On Capacity Scaling in Arbitrary Wireless Networks

Abstract

In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., $n$ nodes are placed uniformly at random in a square region of area $n$). They showed that for small path-loss exponents $\alpha\in(2,3]$ cooperative communication is order optimal, and for large path-loss exponents $\alpha > 3$ multi-hop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node placement. In this paper, we consider the problem of characterizing the throughput scaling in extended wireless networks with arbitrary node placement. As a main result, we propose a more general novel cooperative communication scheme that works for arbitrarily placed nodes. For small path-loss exponents $\alpha \in (2,3]$, we show that our scheme is order optimal for all node placements, and achieves exactly the same throughput scaling as in Ozgur et al. This shows that the regularity of the node placement does not affect the scaling of the achievable rates for $\alpha\in (2,3]$. The situation is, however, markedly different for large path-loss exponents $\alpha >3$. We show that in this regime the scaling of the achievable per-node rates depends crucially on the regularity of the node placement. We then present a family of schemes that smoothly "interpolate" between multi-hop and cooperative communication, depending upon the level of regularity in the node placement. We establish order optimality of these schemes under adversarial node placement for $\alpha > 3$.Comment: 38 pages, 6 figures, to appear in IEEE Transactions on Information Theor

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

“…This is a highly simplified model, but nonetheless one that suffices to demonstrate the fundamental mechanisms that govern capacity scaling. Assuming that all the nodes have perfectly directional transmissions, we also disregard multipath propagation, and simply focus on a line-of-sight channel between each pair of nodes used in [10,11,28]. An underwater acoustic channel is characterized by an attenuation that depends on both the distance r ki between nodes i and k (i, k ∈ {1, .…”

“…We thus assume a narrow-band time-varying channel, whose gain changes to a new independent value for every symbol. Note that this random phase model is based on a far-field assumption [10,11,28], 8 which is valid if the wavelength is sufficiently smaller than the minimum node separation. Based on the above channel characteristics, operating regimes of the network are identified according to the following physical parameters: the absorption a( f ) and the noise PSD N ( f ) which are exploited here by choosing the frequency f based on the number of nodes, n. In other words, if the relationship between f and n is specified, then a( f ) and N ( f ) can be given by a certain scaling function of n from (3) and (5), respectively.…”

“…3, which will provide an upper bound on P (k) L in (11). It is obviously seen that the amount of power transfer under the transformed regular network is greater than that under another regular network with at most log n nodes at each vertex, located at integer lattice positions in a square region of area n. Hence, the upper bound for random networks is boosted by at least a logarithmic factor of n compared to that of regular networks discussed in Sect.…”

“…1 MH schemes are then further developed and analyzed in [3][4][5][6][7][8][9], while their throughput per S-D pair scales far slower than Θ (1). Recent results [10,11] have shown that an almost linear throughput in the radio network, i.e. Θ(n 1− ) for an arbitrarily small > 0, which is the best we can hope for, is achievable by using a hierarchical cooperation (HC) strategy.…”

“…Θ(n 1− ) for an arbitrarily small > 0, which is the best we can hope for, is achievable by using a hierarchical cooperation (HC) strategy. 2 Besides the schemes in [10,11], there have been other studies to improve the throughput of wireless radio networks up to a linear scaling in a variety of network scenarios by using novel techniques such as networks with node mobility [12], interference alignment [13], and infrastructure support [14].…”