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

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 [1] ( 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個數，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。

關鍵字

特徵向量；同調信號；入射方向；特徵分解；信號個數

並列摘要

In array processing, the estimation of DOA( Direction of Arrival ) and the number of signals have been well studied, since MUSIC [1] (Multiple Signal Classification)and ESPRIT [2] ( Estimation of Signal Parameter via Rotational Invariance Techniques )were proposed. However, the signal environment is limited in incoherent signal space in these algorithms. In Spatial Smoothing technique [7][8], we solved the rank deficient problem, and it is unable to estimate the number of signals. If the size of sub-array is less than the coherent signals, we can’t obtain the correct solution. On the other hand, if larger sub-array is used, it will be an inefficient using sensor and increasing the computing cost. In coherent signal environment, different from Spatial Smoothing technique, by the property of eigenvector of signal covariance matrix, we transform the eigenvectors into a new matrix. Base on this new method, we can estimate the number and DOA of signals by the eigenvalues of the auto-covariance matrix of the new matrix, also we may discriminate the groups of coherent signals by counting the rank of signal subspace obtained by increasing P, the dimension of the new matrix, till we find out the whole signal space .

並列關鍵字

eigendeposition ； number of signal ； DOA ； coherent signal ； eigenvector

參考文獻

[1] Schmidt R. O. “Multiple Emitter location and signal parameter estimation.” IEEE Trans. Antennas Propag., vol.AP-34, pp. 276-280, March 1986.

[2] Roy R. and Kailath T. “ESPRIT- Estimation of Signal Parameters via Rotational Invariance Techniques.” IEEE Trans. Acoust., Speech, Signal Process., vol.ASSP-37, pp. 984-995, July 1989.

[3] Wax M. and Kailath T. “Detection of signals by information theoretic criteria.” IEEE Trans. Acoust., Speech, Signal Process., vol.ASSP-33. pp. 387-392, April 1985.

[4] Akaike H. “A new look at the statistical model identification.” IEEE Trans. Autom. Control, vol.AC-19, pp. 716-723, June 1974.

[5] Rissanen J. “Modeling by shortest data description.” Automatica, vol.14, pp. 465-471, 1978.

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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

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