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Secure Communication in MIMOME Movable-Antenna Systems with Statistical Eavesdropper CSI

This paper proposes a joint transmit precoding and movable antenna position optimization framework for MIMOME systems under imperfect eavesdropper channel state information, utilizing random matrix theory to derive an ergodic secrecy rate equivalent and a novel AMSGrad-based alternating optimization algorithm to solve the resulting non-convex problem with guaranteed convergence.

Original authors: Lei Xie, Peilan Wang, Guanxiong Shen, Guyue Li, Weidong Mei, Liquan Chen

Published 2026-01-22

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Lei Xie, Peilan Wang, Guanxiong Shen, Guyue Li, Weidong Mei, Liquan Chen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Moving Target vs. a Static Wall

Imagine you are trying to whisper a secret to a friend (Bob) across a noisy, crowded room. However, there is a spy (Eve) lurking nearby trying to eavesdrop.

In traditional wireless networks, the "speakers" (antennas) are fixed in place, like speakers bolted to a wall. They can only change how they shout (the volume and direction), but they can't move. If the room is full of obstacles or if the spy happens to be standing in a spot where the sound carries perfectly, the fixed speakers are stuck.

This paper proposes a new idea: Movable Antennas (MAs). Imagine the speakers are on wheels. They can physically roll around the room to find the perfect spot to whisper clearly to Bob while making sure the spy hears nothing but static.

The Problem: The Spy is a Ghost

Usually, to outsmart a spy, you need to know exactly where they are standing and what their ears are like. But in the real world, spies are sneaky. They don't tell you where they are.

What the transmitter knows: It knows the direct line of sight (like seeing the spy's silhouette) and some general statistics about the room (like "it's usually echoey in this corner").
What the transmitter doesn't know: The exact, moment-to-moment details of the spy's connection (like the specific way sound bounces off a moving chair right now).

The researchers had to figure out how to optimize the system without knowing the spy's exact location, only their general "habits."

The Solution: A Two-Part Strategy

The paper proposes a smart, two-step dance to maximize the "Secret Rate" (how much secret info can be sent safely).

1. The Math Magic (Random Matrix Theory)

Calculating the average secrecy rate with a "ghost" spy is incredibly hard. It's like trying to predict the average weather for a whole year by simulating every single raindrop. It takes too long.

The authors used a branch of math called Random Matrix Theory to create a "shortcut." Instead of simulating millions of random scenarios, they derived a precise formula that acts like a crystal ball. It predicts the average performance accurately without needing to run endless simulations. This formula is the foundation for the rest of their work.

2. The Optimization Dance (Alternating Optimization)

Once they had the formula, they needed to find the best settings. They used a method called Alternating Optimization, which is like tuning a radio and moving the antenna at the same time, but doing one step at a time:

Step A: Tune the Signal (Precoding). Keep the antennas in their current spots, but adjust the signal (the "voice") to be as clear as possible for Bob and as garbled as possible for Eve. They used a clever algorithm (Majorization-Minimization) to find the best "voice" without getting stuck in a bad spot.
Step B: Move the Antennas. Now, keep the "voice" fixed, but roll the antennas to new positions. The goal is to find a spot where the signal to Bob is strong and the signal to Eve is weak.
- The Challenge: Moving the antennas is tricky because the math is messy. Standard methods fail here.
- The Fix: They invented a new, specialized tool (based on AMSGrad) that uses only the "slope" of the problem to guide the antennas to the best spot, even if the math is too complex for standard tools.

They repeat Step A and Step B over and over until the system settles on the perfect combination of signal and position.

The Results: Why Moving Matters

The researchers ran simulations to test their idea against the old "fixed wall" method.

The Winner: The system with Movable Antennas significantly outperformed the fixed system.
The "Negative" Score: In some scenarios, the fixed system actually failed so badly that the spy could hear more than the friend (a negative secrecy rate). The movable system fixed this.
The "Rich" Environment: The more complex the room (more reflections and bounces), the better the movable antennas performed. They could "surf" the waves of the room to find the perfect spot, whereas fixed antennas were stuck in the deep valleys of bad signal.

Summary

This paper proves that if you can physically move your antennas, you can secure your wireless communications much better, even when you don't know exactly where the eavesdropper is. By using a new mathematical shortcut to predict performance and a smart algorithm to move the antennas, the system can actively reshape the airwaves to protect secrets, leaving the spy in the dark.

Technical Summary: Secure Communication in MIMOME Movable-Antenna Systems with Statistical Eavesdropper CSI

Problem Statement
This paper addresses the challenge of enhancing physical layer security (PLS) in a Multiple-Input Multiple-Output Multiple-Antenna Eavesdropper (MIMOME) system utilizing Movable Antennas (MAs). A critical practical constraint considered is the unavailability of instantaneous Eavesdropper Channel State Information (ECSI). Unlike prior works that often assume perfect ECSI or deterministic Line-of-Sight (LoS) models, this study operates under a more realistic scenario where the transmitter possesses only the instantaneous LoS component and the statistical properties of the Non-Line-of-Sight (NLoS) component of the eavesdropper's channel. The objective is to maximize the Ergodic Secrecy Rate (ESR) by jointly optimizing the transmit precoding matrix and the continuous positions of the movable antennas at the legitimate transmitter, despite the uncertainty in the eavesdropper's channel.

Methodology
The authors propose a comprehensive framework to tackle the intractability of the ESR expression under statistical ECSI and the non-convexity of the joint optimization problem:

Deterministic Equivalent via Random Matrix Theory (RMT):
Since deriving an exact analytical expression for the ESR involves complex expectations over random NLoS components, the authors leverage Random Matrix Theory. They derive a deterministic equivalent (closed-form approximation) for the ESR in the asymptotic regime (as the number of antennas and eavesdroppers approaches infinity). This approximation replaces stochastic objectives with a deterministic surrogate, avoiding the computational burden of Monte Carlo simulations and providing a differentiable objective function for optimization.
Alternating Optimization (AO) Framework:
The joint optimization of the precoding matrix ( $F$ ) and antenna positions ( $T$ ) is formulated as a non-convex problem. The authors employ an Alternating Optimization (AO) framework, iteratively updating $F$ and $T$ while fixing the other variable.
Precoding Optimization (Majorization-Minimization):
For the precoding matrix update, the authors develop a gradient-based algorithm within the Majorization-Minimization (MM) framework. A key technical contribution is the derivation of the gradient for the ESR, which requires solving an implicit fixed-point equation inherent to the deterministic equivalent. The algorithm utilizes a gradient projection method with an Armijo line search to handle power constraints.
Antenna Position Optimization (AMSGrad-based Surrogate):
Optimizing continuous antenna positions is challenging because the complex expression of the ESR with respect to position prevents the construction of a standard MM surrogate function that strictly satisfies majorization conditions. To address this, the authors propose a novel surrogate function based on the AMSGrad optimization algorithm. This method relies solely on gradient information. Although it relaxes strict majorization requirements, the authors provide a rigorous theoretical proof demonstrating that the algorithm converges to a stationary point and achieves a "no-regret" property.

Key Contributions

Theoretical Derivation: The paper derives an explicit deterministic equivalent for the ESR in MIMOME-MA systems with statistical ECSI. This result bypasses the need for time-consuming Monte Carlo simulations and serves as the foundation for subsequent optimization.
Precoding Algorithm: A Majorization-Minimization (MM) based algorithm is developed for transmit precoding, featuring a novel derivation of the gradient via implicit fixed-point equations.
Position Optimization: A novel AMSGrad-based optimization scheme is proposed for continuous antenna position tuning. The paper provides a rigorous convergence proof for this method, ensuring it reaches a stationary point despite relaxing standard MM majorization conditions.
System Design: The work formulates and solves a joint optimization problem for precoding and antenna positioning, demonstrating a practical approach to robust secure communication under imperfect ECSI.

Simulation Results
Numerical simulations validate the theoretical findings and the effectiveness of the proposed scheme:

Accuracy of Approximation: The deterministic equivalent derived via RMT is shown to be highly accurate even in moderate system dimensions (finite $N$ and $M$ ), closely matching empirical Monte Carlo results.
Convergence: Both the GP-based precoding algorithm and the AMSGrad-based position optimization algorithm demonstrate rapid and monotonic convergence. The overall AO framework typically stabilizes within a few iterations.
Performance Gains: The proposed MA-aided scheme significantly outperforms conventional Fixed-Position Antenna (FPA) systems.
- Compared to FPA systems with Zero-Forcing (ZF) precoding, the proposed method achieves substantial gains (approximately 4 bps/Hz in tested scenarios), as ZF alone is sub-optimal for security when ECSI is imperfect.
- Compared to FPA systems using the same advanced GP-based precoding, the MA system shows superior performance. This highlights that the additional spatial degrees of freedom (DoFs) gained by reconfiguring antenna positions allow the system to actively reshape the channel, avoiding deep fading for the legitimate user and degrading the eavesdropper's channel quality.
- The performance gap between MA and FPA systems widens in rich scattering environments (higher number of paths), suggesting that position optimization yields greater gains than precoding optimization alone in such conditions.

Significance
The paper claims that extending PLS frameworks to practical MA systems under statistical ECSI is a significant advancement. By moving beyond the assumption of perfect ECSI, the proposed method offers a more robust solution for real-world scenarios where eavesdroppers are passive and non-cooperative. The work demonstrates that MAs can effectively enhance secrecy capacity by leveraging extra spatial DoFs through position optimization, even when the transmitter lacks full channel knowledge of the adversary. The proposed algorithms provide a computationally efficient and theoretically grounded approach to realizing these gains, validating the potential of MAs in next-generation secure wireless networks.