Cooperative multi-hop schemes for arbitrary wireless networks

We consider the problem of characterizing per node throughput scaling in arbitrary extended wireless networks. For extended networks with random node placement, the following threshold phenomenon exists: for path loss exponent alpha les 3, hierarchical cooperative communication achieves the optimal throughput scaling; for alpha > 3, multi-hop communication achieves the optimal throughput scaling. We establish that for arbitrary node placement, due to the lack of ldquoregularityrdquo, such a threshold phenomenon does not exist. More precisely, while hierarchical cooperative communication is still order optimal for alpha les 3, there are node placements such that multi-hop communication is not order optimal for alpha > 3. We then present a family of schemes that smoothly ldquointerpolatesrdquo between multi-hop and hierarchical cooperative communication, depending upon the ldquolevel of regularityrdquo of the node placement. We establish optimality of these schemes under adversarial node placement for alpha > 3.