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

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

TL;DR

The paper addresses secure downlink transmission in a MIMOME system enhanced with movable antennas under imperfect ECSI. It derives a deterministic Taylor/random-matrix theory-based equivalent for the ergodic secrecy rate to bypass Monte Carlo simulations, and then solves a joint optimization of the precoding matrix and MA positions via alternating optimization. The precoder design uses a majorization-minimization approach with a fixed-point gradient, while the MA-position update employs an AMSGrad-based surrogate and a proven convergence analysis. Empirical results show the deterministic ESR closely matches Monte Carlo estimates and that the MA-enabled scheme substantially outperforms fixed-antenna baselines, highlighting the potential of MA-assisted physical-layer security in dynamic wireless environments.

Abstract

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.

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

TL;DR

The paper addresses secure downlink transmission in a MIMOME system enhanced with movable antennas under imperfect ECSI. It derives a deterministic Taylor/random-matrix theory-based equivalent for the ergodic secrecy rate to bypass Monte Carlo simulations, and then solves a joint optimization of the precoding matrix and MA positions via alternating optimization. The precoder design uses a majorization-minimization approach with a fixed-point gradient, while the MA-position update employs an AMSGrad-based surrogate and a proven convergence analysis. Empirical results show the deterministic ESR closely matches Monte Carlo estimates and that the MA-enabled scheme substantially outperforms fixed-antenna baselines, highlighting the potential of MA-assisted physical-layer security in dynamic wireless environments.

Abstract

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.
Paper Structure (17 sections, 5 theorems, 112 equations, 9 figures, 2 algorithms)

This paper contains 17 sections, 5 theorems, 112 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Eve's channel
  5. Bob's channel
  6. Received Signal Model
  7. Ergodic Secrecy Rate
  8. ESR with Statistic ECSI
  9. Asymptotic Approximation of ESR
  10. Problem Formulation and Solution
  11. Update $\mathbf{F}$ with Fixed $\mathbf{T}_{k}$
  12. Update $\mathbf{T}$ with Given $\mathbf{F}_{k+1}$
  13. Simulation Results
  14. Validation of Proposition \ref{['prop:ergodic_secrecyC']}
  15. Convergence Performance
  16. ...and 2 more sections

Key Result

Proposition 1

Define the matrix $\mathbf{B}$ as where $\mathbf{G}_{\mathrm{LoS}} = \left[\mathbf{g}_1^{\mathrm{LoS}}(\mathbf{T}),\mathbf{g}_2^{\mathrm{LoS}}(\mathbf{T}),\cdots,\mathbf{g}_M^{\mathrm{LoS}}(\mathbf{T})\right]$, and Define two diagonal matrices $\mathbf{D}$ and $\widetilde{\mathbf{D}}$ as Then, define $(\delta,\tilde{\delta})$ as the unique positive solution of the following fixed-point equation

Figures (9)

  • Figure 1: Illustration of the considered MIMOME system.
  • Figure 2: Illustration of the coordinates and spatial angles for the MA.
  • Figure 3: The ergodic secrecy rate $\overline{\mathcal{R}}$ versus $M$.
  • Figure 4: The ergodic secrecy rate $\overline{\mathcal{R}}$ versus $L$.
  • Figure 5: The convergence performance of Algorithm \ref{['alg2']}.
  • ...and 4 more figures

Theorems & Definitions (7)

  • Remark 1
  • Proposition 1
  • Lemma 1: 5429113
  • Remark 2
  • Proposition 2
  • Proposition 3
  • Proposition 4