空中雷達需要具備偵測目標物速度和位置的能力, 然而雷達偵測的能力會被地面回傳 的雜波, 和敵人發射的干擾信號, 以及雷達接收端的熱雜訊所影響. 時空適應性訊號處理可 以抑制雜波和敵人的干擾信號, 並同時保有目標物的增益, 以此技術改善偵測能力. 完整的 時空適應性訊號處理主要有兩個嚴重的問題, 第一個問題是它需要有大量的取樣資料去訓 練, 而雷達所取樣到的資料是有限的, 另一個則是反矩陣的運算導致它的計算複雜度太高. 為了解決這些問題, 需要去研究降維的時空適應性訊號處理. 在取樣資料有限的情況下, 降 維的時空適應性訊號處理通常有比較好的偵測能力, 而且計算複雜度也比較低.
這篇論文會藉由取樣協方差求逆, 以及 Reed,Mallett,Brennan 三人所提出來的法則, 來 研究用來估測的次要資料數量與時空適應性訊號處理的關係. 這篇論文會證明使用較少的 次要資料去估計協方差矩陣時, 比起完整的時空適應性訊號處理, 降維的時空適應性訊號 處理會有比較強的偵測能力. 此外, 在論文中也會比較平面陣列天線和線性陣列天線的性 能, 之後證明出平面陣列天線的性能比較好, 但是計算複雜度比較高. 在時空適應性訊號處 理演算法中, 協方差矩陣的反矩陣運算是很關鍵的, 因為它會主宰整個計算所需要的時間, 論文中會證明降維的時空適應性訊號處理, 花在反矩陣運算上的時間比較少.

Airborne radars are required to provide detection for speed and position of targets. However, the echo of ground clutter, jamming from enemies, and thermal noise at receiver degrades the performance of radars. Space-time adaptive processing (STAP) is a technique for improving detection of radars which can suppress clutter and jamming, and it can also preserve the gain of targets at the same time. There are two main problems for fully adaptive STAP. The first one is the limited sample data of receiver, and it will affect the adaptive weight training. The other one is that its computational complexity is too high because of the computation of inverse covariance matrix. To solve the problems, reduced-dimension STAP is required to be researched. With the limited sample data, the performance of partially STAP is better than fully STAP, and it has lower computational complexity.
In this thesis, a research between the number of secondary data for estimation and performance of STAP algorithms will be discussed with sample matrix inversion (SMI) and Reed, Mallett, and Brennan (RMB) rule. This thesis shows that with the less secondary data to estimate covariance matrix, partially adaptive STAP may provide better performance than fully adaptive STAP. Besides, the comparison of performance between planar array antenna and linear array antenna will also be analyzed. We also show that planar array antenna has the better performance than linear array antenna but it has the higher computational complexity. In the STAP algorithms, the computation of inverse covariance matrix is critical, because it dominates the computation time. This thesis shows that the computation time of inverse covariance matrix for partially adaptive STAP is less.

摘要 i
Abstract ii
Contents iv
1 INTRODUCTION 1
1.1 Foreword ..................................... 1
1.2 Research Motivation and Objective ... 2
1.3 Related works............ . 3
1.4 Proposed method.......... . 5
1.5 Contribution and Achievement . . . 5
1.6 Thesis Organization . . . . . . . . . 6
2 System Model 7
2.1 Pulse Doppler Array Radar System ... 7
2.1.1 Pulse Doppler Array Radar .... 7
2.1.2 Radar CPI Datacube ..... 9
2.2 Target Model for Linear Array Antenna .................... 12
2.3 Noise Model for Linear Array Antenna ..................... 15
2.4 Jammer Model for Linear Array Antenna.................... 16
2.5 Clutter Model for Linear Array Antenna .................... 17
2.5.1 Clutter .................................. 17
2.5.2 Rank of the Clutter Covariance Matrix. . . . . . . . . . . . . . . . . 18
2.5.3 Side looking and Forward looking.................... 19
3 Systems Architecture 21
3.1 STAP General Architecture ........................... 21
3.2 Sample Matrix Inversion............................. 23
3.3 RMB Rule for Sufficient Number of Secondary Data. . . . . . . . . . . . . . 24
4 Fully Space-Time Adaptive Processing 28
4.1 Algorithm of Fully STAP ............................ 28
4.2 Algorithm of Fully STAP for Planar Array................... 30
4.3 Computational Complexity of Fully STAP ................... 32
4.4 STAP Performance Metrics ........................... 33
5 Partially Space-Time Adaptive Processing 35
5.1 Partially STAP Introduction........................... 35
5.2 Element Space STAP............................... 38
5.2.1 Element Space Pre-Doppler STAP ................... 38
5.2.2 Element Space Post-Doppler STAP................... 42
5.3 Beam Space STAP ................................ 46
5.3.1 Beam Space Pre-Doppler STAP..................... 47
5.3.2 Beam Space Post-Doppler STAP .................... 52
5.4 Computational Complexity and Performance of Partially STAP . . . . . . . 55
6 Simulation Results 57
6.1 Comparison and Analysis between Linear Array and Planar Array for Fully STAP ....................................... 58
6.2 Comparison and Analysis of Partially STAP .................. 66
7 Conclusions 79
Bibliography 80

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