Hierarchical Cooperation in Ad Hoc Networks: Optimal Clustering and Achievable Throughput

For a wireless network with
n
nodes distributed in an area
A
, and with
n
source-destination pairs communicating with each other at some common rate, the hierarchical cooperation scheme proposed in (Ozgur, Leveque, and Tse, 2007) is analyzed and optimized by choosing the number of hierarchical stages and the corresponding cluster sizes that maximize the total throughput. It turns out that increasing the number of stages does not necessarily improve the throughput, and the closed-form solutions for the optimization problem can be explicitly obtained. Based on the expression of the maximum achievable throughput, it is found that the hierarchical scheme achieves a scaling with the exponent depending on
n
. In addition, to apply the hierarchical cooperation scheme to random networks, a clustering algorithm is developed, which divides the whole network into quadrilateral clusters, each with exactly the number of nodes required.