Bistatic invariance principle for multi-static active geometries

Abstract

The invariance principle describes the spatial interference patterns resulting from the coherent addition of propagating normal modes in the ocean channel. The relationship simplifies propagation structure into a scalar invariant which is approximately unity for many shallow-water environments. For passive sonar geometries (i.e., source to receiver) this valuable relationship has been extensively explored and applied to the interpretation of passive lofargrams. In active bistatic geometries, a transmitted pulse travels over two distinct propagation pathways (i.e., source-to-target and target-to-receiver). Assuming a distributed network (i.e., long-range propagation), each of these paths in isolation would produce interference patterns as dictated by the invariance principle. However, for bistatic active applications, the received pulse is a product of both propagation paths and a target-dependent scattering matrix which introduces mode coupling. For broadband waveforms, the question arises as to whether there is an observable interference pattern for a moving source. In this presentation, a derivation of the bistatic invariance principle is presented and discussed. Simulation results for the predicted time-frequency structure in a shallow-water channel are presented for specific sensor geometries and choices of target scattering matrix. Implications for application to multi-static active target tracking are presented in a companion paper.