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 pathloss exponents $\alpha\in(2,3]$ cooperative communication is order optimal, and for large pathloss exponents $\alpha > 3$ multihop 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 pathloss 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 pathloss exponents $\alpha >3$. We show that in this regime the scaling of the achievable pernode rates depends crucially on the regularity of the node placement. We then present a family of schemes that smoothly "interpolate" between multihop 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 $\alpha > 3$.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2745
 Bibcode:
 2007arXiv0711.2745N
 Keywords:

 Computer Science  Information Theory
 EPrint:
 38 pages, 6 figures, to appear in IEEE Transactions on Information Theory