On the Capacity of the Underwater Acoustic Channel with Dominant Noise Sources

TL;DR

This paper derives an upper bound for the capacity of underwater acoustic channels with impulsive noise and fading, showing it closely relates to the Gaussian noise capacity with a quantifiable gap, and explores secrecy rate implications.

Contribution

It introduces a novel upper bound for UWA channel capacity considering generalized Gaussian noise and $ extit{ ext{α-μ}}$ fading, extending capacity analysis beyond Gaussian assumptions.

Findings

Capacity is upper bounded by Gaussian channel capacity plus a constant gap.

The same gap applies to ergodic capacity with $ extit{ ext{α-μ}}$ fading.

Secrecy rates depend on the noise shaping parameters of the channels.

Abstract

This paper provides an upper-bound for the capacity of the underwater acoustic (UWA) channel with dominant noise sources and generalized fading environments. Previous works have shown that UWA channel noise statistics are not necessary Gaussian, especially in a shallow water environment which is dominated by impulsive noise sources. In this case, noise is best represented by the Generalized Gaussian (GG) noise model with a shaping parameter $\beta$. On the other hand, fading in the UWA channel is generally represented using an $\alpha$-$\mu$ distribution, which is a generalization of a wide range of well known fading distributions. We show that the Additive White Generalized Gaussian Noise (AWGGN) channel capacity is upper bounded by the AWGN capacity in addition to a constant gap of $\frac{1}{2} \log \left(\frac{\beta^{2} \pi e^{1-\frac{2}{\beta}} \Gamma(\frac{3}{\beta})}{2(\Gamma(\frac{1}{\beta}))^{3}} \right)$ bits. The same gap also exists when characterizing the ergodic capacity of AWGGN channels with $\alpha$-$\mu$ fading compared to the faded AWGN channel capacity. We justify our results by revisiting the sphere-packing problem, which represents a geometric interpertation of the channel capacity. Moreover, UWA channel secrecy rates are characterized and the dependency of UWA channel secrecy on the shaping parameters of the legitimate and eavesdropper channels is highlighted.