Analytical results in detecting broadband signals in reverberant dispersive environments

In previous work, the utility of using broadband waveforms was investigated as a means of improving active sonar performance against slow moving or stationary targets in littoral waters. This work was motivated by the fact that, in principle, the use of a wide spectrum permits the design of waveforms with nearly ideal "thumbtack-like" ambiguity functions. However, it is widely known that the ocean has dispersive characteristics in both time and frequency that can prevent the idealized broadband gains from being realized. These dispersive effects, or coherence losses, result in non-idealized signal-echo cross-ambiguity function properties. Currently, it is not well understood how coherence losses affect the cross-ambiguity function. Thus, the previous related effort, for a given fixed bandwidth and time duration waveform, studied and quantified the effects of coherence losses on detection in reverberation-limited environments, where coherence losses were assumed to be uniformly distributed. Given that, the work reported in this paper discusses the extension of previous results by investigating coherence losses for an arbitrary time duration and bandwidth waveform. Further, additional results have been obtained to simulate time/frequency dispersion losses that are assumed to be either uni-modally or multi-modally Gaussian distributed