On the Order Optimality of Large-scale Underwater Networks
چکیده
Capacity scaling laws are analyzed in an underwater acoustic network with n regularly located nodes on a square, in which both bandwidth and received signal power can be limited significantly. 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. Cut-set upper bounds on the throughput scaling are then derived in both extended and dense networks having unit node density and unit area, respectively. It is first analyzed that under extended networks, the upper bound is inversely proportional to the attenuation parameter, thus resulting in a highly power-limited network. Interestingly, it is seen that the upper bound for extended networks is intrinsically related to the attenuation parameter but not the spreading factor. On the other hand, in dense networks, we show that there exists either a bandwidth or power limitation, or both, according to the path-loss attenuation regimes, thus yielding the upper bound that has three fundamentally different operating regimes. Furthermore, we describe an achievable scheme based on the simple nearest-neighbor multi-hop (MH) transmission. We show that under extended networks, the MH scheme is order-optimal for all the operating regimes. An achievability result is also presented in dense networks, where the operating regimes that guarantee the order optimality are identified. It thus turns out that frequency scaling is instrumental towards achieving the order optimality in the regimes. Finally, these scaling results are extended to a random network realization. As a result, vital information for fundamental limits of a variety of underwater network scenarios is provided by showing capacity scaling laws. Index Terms Achievability, attenuation parameter, bandwidth, capacity scaling law, carrier frequency, cut-set upper bound, dense network, extended network, multi-hop (MH), operating regime, path-loss attenuation regime, 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 was presented in part at the IEEE International Symposium on Information Theory, Austin, TX, June 2010 and was submitted in part to the 2011 IEEE International Symposium on Information Theory. 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 was with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. He is now with the Instituto de Telecomunicacoes, Universidade do Porto, Porto 4200-465, Portugal (E-mail: dlucani@fe.up.pt). M. Médard is with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (E-mail: medard@mit.edu). M. Stojanovic is with the ECE Department, Northeastern University, Boston, MA 02115 USA (E-mail: millitsa@mit.edu). SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 2