- 期刊
在同調信號環境下利用信號特徵向量矩陣運算判斷信號個數、信號組成以及估測信號入射方向
Number and DOA of Coherent Signals Determination by Eigenvector Matrix Operation
摘要
在陣列天線信號處理領域之中，信號的個數以及信號入射方向的估測一直是相當重要的課題。過去已有相當多專家學者投注心力從事這方面的研究，諸如MUSIC[l](Multiple Signal Classification)、ESPRIT[2](Estimation of Signal Parameter via Rotational Invariance Techniques)已是大家耳熟能詳的方向估測演算法；然而其環境僅限於非同調信號，一旦考慮到傳輸信號因障礙物產生物理折射、反射而造成的同調信號(coherent signal)環境，便無法藉由將信號的自相關矩陣(auto-correlation matrix)做特徵值分解(eigen-decomposition)，再將特徵值利用AIC[4](Akaike Information Criterion)或是MDL[5][6](Minimum Description Length)方法來估計信號的個數[3]，因此以往方向估測的演算法此時皆無法使用。直到提出了Spatial Smoothing技術[7][8]，才解決了因同調信號造成的秩不足(rank deficient)問題；不過由於仍舊無法得知入射信號結構，導致在使用此技術時所必須要決定的子陣列(sub-array)維度大小沒有辦法有效確定。倘若子陣列維度不夠，則無法消除秩不足的狀況；然而將子矩陣維度過度增加，不但對天線使用上是種浪費，同時也增加了計算成本。因此這個部分至今還是個待大家共思解決之道的問題。 本篇論文中，不同於Spatial Smoothing技術將陣列天線分割成數個子陣列，我們利用同調信號特徵向量(eigenvector)的特性構成一個新的運算矩陣，相較於Spatial Smoothing技術，我們並不需要額外再對子陣列進行運算步驟便足以避免秩不足的問題產生。不但可以藉由此新矩陣其自相關矩陣的特徵值判斷出入射信號的個數，進而將各信號入射方向估測出來；也能夠藉由此一新矩陣不同維度時所得到的資訊判斷出同調信號間各組信號其組成的狀況。
並列摘要
In array processing, the estimation of DOA (Direction of Arrival) has been well studied, since MUSIC [1] (Multiple Signal Classification) and ESPRIT [2] (Estimation of Signal Parameter via Rotational Invariance Techniques) were proposed. However these two algorithms fail to apply to coherent signals. In Spatial Smoothing technique [7] [8], the DOA of the coherent signal can be solved, but the technique is unable to estimate the structure of the signals. The other drawback of Spatial Smoothing is the inefficient use of sensors. Here by exploiting the property of eigenvector of coherent signals covariance matrix, we propose a new method to estimate DOA and can overcome the unclassified structure of the coherent signal. We transform the eigenvectors into a new matrix, and then we can estimate the structure of the signal by this new matrix. This is to count the rank of signal subspace obtained by increasing the dimension of the new matrix, till we find the whole signal space. The DOA of signals can also be derived by the operations on the new matrix.
延伸閱讀
- Wu, Y. N. (2005). 在同調信號環境下利用特徵向量矩陣運算判斷信號個數、信號組成以及估測信號入射方向 [master's thesis, Chung Yuan Christian University]. Airiti Library. https://doi.org/10.6840/cycu200500130
- Wu, W. C., Hung, H. F., & Jeng, Y. W. (2004). 應用空時信號處理方法估計多重路徑分碼多工信號之空間特徵波形. 大葉學報, 13(1), 89-94. https://doi.org/10.7119/JDYU.200406.0089
- Wang, Y. T. (2008). 應用因子圖形與和積演算法於時變通道中正交分頻多工系統之信號偵測 [master's thesis, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-2002201315000284
- 丁振發（1994）。寬頻同調信號之方位角估測及波束成型〔碩士論文，元智大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0009-3004200913341378
- Wu, X. C. (2009). System-level Power Estimation for Digital Signal Processor [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2009.01377