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arXiv:2301.11515

Secrecy Analysis for MISO Broadcast Systems with Regularized Zero-Forcing Precoding

Zhang, Xin, Shenghui Song, Yonina C. Eldar

Published Jan 27, 2023• 3 citations
arXivHTMLPDF

Abstract

As an effective way to enhance the physical layer security (PLS) for the broadcast channel (BC), regularized zero-forcing (RZF) precoding has attracted much attention. However, the reliability performance, i.e., secrecy outage probability (SOP), of RZF is not well investigated in the literature. In this paper, we characterize the secrecy performance of RZF precoding in the large multiple-input single-output (MISO) broadcast system. For this purpose, we first consider a central limit theorem (CLT) for the joint distribution of the users' signal-to-interference-plus-noise ratio (SINR) and the eavesdropper's (Eve's) signal-to-noise ratio (ESNR) by leveraging random matrix theory (RMT). The result is then utilized to obtain a closed-form approximation for the ergodic secrecy rate (ESR) and SOP of three typical scenarios: the case with only external Eves, the case with only internal Eves, and that with both. The derived results are then used to evaluate the percentage of users in secrecy outage and the required number of transmit antennas to achieve a positive secrecy rate. It is shown that, with equally-capable Eves, the secrecy loss caused by external Eves is higher than that caused by internal Eves. Numerical simulations validate the accuracy of the theoretical results.

DOI
10.48550/arxiv.2301.11515

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As an effective way to enhance the physical layer security (PLS) for the broadcast channel (BC), regularized zero-forcing (RZF) precoding has attracted much attention. However, the reliability performance, i.e., secrecy outage probability (SOP), of RZF is not well investigated in the literature. In this paper, we characterize the secrecy performance of RZF precoding in the large multiple-input single-output (MISO) broadcast system. For this purpose, we first consider a central limit theorem (CLT) for the joint distribution of the users' signal-to-interference-plus-noise ratio (SINR) and the eavesdropper's (Eve's) signal-to-noise ratio (ESNR) by leveraging random matrix theory (RMT). The result is then utilized to obtain a closed-form approximation for the ergodic secrecy rate (ESR) and SOP of three typical scenarios: the case with only external Eves, the case with only internal Eves, and that with both. The derived results are then used to evaluate the percentage of users in secrecy outage and the required number of transmit antennas to achieve a positive secrecy rate. It is shown that, with equally-capable Eves, the secrecy loss caused by external Eves is higher than that caused by internal Eves. Numerical simulations validate the accuracy of the theoretical results.
With its capability to obtain a good tradeoff between complexity and performance, regularized zero-forcing (RZF) has been widely investigated to enhance the physical layer security. However, the associated reliability performance, i.e., secrecy outage probability (SOP), is not yet available in the literature. In this paper, we characterize the secrecy performance of RZF in the multi-user, downlink multiple-input single-output system. For this purpose, we first set up a central limit theorem for the joint distribution of users’ signal-to-interference-plus-noise ratio and eavesdropper’s signal-to-noise ratio by leveraging random matrix theory. The result is then utilized to obtain a closed-form approximation for the ergodic secrecy rate and SOP of three typical scenarios: the case with only external Eves, the case with only internal Eves, and that with both. The derived results are then used to evaluate the percentage of users in secrecy outage and the required number of transmit antennas to achieve a positive secrecy rate. It is shown that, with equally-capable Eves, the secrecy loss caused by external Eves is higher than that caused by internal Eves. Numerical simulations validate the accuracy of the theoretical results and demonstrate the advantage of RZF over other linear transmitters such as ZF.
Secrecy performance in the near-field (NF) presents a compelling topic for sixth-generation (6G) wireless networks. In this paper, we investigate the physical layer security (PLS) of NF downlink networks serving a single legitimate user in the presence of an eavesdropper. To characterize the performance of the network, through the central limit theorem (CLT), the expected value of the eavesdropping channel statistics is derived for the downlink link in the case of Rayleigh fading. Furthermore, the performance of the proposed network is evaluated in terms of the secrecy outage probability (SOP). The closed-form expressions of the SOP and the floor of SOP under high signal-to-noise ratio (SNR) conditions are derived. We also contrast the impact of the number of antennas as well as the target secrecy rate on the overall secrecy performance of the considered network, and analyze the impact of the eavesdropper on the SOP of the considered network. We finally show that: The SOP of the system decreases with the increase of the transmit power, and finally converges to a fixed value. Our Monte Carlo simulations perfectly illustrate the analytical results.
In this paper, we study the performance of regularized channel inversion (RCI) precoding in large MISO broadcast channels with confidential messages (BCC). We obtain a deterministic approximation for the achiev-able secrecy sum-rate which is almost surely exact as the number of transmit antennas M and the number of users K grow to infinity in a fixed ratio β = K/M. We derive the optimal regularization parameter ξ and the optimal network load β that maximize the per-antenna secrecy sum-rate. We then propose a linear precoder based on RCI and power reduction (RCI-PR) that significantly increases the high-SNR secrecy sum-rate for 1 < β < 2. Our proposed precoder achieves a per-user secrecy rate which has the same high-SNR scaling factor as both the following upper bounds: (i) the rate of the optimum RCI precoder without secrecy requirements, and (ii) the secrecy capacity of a single-user system without interference. Furthermore, we obtain a deterministic approximation for the secrecy sum-rate achievable by RCI precoding in the presence of channel state information (CSI) error. We also analyze the performance of our proposed RCI-PR precoder with CSI error, and we determine how the error must scale with the SNR in order to maintain a given rate gap to the case with perfect CSI. Index Terms Physical layer security, broadcast channel, random matrix theory, linear precoding, multi-user systems. ar X iv
Multiuser multiple-input multiple-output (MIMO) wireless techniques have received tremendous attention as a way to achieve high spectral efficiency in current mobile communication systems such as Long Term Evolution (LTE) [1]. Due to the broadcast nature of the physical medium, wireless multiuser communications are very susceptible to eavesdropping, and it is critical to secure the transmitted information. In this work, consider the broadcast channel with confidential messages and external eavesdroppers (BCCE), where a multi-antenna base station [2] simultaneously communicates to multiple potentially malicious users, in the presence of randomly located external eavesdroppers. The secrecy capacity is measured in terms of outage probability and provides a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. Using the proposed model, the secrecy rates is achieved with regularized channel inversion (RCI) precoding and analyzed by performing a large-system analysis where the number of users K and the number of transmit antennas N both grow to infinity in a fixed ratio. Finally an explicit expression for the probability of secrecy outage and the system performance is analyzed in the presence of both colluding and non-colluding eavesdroppers.
Massive Multiple Input Multiple Output (MIMO) has been considered as an emerging technology to enhance the spectral and energy efficiency for the upcoming wireless communication systems. This paper derives a closed-form approximation for the Ergodic Achievable Secrecy Sum-Rate (EASSR) by considering the joint impact of eavesdroppers and jammers. Two widely used linear precoding techniques, Zero-Forcing (ZF) and Maximum Ratio Transmission (MRT), were used in conjunction with matrix and vector normalization to analyze the secrecy performance. Closed-form expressions are used to explain how the secrecy performance is affected when using the ZF and MRT precoding in the eavesdropping and jamming attack models. We also analyze and compare the performances of different combinations of normalization method and precoding technique in various scenarios. From the analytical expressions and simulation results, we observe that the vector and matrix normalization perform better for the ZF precoding than for the MRT precoding in high Signal-to-Noise Ratio (SNR) scenarios. However, in low SNR, the MRT with matrix normalization outperforms the ZF with vector normalization regardless of the number of users in the system. Further, we observe that the MRT fails to serve more than two users in high SNR scenario. Numerical results obtained from Monte Carlo simulation are used to corroborate the accuracy of the asymptotic secrecy analysis.
In this paper, we consider the broadcast channel with confidential messages and external eavesdroppers (BCCE), where a multi-antenna base station simultaneously communicates to multiple potentially malicious users, in the presence of randomly located external eavesdroppers. Using the proposed model, we study the secrecy rates achievable with regularized channel inversion (RCI) precoding by performing a large-system analysis that combines results from stochastic geometry and random matrix theory, where the number of users K and the number of transmit antennas N both grow to infinity in a fixed ratio. We obtain explicit expressions for the probability of secrecy outage and an upper bound on the rate loss due to the presence of external eavesdroppers. We show that both these quantities scale as \fraclambda_esqrt{N} as the density of external eavesdroppers λ_e grows, irrespective of their collusion strategy. Furthermore, we derive a practical rule for the choice of the regularization parameter, which is agnostic of channel state information and location of eavesdroppers, and yet provides close to optimal performance.