  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.
