On Simultaneous Connectivity of Heterogeneous Networks

One of the most desirable properties of networks in communication theory is connectivity as this property is crucial to the ability to pass massages between nodes in the networks. The connectivity of large-scale homogeneous networks has a strong link to continuum percolation theory, and it can be considered as one of its applications.  In recent years, due to the scarcity of free static spectrum resources, a new concept dubbed Cognitive Radio has emerged. The overarching goal of cognitive radio networks is to improve spectrum utilization by giving communication opportunities to cognitive (secondary) nodes while limiting their interference on non-cognitive (primary) nodes in the network. Several works have considered the connectivity of non-cooperative networks with heterogeneous nodes. These significant works consider heterogeneous systems with primary and secondary networks, nevertheless, the discussion therein is restricted to the connectivity of the secondary network. This leads to models in which the secondary nodes are components of a multi-hop network, but the primary nodes are a part of a single-hop network in which each primary transmitter has one primary receiver and vice-versa. This assumption may be non-applicable at times since it does not consider multi-user communication in the primary network. Hence the motivation to analyze a new heterogeneous model that captures the connectivity demands of the multi-hop primary network in which both the primary and secondary networks are multi-hop networks. 

In this talk I will discuss the connectivity of both the secondary network and the primary network, a state called simultaneous connectivity. In this state both random primary and random secondary networks co-exist and each of them includes an infinite connected component. I will review the Gilbert disk model which is composed of a homogeneous Poisson point process (PPP) where each point is a center of a transmission disk, and explain its relation to the homogeneous network model.  I will then discuss the simultaneous connectivity of two Gilbert disk models with independent PPPs. These two models represent the primary and secondary networks and are connected through excluding disks, which prevent elements of the secondary PPP to be active in the vicinity of the primary network nodes. Under these assumptions we will ensure the feasibility of this model and characterize the region of densities of the two PPPs in which the two models both have a unique infinite connected component. As described above, the motivation for this work is the co-existence of two cognitive radio networks.   

* This research was carried out towards the PhD Degree in Electrical Engineering at Bar-Ilan University, under the supervision of Dr. Anelia Somekh-Baruch and Prof. Amir Leshem. 

 * Joint work with Anelia Somekh-Baruch, Reuven Cohen and Amir Leshem