Movable Antenna Secure Transmission

• Movable Antenna Secure Transmission is a technique using reconfigurable arrays to jointly optimize antenna positions and beamforming for enhanced physical-layer security.
• It employs alternating optimization and advanced algorithms to dynamically reshape propagation channels, maximizing legitimate link gain and mitigating interference.
• Practical implementations demonstrate significantly improved secrecy rates and robustness even with imperfect eavesdropper CSI, applicable in cellular, IoT, UAV, and mmWave systems.

Movable Antenna (MA) Empowered Secure Transmission refers to the use of antenna arrays whose constituent elements can be physically repositioned—within a prescribed region and under strict spatial constraints—to enhance the physical-layer security (PLS) of wireless communication systems. By treating antenna locations as optimization variables alongside traditional beamforming weights, MA architectures introduce an additional spatial degree of freedom (DoF). This flexibility provides the ability to dynamically reshape propagation channels, maximize legitimate link gain, and suppress eavesdropping, jamming, or self-interference more effectively than fixed-position antenna (FPA) arrays.

1. Fundamental Principles of Movable Antenna Arrays

Movable antennas depart from the static geometry of FPA arrays by supporting continuous or discretized location adjustment of the array elements. The array steering vector for direction $\theta$ with position vector $\mathbf{x} = [x_1, \ldots, x_N]^T$ is given by

$$\mathbf{a}(\mathbf{x}, \theta) = \big[ e^{j\frac{2\pi}{\lambda}x_1\cos{\theta}}, \ldots, e^{j\frac{2\pi}{\lambda}x_N\cos{\theta}} \big]^T$$

where $\lambda$ is the wavelength and $N$ denotes the number of antennas. Unlike FPAs, MA arrays relinquish predetermined array manifolds, so their spatial signature becomes a direct function of the location vector, federating beamforming and geometry into a coupled design problem.

This architectural reconfigurability not only allows more stringent null-steering toward eavesdroppers but also empowers the system to maximize beam gain at intended receivers. Importantly, the physical constraints include bounded movement regions for each antenna and a minimum inter-element spacing $d_{\min}$ to avoid mutual coupling.

2. Optimization-Based Secure Transmission Architectures

The core of MA-empowered PLS is the joint optimization of beamforming vectors and antenna positions, subject to region, power, and spacing constraints. Representative design problems include:

• Secrecy Rate Maximization:

$$\max_{\mathbf{x}, \mathbf{w}}\, R_{\text{sec}}(\mathbf{x}, \mathbf{w})$$

subject to: $\|\mathbf{w}\|^2 \leq P_A$, $x_n \in [0, L]$, $|x_n - x_m| \geq d_{\min}$ for $n \neq m$

where

$$R_{\text{sec}}(\mathbf{x},\mathbf{w}) = \left[ \log_2\left(1 + \frac{|\mathbf{a}^H(\mathbf{x},\theta_0)\mathbf{w}|^2}{\sigma^2} \right) - \log_2\left( 1 + \sum_{i=1}^M \frac{|\mathbf{a}^H(\mathbf{x},\theta_i)\mathbf{w}|^2}{\sigma^2} \right) \right]^+$$

with $\theta_0$ the legitimate user's angle and $\{\theta_i\}$ the eavesdroppers' angles.

• Joint Power Minimization and Beamforming:

Subject to a target secrecy rate constraint, the goal is to minimize the transmit power by jointly optimizing beamforming and positions. This leads to Rayleigh quotient or eigenvalue subproblems for $\mathbf{w}$ and non-convex position updates for $\mathbf{x}$ (Cheng et al., 2023).

Solution strategies universally apply alternating optimization, decomposing the non-convex design into tractable subproblems:

• Beamforming subproblem: For fixed positions, optimal $\mathbf{w}$ is obtained by solving an eigenvalue problem, e.g.,

$\mathbf{w}^* = \sqrt{P_A} \cdot \mathbf{o}_{\max}$

where $\mathbf{o}_{\max}$ is the principal eigenvector of a matrix formed from the steering vectors of all users and eavesdroppers.

• Antenna position subproblem: For fixed beamforming, $\mathbf{x}$ is updated by projected gradient ascent or MM (majorization-minimization), ensuring inter-element distance and region restrictions (Hu et al., 2023, Tang et al., 7 Mar 2024). For discrete-position problems, combinatorial path search (e.g., graph-theoretic algorithms) can be used (Mei et al., 1 Aug 2024).

3. Extensions: MIMO, Full-Duplex, Cooperative and RIS-Aided Secure Transmission

The basic MA empowered architecture has been generalized to several advanced system models:

• MIMO and Artificial Noise (AN): In MIMO settings, secrecy is maximized via joint optimization over transmit precoding matrices, artificial noise covariance, and the MA array geometry (Tang et al., 7 Mar 2024). The MMSE-based reformulation decomposes the challenge into convex QCQP for precoding/AN subproblems and surrogate-based block updates for positions.
• Full-Duplex (FD) and Multiuser Scenarios: MA arrays for both transmit and receive chains in an FD BS facilitate simultaneous uplink/downlink secrecy (SSR maximization). These designs must handle SI (self-interference), multiple legitimate and eavesdropper users, and non-convex joint beamforming/position optimization (Ding et al., 15 Jul 2024). PSO or MVPSO algorithms are used for high-dimensional position search.
• Cell-Free and Symbiotic Radio Networks: Distributed APs with MAs, sometimes in tandem with RIS, can collaboratively optimize their beamforming weights and antenna locations—jointly maximizing primary user secrecy rates under QoS and AP region constraints (Guan et al., 8 Aug 2024, Lyu et al., 23 Apr 2025, Lyu et al., 9 Aug 2025).
• RIS-ISAC Systems: Joint design of MA positions, BS/RIS beamforming, and sensing waveform is used to maximize user sum-rates under both secrecy leakage and radar SNR constraints. Fractional programming, penalty-based block optimization, and MM are key algorithmic ingredients (Ma et al., 4 Oct 2024).
• Directional Modulation and FDA: For directionally insecure mmWave/THz bands where LoS dominates, MA arrays combined with frequency-diverse arrays (FDAs) are used to jointly optimize both position and frequency distribution of array elements to secure signals in both angle and range dimensions, using closed-form or simulated annealing optimization (Li et al., 30 Jun 2025, Li et al., 10 Apr 2025).

4. Secure Transmission Without Eavesdropper CSI and Robust/Covert Transmission

MA arrays show distinctive advantages when eavesdropper CSI is unknown or only statistically modeled:

• Secrecy Outage Probability Minimization: In Rician fading or only partial eavesdropper CSI, secrecy performance is evaluated via outage probability, with optimization via linearization (e.g., Laguerre series) of the involved gamma functions. APGA or ZF-based position/beamforming optimization is shown to yield large performance gains (Hu et al., 4 Apr 2024, Feng et al., 25 May 2024).
• Jamming/AN under Unknown Eavesdropper: Systems can minimize the information rate using MA location optimization so as to maximize the available jamming power (residual after serving the legitimate SNR constraint) for transmission in the legitimate channel's null space (Cheng et al., 27 Dec 2024).
• Covert Communications with Noise Uncertainty: When the adversary faces bounded but uncertain noise variance, discrete-position MA arrays (solved via discrete projected gradient descent) can simultaneously ensure ultra-reliable transmission and perfect covertness by exploiting regions where the transmit power seen by the warden is below the uncertainty-induced detection threshold (Wang et al., 29 Dec 2024).
• Jammer Threats and Countermeasures: MA-equipped jammers present an increased PLS threat by being able to maximize interference projection to targeted users; simulation shows sum rate and outage probability can be significantly more degraded than with FPA jammers, prompting the need for localization, adaptive beamforming, and regulatory countermeasures (Maghrebi et al., 9 Nov 2024).

5. Algorithmic Structures and Performance Insights

Prominent algorithmic strategies and their salient performance traits include:

• Alternating Optimization: Decoupling joint (beamforming, position, power, AN, RIS-phase) problems by repeatedly solving one block while holding others fixed.
• Projected Gradient/Block Coordinate Descent/MM: For continuous variables, projected gradient or majorization-minimization are used for position updates; block coordinate descent is often used at the top level (Hu et al., 2023, Tang et al., 7 Mar 2024).
• Stochastic/Combinatorial and Metaheuristic Methods: Discrete position problems employ graph-based enumeration, sequential update, or evolutionary metaheuristics (PSO, MVPSO, GA-PSO, SA-PSO, DPGD). These methods efficiently search high-dimensional and/or combinatorially structured position spaces (Mei et al., 1 Aug 2024, Guan et al., 8 Aug 2024, Ding et al., 15 Jul 2024, Lyu et al., 23 Apr 2025).
• Fractional Programming/SCA/SDR: For non-convex rate expressions, fractional programming, SCA, and semidefinite relaxation (SDR) techniques are used, often yielding closed-form updates in certain blocks (Ma et al., 4 Oct 2024, Shen et al., 4 Jul 2025).
• Complexity and Convergence: Simulations show that PGA, MM, AO, and hybrid metaheuristics typically converge in tens to hundreds of iterations; for most practical systems, moderate MA movement regions provide almost all achievable benefits, with diminishing returns for increasing movement freedom (Cheng et al., 2023, Lyu et al., 9 Aug 2025). Discrete approaches approach the performance of continuous optimization when enough candidate points are provided (Mei et al., 1 Aug 2024).

6. Practical Implications, Research Directions, and Applications

Experimental and simulation results across all models confirm the consistent advantage of MAs for secure transmission over FPA-based reference systems:

• Secrecy performance benefits are substantial, often yielding 20–70% higher secrecy rates or significant reductions in secrecy outage, transmit power, and hardware count.
• Flexible, adaptive deployment: MA arrays support secure communications in cellular, IoT, vehicular, UAV, satellite, THz/mmWave, and integrated sensing-and-communication systems, and can be extended to pragmatic architectures where only discrete position sets are physically viable.
• Robustness to uncertainty: MA empowered authentication and secrecy mechanisms are effective even in the absence of full eavesdropper CSI, or when challenged by noise uncertainty, strong jammers, or mobile environments.
• Risks and Regulation: The dual-use of MA devices for destructive jamming highlights the urgency of authentication, anomaly detection, and regulatory frameworks to harness MA benefits safely (Maghrebi et al., 9 Nov 2024, Ma et al., 31 Aug 2025).

Emerging directions include integrating MAs with intelligent surfaces (RIS), generalizing to near-field and six-dimensional (6DMA, combining orientation and position) architectures, and leveraging machine learning for real-time, low-complexity joint position/beamforming adaptation.

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The body of research on MA empowered secure transmission conclusively demonstrates that spatial reconfigurability—in concert with advanced optimization—substantially enhances physical-layer security, enabling both more robust and more flexible defense against evolving wireless threats.