Study On Fast Subspace Estimation Method And Its Applications To Array Signal Processing

It is interesting to fast estimate signal subspace and noise subspace in the area of optimization, differential equation, communication, signal processing and system science. Especially in the field of array signal processing, it is crucial to correctly estimate the subspaces since a large number of super-resolution algorithms for parameter estimation are based on the signal subspace or the noise subspace. Normally, the conventional method for subspace estimation resorts to estimating the array covariance matrix and performing the eigenvalue decomposition (EVD) to the estimate of the array covariance matrix. However, the EVD technique tends to be computationally intensive, in particular for the case of large array. On the other hand, presuming the formation of a sample covariance matrix indicates that it is necessary to have sufficient sample support. Nevertheless, in many practical applications such as in low sample support or when the signal statistics are rapidly time-varying, we may not have enough sample to form the sample covariance matrix. Therefore, it is very interesting to obtain the subspaces without the estimate of the sample covariance matrix and its EVD. In this thesis, we develop a fast subspace estimation method without eigendecomposition (FSE-E) to acquire the signal subspace and the noise subspace, and exploit the subspace estimations to resolve the narrow-band signals impinging upon a uniform linear array (ULA).· The fundamental algorithms for reduced-rank adaptive filters are systematically addressed. To facilitate the discussion of the coming chapters, the data model of array signals is firstly given. Then, the conventional reduced-rank adaptive filtering algorithms, i. e., the principal component (PC) method, the cross-spectral metric (CSM) and the multi-stage wiener filter (MSWF) is presented. Emphasis is placed on the review of the MS WF.· Some useful properties of the MSWF are studied to provide the theory to develop a fast detection algorithm for the number of signal sources. It is proved that, after P multi-stage decompostition, the array data matrix becomes a temporal white random process. Furthermore, all the data matrices after the Pth stage are also white random processes, and take the special forms. Numerical results are consistent with theanalysis, thereby indicating the discussion of the properties of the MSWF is valid.· Based on the multi-stage decomposition of the MSWF, a fast algorithm for estimating the signal subspace and the noise subspace is proposed. In view of the relationship between the Krylov subspace and the MSWF, a novel basis is derived for fast subspace estimation. The novel signal subspace attained by the fast algorithm is completely equivalent to that yielded by the classical EVD based method. Furthermore, considering the orthogonality of the matched filters of the MSWF based on the correlation subtractive architecture (CSA) (CSA-MSWF), a new method for fast noise subspace estimation is developed. Noting that after pre-filtered, the sample covariance matrix becomes a tridiagonal matrix, we propose two efficient methods for detennining the number of signal sources. Moreover, it is proved that the proposed criterion functions converge to the classical AIC and MDL criterion functions with probability one when the number of snapshots tends to infinity. The effectiveness of the proposed methods is strengthened by numerical results.· Since the signal subspace and the noise subspace are capable of being readily obtained by the fast subspace estimation method without eigendecomposition (FSE-E), the classical subspace based methods, more specifically the MUSIC and ESPRIT algorithms, can be exploited to estimate the directions of arrival (DOAs) of narrow-band signals impinging upon a uniform linear array (ULA). For complete correlated (coherent) signal sources, we proposed two different smoothing schemes to decorrelate the coherent signals. In the case where the sample covariance matrix is given, we perform the spatially smoothed Lanczos algorithm to fast compute...