On the Order Optimality of Large-scale Underwater Networks—Part I: Extended Network Model

In this two-part paper, information-theoretic 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. Parts I and II deal with an extended network of unit node density and a dense network of unit area, respectively. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of n. We first 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. It is 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 is intrinsically related to the attenuation parameter but not the spreading factor. Furthermore, we describe an achievable scheme based on the nearest-neighbor multi-hop (MH) transmission, which is suitable due to the low propagation speed of acoustic channel. We show that the MH scheme is order-optimal for all the operating regimes of extended networks. W.-Y. Shin · V. Tarokh School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA E-mail: {wyshin, vahid}@seas.harvard.edu D. E. Lucani Instituto de Telecommunicacoes, Universidade do Porto, Porto 4200-465, Portugal E-mail: [email protected] M. Médard Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA E-mail: [email protected] M. Stojanovic Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA E-mail: [email protected] 2 Won-Yong Shin et al. Finally, these scaling results are extended to a random network realization. As a result, vital information for the fundamental limits of extended underwater networks is provided by showing capacity scaling laws.