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The design of a cellular underwater network is addressed from the viewpoint of determining the cell size and the frequency reuse pattern needed to support a desired number of users operating over a given area within a given system bandwidth. By taking into account the basic laws of underwater acoustic propagation, it is shown that unlike in the terrestrial radio systems, both the cell radius R and the reuse number N must satisfy a set of constraints to constitute an admissible solution (which sometimes may not exist). The region of admissible (R,N) , which defines the possible network topologies, is determined by the user density and the system bandwidth (rho,B) , and by the required signal-to-interference ratio and per-user bandwidth (SIR0,W 0) . The system capacity is defined as the maximal user density rhomax that can be supported within a given bandwidth, and it is derived analytically. Numerical examples are used to illustrate the results. It is shown that capacity-achieving architectures are characterized by N, which grows with rhomax. The capacity, as well as the range of admissible solutions, is heavily influenced by the choice of frequency region to which the bandwidth is allocated. Moving to a higher frequency region than that dictated by signal-to-noise ratio (SNR) maximization improves the SIR and yields a greater capacity. Although higher frequencies demand greater transmission power to span the same distance, they also imply a reduction in the cell size, which, in turn, provides an overall reduction in the transmission power. While complex relationships are involved in system optimization, the analysis presented offers a simple tool for the design of future ocean observation systems based on cellular types of network architecture for wide area coverage.