Spatial analysis in passive listening using adaptive techniques

The various known methods intended for continuous analysis of uncorrelated source fields (MEM-AR, Capon, Borgiotti-Lagunas, Bienvenu-Schmidt) are shown to be based upon a unique conventional diagram, namely one of a spatial linear multiport filter followed by a variance estimator. This filter has K inputs corresponding to K sensors and a single output, and acts as a scalar product system. A fundamental property is then the possibility of having zero responses for the signals coming from K - 1 directions. Using the classical matched filter principle for minimization of undesirable signals (when looking in a given direction), a general class of data-adaptive spatial filters, from which all the above-mentioned methods can be derived with specific choices of parameters, is defined. These filters can be further submitted to normalizing constraints; two examples of this are discussed. This new interpretation leads to the consideration of the above-mentioned methods as special applications of the well-known adaptive array techniques to the estimation problem. Moreover, the asymptotic behaviors are examined when a noise subtraction technique based upon the reduction of the smallest cross-spectral matrix eigenvalue is applied. The convergence toward the Pisarenko solution is ascertained for the estimated directions of the sources, whereas it is not for their estimated intensities (except in the case of the Capon method). In the case of partially correlated sources, the above-mentioned methods are still valid for the localization of sources, but not for their intensities. Other appropriate techniques, such as those of Schmidt, Wax, Shan, and Kailath, must then be considered.