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We expose some concepts concerning the channel impulse response (CIR) oflinear time-varying (LTV) channels to give a proper characterization of themobile-to-mobile underwater channel. We find different connections between thelinear time-invariant (LTI) CIR of the static channel and two definitions ofLTV CIRs of the dynamic mobile-to-mobile channel. These connections are usefulto design a dynamic channel simulator from the static channel models availablein the literature. Such feature is particularly interesting for overspreadchannels, which are hard to characterize by a measuring campaign. Specifically,the shallow water acoustic (SWA) channel is potentially overspread due thesignal low velocity of propagation which prompt long delay spread responses andgreat Doppler effect. Furthermore, from these connections between the LTIstatic CIRs and the LTV dynamic CIRS, we find that the SWA mobile-to-mobile CIRdoes not only depend on the relative velocity between transceivers, but also onthe absolute velocity of each of them referred to the velocity of propagation.Nevertheless, publications about this topic do not consider it and formulatetheir equations in terms of the relative velocity between transceivers. Weillustrate our find using two couples of examples where, even though therelative velocity between the mobiles is the same, their CIRs are not.

On the Mobile-to-Mobile Linear Time-Variant Shallow-Water Acoustic Channel Response