Modeling the large scale transmission loss in underwater acoustic channels

Pre-deployment calculations of the received signal strength in an underwater acoustic channel typically rely on beam tracing of a single-frequency signal for a given (frozen) ocean geometry. The results of such modeling provide an accurate but limited view of transmission loss since acoustic communication systems are necessarily wideband (a typical system might operate between 5 and 15 kHz), and have to be designed for a variety of surface conditions, deployment locations and transmitter/receiver distances. In this paper, we offer a statistical model for the acoustic transmission loss calculated for a wide band of frequencies. The model incorporates the physical laws of acoustic propagation (frequency-dependent attenuation, bottom/surface reflection), as well as the effects of inevitable random local displacements. Our focus is on large-scale phenomena that affect locally-averaged received power and occur due to path-length variation caused by the surface and system displacements (small-scale effects, such as scattering, are responsible for faster variations of the instantaneous signal strength). We argue for a log-normal model, whose mean follows a log-distance dependence with frequency-dependent path loss exponent, and whose variance depends on the signal bandwidth. Assuming a Gauss-Markov auto-regressive (AR) model for the path length variation, we also investigate the possibility to model the large-scale transmission loss as an AR process itself. We illustrate the results through numerical simulation and show experimental data that support our theory.