Topology Formation in Degree-Constrained Directional Antenna Networks

In a network with sophisticated directional antennas, the antenna pattern can approach an ideal where the beam width and side lobe intensity both approach zero. Assuming transmission power remains constant, the effective range of such an antenna approaches infinity and the probability of co-channel interference approaches zero. In such a network, any two nodes can have a direct link with each other, regardless of the physical distance between them. However, such a system implies both a time-division scheme that constrains the number of links each node may form, and a relatively slow in-band neighbor discovery process. In this paper, we first study a simple scheme that forms a link with every node it discovers until the node is saturated. Under certain node arrival assumptions, this creates network distances (in terms of hops) far higher than a centralized algorithm would optimally produce. A simple heuristic that rejects links if nodes share a certain number of common neighbors produces far shorter paths across the network.