Connectivity of Intelligent Reflecting Surface Assisted Network via Percolation Theory

The integrated access and backhaul (IAB) technology enables cost-effective ultradense network deployment, by replacing wired transmission infrastructure. However, IAB is hindered by high energy consumption, fragile wireless links, and coverage holes. With the capability of enhancing coverage and smart configuration of the radio environment at a low cost, intelligent reflecting surfaces (IRSs) can well address the challenges in IAB. This paper focuses on forming heterogeneous communication between base station (BS) and IRS in large-scale IAB networks, achieving percolation-based connectivity of BSs to ensure further cost-effective BSs deployment and successful data packet delivery between users. The dependency between the two node processes and the asymmetry of communication links introduce new challenges for connectivity in IRS-assisted IAB networks. To address these challenges, continuum percolation theory is applied to scrutinize the topological and analytical properties of the IRS-assisted wireless network. Specifically, the analysis demonstrates the uniqueness of the infinite connected component and proves the topological connectivity within the corresponding connectivity region. Additionally, the paper establishes the necessary and sufficient conditions for achieving network connectivity manifested in the critical densities of both BS and IRS nodes. The theoretical analysis is validated through simulations, confirming alignment between derived bounds and Monte Carlo results.