A Study of Spatial Processing Gain in Underwater Acoustic Communications

Spatial processing, including beamforming and diversity combining, is widely used in communications to mitigate intersymbol interference (ISI) and signal fading caused by multipath propagation. Beamforming suppresses ISI (and noise) by eliminating multipath (and noise) arrivals outside the signal beam. Beamforming requires the signals to be highly coherent between the receivers. Diversity combining combats ISI as well as signal fading by taking advantage of the independent information in the signal. Classical (spatial) diversity requires that signals are independently fading, hence are (spatially) uncorrelated with each other. In the real world, the received signals are neither totally coherent nor totally uncorrelated. The available diversity is complex and not well understood. In this paper, we study the spatial processing gain (SPG) as a function of the number of receivers used, receiver separation, and array aperture based on experimental data, using beamforming and multichannel combining algorithms. We find that the output symbol signal-to-noise ratio (SNR) for a multichannel equalizer is predominantly determined by the array aperture divided by the signal coherence length, with a negligible dependence on the number of receivers used. For a given number of receivers, an optimal output symbol SNR (OSNR) is achieved by spacing the receivers equal to or greater than the signal coherence length. We model the SPG in decibels as the sum of the noise suppression gain (NSG, equivalent to signal-to-noise enhancement) and the ISI suppression gain (ISG, equivalent to signal-to-ISI enhancement) both expressed in decibels; the latter exploits the spatial diversity and forms the basis for the diversity gain. Data are interpreted using the modeled result as a guide. We discuss a beam-domain processor for sonar arrays, which yields an improved performance at low-input SNR compared to the element-domain processor because of the SNR enhancement from beamforming many sensors.