Detection of Random Acoustic Signals by Receivers with Distributed Elements: Optimum Receiver Structures for Normal Signal and Noise Fields

Abstract

This paper deals with the passive detection of noiselike signals in the presence of both external (environmental) noise and self-generated (receiver) noise, using an array of transducers. Starting with the Bayesian formulation of the general detection problem, a set of matrix integral equations is derived whose solution yields the optimum detector function. By regarding the resultant time-varying filters as operators and the defining matrix integral equations as a set of operational equations, it is possible to examine the underlying structure of the optimum detector most easily. It is shown, thereby, that factorization of the space-time operations (i.e., separation of the required filter into two successive operations—the first depending only on the geometry of the array, the second depending only on the statistics of the noise processes) is not, in general, possible in optimum systems. Only in the strong-signal case has it been possible to show that factorization analogous to conventional beam forming can be utilized in optimum array detection. Another interesting conclusion is that an optimum detector is not superdirective in the limiting case of strong external directive noise.