Source-linked AI summary
Secure Wireless Communication via Movable-Antenna Array
Guojie Hu, Qingqing Wu, Kui Xu, Jiangbo Si, Naofal Al-Dhahir
TL;DR
The paper addresses secure communication for an MA array-enabled transmitter communicating with Bob amid multiple colluding eavesdroppers. It jointly optimizes transmit beamforming and movable-antenna positions with PGA and alternating optimization, and simulations show significantly higher secrecy rates than FPA arrays.
Problem
The paper investigates whether movable-antenna arrays can enhance physical-layer security against multiple colluding eavesdroppers beyond fixed-position antenna arrays.
Method
The approach jointly optimizes Alice's transmit beamforming and all movable-antenna positions using projected gradient ascent and alternating optimization.
Results
Simulations show that MA arrays significantly enhance secrecy rate and security performance compared with conventional FPA arrays.
Takeaways & Limitations
Flexible antenna positions provide an additional spatial degree of freedom for improving secure communication performance.
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
Conventional FPA beamforming is limited by static steering vectors and spatial correlation, while MA arrays add adjustable antenna positions to reconfigure channels. This letter applies that spatial flexibility to secure communication and jointly optimizes beamforming and antenna positions to improve secrecy rate.
- FPA beamforming uses fixed antenna positions, producing static steering vectors and weakened secure beamforming gains under spatial correlation.
- MA arrays exploit adjustable antenna positions within a specified region to vary steering vectors, reconfigure wireless channels, and achieve higher communication capacity.
- The letter studies MA-assisted secure communication from Alice to a single-antenna Bob with multiple single-antenna eavesdroppers.
- Transmit beamforming and all antenna positions are jointly optimized to maximize achievable secrecy rate using PGA and alternating optimization.The formulated problem is highly non-convex.
- Simulations show that MA arrays greatly improve secrecy rate relative to conventional FPA arrays by exploiting additional spatial degrees of freedom.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system places a linear MA array at Alice and fixed single antennas at Bob and multiple eavesdroppers. The secrecy-rate maximization jointly selects beamforming and antenna positions under spacing, region, and power constraints, forming a highly non-convex problem.
- Alice uses a linear MA array with N movable antennas, while Bob and M colluding eavesdroppers each use a single fixed-position antenna.
- The antenna-position vector is x = [x1, x2, ..., xN]T, and the MA steering vector depends on x and steering angle θ.
- The achievable secrecy rate is defined for the worst case in which all eavesdroppers cooperatively process their received confidential information.
- The optimization jointly chooses antenna positions x and transmit beamforming w to maximize Rsec(x, w).
- A minimum antenna spacing avoids coupling, antenna positions remain within a specified region, and Alice's transmit power is bounded by PA.The region length L must satisfy L ≥ (N − 1)dmin for the spacing constraint to remain feasible.
- The problem is highly non-convex because the objective is non-concave in x and w, and the two variables are coupled.Alternating optimization therefore updates x and w iteratively while holding the other variable fixed.
A. Optimizing w Given x
With antenna positions fixed, the beamforming subproblem is formulated and solved using its established optimal solution.
- Given x, the problem of optimizing transmit beamforming w is expressed as a separate subproblem.
- The optimal solution to this beamforming subproblem is the normalized eigenvector associated with the largest eigenvalue of a specified matrix.
- The solution expression uses the inverse operation for the relevant matrix term.
B. Optimizing x Given w
With w fixed, the antenna-position subproblem remains highly non-convex, so the paper applies projected gradient ascent with projection to maintain feasible MA positions.
- The antenna-position problem is highly non-convex because its objective is complex.
- Projected gradient ascent iteratively updates antenna positions to seek a locally optimal solution.The update uses a gradient-ascent step with step size δ.
- A projection function enforces the position constraints after each update when necessary.The projection keeps each antenna position within its feasible range while respecting minimum separation.
- The feasible range for each ordered position x_n is determined by the array length and minimum antenna separation.For n = 1, ..., N, x_n lies between x_{n−1} + dmin and L −(N −n)dmin, with x_0 = −dmin for convenience.
- The alternating-optimization procedure initializes positions uniformly, updates w, and repeats until the objective converges to a prescribed accuracy.
- The PGA inner loop has computational complexity about O(((M + 1)N + (M + 1)^2)T_inner).T_inner denotes the number of iterations in the inner layer.
C. Alternating Optimization
The paper alternates between beamforming and antenna-position updates to solve the secrecy-rate problem, with convergence supported by a nondecreasing bounded objective and reported convergence behavior.
- The overall alternating algorithm solves the joint secrecy-rate problem by iteratively updating beamforming and antenna positions.
- The secrecy rate is nondecreasing over iterations and has an upper bound, guaranteeing convergence of the alternating algorithm.
- Fig. 2 compares convergence behavior for the PGA method and the alternating optimization algorithm in separate subfigures.
- The algorithm’s overall complexity includes an outer-loop term and the PGA inner-loop term, with T_outer denoting outer iterations.
IV. SIMULATION RESULTS
Simulations show that optimized movable-antenna positions improve beam control and secrecy performance over fixed-position arrays, while the proposed algorithms converge efficiently.
- Convergence behavior: The inner and outer objectives converge to constants within at most 50 and 4 iterations, respectively, for the tested N = 3 case.These convergence behaviors support the reported computational efficiency of the proposed algorithms.
- Optimized antenna positions: Optimized MA positions are nonuniform, unlike the uniformly spaced FPA positions xFPA = [0, dmin, ..., (N−1)dmin]T.The MA positions are optimized separately for N = 4 and N = 3.
- Beam gain: For N = 4, both arrays null-steer toward the two eavesdropper angles, while the MA array achieves higher gain toward Bob.The MA advantage comes from exploiting flexible antenna positions as an additional spatial degree of freedom.
- Beam gain: For N = 3, the MA array nearly null-steers toward both eavesdroppers and retains preferable Bob gain, whereas the FPA array leaks toward θ1 and has lower Bob gain.Beamforming performance deteriorates for both arrays when the antenna count decreases from four to three.
- Secrecy rate: As N increases, secrecy rates rise for both arrays, while the MA array achieves a significant gain over the FPA array under different Alice power budgets.The reported increase is attributed to larger spatial diversity and multiplexing gains, together with flexible MA positions.
V. CONCLUSION
The conclusion presents an MA-array secure communication system and optimization methods for jointly designing transmit beamforming and movable-antenna positions. Simulations show that the resulting additional spatial degrees of freedom significantly enhance security performance over conventional FPA arrays.
- Conclusion: The paper jointly optimizes transmit beamforming and all movable-antenna positions at Alice to maximize achievable secrecy rate.It develops projected gradient ascent and alternating optimization methods for this design.
- Conclusion: Simulations show that antenna-position optimization provides additional spatial degrees of freedom and significantly improves security performance over conventional FPA arrays.