Physical-layer security has been widely accepted as the strict notion of perfect secrecy in wireless networks. By exploring the quality gap of the legitimate and wiretap channels, and with the assistance of secure coding, wireless communication can be established between two nodes in the network. Secure connectivity is the key property to describe the networks’ ability to establish secure communications. Existing results on a secure graph, which is a model of ad hoc network, are inadequate to fully characterize the properties of infrastructure-based networks. In this paper, we study the secure connectivity of infrastructure-based 1-D networks protected by physical-layer security. The network consists of three types of nodes: powerful nodes (PNs), which are the access points (AP) to the infrastructure and fixed along the network, ordinary nodes (ONs), and eavesdroppers, both of which are Poissonly distributed in the segment bounded by two adjacent PNs. We aim to characterize the secure connections between ONs and PNs in terms of secure connectivity probability (SCP) and secure segment probability (SSP). To obtain the two metrics, we establish an analytical framework by defining secure segments and secure scenarios. Analytical results of SCP and SSP, verified by the simulation experiments, reveal the relations between secure connectivity and system parameters of the infrastructure-based 1-D networks, such as distance between adjacent PNs, distribution density of ONs, and eavesdroppers.
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