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Scientific Reports

Ergodic secrecy rate and outage probability in NOMA IRS massive MIMO networks with jamming

Min Zhu, Hamid Gholizadeh Fard, Bahar Hazrati, Behrooz Mosallaei, Alhussein G. Alkhayer, Kai Jin, Jingyu Zhang

Published Jul 7, 2025• 2 citations
Publisher

Abstract

This research paper considers a wireless system that assumes massive multiple-input multiple-output (MIMO) technical solutions for the Base Station (BS), while both near and far users have just one antenna. This study primarily aims to examine the security implications of the physical layer in this system using Non-Orthogonal Multiple Access (NOMA) along with an Intelligent Reconfigurable Surface (IRS). It is assumed that the BS broadcasts signals to pairs of NOMA users, and both categories of users also receive signals from the IRS. Additionally, the far user is regarded as untrusted, while the jammer is present. Moreover, to assess the confidentiality performance of the studied system, the Ergodic Secrecy Rate (ESR) and Secrecy Outage Probability (SOP) are considered, and their closed-form expressions are provided. Our findings indicate that the integration of IRS leads to an exponential enhancement in the ESR, consequently reducing the SOP. Additionally, our observations highlight the superior efficiency of networks featuring a jamming mechanism. Furthermore, the employment of a massive multi-antenna setup amplifies the transfer Signal-to-Noise Ratio (SNR), leading to heightened ESR and a simultaneous reduction in the SOP.

DOI
10.1038/s41598-025-06059-w

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This research paper considers a wireless system that assumes massive multiple-input multiple-output (MIMO) technical solutions for the Base Station (BS), while both near and far users have just one antenna. This study primarily aims to examine the security implications of the physical layer in this system using Non-Orthogonal Multiple Access (NOMA) along with an Intelligent Reconfigurable Surface (IRS). It is assumed that the BS broadcasts signals to pairs of NOMA users, and both categories of users also receive signals from the IRS. Additionally, the far user is regarded as untrusted, while the jammer is present. Moreover, to assess the confidentiality performance of the studied system, the Ergodic Secrecy Rate (ESR) and Secrecy Outage Probability (SOP) are considered, and their closed-form expressions are provided. Our findings indicate that the integration of IRS leads to an exponential enhancement in the ESR, consequently reducing the SOP. Additionally, our observations highlight the superior efficiency of networks featuring a jamming mechanism. Furthermore, the employment of a massive multi-antenna setup amplifies the transfer Signal-to-Noise Ratio (SNR), leading to heightened ESR and a simultaneous reduction in the SOP.
We have proposed and analyzed secrecy performance of a network architecture which contains a source, two destinations, a friendly jammer (FJ) and an eavesdropper (Eve). To jam the Eve in order to secure the confidential information of both users, the FJ sends a jamming signal while the source sends the combined information signal using non-orthogonal multiple access (NOMA) technique to both the users. A known jamming is considered which is known by both the users. Both the users subtract the known jamming from the received signal and then decode the information signal as per the NOMA technique. We analyzed the physical layer security of the network in terms of the secrecy outage probability (SOP) where the two users have different target secrecy rates. A closed form expression of the SOP is developed. We have analyzed the SOP under the impact of several numerical parameters such as: source transmit signal to noise ratio (SNR), FJ transmit SNR, fraction of source transmit power, and different target secrecy rates. For a fixed transmit SNR of the FJ, we obtain an optimal value of the source transmit SNR at which SOP is minimized. These analyzed results are also supported by the MATLAB based simulation results.
In non-orthogonal multiple access (NOMA) systems, serving multiple users in shared resource blocks can allow untrusted users to overhear the messages of other users. In this context, we study a network consisting of a base station (BS), a near user and a far user, where the latter attempts to overhear the message of the former. The near user is a full-duplex (FD) node that can also act as a relay. Two operating scenarios are considered: 1) friendly jammer (FJ), where the FD node broadcasts noise for degrading the channel between the BS and the far user, while receiving data from the BS; and 2) friendly jammer relay (FJR), where, in addition to degrading the channel between the BS and the far user, the FD node relays the message of the far user. We investigate the secrecy performance of the network by characterizing the secrecy outage probability (SOP) in both scenarios. We obtain the exact SOP of the FJ case, and an approximation for the SOP of the FJR scenario, both expressed in closed-form. Numerical results confirm the accuracy of the analytical results. For a given BS power budget and power allocation to the users, it is demonstrated that the jamming and relaying powers are prominent factors to make the NOMA-FJR scheme superior to NOMA-FJ, as well as to conventional and cooperative NOMA schemes.
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.
This paper investigates the uplink secrecy performance of a reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) network. In the proposed system model, users communicate with the base station (BS) via a strategically partitioned RIS. However, a silent passive eavesdropper overhears the data through a direct link. As part of the proposed security design, we propose a user-centric artificial noise (AN) transmission strategy that degrades the decoding ability of the eavesdropper without sacrificing the power budget. The AN is nullified in the composite channel utilizing singular value decomposition. After analyzing the channel statistics, which consider all channels experiencing Nakagami-mmmfading, we derive theoretical closed-form expressions for the ergodic secrecy rate (ESR) for each user in the NOMA pair using Gauss-Chebyshev quadrature and Taylor-Maclaurin expansions. Monte Carlo simulations validate the correctness of our analysis. The numerical results confirm that our proposed scheme consistently achieves a positive ESR. We also explore the impact of channel fading and RIS-partitioning ratio on the uplink ESR and comment on optimal power allocation. Notably, the results also confirm that the proposed system outperforms the benchmark MIMOorthogonal multiple access-based scheme.
This paper investigates the security aspects of a multiple-input multiple-output (MIMO) network that utilizes a relay and non-orthogonal multiple access (NOMA) to serve multiple users under a potential eavesdropping scenario. Given the security vulnerabilities inherent in spectrally efficient systems, our work establishes a mathematical framework to analyze this specific architecture. We derive new closed-form expressions to characterize the secrecy outage probability (SOP) for individual users and the system as a whole. Through extensive simulations covering various antenna configurations and signal-to-noise conditions, our analysis confirms that the NOMA protocol can provide superior security compared to conventional orthogonal multiple access (OMA) in certain operational domains. These findings underscore the viability of NOMA as a foundational technology for constructing secure, next-generation wireless systems.
NOMA (Non-Orthogonal Multiple Access) has been recognized as new multiple access technology for wireless communication networks of the fifth generation and beyond, owing to its ability to improve spectral efficiency, support massive connectivity, and provide user fairness. However, it has been observed that the superposition-based transmission principle of NOMA is highly susceptible to eavesdropping attacks, especially in an open wireless network where all wireless communications are inherently broadcast in nature. Hence, ensuring secure wireless communications for NOMA systems has now become an important area of research. This research aims to improve the secrecy level of wireless communications for NOMA systems by employing Physical Layer Security (PLS) techniques. Specifically, two prominent PLS techniques, Artificial Noise (AN) and Cooperative Jamming (CJ), have been employed to provide security against passive eavesdropping attacks. The cooperative NOMA system architecture is considered, and the secrecy enhancement is analyzed for two possible scenarios when the eavesdropper is close to the relay node and when the eavesdropper is close to the base station. The secrecy performance of the proposed system is analyzed through various parameters, namely, Secrecy Outage Probability (SOP), Secrecy Capacity (SC), Secrecy Rate (SR), and Secrecy Energy Efficiency (SEE) in terms of the Signal to Noise Ratio (SNR). The numerical results for the secrecy metrics are obtained through MATLAB-based simulations, whereas the system-level model is developed using the Simulink platform to verify the suggested system's functionality in the presence of AN and CJ for the legitimate NOMA users and the eavesdropper. The results show that the secrecy performance is significantly enhanced with the introduction of AN and CJ, and the system shows robust performance in terms of energy efficiency. This paper provides significant insights into the design of the NOMA system from the secrecy perspective and validates the potential of PLS techniques for the design of the future wireless system.