Estimation of the Dimensionality of the Signal Subspace

ESTIMATION OF THE DIMENSIONALITY OF THE SIGNAL SUBSPACE. John A. Uber, Ph.D. George Mason University, 2003 Dissertation Director: Dr. Harry L. Van Trees This dissertation develops a novel technique for estimating the dimensionality of the signal subspace and thus detecting the number of signals impinging on the receive array of a signal exploitation system. Previous work relied solely on either statistical analysis or the development of a model-order selection (MOS) approach to develop a detection algorithm emphasizing an information-theoretic (IT) criterion. Our proposed MOS solution utilizes the fundamental principles of both information theory and statistical analysis in developing a unified approach to signal subspace dimensionality enumeration. Eigen-decomposition of the sample spatial autocovariance matrix develops a sufficient statistic for the separable detection of the number of signals. An IT-based MOS technique is developed by exploiting the assumed knowledge of the signal-structured model (SSM) of the receive array. The SSM allows us to separate the source signal into its spatial and temporal components, simplifying the IT-MOS parameterization problem. Statistical analysis of the IT-based SSM produces an empirically-tailored model (ETM) for characterizing detection performance over the full extent of the array parameter space. Together, the IT-based SSM and the statistically-based ETM allow for the development of the Combined Dimensionality Enumeration (CDE) detection algorithm. The inspiration for the CDE algorithm is to establish and maintain a stable false alarm rate (FAR) while detecting an unknown number of signals. Additional utility results from the introduction of a statistical scaling parameter, enabling the CDE algorithm to have an adjustable FAR. The primary advantage of the CDE results from robust detection performance with the ability to control the desired probability of false alarm over the full operational scenario space.