freedom (DOF). They enable better direction-of-arrival (DOA) estimation via their structured difference coarrays. However, due to the non-uniform sensor placement, the conventional beam patterns of MRAs, NAs, and CAs have certain limitations. Compared to ULAs, they may exhibit higher sidelobe levels or irregular mainlobe shapes. They may lack well-defined nulls, making it difficult to distinguish between the mainlobe and sidelobe regions. Moreover, most existing beam pattern synthesis methods have not sufficiently addressed these sparse arrays. In this thesis, we propose an algorithm for designing beamforming weights based on minimizing the Integrated Sidelobe Level (ISLL). The approach involves placing the first null to define the mainlobe and sidelobe regions. The algorithm adopts the Adaptive Moment Estimation (Adam) to solve the problem iteratively. Our algorithm is not limited to a specific array configuration. It allows flexible placement of the first null to explicitly define mainlobe and sidelobe regions, enabling better sidelobe suppression or more concentrated mainlobe energy. The simulation results demonstrate the performance of the proposed algorithm across different array configurations. For ULAs, our method achieves lower ISLL and mean sidelobe levels (MSLL) than existing designs with the same mainlobe width. We apply the proposed method to NAs and CAs, and evaluate the beam patterns under various parameter settings and sensor counts. The results show that sidelobe suppression and the quality of the mainlobe shape are closely influenced by the choice of the first null and the regularization parameter. Furthermore, we demonstrate the effectiveness of the proposed beamforming weights in different interference scenarios through signal reconstruction experiments. We also present the potential application of the proposed method in beamforming codebook design.