臺灣博碩士論文加值系統

摘要
使用陣列天線或水下感音器估測訊號源方位廣泛地應用於雷達、通訊和聲納研究上，其研究領域已漸漸由窄頻訊號延伸至寬頻訊號。文獻中，亦有多種高解析度寬頻訊號源方位估測法相繼被提出，但在以聚焦結構處理寬頻信號之演算法中，大多都需要先進行方位預估的步驟，如此便造成其性能對預估方位誤差之敏感性。
本論文中首先使用高解析度之信號子空間聚焦法來進行寬頻信號源之方位估測，利用此法便可省去方位預估之步驟。接著我們提出兩種行向量聚焦快速解根法，此兩種方法以簡易信號子空間估測法來取代信號子空間聚焦法，省去估測每一頻率信號子空間所需的特徵分解，並結合快速多項式解根法，來降低多項式解根的階數。由於多項式的階數由信號源個數決定，而不像MUSIC根值法中的多項式階數是由感測陣列的個數來決定，因此可大大降低計算量。最後利用電腦模擬來比較和驗證信號子空間聚焦法及行向量聚快速解根法應用於寬頻訊號源之效能。



關鍵詞: 方位估測，陣列訊號處理，寬頻訊號，近場，聚焦矩陣

Abstract
Direction-of-arrival (DOA) estimation of signal sources based on antenna or hydrophone array has been extensively explored in the areas of radar, communication and sonar. Its research trend gradually moves from narrowband signals to wideband signals. In the literature, there are several high resolution techniques developed for DOA estimation of wideband signals, but wideband signal processing using focusing schemes requires preliminary DOA estimate, thus resulting in perfor- mance sensitive to the estimation errors.
In the thesis, we first adopt the signal subspace focusing method (SSF) for DOA estimation of wideband sources, which does not require preliminary DOA estimates. Then, we develop two methods which combine column vector focusing (CVF) with fast polynomial rooting. Using these methods, we can avoid the eigenvalue decomposition in each frequency bin as required when each signal subspace in SSF is estimated and reduce order of polynomial rooting . Unlike Root MUSIC that uses a polynomial with an order determined by the number of sensors, each of them exploits a polynomial with only signal-related roots, therefore greatly reducing the computational complexity. Finally, computer simulations are provided to compare the performances of SSF or CVF based methods for the DOA estimation of wideband sources.

Keywords : direction of arrival, array signal processing, wideband signal, near field, focusing matrix.

目 錄
第一章 緒論…………………….…………………………….…… 1
1.1 簡介………………………………………………… 1
1.2 研究動機與目地…………………………………… 4
1.3 論文架構介紹……………………………………… 6

第二章 窄頻訊號源之方位估測…………………………………... 7
2.1 簡介…………………………………………………… 7
2.2. 窄頻遠場源的接收訊號模式………………………… 9
2.3. 窄頻近場源的接收訊號模式………………….……... 12
2.4. MUSIC演算法………..……………………………… 15

第三章 近場寬頻訊號源之方位估測…………….……………….. 19
3.1 寬頻遠場源的接收訊號模式………………..……….. 19
3.2 寬頻遠場源之方位估測……..……………………….. 23
3.2.1信號子空間聚焦法……………………………... 23
3.2.2行向量聚焦法…………………………………... 28
3.3 寬頻近場源之方位估測………………….…. ……..... 33
3.4 電腦模擬.……………………………………………... 38

第四章 寬頻遠場源之快速方位估測……………………………... 47
4.1 簡介………………………………………………….... 47
4.2 多項式解根的方位估測演算法……………………… 48
4.2.1 Root MUSIC 演算法…………………………... 48
4.2.2 Fast Root MUSIC 演算法……………………… 50
4.2.3 Reduced-Order Root MUSIC…………………… 52
4.3 行向量聚焦快速解根演算法..……………………….. 56
4.3.1以行向量聚焦法為主的快速Root-MUSIC演算法………………………………………………………
56
4.3.2以行向量聚焦法為主的降階Root-MUSIC演算法………………………………………………………
59
4.4. 電腦模擬……………………………………………… 64

第五章 結論與未來展望………………………………………… 73

參考文獻……………………………………………………………... 75












圖表目錄
圖 2.1 訊號源的入射波到達感測器陣列之情形……………... 10
圖 2.2 在近場時，感測器與訊號源的幾何佈置圖…………... 14
圖 3.1 陣列功率頻譜密度矩陣子行向量之選取……………... 33
圖 3.2 使用聚焦結構及未使用聚焦結構之MUSIC頻譜比較圖………………………………………………………...
39
圖 3.3 使用同調信號子空間聚焦法之頻譜圖…………...….... 41
圖 3.4 使用行向量聚焦法之頻譜圖…………….………...…... 41
圖 3.5 使用信號子空間聚焦法之頻譜圖...…………………… 42
圖 3.6 以二維MUSIC空間頻譜為主的信號子空間聚焦法估測寬頻近場源之二維空間頻譜分佈圖………………...
44
圖 3.7 圖3.6之等值頻譜(俯視)圖…………………………….. 44
圖 3.8 以二維MUSIC空間頻譜為主的行向量聚焦法估測寬頻近場源之二維空間頻譜分佈圖……………………...
45
圖 3.9 圖3.8之等值頻譜(俯視)圖…………………………….. 45
圖 4.1 行向量聚焦快速Root MUSIC演算法之流程圖………. 58
圖 4.2 行向量聚焦降階Root MUSIC演算法之流程圖………. 63

圖 4.3 SSF-RMUSIC、SSF-RORMUSIC、CVF-RMUSIC、
CVF-RORMUSIC、CVF-FRMUSIC 的均方誤差效能比較圖…………………………………………………... 65
圖 4.4 SSF-RMUSIC演算法之多項式根分佈圖…...………… 70
圖 4.5 CVF-RMUSIC演算法之多項式根分佈圖…...………... 70
圖 4.6 SSF-RORMUSIC演算法之多項式根分佈圖………...... 71
圖 4.7 CVF-RORMUSIC演算法之多項式根分佈圖…………. 71
圖 4.8 CVF-FRMUSIC演算法之多項式根分佈圖………...…. 72
表 3.1 SSF與CVF的方位估測統計分析表..……..................... 42
表 4.1 SSF-RMUSIC與SSF-RORMUSIC的估測誤差統計分析表……………………………………………………...
66
表 4.2 CVF-RMUSIC與CVF-FRMUSIC的估測誤差統計分析表……………………………………………………...
67
表 4.3 CVF-RORMUSIC的估測誤差統計分析表……………. 68
表 4.4 運算時間比較表………………………………………... 69

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