Capacity Scaling Laws for Underwater Networks

The underwater acoustic channel is characterized by a path loss that depends not only on the transmission distance, but also on the signal frequency. Signals transmitted from one user to another over a distance $l$ are subject to a power loss of $l^{-\alpha}{a(f)}^{-l}$. Although a terrestrial radio channel can be modeled similarly, the underwater acoustic channel has different characteristics. The spreading factor $\alpha$, related to the geometry of propagation, has values in the range $1 \leq \alpha \leq 2$. The absorption coefficient $a(f)$ is a rapidly increasing function of frequency: it is three orders of magnitude greater at 100 kHz than at a few Hz. Existing results for capacity of wireless networks correspond to scenarios for which $a(f) = 1$, or a constant greater than one, and $\alpha \geq 2$. These results cannot be applied to underwater acoustic networks in which the attenuation varies over the system bandwidth. We use a water-filling argument to assess the minimum transmission power and optimum transmission band as functions of the link distance and desired data rate, and study the capacity scaling laws under this model.