- 學位論文
帶蓋式盒狀陣列：一種基於感測器錯誤具有增強穩健性的新型二維稀疏陣列設計
Lidded Box Arrays: A Novel 2-D Sparse Array Design for Robustness to Sensor Failures
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摘要
近年來，陣列訊號處理在各種應用中被廣泛使用，利用多個感測器接收來自發射源的訊號。稀疏陣列因為差異協列有中心均勻線性陣列段，因此比傳統的均勻線性陣列有更好的效能。當中心均勻線性陣列段大小與差異協列的大小一樣時，則被稱為無洞差異協列。中心均勻線性陣列段越大，越能進一步提高效能。到達方向估計是稀疏陣列的一個應用，可以估計一維陣列和二維陣列中源的角度。然而，每個感測器在使用一段時間後都會有隨機錯誤的問題，導致接收訊號不正確。雖然一些方法解決了一維陣列中的這個問題，例如通過定義脆弱性來量化陣列的穩健性，但二維陣列的方法仍需要進一步研究。因此，我們開發了一種新型的二維稀疏陣列，稱為帶蓋式盒狀陣列。 帶蓋式盒狀陣列的陣列幾何形狀類似於開放式盒狀陣列順時針旋轉90度後帶有蓋子，其大小取決於參數W、H和S。帶蓋式盒狀陣列具有無洞差異協列。我們將根據移除感測器的影響來定義二維陣列的脆弱性，並證明帶蓋式盒狀陣列具有與均勻矩形陣列一樣最小的脆弱性。我們提出了一種方法來減少選擇帶蓋式盒狀陣列參數的搜尋範圍，主要是解決兩種情況。第一個情況是在固定N個感測器數量下最大化差異協列的大小。第二個情況是在在給定面積A的情況下最小化感測器的數量。 我們模擬了二維到達方向估計，比較了使用不同快照數量、信噪比和感測器錯誤機率p的帶蓋式盒狀陣列、均勻矩形陣列和開放式盒狀陣列的效能。雖然均勻矩形陣列和開放式盒狀陣列都有無洞差異協列，但開放式盒狀陣列的脆弱性相對於均勻矩形陣列和帶蓋式盒狀陣列更大。在相同數量的感測器下，開放式盒狀陣列由於具有最大的差異協列而表現最佳，其次是帶蓋式盒狀陣列，然後是均勻矩形陣列。但是，感測器錯誤會顯著影響開放式盒狀陣列的效能。當p增加時，在特定條件下，帶蓋式盒狀陣列的效能可以與開放式盒狀陣列相當甚至更好。
並列摘要
Array signal processing has found various applications in recent years, utilizing multiple sensors to receive signals from emitting sources. Sparse arrays offer better performance than traditional uniform linear arrays (ULAs) due to the difference coarrays with the central ULA segment. A hole-free difference coarray is achieved when the central ULA segment size matches the size of the difference coarray. A larger central ULA segment further improves performance. Direction-Of-Arrival (DOA) estimation is an application for sparse arrays which can estimate the angles of sources in one-dimensional (1-D) arrays and two-dimensional (2-D) arrays. However, each sensor has the problem of random failure after being used for some time, leading to incorrect signal reception. While some methods address this problem in 1-D arrays, such as by defining the fragility to quantify the robustness of the array, methods for 2-D arrays remain to be further investigated. Therefore, we develop a novel 2-D sparse array called the Lidded Box Array (LBA). The LBA has an array geometry similar to an Open Box Array (OBA) rotated 90 degrees clockwise with a lid. Its size depends on the parameters: W, H, and S. The LBA has a hole-free difference coarray. We define the fragility of 2-D arrays based on the influence of removing a sensor and prove that the LBA has the minimum fragility as Uniform Rectangular Arrays (URAs). We propose a method to reduce the search range for selecting the parameters of the LBA by addressing two conditions. The first condition aims to maximize the size of the difference coarray with a fixed number of N sensors. The second condition aims to minimize the number of sensors for a given area A. We simulate the 2-D DOA estimation and compare the LBA with the URA and OBA under various numbers of snapshots, Signal-to-Noise Ratios (SNR), and probability p of sensor failures. Both the URA and OBA have the hole-free difference coarrays, but the fragility of the OBA is larger compared to the URA and LBA. With the same number of sensors, the OBA performs the best due to the largest difference coarray, followed by the LBA, and then the URA. However, sensor failures significantly affect the performance of the OBA. As p increases, the performance of the LBA becomes comparable to or even better than that of the OBA under certain conditions.
參考文獻
[1] S. Haykin, Array Signal Processing. Englewood Cliffs, NJ, USA: Prentice-Hall, 1984.
[2] H. L. V. Trees, Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory. John Wiley and Sons, Ltd, 2002.
[3] M. I. Skolnik, Introduction to Radar Systems, 3rd ed. New York, NY, USA: McGraw-Hill, 2001.
[4] P. Pal and P. P. Vaidyanathan, “Nested arrays: A novel approach to array processing with enhanced degrees of freedom,” IEEE Transactions on Signal Processing, vol. 58, no. 8, pp. 4167 – 4181, Aug. 2010.
[5] ——, “Coprime sampling and the MUSIC algorithm,” 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), 2011.