On the virtual array concept for higher order array processing

For about two decades, many fourth order (FO) array processing methods have been developed for both direction finding and blind identification of non-Gaussian signals. One of the main interests in using FO cumulants only instead of second-order (SO) ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array, which eventually introduces the FO Virtual Array concept presented elsewhere and allows, in particular, a better resolution and the processing of more sources than sensors. To still increase the resolution and the number of sources to be processed from a given array of sensors, new families of blind identification, source separation, and direction finding methods, at an order m=2q (q≥2) only, have been developed recently. In this context, the purpose of this paper is to provide some important insights into the mechanisms and, more particularly, to both the resolution and the maximal processing capacity, of numerous 2qth order array processing methods, whose previous methods are part of, by extending the Virtual Array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space, angular and/or polarization diversity.