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IEEE Transactions on Wireless Communications

Secrecy Performance Analysis of Analog Cooperative Beamforming in Three-Dimensional Gaussian Distributed Wireless Sensor Networks

Haejoon Jung, In-Ho Lee

Published Feb 12, 2019• 42 citations
Publisher

Abstract

A wireless sensor network (WSN) refers to a network of sensor nodes that collaboratively work to sense, monitor, and control their surrounding environments. As WSNs are integrated into the Internet of Things, it is crucial to protect the network against malicious security attacks considering its wide applicability, such as military monitoring, healthcare, and civilian applications. Thus, in this paper, we consider a physical-layer security technique exploiting analog cooperative beamforming (ACB), where multiple sensor nodes create a virtual antenna array (VAA) and locally adapt their phases. As WSNs inherently have clustered topology, we model the VAA elements' locations by Gaussian distributions. The secrecy capacity of the ACB with the Gaussian-distributed elements is derived in a closed-form expression. The theoretical and numerical results indicate that the ACB-based schemes provide a better secrecy rate compared to the conventional co-located antenna array-based schemes. In addition, the ACB with Gaussian-distributed elements can better suppress side-lobe, which causes undesired information leakage to certain directions, compared to the ACB with uniformly distributed elements. Furthermore, we investigate the impacts of fading channel and phase estimation error in the ACB.

DOI
10.1109/twc.2019.2897763

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A wireless sensor network (WSN) refers to a network of sensor nodes that collaboratively work to sense, monitor, and control their surrounding environments. As WSNs are integrated into the Internet of Things, it is crucial to protect the network against malicious security attacks considering its wide applicability, such as military monitoring, healthcare, and civilian applications. Thus, in this paper, we consider a physical-layer security technique exploiting analog cooperative beamforming (ACB), where multiple sensor nodes create a virtual antenna array (VAA) and locally adapt their phases. As WSNs inherently have clustered topology, we model the VAA elements' locations by Gaussian distributions. The secrecy capacity of the ACB with the Gaussian-distributed elements is derived in a closed-form expression. The theoretical and numerical results indicate that the ACB-based schemes provide a better secrecy rate compared to the conventional co-located antenna array-based schemes. In addition, the ACB with Gaussian-distributed elements can better suppress side-lobe, which causes undesired information leakage to certain directions, compared to the ACB with uniformly distributed elements. Furthermore, we investigate the impacts of fading channel and phase estimation error in the ACB.
As the importance to guarantee confidentiality against security attacks by eavesdroppers has attracted significant attention, there has been much effort to enhance the security performance through cooperative beamforming (CB) in the context of physical layer security (PLS). In particular, analog CB (ACB), which requires vastly lower overhead compared to digital CB, can provide significantly higher secrecy rate compared to the PLS methods with co-located array. In this letter, we focus on ACB with open-loop architecture that requires low complexity, and consider phase offsets across multiple virtual antenna array (VAA) elements for ACB, which are caused by position estimation error of VAA. We investigate the impact of the phase offsets in ACB in terms of the secrecy throughput loss.
Analog cooperative beamforming (ACB) improves physical-layer security (PLS) by enabling phase-coordinated transmissions among spatially distributed nodes without exchanging channel state information (CSI). However, previous studies have relied on predefined node distributions and two-dimensional (2D) network models, limiting the practical applicability of ACB. Motivated by this limitation, we propose a three-dimensional (3D) ACB-based PLS framework that predicts the secrecy performance of ACB under arbitrary node distributions by explicitly considering both LoS and NLoS channel components. Using kernel density estimation (KDE), we estimate the unknown spatial node distribution and derive closed-form expressions for the secrecy rate by analyzing the array gain statistics at the legitimate receiver and the eavesdropper.We verify the proposed framework through simulations and conduct a detailed analysis to examine the impact of network parameters, such as cluster size and the number of nodes.
Physical-layer security (PLS) is a promising alternative or complement to cryptography-based solutions, because security key management and distribution required in such schemes are challenging in future wireless technologies with a distributed nature (e.g., Internet-of-Things (IoT) and massive machine-type communication). Motivated by this fact, in this paper, we investigate a PLS algorithm using linear virtual antenna array (VAA) constructed by multiple single-antenna nodes in mobile ad hoc networks such as unmanned aerial vehicles (UAVs) and mobile robots. Digital cooperative beamforming (CB) has been extensively explored such as cooperative null-steering or jamming. However, in spite of their effectiveness, the digital CB-based schemes incur prohibitive overhead and complexity, which creates difficulty in networks with limited hardware (e.g., IoT). To overcome this issue, we consider an analog CB-based PLS with linearly distributed VAA, which can be implemented in a fully distributed manner. In the proposed scheme, the received signal at the intended receiver is co-phased, while other receivers capture noise-like signals through randomized radiation patterns using the linear VAA. Assuming Rician channels, we derive secrecy rate of the proposed algorithm in a closed-from expression for an arbitrary K-factor, which is not available in previous work on the analog CB-based PLS. Furthermore, we show that the random location perturbations of the VAA elements following Gaussian distributions can enhance the secrecy performance by resolving the angle-of-departure ambiguity issue in linear arrays.
With the rapid increase in connectivity and complexity of 6G-enabled Internet-of-Things (IoT) networks, security has become a critical concern due to the integration of various devices. Analog cooperative beamforming (ACB)-based physical layer security (PLS) algorithms have been investigated to effectively cope with such a security issue in massive IoT networks with limited hardware capabilities. However, in the existing work on ACB-based PLS, IoT nodes are typically assumed to follow Gaussian or uniform distributions, which limits the applicability in general IoT networks with arbitrary node distributions. For this reason, we propose a novel approach to analyze the secrecy rate of the ACB-based PLS scheme with arbitrarily distributed nodes using the non-parametric kernel method, where a kernel function is introduced to better estimate the actual node distribution from survey data.
With the rapid proliferation of the Internet of Things (IoT), small devices in various applications generate, process, and exchange security and safety-critical data as well as privacy-sensitive information. However, due to limited hardware capabilities of such small devices, the IoT networks are inherently vulnerable to security attacks. In this context, the analog cooperative beamforming (ACB)-based physical layer security (PLS) technique can be a suitable solution to guarantee security in the IoT networks by creating a virtual antenna array with multiple IoT devices. Nevertheless, such techniques suffer from poor secrecy performance, when an eavesdropper is located within the main beam toward the legitimate receiver. Motivated by this limitation, in this article, we propose a fully distributed null-steering beamformer, which is suitable for IoT networks following decentralized architecture. Through analysis and simulation, we show that the proposed PLS algorithm outperforms the existing ACB-based PLS scheme. Furthermore, we show that there exists an optimal degree of nulling that maximizes the secrecy performance, which can be estimated based on the analytical results.
In this letter, we propose an analog cooperative beamforming (ACB) technique using random antenna arrays for physical-layer (PHY) secure communications, where the array elements are assumed to be uniformly distributed in a spherical volume. Motivated by the fact that the sidelobe of radiating elements at undesired directions can be used for eavesdropping, the proposed ACB aims at randomizing the radiation pattern at the undesired directions for PHY secure communications. To achieve this aim, it allows the radiating elements to be randomly selected and adapt their phases to a desired direction. To evaluate the PHY security performance, we derive the average secrecy capacity by subtracting the channel capacity for a given undesired direction from that for a desired direction. The analysis and simulation results indicate that the proposed ACB outperforms the existing PHY security technique with a fixed antenna array especially when its array elements are widely dispersed.