The underwater acoustic channel is characterized by a path loss that depends not only on the transmission distance, but also on signal frequency. Signals transmitted from one user to another over a distance _l_ are subject to a power loss of _l_^−α_a_(_f_)^−l. Although a terrestrial radio channel can be modeled similarly, the underwater acoustic channel has different characteristics. The spreading factor α, related to the geometry of propagation, has values in the range 1⩽α⩽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 hertz. Existing results for capacity of radio wireless networks correspond to scenarios for which _a_(_f_)=1, or a constant greater than one, and α⩾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 minimal transmission power and optimal transmission band as functions of the link distance and desired data rate, and study the capacity scaling laws under this model. We show that the transport capacity increases at most at a rate , where _W_₀ represents the branch zero of the Lambert W function, for the cases in which the transmission band is either fixed a priori or assigned in relation to the transmission distance. This means that the transport capacity increases much more slowly than that of multihop routing in wireless scenarios, which is bounded by _O_(_n_^1/2). Finally, we show that scaling the frequency of the transmission band with the number of nodes provides a means to exploit characteristics of the acoustic channel in order to overcome the previous pessimistic results.

Capacity Scaling Laws for Underwater Networks