On the Connectivity of Hierarchical Directional Optical Sensor Networks

In this paper, we investigate the fundamental property of connectivity in a hierarchical ad-hoc optical sensor network (OSN) communicating with broad beam lasers. The OSN is modeled as a random sector graph, in which the randomly deployed sensors can send data within a contiguous and randomly oriented sector of communication. Hierarchy is achieved by employing passive and active free space optical devices. Connectivity analysis in this hierarchical network model is vital in order to assess the feasibility of routing, security and network protocols. To this end, this paper provides probabilistic bounds on network parameters for hierarchical connectivity in OSNs, using a novel approach that directly considers directionality. In particular, we prove probabilistic bounds on the jointly minimum radius of communication as well as angle of the communication sector (i.e., beam width) required for network connectivity.