Multidimensional detection and extraction of signals in random media

An approach to the general problem of detecting and extracting signals from random media with the help of multichannel (i.e., multidimensional) receivers is described, based on standard decision theory methods and stressing the key role of channel physics and geometry. The principal aim is to provide an illustrative outline of a unified treatment, emphasizing the interdisciplinary character of the methods used and the critical nature of the channel model for both optimal and suboptimal systems. Included is a discussion of system apertures (arrays), the dynamical equations of propagation in elastic media and for electromagnetic phenomena, scattering, ambient (self-) noise fields, preformed and adaptive beams, Poisson and Gaussian field statistics, and general methods for obtaining the statistical description of noise and signal fields. Two illustrative examples of some recent results are briefly considered, and a number of important current problems are described, whose solutions depend on the approach developed here.