⚡ electrical engineering

Secure Multiuser Beamforming With Movable Antenna Arrays

This paper proposes a secure multiuser transmission framework utilizing movable antenna arrays, where a joint optimization algorithm for digital beamforming and antenna placement is developed to maximize the sum secrecy rate, demonstrating superior performance over conventional fixed-position antenna systems.

Original authors: Zhenqiao Cheng, Chongjun Ouyang, Boqun Zhao, Xingqi Zhang

Published 2026-06-04

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CC BY 4.0

Original authors: Zhenqiao Cheng, Chongjun Ouyang, Boqun Zhao, Xingqi Zhang

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

Imagine you are a radio station trying to broadcast a secret message to a group of friends (the Legitimate Users) while a group of spies (the Eavesdroppers) are lurking nearby, trying to steal that message.

In a traditional radio setup, your antennas are like fixed streetlights. They are bolted to the ground in a specific pattern. You can change the direction of the light beam (digital beamforming), but you can't move the lightbulbs themselves. If the spies happen to be standing in a spot where the light naturally spills over, they can hear your secret.

This paper introduces a new, smarter way to do things using Movable Antennas (MAs). Think of these antennas not as streetlights, but as flashlights held by people who can walk around.

Here is the breakdown of what the paper does, using simple analogies:

1. The Problem: The "Fixed Light" Limitation

In the old way (Fixed-Position Antennas), the signal has to travel through a messy environment full of walls and reflections. Sometimes, the signal bounces off a wall and accidentally shines right into the spies' ears. Because the antennas are stuck in place, you can't easily dodge these "bad bounces" or aim the light perfectly to avoid the spies.

2. The Solution: The "Dancing Flashlights"

The authors propose a system where the antennas can physically move within a certain area (like a dance floor).

The Idea: Instead of just turning the beam, the system physically moves the antennas to find the "sweet spot."
The Goal: Move the antennas so the signal hits your friends brightly but creates a "shadow zone" where the spies hear nothing. It's like a magician moving a spotlight to illuminate the audience while keeping the stage dark for the villains.

3. The Challenge: Too Many Choices

The problem is that moving the antennas is hard.

You have to decide where to put every single antenna (the "dance moves").
You also have to decide how to beam the signal (the "volume and direction").
These two things are linked: moving an antenna changes how the beam works, and changing the beam might require moving the antenna again. It's a giant, messy puzzle with millions of possible combinations.

4. The Method: The "Step-by-Step Puzzle Solver"

The paper creates a smart algorithm (a set of rules for a computer) to solve this puzzle. They don't try to solve everything at once because that's too hard. Instead, they use a method called Block Coordinate Descent, which is like solving a jigsaw puzzle one piece at a time:

Freeze the positions: Assume the antennas are stuck where they are, and find the best way to beam the signal.
Freeze the beam: Assume the signal pattern is fixed, and find the best place to move the antennas to improve it.
Repeat: Keep switching back and forth, making tiny improvements each time, until the signal is as strong as possible for your friends and as weak as possible for the spies.

They also use some mathematical "tricks" (like Fractional Programming) to turn a very complicated math problem into a series of simpler steps that a computer can solve quickly.

5. The Results: Moving Wins

The authors ran computer simulations to test their idea.

The Test: They compared their "Dancing Flashlights" (Movable Antennas) against the "Fixed Streetlights" (Traditional Antennas).
The Outcome: The movable system consistently achieved a higher "Secret Rate." This means they could send more secret information per second without the spies catching a single word.
The Catch: As they added more spies, the secret rate went down (because the spies could pool their hearing power), but the movable system still did better than the fixed one.
The Sweet Spot: They found that having a larger area to move the antennas in (a bigger dance floor) and having more antennas generally led to better security.

Summary

In short, this paper proves that if you let your antennas move around instead of keeping them stuck in one spot, you can physically reshape the airwaves to hide your secrets from eavesdroppers much better than ever before. They built a smart computer program to figure out exactly where to move them, and the results show it works significantly better than the old, static way.

Technical Summary: Secure Multiuser Beamforming With Movable Antenna Arrays

Problem Statement
The paper addresses the challenge of enhancing physical-layer security in multiuser multiple-input multiple-output (MIMO) systems. While movable antenna (MA) architectures have shown promise in improving throughput and reducing fading in single-user or restrictive multiuser settings, a general framework for secure multiuser transmission remains underexplored. Specifically, existing literature often limits analysis to single-user scenarios, single-eavesdropper cases, or specific channel conditions. The authors identify a gap in developing a framework that accommodates arbitrary numbers of legitimate users, data streams, and cooperating eavesdroppers, while jointly optimizing digital beamforming and the physical placement of antennas to maximize the sum secrecy rate.

System Model and Formulation
The proposed system consists of a base station (BS) equipped with $M$ movable antennas, serving $K$ legitimate user terminals (UTs) while facing $J$ cooperating eavesdroppers. The BS operates in time-division duplexing (TDD) mode with perfect channel state information (CSI) acquired via uplink pilot training. The channel model utilizes a field-response approach, where the channel vectors depend explicitly on the physical coordinates of the antennas within a prescribed two-dimensional transmit region.

The objective is to maximize the achievable sum secrecy rate, defined based on secure channel coding theory. The secrecy rate for each user is the difference between the capacity of the legitimate link and the aggregated capacity of the eavesdroppers' links, bounded by zero. The optimization problem involves jointly determining the transmit beamforming matrix and the coordinates of the $M$ antennas, subject to a total transmit power constraint and a minimum spacing constraint to mitigate mutual coupling. The problem is inherently difficult due to the non-concave nature of the objective function with respect to both variables and the non-convex constraints on antenna placement.

Methodology
To solve the non-convex joint optimization problem, the authors propose a framework combining Fractional Programming (FP) and Block Coordinate Descent (BCD).

Reformulation: The original problem, which includes a non-smooth $[\cdot]_+$ operator, is first transformed into an equivalent form using an auxiliary binary variable vector. Subsequently, the sum-of-ratios structure is addressed by introducing auxiliary variables ( $\alpha, \beta, \eta$ ) to convert the objective into a more tractable form via the FP framework. This results in a variational representation where the optimal beamforming and placement variables remain unchanged.
BCD Algorithm: The transformed problem is solved using a BCD approach, where variables are updated iteratively while others are fixed:
- Beamforming ( $W$ ): With fixed antenna positions, the subproblem becomes a convex quadratically constrained quadratic program (QCQP). The optimal beamformers are derived using Karush-Kuhn-Tucker (KKT) conditions, solved via eigen-decomposition and a bisection search for the Lagrange multiplier.
- Antenna Placement ( $T$ ): With fixed beamforming, the placement update is non-convex and coupled. The authors employ an element-wise alternating optimization strategy. Each antenna coordinate ( $x$ and $y$ ) is updated sequentially via a low-complexity one-dimensional search over a finite grid, ensuring minimum spacing constraints are met.
- Auxiliary Variables: The auxiliary variables ( $b, \alpha, \beta, \eta$ ) are updated using closed-form expressions derived from the optimality conditions.

The proposed algorithm is proven to converge, as the objective value is non-decreasing in each iteration and upper-bounded.

Key Contributions

Framework Development: The paper establishes a general MA-enabled multiuser secure transmission framework that supports arbitrary numbers of users and cooperating eavesdroppers, extending beyond previous single-user or restrictive multiuser studies.
Theoretical Characterization: Novel expressions for the achievable sum secrecy rate are derived based on secure channel coding theorems, explicitly accounting for the dependency of channel characteristics on physical antenna positions.
Algorithm Design: A joint optimization algorithm is developed that efficiently handles the strong coupling between digital beamforming and MA placement. The method ensures that every variable update admits either a closed-form solution or a low-complexity search, facilitating efficient implementation.

Numerical Results
Simulation results validate the effectiveness of the proposed method against a benchmark using conventional fixed-position antenna arrays (FPAs) with uniform linear arrays.

Performance Gain: The MA-enabled design consistently achieves higher sum secrecy rates than the FPA benchmark across various scenarios, including different numbers of eavesdroppers, transmit antennas, and users.
Impact of Parameters:
- Increasing the number of transmit antennas ( $M$ ) or the size of the transmit region ( $A$ ) improves the secrecy rate by providing greater spatial diversity and degrees of freedom for leakage suppression.
- The secrecy rate generally increases with the number of users ( $K$ ) when sufficient antennas are available to manage interference. However, in RF-limited cases (e.g., $M=2$ ), the rate may decrease as $K$ grows due to the inability to simultaneously suppress interference and leakage.
- As the number of cooperating eavesdroppers increases, the secrecy rate decreases, reflecting the increased capability of the eavesdroppers to capture leaked energy.
Convergence: The algorithm demonstrates monotonic convergence in a few iterations. Additionally, increasing the grid search resolution for antenna placement yields performance gains that diminish as the resolution becomes very fine.

Significance and Claims
The paper claims that the proposed MA-enabled design offers a significant advantage over conventional fixed-position arrays for multiuser secure transmission. By leveraging the flexibility of antenna movement to reshape the wireless channel, the system can more effectively steer energy toward legitimate users and minimize information leakage to eavesdroppers. The authors position this work as a step toward next-generation MIMO systems, demonstrating that joint optimization of physical placement and digital processing is a viable and effective strategy for enhancing physical-layer security. The study acknowledges that future work will need to address robust designs under imperfect CSI, practical mobility constraints, non-cooperative eavesdropping, and frequency-selective channels.