On Capacity Scaling in Arbitrary Wireless Networks

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

isin

(2,3]
, cooperative communication is order optimal, and for large path-loss 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 path-loss exponents
alpha

isin

(2,3]
, we show that our scheme is order optimal for all node placements, and achieves exactly the same throughput scaling as in Ozgur. This shows that the regularity of the node placement does not affect the scaling of the achievable rates for
alpha

isin

(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 ldquointerpolaterdquo 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
.