On Capacity Scaling of Underwater Networks: An Information-Theoretic Perspective

Capacity scaling laws are analyzed in an underwater acoustic network with n regularly located nodes on a square. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of n. In the network, we characterize an attenuation parameter that depends on the frequency scaling as well as the transmission distance. A cut-set upper bound on the throughput scaling is then derived in extended networks. Our result indicates that the upper bound is inversely proportional to the attenuation parameter, thus resulting in a highly power-limited network. Interestingly, it is seen that unlike the case of wireless radio networks, our upper bound is intrinsically related to the attenuation parameter but not the spreading factor. Furthermore, we describe an achievable scheme based on the simple nearest-neighbor multi-hop (MH) transmission. It is shown under extended networks that the MH scheme is order-optimal as the attenuation parameter scales exponentially with √ n (or faster). Finally, these scaling results are extended to a random network realization. Index Terms Attenuation parameter, capacity scaling law, carrier frequency, cut-set upper bound, extended network, multihop (MH), power-limited, underwater acoustic network. This work was supported in part by the National Science Foundation under grants No. 0520075, 0831728 and CNS-0627021, and by the ONR MURI grant No. N00014-07-1-0738, subcontract # 060786 issued by BAE Systems National Security Solutions, Inc., and supported by the Defense Advanced Research Projects Agency (DARPA) and the Space and Naval Warfare System Center (SPAWARSYSCEN), San Diego under Contract No. N66001-06-C-2020 (CBMANET), by the National Science Foundation under grant No. 0831728, and by the ONR grant No. N00014-09-1-0700. The material in this paper is to be presented in part at the IEEE International Symposium on Information Theory, Austin, TX, June 2010. W.-Y. Shin and V. Tarokh are with the School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA (E-mail:{wyshin, vahid}@seas.harvard.edu). D. E. Lucani and M. Médard are with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (E-mail: {dlucani, medard}@mit.edu). M. Stojanovic is with the ECE Department, Northeastern University, Boston, MA 02115 USA (E-mail: [email protected]). SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 2