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IEEE Transactions on Communications

Random Matrix Analysis of Secrecy Outage Probability for MISO Systems With RZF Precoding

Xin Zhang, Jingjing Wang, Shenghui Song, Merouane Abdelkader Debbah

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2026.3669497

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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.
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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.
This paper proposes a novel usage of zero-forcing beamforming (ZFB) for secure transmission in multiple-input single-output (MISO) wiretap channels. When using ZFB for secure transmission, the difficulty lies in the legitimate transmitter (Alice) hardly knowing the channel to eavesdroppers (Eves). The knowledge of the channel to Eves is essential when Alice builds a ZFB precoder that could eliminate the information leakage to Eves. To overcome this difficulty, this paper introduces a torch node that is assumed to be close to an Eve and helps Alice to estimate the channel to the Eve though the estimation is prone to errors. An exact secrecy outage probability (SOP) of the proposed ZFB with torch nodes as well as its asymptotic analysis is provided in this paper. Due to the channel estimation errors, a torch node is not always beneficial to reducing SOP. For a typical problem with a single Eve, a sub-optimal threshold that supports the usage of a torch node is provided in close-form. Numerical results show that the proposed ZFB with torch nodes significantly improves SOP.
Intelligent reflecting surface (IRS) provides an energy-efficient way to construct channels and enables the joint transceiver and channel design. In this paper, we consider the analysis and design of IRS-aided multiple-input multiple-output (MIMO) secure communications. We first investigate the fundamental limits of IRS-aided wiretap MIMO communications by determining the ergodic secrecy rate (ESR) and secrecy outage probability (SOP), which are not yet available in the literature. For that purpose, we derive the central limit theorem (CLT) for the joint distribution of the mutual information (MI) statistics over IRS-aided MIMO wiretap channels by utilizing random matrix theory (RMT). The CLT is then used to obtain the closed-form expressions for ESR and SOP, which are also extended to the scenario with multiple multi-antenna eavesdroppers. Based on the theoretical results, algorithms for maximizing the artificial noise (AN)-aided ESR and minimizing SOP are proposed. Numerical simulations validate the accuracy of the theoretical results and effectiveness of the proposed optimization algorithms.
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