On the relationship between capacity and distance in an underwater acoustic communication channel

Path loss of an underwater acoustic communication channel depends not only on the transmission distance, but also on the signal frequency. As a result, the useful bandwidth depends on the transmission distance, a feature that distinguishes an underwater acoustic system from a terrestrial radio one. This fact influences the design of an acoustic network: a greater information throughput is available if messages are relayed over multiple short hops instead of being transmitted directly over one long hop. We asses the bandwidth dependency on the distance using an analytical method that takes into account physical models of acoustic propagation loss and ambient noise. A simple, single-path time-invariant model is considered as a first step. To assess the fundamental bandwidth limitation, we take an information-theoretic approach and define the bandwidth corresponding to optimal signal energy allocation -- one that maximizes the channel capacity subject to the constraint that the transmission power is finite. Numerical evaluation quantifies the bandwidth and the channel capacity, as well as the transmission power needed to achieve a pre-specified SNR threshold, as functions of distance. These results lead to closed-form approximations, which may become useful tools in the design and analysis of acoustic networks.