| This dissertation addresses the problem of determining the number of wideband sources and estimating their directions of arrival (doa) using a passive sensor array. The essential feature of the approach, called Coherent Signal-subspace Method (CSM), is a data reducing step which involves the alignment and averaging of the signal subspaces of the narrowband components within the common bandwidth of the signals. Information Criteria and narrowband signal-subspace estimators are then used for detection (determination of the number of sources) and doa estimation respectively.; The detection and estimation performances of the CSM strongly depend on the quality of the focussing matrices used in the data reduction step of constructing the Approximately Coherently Averaged Correlation Matrix (ACACM). From information-preserving point of view, we investigate the degree of statistical sufficiency of the ACACM via a relatively efficiency measure, termed the Relative Information Index (RII), for several classes of focussing matrices. It is demonstrated that a small value of RII indicating large information loss in the statistic-formulation stage is always accompanied by poor performance in terms of detection and resolution thresholds, bias and variance measures.; Based on theoretical and simulation results, the specific structure of the focussing matrix is shown to have profound consequences in the statistical characteristics of the doa estimates. Specifically, we show that a good focussing matrix is unitary. Within the unitary class, we derive a new class of focussing matrices, termed Rotational-Signal-Subspace class, which performs substantially better than the previously suggested classes for detection and doa estimation in the multi-group cases.; The direction estimation performance can be further improved by a 'good' narrowband signal-subspace estimator, for example Minimum-Norm or ESPRIT algorithm. The wideband Minimum-Norm and ESPRIT algorithms are derived and their connections with DSM are established. Finally, when the signal-to-noise ratio is non-uniform across the receiver bandwidth, a weighted ACACM is shown to be the most appropriate data reduction for the CSM. |
