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arXiv:2507.05878

An Effective Equivalence Model of Analyzing PLS of Multiple Eavesdroppers Facing Low-altitude Communication Systems

Yujia Zhao, Zhiyong Feng, Yu, Kan, Zhang, Qixun, Li, Dong

Published Jul 8, 2025• 0 citations
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Abstract

In low-altitude wireless communications, the increased complexity of wireless channels and the uncertainty of eavesdroppers (Eves)--caused by diverse altitudes, speeds, and obstacles--pose significant challenges to physical layer security (PLS) technologies based on fixed-position antennas (FPAs), particularly in terms of beamforming capabilities and spatial efficiency. In contrast, movable antennas (MAs) offer a flexible solution by enabling channel reconstruction through antenna movement, effectively compensating for the limitations of FPAs. In this paper, we aim to derive a closed-form expression for the secrecy rate, a key metric in PLS, which is often unattainable in current studies due to the uncertainty of Eves. We construct an equivalent model that leverages the reconfigurable nature of MAs, equating the secrecy rates obtained by multiple Eves with single FPAs to those achieved by a single virtual Eve equipped with an MA array. To minimize the gap between these two types of secrecy rates, we formulate and solve an optimization problem by jointly designing the equivalent distance between the transmitter and the virtual Eve} and the antenna positions of MAs at the virtual Eve. Numerical simulations validate the effectiveness of the proposed equivalent model, offering a new perspective for PLS strategies. This work provides significant insights for network designers on how system parameters affect PLS performance.

DOI
10.48550/arxiv.2507.05878

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In low-altitude wireless communications, the increased complexity of wireless channels and the uncertainty of eavesdroppers (Eves)--caused by diverse altitudes, speeds, and obstacles--pose significant challenges to physical layer security (PLS) technologies based on fixed-position antennas (FPAs), particularly in terms of beamforming capabilities and spatial efficiency. In contrast, movable antennas (MAs) offer a flexible solution by enabling channel reconstruction through antenna movement, effectively compensating for the limitations of FPAs. In this paper, we aim to derive a closed-form expression for the secrecy rate, a key metric in PLS, which is often unattainable in current studies due to the uncertainty of Eves. We construct an equivalent model that leverages the reconfigurable nature of MAs, equating the secrecy rates obtained by multiple Eves with single FPAs to those achieved by a single virtual Eve equipped with an MA array. To minimize the gap between these two types of secrecy rates, we formulate and solve an optimization problem by jointly designing the equivalent distance between the transmitter and the virtual Eve} and the antenna positions of MAs at the virtual Eve. Numerical simulations validate the effectiveness of the proposed equivalent model, offering a new perspective for PLS strategies. This work provides significant insights for network designers on how system parameters affect PLS performance.
Physical layer security (PLS) technology based on the fixed-position antenna (FPA) has attracted widespread attention. Due to the fixed feature of the antennas, current FPA-based PLS schemes cannot fully utilize the spatial degree of freedom, and thus a weaken secure gain in the desired/undesired direction may exist. Different from the concept of FPA, movable antenna (MA) is a novel technology that reconfigures the wireless channels and enhances the corresponding capacity through the flexible movement of antennas on a minor scale. MA-empowered PLS enjoys huge potential and deserves further investigation. In this paper, for the first time, we investigate the secrecy performance of MA-enabled PLS system where a MA-based base station (BS) transmits the confidential information to multiple single-antenna Bobs, in the presence of the single-antenna eavesdropper (Eve) with no location information, by jointly optimizing the beamforming and antenna positions at the BS. Furthermore, the non-convex optimization problem can be solved via the methods of projected gradient ascent and alternating optimization. Also, and simulated annealing is adopted to find a high-quality feasible solution. Simulation results demonstrate the effectiveness and correctness of the proposed method. In particular, MA-enabled PLS scheme can significantly enhance the secrecy rate compared to the conventional FPA-based ones for different settings of key system parameters.
Physical layer security (PLS) technology based on the fixed-position antenna (FPA) has {attracted widespread attention}. Due to the fixed feature of the antennas, current FPA-based PLS schemes cannot fully utilize the spatial degree of freedom, and thus a weaken secure gain in the desired/undesired direction may exist. Different from the concept of FPA, mobile antenna (MA) is a novel technology that {reconfigures} the wireless channels and enhances the corresponding capacity through the flexible movement of antennas on a minor scale. MA-empowered PLS enjoys huge potential and deserves further investigation. In this paper, we, for the first time, investigate the secrecy performance of MA-enabled PLS system where a MA-based Alice transmits the confidential information to multiple single-antenna Bobs, in the presence of the single-antenna eavesdropper (Eve) {in the absence} of perfect channel state information (CSI). For the purpose of the secrecy rate maximization of the worst Bob, we jointly design the transmit beamforming and antenna positions at the Alice, subject to the minimum moving distance of the antenna, uncertainty CSI of Eve, and maximum transmit power. Furthermore, the projected gradient ascent (PGA), alternating optimization (AO), and simulated annealing (SA) {are} adopted to solve the non-convex characteristics of the problem of the secrecy rate maximization. Simulation results demonstrate the effectiveness and correctness of the proposed method. In particular, MA-enabled PLS scheme can significantly enhance the secrecy rate compared to the conventional FPA-based ones for different settings of key system parameters.
This paper considers a movable antenna (MA)-aided secure multiple-input multiple-output (MIMO) communication system consisting of a base station (BS), a legitimate information receiver (IR) and an eavesdropper (Eve), where the BS is equipped with MAs to enhance the system’s physical layer security (PLS). Specifically, we aim to maximize the secrecy rate (SR) by jointly optimizing the transmit precoding (TPC) matrix, the artificial noise (AN) covariance matrix and the MAs’ positions under the constraints of the maximum transmit power and the minimum spacing between MAs. To solve this non-convex problem with highly coupled optimization variables, the block coordinate descent (BCD) method is applied to alternately update the variables. Specifically, we first reformulate the SR into a tractable form, and derive the optimal TPC matrix and the AN covariance matrix with fixed MAs’ positions by applying the Lagrangian multiplier method in semi-closed forms. Then, the majorization-minimization (MM) algorithm is employed to iteratively optimize each MA’s position while keeping others fixed. We also extend this work to the more general multicast scenario. Finally, simulation results are provided to demonstrate the effectiveness of the proposed algorithms and the significant advantages of the MAs over conventional fixed position antennas (FPAs) in enhancing system’s security.
A pioneering secure transmission scheme is proposed, which harnesses movable antennas (MAs) to optimize antenna positions for augmenting the physical layer security. Particularly, an MA-enabled secure wireless system is considered, where a multi-antenna transmitter communicates with a single-antenna receiver in the presence of an eavesdropper. The beamformer and antenna positions at the transmitter are jointly optimized under two criteria: power consumption minimization and secrecy rate maximization. For each scenario, a novel suboptimal algorithm was proposed to tackle the resulting nonconvex optimization problem, capitalizing on the approaches of alternating optimization and gradient descent. Numerical results demonstrate that the proposed MA systems significantly improve physical layer security compared to various benchmark schemes relying on conventional fixed-position antennas (FPAs).
Movable antenna (MA) array is a novel technology recently developed where positions of transmit/receive antennas can be flexibly adjusted in the specified region to reconfigure the wireless channel and achieve a higher capacity. In this letter, we, for the first time, investigate the MA array-assisted physical-layer security where the confidential information is transmitted from a MA array-enabled Alice to a single-antenna Bob, in the presence of multiple single-antenna and colluding eavesdroppers. We aim to maximize the achievable secrecy rate by jointly designing the transmit beamforming and positions of all antennas at Alice subject to the transmit power budget and specified regions for positions of all transmit antennas. The resulting problem is highly non-convex, for which the projected gradient ascent (PGA) and the alternating optimization methods are utilized to obtain a high-quality suboptimal solution. Simulation results demonstrate that since the additional spatial degree of freedom (DoF) can be fully exploited, the MA array significantly enhances the secrecy rate compared to the conventional fixed-position antenna (FPA) array.
This paper investigates the potential of movable antennas (MAs) to enhance physical layer security within a multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) system. We consider a practical scenario where the transmitter operates with imperfect eavesdropper channel state information (ECSI), knowing only the instantaneous line-of-sight (LoS) component and the statistical properties of non-line-of-sight (NLoS) component. To rigorously quantify secrecy performance under the ECSI uncertainty, we adopt the ergodic secrecy rate (ESR) as the metric. Since deriving an exact analytical expression for the ESR is intractable, we leverage random matrix theory to derive a deterministic equivalent. This avoids heavy Monte Carlo simulations and also provides explicit insights into the effects of channel spatial statistics on secrecy performance. Building upon the deterministic equivalent, we formulate a joint maximization problem for the transmit precoding matrix and the antenna positions at the legitimate transmitter. To tackle the non-convexity of this optimization problem, we develop a comprehensive alternating optimization framework. Specifically, the precoding matrix is optimized via a majorization-minimization (MM) algorithm, where the gradient is computed by solving an implicit fixed-point equation. For the antenna position optimization, the complexity of the objective function prevents the construction of standard MM surrogate. To this end, we further propose a novel AMSGrad-based surrogate function that relies solely on gradient information. We provide a rigorous theoretical proof that guarantees the convergence of this proposed algorithm despite relaxing the strict majorization conditions.