Angle of Arrival Distribution in an Underwater Acoustic Communication Channel with Incoherent Scattering

Angle of arrival (AoA) analysis is essential for the statistical characterization of the underwater (UW) channel where the acoustic signal propagation is confined to a restricted geometry. In UW channels, the acoustic signal reaches the receiver either through the line of sight path or through scattering from the sea surface and bottom. Low-frequency acoustic signals (few Hz) undergo reflection from the sea surface and bottom. This is called coherent scattering, where the scattered paths are assumed to be in phase and concentrated around the specular paths. At relatively higher frequencies (above 10 kHz), incoherent scattering occurs, resulting in an omnidirectional scattering pattern at each point of interaction with the sea surface. In this work, we derive a closed-form expression for the AoA distribution for a single bounce (SB) path that undergoes incoherent scattering from the surface/bottom in an UW channel. The analysis is extended to the case of paths involving multiple bounces (MB). The AoA distribution is further used to evaluate the Doppler spread in an UW channel.