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IET Information Security

ESR analysis over ST‐MRC multi‐input multi‐output Nakagami fading channels

Jin‐Yuan Wang, Sheng‐Hong Lin, Wei Cai, Jianxin Dai

Published Mar 5, 2019• 3 citations
Publisher

Abstract

Different from conventional key‐based cryptography schemes, physical‐layer security (PLS) techniques have drawn much attention recently to realise unconditional security from the information theory perspective. As an important performance metric in PLS, the ergodic secrecy rate (ESR) for a multi‐input multi‐output wireless communication network over a Nakagami fading channel is analysed. The network is consisted of a multi‐antenna transmitter (Alice), a multi‐antenna legitimate receiver (Bob), and a multi‐antenna eavesdropper (Eve). By using the selective transmission (ST) at Alice and the maximum ratio combining (MRC) at Bob and Eve, an exact expression of the ESR is derived. However, due to the infinite summation, it is very hard to evaluate the ESR performance. To reduce computational complexity and obtain more insights, a lower bound of the ESR is then obtained, which is in a closed form. As special cases, the lower bounds of the ESR for the signal‐antenna scenario and Rayleigh fading channel are also obtained, respectively. Numerical results show that the derived expressions of the ESR and its lower bound are very accurate to evaluate system performance.

DOI
10.1049/iet-ifs.2018.5185

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Different from conventional key‐based cryptography schemes, physical‐layer security (PLS) techniques have drawn much attention recently to realise unconditional security from the information theory perspective. As an important performance metric in PLS, the ergodic secrecy rate (ESR) for a multi‐input multi‐output wireless communication network over a Nakagami fading channel is analysed. The network is consisted of a multi‐antenna transmitter (Alice), a multi‐antenna legitimate receiver (Bob), and a multi‐antenna eavesdropper (Eve). By using the selective transmission (ST) at Alice and the maximum ratio combining (MRC) at Bob and Eve, an exact expression of the ESR is derived. However, due to the infinite summation, it is very hard to evaluate the ESR performance. To reduce computational complexity and obtain more insights, a lower bound of the ESR is then obtained, which is in a closed form. As special cases, the lower bounds of the ESR for the signal‐antenna scenario and Rayleigh fading channel are also obtained, respectively. Numerical results show that the derived expressions of the ESR and its lower bound are very accurate to evaluate system performance.
Summary In this work, we analyze the physical layer security (PLS) for a multiuser (MUS) multi‐input multi‐output multi‐eavesdropper (MIMOME) wireless network using selection transmission (ST) at the base station (BS) with maximum ratio combining (MRC) at both of the receivers, receivers of legitimate users (LUs) as well as the receivers of illegitimate users over an uncorrelated Rayleigh fading channel. In this scenario, multiple users communicate to a BS at the same time multiple eavesdropper user may intercept the transmission. Next, we drive exact closed‐form expression for probability of nonzero secrecy capacity (PNZSC) and secrecy outage probability (SOP) in the presence of imperfect channel state information (ICSI). At last, we present the simulation results to authenticate the analytical results and analyze the impact of ICSI on PLS of MUS‐MIMOME system.
Abstract Transmit antenna selection (TAS) in wiretap channels has arisen as a simple promising scheme to improve physical layer security. However, up to now, TAS schemes have aimed at maximising the instantaneous signal‐to‐noise ratio of the legitimate receiver, which by its essence is a sub‐optimal strategy from a secrecy point of view. In this paper, unlike previous works, we propose a novel TAS scheme for multiple‐input multiple‐output wiretap channels by exploiting full channel state information. The proposed scheme achieves higher secrecy performance by selecting an antenna that maximises the secrecy rate. In our analysis, we assume that the receiver (Rx) and the eavesdropper employ either selection combining (SC) or maximal‐ratio combining (MRC) to combine the received signals, and this results in four different receiver combining arrangements. By considering Nakagami‐m fading, secrecy performance is analysed. Specifically, closed‐form expressions for the secrecy outage probability are derived, which can be used as a quality of service metric. Moreover, an asymptotic analysis is carried out and the respective diversity/array gains are obtained. The ergodic secrecy rate is also investigated for the case of multiple‐input single‐output wiretap channels. Insightful discussions are attained from our analysis. For instance, it is shown that the performance gain of MRC over SC at the Rx does not depend on the number of antennas and combining scheme at the eavesdropper. More interestingly, we observe that such a performance gain is independent of the TAS scheme used at the transmitter (Tx). On the other hand, it is shown that the secrecy gap between SC and MRC at the eavesdropper is independent of the number of antennas at the Tx, but it depends on the number of antennas at the Rx. Finally, it is demonstrated that the diversity gain is the same for all antenna configurations. Copyright © 2016 John Wiley & Sons, Ltd.
Physical Layer Security of MRC in Fisher–Snedecor FFF Fading Channels
The physical layer security (PLS) is explored in quasi-static Fisher-Snedecor F Fading Channels with maximal ratio combining (MRC), which have been used to model the conventional and emerging realistic wireless communication channels. We consider the secure transmission of privileged information from a single antenna legitimate transmitter to L-antenna legitimate receiver are wiretapped by L-antenna eavesdropper. The receiver maximizes the probability of secure transmission by adopting MRC, whereas eavesdropper maximizes the probability of eavesdropping by adopting MRC. We derive PLS secrecy metrics for a system setup where the transmitter is having no channel state information (CSI) of both the receiver and eavesdropper. Specifically, we derive a novel closed-form expressions for secure outage probability (SOP) and strictly positive secrecy capacity (SPSC). Furthermore, to obtain important insight into the effect of channel parameters on the secrecy performance, an asymptotic analysis is conducted for SOP at high signal-to-noise ratio (SNR) regime.
This paper investigates the role of the Maximum Ratio Combining (MRC) diversity scheme in enhancing security for multicast communications over a Nakagami-0.5 fading channel in the presence of multiple eavesdroppers. The considered scenario involves a singleantenna transmitter communicating confidentially with multiple legitimate receivers, while multiple eavesdroppers attempt to intercept the transmission. Explicit mathematical formulation have been established to evaluate the likelihood of achieving a positive secrecy multicast capacity and the probability of a secure outage, providing a theoretical framework to evaluate the secrecy performance. The analysis highlights the impact of critical system parameters, including the number of legitimate receivers, the number of eavesdroppers and the number of antennas employed at both legitimate receivers and eavesdroppers. By employing MRC, which coherently combines signals from multiple antennas to maximize the received signal-to-noise ratio, the study demonstrates significant improvements in the secrecy performance of multicast systems. The findings contribute valuable insights into designing more secure multicast communication networks in the presence of severe fading and adversarial interception.
In this paper, multiple-input-multiple-output wireless communication network is considered: with a base station Alice having multiple antennas, one desired information receiver Bob and one eavesdropper with multiple antennas. A closed-form mathematical expression for the ergodic secrecy capacity under Nakagami-m Fading Channels is derived. The derived expression highlights the variation of the ergodic secrecy capacity with number of antennas in Bob and Nakagami-m pararmeter, which is depicted with numerical analysis.
Quantum computing threatens traditional encryption methods like RSA and ECC, as quantum algorithms such as Shor's algorithm can break them efficiently. Physical Layer Security (PLS) offers a resilient alternative by leveraging the inherent properties of communication channels, making it immune to quantum advancements. This paper investigates the secrecy capacity of modified Nakagami‐ q fading channels in the presence of a multi‐antenna eavesdropper. The multiple antennas at the receivers are assumed to be independent and identically distributed (i.i.d.). We apply a small limit argument approximation (SLAA) to the zeroth‐order modified Bessel function of the first kind within the conventional Nakagami‐ q probability density function. This modification eliminates the mathematical intractability associated with the Bessel function, enabling the derivation of novel, simple, and closed‐form analytical expressions for key secrecy metrics. Specifically, we derive and analyze the probability of positive secrecy capacity, secure outage probability, and ergodic secrecy capacity. The validity of the proposed approximation is confirmed through high‐fidelity Monte Carlo simulations ( samples), which demonstrate a negligible Root Mean Square Error (RMSE) of from the conventional model. Results show that the system maintains positive secrecy capacity even when the eavesdropper has a higher SNR than the legitimate channel, particularly in low‐SNR regions where eavesdropper antenna count has minimal impact. Special cases, such as Rayleigh fading with single‐antenna setups, further validate these findings. This research highlights the robustness of PLS in protecting communications against quantum threats and provides a mathematically tractable framework for secrecy analysis in generalized fading environments. © 2026 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.