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Spatial Secrecy Outage Probability Design Under Nakagami-m Wiretap Channel in the Industrial Internet of Things

Xiaokai Liu, Fangmin Xu, Lina Ning, Quanzhong Li, Chenglin Zhao

Published Jan 24, 2025• 0 citations
Publisher

Abstract

The rapid evolution of the Industrial Internet of Things (IIoT) has created significant opportunities for industrial transformation, while simultaneously presenting substantial challenges to network security. Among these challenges, physical layer security emerges as a critical factor in ensuring the integrity and reliability of message transmission across interconnected devices and sensors within complex industrial environments. In our previous work, we proposed a mechanism for assessing the Spatial Secrecy Outage Probability (SSOP) in a Rayleigh Channel with a single eavesdropper, achieving promising simulation results. This paper focuses on the Nakagami-m Wiretap Channel and multiple eavesdroppers assuming that the location of legitimate devices is known, while the eavesdropper devices have a spatially homogeneous Poisson point process distribution of locations, forming the SSOP models related to the device locations from the perspective of insecure regions (ISRs) and secure regions (SRs), and the closed-form expression for its upper bound is derived. Subsequently, under the constraints imposed by SSOP conditions, we establish an optimization model aimed at maximizing system secrecy throughput. Finally,we analyze ISRs and SRs based on geographical location information through the lens of Secrecy Outage Probability (SOP), evaluating the security performance of our system. Through advanced modeling and simulation in MATLAB, we validated the accuracy of the proposed definition and derived the upper bound for the SSOP under Nakagami-m Channel. The experimental results further demonstrate the deep relationship between Secrecy Rate and Throughput. Additionally, it was observed that as the secrecy rate increases, the secrecy outage probability also rises, necessitating careful consideration of the trade-off. These insights are crucial for understanding and enhancing the security performance of IIoT communication systems.

DOI
10.20944/preprints202501.1851.v1

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The rapid evolution of the Industrial Internet of Things (IIoT) has created significant opportunities for industrial transformation, while simultaneously presenting substantial challenges to network security. Among these challenges, physical layer security emerges as a critical factor in ensuring the integrity and reliability of message transmission across interconnected devices and sensors within complex industrial environments. In our previous work, we proposed a mechanism for assessing the Spatial Secrecy Outage Probability (SSOP) in a Rayleigh Channel with a single eavesdropper, achieving promising simulation results. This paper focuses on the Nakagami-m Wiretap Channel and multiple eavesdroppers assuming that the location of legitimate devices is known, while the eavesdropper devices have a spatially homogeneous Poisson point process distribution of locations, forming the SSOP models related to the device locations from the perspective of insecure regions (ISRs) and secure regions (SRs), and the closed-form expression for its upper bound is derived. Subsequently, under the constraints imposed by SSOP conditions, we establish an optimization model aimed at maximizing system secrecy throughput. Finally,we analyze ISRs and SRs based on geographical location information through the lens of Secrecy Outage Probability (SOP), evaluating the security performance of our system. Through advanced modeling and simulation in MATLAB, we validated the accuracy of the proposed definition and derived the upper bound for the SSOP under Nakagami-m Channel. The experimental results further demonstrate the deep relationship between Secrecy Rate and Throughput. Additionally, it was observed that as the secrecy rate increases, the secrecy outage probability also rises, necessitating careful consideration of the trade-off. These insights are crucial for understanding and enhancing the security performance of IIoT communication systems.
The rapid development of the Industrial Internet of Things (IIoT) has brought enormous opportunities to the industrial environment, but has also posed significant challenges to network security, especially physical layer security, which is crucial for the reliable transmission of messages among interconnected devices and sensors. Focusing on enhancing the physical layer security in IIoT communication, this paper proposes a mechanism for the Spatial Secrecy Outage Probability (SSOP) to ensure the secure transmission of data. The SSOP algorithm assumes that the location of legitimate devices is known, while the eavesdropper devices have a random distribution of locations, forming the SSOP model related to the device locations from the perspective of insecure regions (ISRs) and secure regions (SRs), and the closed-form expression for its upper bound is derived. Subsequently, under the constraint of the SSOP conditions, we establish an optimization model with the objective of system throughput maximization based on the Spatial Secrecy Outage Probability (SRM-SSOP). By optimizing the transmission rate of legitimate channels or controlling the transmission power, the maximization of the system throughput can be achieved, thus reducing the consumption of communication resources. Through sophisticated modeling and simulation in MATLAB, we verified the accuracy of the definition and derived the upper bound of the SSOP. The experimental results also show that the SSOP algorithm gradually converges to a specific value as the number of antenna elements increases. In addition, we observed that, when the receiver device is aligned with the normal direction of the transmit antenna array, the SSOP reaches a minimum value. This performance is crucial for understanding and optimizing the security performance of IIoT communication systems.
With the increasing number of antennae in base stations, there is considerable interest in using beamforming to improve physical layer security, by creating an “exposure region” that enhances the received signal quality for a legitimate user and reduces the possibility of leaking information to a randomly located passive eavesdropper. This paper formalizes this concept by proposing a novel definition for the security level of such a legitimate transmission, called the spatial secrecy outage probability (SSOP). By performing a theoretical and numerical analysis, it is shown how the antenna array parameters can affect the SSOP and its analytic upper bound. While this approach may be applied to any array type and any fading channel model, it is shown here how the security performance of a uniform linear array varies in a Rician fading channel by examining the analytic SSOP upper bound.
This paper investigates physical layer security (PLS) of uplink non-orthogonal multiple access (NOMA) in Internet of Things (IoT) networks, where two devices transmit secret information to base station or access point simultaneously under the intercepting of an eavesdropper (Eve). The new closed-form expressions of joint connection outage probability (JCOP), joint secrecy outage probability (JSOP) and sum secrecy throughput (SST) are derived over Nakagami-m fading channels to indicate the impact of parameters, i.e., transmit power and codeword rates, on secrecy performance. Simulation results are obtained to verify our analysis and allow an easy design of transmit power and wiretap code rates which maximizes the SST.
With increasing number of antennae in base stations, there is considerable interest in using beamfomining to improve physical layer security, by creating an `exposure region' that enhances the received signal quality for a legitimate user and reduces the possibility of leaking information to a randomly located passive eavesdropper. The paper formalises this concept by proposing a novel definition for the security level of such a legitimate transmission, called the `Spatial Secrecy Outage Probability' (SSOP). By performing a theoretical and numerical analysis, it is shown how the antenna array parameters can affect the SSOP and its analytic upper bound. Whilst this approach may be applied to any array type and any fading channel model, it is shown here how the security performance of a uniform linear array varies in a Rician fading channel by examining the analytic SSOP upper bound.
The multiple-input-multiple-output (MIMO) scheme enhances the capacity and reliability of secure Internet of Things (IoT) communication systems. In this article, an MIMO secure IoT communication system which includes a multiantenna transmitter, a multiantenna legitimate receiver, and a multiantenna eavesdropper is investigated. Considering that the transmitter and receiver are deterministic whereas the eavesdropper is either deterministic or randomly distributed, we theoretically derive the secrecy outage probabilities (SOPs) in independent and identically distributed (i.i.d.) as well as full-correlated Rayleigh fading channels. The i.i.d. or full-correlated Wishart matrices are introduced to express the mutual information rates from the transmitter to the legitimate receiver and eavesdropper. By analyzing the joint probability density functions of unordered eigenvalues of Wishart matrices, we obtain the moment generating functions (MGFs) of mutual information rates. Employing inverse Laplace transforms of the MGFs, the SOPs are obtained. Simulation results show the close agreement between the simulated and analytical results.
In this paper, we propose a secure transmission scheme from a source to a destination in the presence of spatially random eavesdroppers, the distribution of which is modeled as a homogeneous Possion point process (PPP). In addition to transmitting the message signal, the source is allowed to use part of its power to transmit jamming signals in order to interfere the eavesdroppers. We assume the destination has the knowledge of the jamming signals. Based on the stochastic geometry and point process theory, we derive the closed-form expressions for the connection outage probability and the secrecy outage probability to characterize the reliability and the security performance, respectively. And we determine the optimal power allocation factor and wiretap code rates which maximize the secrecy throughput of the wiretap channel under secrecy outage probability constraint.