Capacity-achieving input for parametric underwater communications

In parametric underwater communications, nonlinear effects occurring during the propagation of intense acoustic waves in the underwater channel are beneficially used for data transmission. Due to the nonlinearity, the underlying parametric channel significantly complicates information theoretical analyses. This paper investigates the impact of the channel nonlinearity from an information theoretical point of view. Considering a simplified model, capacity lower bounds are analytically derived for the nonlinear channel. The approximation error converges to zero if the signal-to-noise ratio tends to zero or infinity, respectively. As a result, the paper proposes the weighted superposition of a circularly-symmetric Gaussian probability density function and an annular-shaped probability density function to be a good approximation for the optimal input distribution of the nonlinear parametric channel. The analytical results are in a good agreement with numerical results.