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IEICE Communications Express

Secrecy Performance Analysis of Keyhole MIMOME Wiretap Channels with Imperfect CSI

Xujie Zang, Hongwen Yang

Published Feb 13, 2026• 1 citation
Publisher

Abstract

This paper investigates physical layer security in multi-antenna keyhole systems with imperfect channel state information (CSI). In dense urban environments, rank-deficient channels, specifically the rank-one keyhole effect, significantly degrade secrecy performance. We derive closed-form asymptotic expressions for the secrecy outage probability (SOP) and average secrecy rate (ASR) in the high signal-to-noise ratio (SNR) regime. Based on the analytical results and Monte-Carlo simulations, the impacts of key parameters, such as Alice's antenna number and CSI error variance, are quantified and discussed, which provides insights into robust secrecy design.

DOI
10.23919/comex.2026xbl0001

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This paper investigates physical layer security in multi-antenna keyhole systems with imperfect channel state information (CSI). In dense urban environments, rank-deficient channels, specifically the rank-one keyhole effect, significantly degrade secrecy performance. We derive closed-form asymptotic expressions for the secrecy outage probability (SOP) and average secrecy rate (ASR) in the high signal-to-noise ratio (SNR) regime. Based on the analytical results and Monte-Carlo simulations, the impacts of key parameters, such as Alice's antenna number and CSI error variance, are quantified and discussed, which provides insights into robust secrecy design.
The inherent openness of wireless networks exposes them to eavesdropping threats. In dense urban environments, signal propagation is frequently characterized by the keyhole effect, which causes channel rank deficiency and cascaded fading, challenging the assumptions of conventional multiple-input multiple-output (MIMO) physical layer security. This paper investigates the secrecy performance of MIMO multiple-antenna-eavesdropper (MIMOME) systems over keyhole channels with independent legitimate and eavesdropper links. We analyze the secrecy performance under three progressive scenarios: perfect CSI without artificial noise (AN), perfect CSI with AN-aided transmission, and practical imperfect CSI with AN. Specifically, we derive closed-form asymptotic expressions for the secrecy outage probability (SOP) and average secrecy rate (ASR) in the high signal-to-noise ratio (SNR) regime using Meijer G-functions and Gauss hypergeometric functions, from which the secrecy diversity order and secrecy array gain are explicitly extracted. The analytical results reveal that AN injection successfully restores the secrecy diversity order from zero to one, while imperfect CSI causes AN leakage that leads to ASR saturation and an SOP floor. The derived asymptotic expressions are verified by Monte Carlo simulations. Our findings provide theoretical guidelines by quantifying the trade-off between AN suppression capabilities and self-interference in cascaded fading environments.
Ensuring physical layer security for low-altitude economic networking (LAENet) is critical due to the broadcast nature of wireless channels. In dense urban environments, multi-antenna LAENet systems are often impaired by the keyhole effect, which induces rank deficiency and poses significant security challenges. This paper investigates the secrecy performance of a multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) system in LAENet with keyhole channels. Depending on the availability of channel state information (CSI) at the transmitter, three wiretap scenarios are considered: (i) broadcasting, (ii) passive eavesdropping, and (iii) spoofing. For each scenario, the optimal precoder is designed to maximize the secrecy transmission rate. Based on these designs, we derive closed-form expressions for the secrecy outage probability (SOP) and average secrecy rate (ASR). To provide insights into the effect of keyholes on secrecy diversity order and array gain under this severe rank-deficiency structure, we also obtain asymptotic expressions for SOP and ASR in the high signal-to-noise ratio (SNR) regime using the Mellin transform. Numerical results validate the analytical expressions and illustrate the influence of key parameters on secrecy performance. These findings provide meaningful guidance for the secure design of future LAENet deployments.
Multiple antennas aided wireless communications under dense urban environments often suffer from keyhole effect, which leads to rank deficiency. Secrecy performance of artificial noise (AN) aided multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) keyhole channels is investigated in this paper. Expressions of the asymptotic lines of some vital secrecy metrics are obtained in terms of secrecy outage probability (SOP) and average secrecy rate (ASR) in the high signal-to-noise ratio (SNR) regime, and are verified by Monte-Carlo simulations. It is shown that the secrecy performance is influenced by the antenna numbers at the transceiver and the eavesdropper. Most importantly, by comparing the scheme aided with AN to that without AN, it is found that AN plays a great role in enhancing security of MIMOME keyhole channels.
In this paper, we investigate the physical layer security of a multiple-input and multiple-output (MIMO) relay system under imperfect channel state information (CSI). We propose using multiple antennas at the source and destination to increase the signal-to-noise (SNR) gain of the primary channel, thus improving the system's security performance. Exact closed-form expression of the secure outage probability (SOP) and secrecy capacity (SC) are derived and verified by Monte-Carlo simulations. A close match between the theoretical and simulation results confirms the accurateness of our mathematical analysis. We show that the SOP decreases while the SC increases as the average SNR is higher. Furthermore, the saturated minimum and maximum values highly depend on the number of antennas at source and destination, the degree of imperfect CSI, and the location of eavesdropper.
Physical layer security (PLS) is investigated in a multiple-input multiple-output multiple-antenna eavesdropper keyhole channel over Rayleigh fading. Specifically, the secrecy performance is evaluated by two secrecy performance metrics including the secrecy outage probability (SOP) and average secrecy rate (ASR). By assuming that the transmitter has full channel state information of the main channel, the SOP and ASR are analyzed. To glean further insights, asymptotic analyses are performed to the SOP and ASR by considering an infinite amount of transmit power. It is found that the asymptotic SOP and ASR converge to some constant and the corresponding rate of convergence is determined by the diversity order and array gain.
Transmit antenna selection (TAS) is an emerging technology in physical layer security. To provide new insights into the achievable secrecy performance of TAS in practical communication systems, this paper investigates the average secrecy rate (ASR) and secrecy outage probability (SOP) under practical modulation schemes in TAS aided multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) wiretap channels over Rayleigh fading. Particularly, this research concentrates more on the square M-ary quadrature amplitude modulation (M-QAM). Furthermore, in the considered MIMOME channel, a single antenna is selected to transmit the secret message, and selection combining (SC) or maximal-ratio combining (MRC) is utilized at the legitimate receiver and the eavesdropper. Based on this system model, novel expressions for the ASR and SOP are formulated to characterize the secrecy performance of the finite-alphabet driven MIMOME channel. Besides exact analysis, an asymptotic analysis is performed using the considered performance metrics in high signal-to-noise ratio (SNR) regime. Theoretical analyses suggest that the asymptotic ASR and SOP converge to finite constants in high SNR regime due to the discrete constellation constraint, and we find that the asymptotic behaviour of discrete inputs differs from that of Gaussian inputs. Furthermore, we derive concise expressions to characterize the rate of convergence (ROC) of the ASR and SOP, respectively. To unveil more system design insights, we discuss the relationship between the ROC and several important system parameters such as the antenna number and the modulation order.