On the Effects of Frequency Scaling Over Capacity Scaling in Underwater Networks—Part I: Extended Network Model

Abstract

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. In both cases, a narrow-band model is assumed where the carrier frequency is allowed to scale as a function of n, which is shown to be crucial for achieving the order optimality in multi-hop (MH) mechanisms. We first characterize an attenuation parameter that depends on the frequency scaling as well as the transmission distance. Upper and lower bounds on the capacity scaling are then derived. In Part I, we show that the upper bound on capacity for extended networks is inversely proportional to the attenuation parameter, thus resulting in a highly power-limited network. Interestingly, it is shown that the upper bound is intrinsically related to the attenuation parameter but not the spreading factor. propose an achievable communication scheme based on the nearest-neighbor MH transmission, which is suitable due to the low propagation speed of acoustic channel, and show that it is order-optimal for all operating regimes of extended networks. Finally, these scaling results are extended to the case of random node deployments providing fundamental limits to more complex scenarios of extended underwater networks.

On Capacity and Delay Scaling Laws in Underwater Acoustic Networks

“…Moreover, sensor nodes are usually deployed widely and sparsely in UWANs since the phenomena in the ocean usually happen widely and a sensor node is expensive. The underwater acoustic channel is characterized by an attenuation that depends on both the transmission distance and the signal frequency as [6,7] …”

“…Under a model in which the water-filling method is considered to achieve the minimal transmission power and optimal transmission bandwidth, the scaling of the link distance and desired data rate is studied in [6]. Using the water-filling method and Lambert W function, a new result, that the transport capacity increases at most with a rate of…”

“…In [8], the capacity scaling laws are analyzed under an extended network model with n regularly located nodes on a square and unit node density. And the results obtained in [8] are extended to a dense network model of unit area in [9].…”

“…In [8], the capacity scaling laws are analyzed under an extended network model with n regularly located nodes on a square and unit node density. And the results obtained in [8] are extended to a dense network model of unit area in [9]. characteristics, network coding schemes were presented for underwater acoustic channels in [11], and it is indicated that network coding outperform than the multi-hop routing, in terms of the transmission power.…”

“…Besides the feature that the path loss depends on both the transmission distance and the signal frequency [12], there are many other special characteristics in UWANs, such as the 3D network topology, the widely and sparsely deployed nodes, and the spreading fading characteristic in underwater channel [6]. These characteristics make the capacity scaling in UWANs be quite different from those in terrestrial wireless networks.…”