Connectivity of two-tier networks

In this paper, we investigate the connectivity of a two-tier network, which is composed of a primary tier and a secondary tier according to their different spectrum access priorities. The primary nodes and secondary nodes are both distributed over the same Euclidean space following two independent Poisson point processes of densities λ_P and λ_S, respectively. The two tiers operate over a synchronized time-slotted protocol structure. A primary link that exists between two primary nodes within a certain distance is active with probability p_a at each time slot, while two secondary nodes within a certain distance could communicate only if the communication leads to no interference to the primary communication. We first introduce the definitions of the aggressive and conservative operation regions of the primary tier, which is determined by the critical primary link connection probability p_a^*(λ_P). We then show that the percolation-based connectivity for both the primary tier and the secondary tier cannot hold simultaneously with an aggressive primary tier under practical setups. In addition, we investigate the condition for a conservative primary tier to achieve a certain long-term connectivity, and the corresponding minimum density required for the secondary-tier to achieve percolation-based connectivity.