We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, ¿ = 1, and the eavesdroppers have an intensity of ¿e= O((log n)-2), almost all of the nodes achieve a perfectly secure rate of ¿ (1/¿n). The achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Remarkable, under these assumptions, securing the transmissions of nodes does not entail a loss in the per-node throughput in terms of scaling.
We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, ¿ = 1, and the eavesdroppers have an intensity of ¿e= O((log n)-2), almost all of the nodes achieve a perfectly secure rate of ¿ (1/¿n). The achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Remarkable, under these assumptions, securing the transmissions of nodes does not entail a loss in the per-node throughput in terms of scaling.
This paper studies the achievable secure rate per source-destination pair in wireless networks. First, a path loss model is considered, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes with intensities λ and λe, respectively. It is shown that, as long as λe/λ =o((logn)-2), almost all of the nodes achieve a perfectly secure rate of Ω(1/√n) for the extended and dense network models. Therefore, under these assumptions, securing the network does not entail a loss in the per-node throughput. The achievability argument is based on a novel multihop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Second, an ergodic fading model withnsource-destination pairs and neeavesdroppers is considered. Employing the ergodic interference alignment scheme with an appropriate secrecy precoding, each user is shown to achieve a constant positive secret rate for sufficiently largen. Remarkably, the scheme does not require eavesdropper CSI (only the statistical knowledge is assumed) and the secure throughput per node increases as we add more legitimate users to the network in this setting. Finally, the effect of eavesdropper collusion on the performance of the proposed schemes is characterized.
This work studies the achievable secure rate per source-destination pair in wireless networks. First, a path loss model is considered, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes with intensities λ and λe, respectively. It is shown that, as long as λe/λ=o((logn)−2), almost all of the nodes achieve a perfectly secure rate of Ω(n1) for the extended and dense network models. Therefore, under these assumptions, securing the network does not entail a loss in the per-node throughput. The achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Secondly, an ergodic fading model with n source-destination pairs and ne eavesdroppers is considered. Employing the ergodic interference alignment scheme with an appropriate secrecy pre-coding, each user is shown to achieve a constant positive secret rate for sufficiently large n. Remarkably, the scheme does not require eavesdropper CSI (only the statistical knowledge is assumed) and the secure throughput per node increases as we add more legitimate users to the network in this setting. Finally, the effect of eavesdropper collusion on the performance of the proposed schemes is characterized.
Secure communication over large-scale decentralized wireless networks is an extremely challenging task due to the cost and difficulty in establishing secret keys among all the nodes in a distributed manner. For this reason, the notion of physical layer security has recently drawn significant attention, which may assist with key exchange and provide an additional layer of protection in such networks. In this paper, we investigate how the physical layer security constraints affect the network throughput. We consider a random network in which the legitimate and eavesdropper nodes are located according to independent Poisson point processes. We introduce a new metric "secrecy transmission capacity" to characterize the network throughput in terms of the area spectral efficiency of secure transmissions, subject to constraints on both the quality of service and the level of security. This capacity framework allows us to quantitatively study the throughput cost of physical layer security constraints. We observe that the throughput cost of achieving a moderate level of security is quite low, while throughput must be significantly sacrificed to realize a highly secure network.
In a powerful secrecy attack, eavesdroppers can collude, i.e., they can share their observations. Securing information in such a scenario will be an even more challenging task compared to non-colluding case. We here analyze the effect of eavesdropper collusion on the achievable performance in both the path loss and ergodic multi-path fading models. We provide two results: 1) For the Poisson point process model in a random extended network, if the legitimate nodes have unit intensity (λ = 1) and the colluding eavesdroppers have an intensity of λe= O((log n)-(2+p)) for any p > 0, almost all of the nodes can achieve a secure rate of Ω(1/(√n)); I and 2) In the K-user Gaussian interference channel with E external colluding eavesdroppers, a secure degrees of freedom of η =[1/2-E/K]+per frequency-time slot is achievable for each user in the ergodic setting (in the absence of the eavesdropper channel state information).
Due to the nature of a wireless medium, a wireless channel is susceptible to malicious nodes, which encourages the consideration of secrecy in many applications such as satellite networks, social networking services, etc. Motivated by the social characteristic that makes nodes more likely to communicate with nearby neighbors, we study the secrecy capacity of large-scale wireless networks with social relationships. We consider two distributions of legitimate nodes: They are homogeneously placed based on a Poisson point process (PPP), or they are inhomogeneously distributed as multiclustering topology. In particular, we consider two scenarios: 1) the noncolluding case, where each eavesdropper decodes its receiving message independently; and 2) the colluding case, where eavesdroppers can cooperate to decode the message. We adopt a rank-based model to describe the social characteristic and investigate its impact on the secrecy capacity using the technique of self-interference cancelation. We employ a passive attack model, where eavesdroppers can only listen to transmissions among legitimate nodes. Our important findings include the following: 1) In the noncolluding case, secrecy capacity is not influenced by eavesdroppers in order sense, but it varies with the density of eavesdroppers and social impacts in the colluding case. 2) The proposed scheme can achieve optimal secrecy throughput neglecting polylogarithmic factor in homogeneous wireless networks.
In this paper, we combine sectorized transmission with artificial noise to establish secrecy in decentralized wireless networks. The locations of the legitimate nodes and the eavesdroppers are both modeled by homogeneous Poisson point processes. Using sectorized antennas, each legitimate transmitter sends an information signal in the sector which contains its intended receiver, while simultaneously emitting artificial noise in other sectors, in order to provide secrecy against the eavesdroppers. We first separately characterize the reliability performance of the legitimate link and the secrecy performance against malicious eavesdropping. Then, we derive the secrecy transmission capacity to measure the networkwide secrecy throughput. To facilitate the practical system design, we provide a sufficient condition, in terms of the system parameters and constraints, under which a positive secrecy transmission capacity is achievable. The optimal transmit power allocation between the information signal and the artificial noise for achieving the maximal secrecy transmission capacity is also investigated. Our analysis indicates that sectorized transmission provides significant secrecy enhancements in decentralized wireless networks.