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Robust Secure UAV Communications with the Aid of Reconfigurable Intelligent Surfaces
Li Sixian, Duo Bin, Marco Di Renzo, Tao Meixia, Yuan Xiaojun
TL;DR
The paper addresses secure bidirectional UAV–ground-user communication assisted by an RIS when eavesdropping-channel CSI is imperfect. It develops a robust joint design using alternating optimization and reports improved secrecy-rate performance and robustness relative to benchmark schemes. The study is scoped to a single-user setting, with multi-user extensions left for future work.
Problem
The paper addresses limited research on RIS-aided UAV secure communications under imperfect eavesdropping-channel CSI, which is difficult to obtain because eavesdroppers avoid detection.
Method
It uses alternating optimization to jointly design the UAV trajectory, RIS passive beamforming, and legitimate transmit powers for DL and UL secrecy-rate optimization.
Results
The proposed algorithm exceeds the benchmark schemes in average worst-case secrecy rate and converges quickly, after around 10 iterations in the reported simulation.
Takeaways & Limitations
The results support robust joint trajectory, passive-beamforming, and power control as an effective design for improving secrecy-rate performance under eavesdropping-channel uncertainty.
Takeaways & Limitations
The proposed single-user scheme does not directly apply to non-orthogonal multi-user access, where interference cancellation would be required; this extension is left for future work.
Abstract
from arXiv · showhide
This paper investigates a novel unmanned aerial vehicles (UAVs) secure communication system with the assistance of reconfigurable intelligent surfaces (RISs), where an UAV and a ground user communicate with each other, while an eavesdropper tends to wiretap their information. Due to the limited capacity of UAVs, a RIS is applied to further improve the quality of the secure communications. The time division multiple access (TDMA) protocol is applied for the communications between the UAV and the ground user, namely, the downlink (DL) and the uplink (UL) communications. In particular, the channel state information (CSI) of the eavesdropping channels is assumed to be imperfect. We aim to maximize the average worst-case secrecy rate by the robust joint design of the UAV's trajectory, RIS's passive beamforming, and transmit power of the legitimate transmitters. It is challenging to solve the Joint UL/DL optimization problem due to its non-convexity. To this end, we develop an efficient algorithm based on the alternating optimization (AO) technique. Specifically, the formulated problem is divided into three sub-problems, and the successive convex approximation (SCA), S-Procedure, and semidefinite relaxation (SDR) are applied to tackle these non-convex sub-problems. Numerical results demonstrate that the proposed algorithm can considerably improve the average secrecy rate compared with the benchmark algorithms, and also confirm the robustness of the proposed algorithm.
I. INTRODUCTION
The paper studies secure UAV–ground-user communications assisted by an RIS, addressing the practical challenge of imperfect eavesdropping-channel CSI. It jointly considers UAV mobility, RIS reflection control, and bidirectional DL/UL transmission.
- UAVs offer flexible deployment and LoS-dominated links, while RISs adjust passive element phases to shape propagation and enhance received signal energy.
- Existing RIS-aided UAV secure-communication research is limited and commonly assumes perfect CSI for eavesdropping channels.
- The considered system supports UAV-to-user downlink and user-to-UAV uplink communications under TDMA during a single flight period.
- A building-mounted RIS assists secure transmission, while CNPC links support transmission of control signals among the UAV, RIS, and ground user.
- The UAV flies at constant altitude over N time slots, with trajectory updates constrained by its maximum speed and fixed initial and final locations.
1) DL Transmission:
The downlink models the UAV as the legitimate transmitter and the ground user as the legitimate receiver, with RIS-assisted propagation and constrained UAV transmit power.
- DL Transmission:: The UAV transmit power is constrained by both average and peak power limits over time.
- DL Transmission:: All communication links use Rician fading, including a UAV-to-RIS channel whose small-scale fading depends on the UAV trajectory.
- DL Transmission:: The model includes RIS-reflected UAV-to-user and UAV-to-eavesdropper links alongside direct links with distance-dependent path loss.
- DL Transmission:: The UAV transmits to the ground user in the downlink, while achievable rates are derived from the received SNRs of the ground user and eavesdropper.
2) UL Transmission:
The uplink models the ground user as the legitimate transmitter and the UAV as the legitimate receiver, with RIS-assisted and direct paths to both legitimate and eavesdropping receivers.
- UL Transmission:: The ground-user-to-eavesdropper link is modeled with Rayleigh fading and a distance-dependent path loss.
- UL Transmission:: The ground-user-to-RIS-to-UAV and ground-user-to-UAV links are represented through distance-dependent path-loss models.
- UL Transmission:: In the uplink, the ground user transmits to the UAV, and received SNRs and achievable rates are specified for the UAV and eavesdropper.
- UL Transmission:: The uplink includes a ground-user-to-RIS-to-eavesdropper path whose large-scale fading and RIS phase-shift matrix enter the received-signal model.
B. CSI Assumption
The legitimate-link CSI is assumed available at a central controller, whereas eavesdropping-link CSI is modeled as uncertain within bounded error sets.
- B. CSI Assumption: The central controller is assumed to have perfect CSI for legitimate links, based on periodic updates, uplink pilots, and RIS-related channel-estimation techniques.
- B. CSI Assumption: The eavesdropping channels in the DL and UL are represented using a deterministic CSI-uncertainty model.
- B. CSI Assumption: The uncertainty sets contain all possible channel errors whose Euclidean norms are bounded by the radii ǫ1 and ǫ2.
- B. CSI Assumption: Because the UAV location changes, the worst-case eavesdropping-channel setup and uncertainty terms vary with the time slot.
C. Problem Formulation
The formulation defines worst-case secrecy rates for DL and UL transmissions and maximizes their average by jointly designing UAV trajectory, RIS phase shifts, and both transmit powers.
- Worst-case secrecy rates are defined separately for the DL and UL transmissions, using the nonnegative-part operator [x]+ ≜ max(x, 0).The average objective aggregates these slot-wise secrecy rates across the communication period.
- The optimization jointly selects the UAV trajectory, DL and UL RIS phase-shift matrices, UAV transmit power, and ground-user transmit power.The objective is the average worst-case secrecy rate Rsec.
- Although the constraints are convex, the objective is highly non-concave in the trajectory, phase shifts, and transmit powers.This non-concavity motivates the efficient solution algorithm developed next.
III. PROPOSED SOLUTION FOR JOINT UL/DL OPTIMIZATION
The joint UL/DL problem is reorganized to remove non-smoothness without performance loss, then solved through alternating optimization over power, RIS phase shifts, and UAV trajectory.
- The optimal UAV and ground-user transmit powers are zero when eavesdropping channels outperform legitimate channels in a time slot.This reformulation addresses the non-smoothness without performance loss.
- Alternating optimization divides the problem into transmit-power, RIS-phase-shift, and UAV-trajectory sub-problems.Each sub-problem optimizes its variables while holding the other two variable groups fixed.
- Sub-problem 1 optimizes p and g, sub-problem 2 optimizes Φd and Φu, and sub-problem 3 optimizes Q under the remaining variables fixed.
A. Solution to Sub-Problem 1
Sub-problem 1 handles transmit-power optimization by exploiting the objective structure and analytically addressing worst-case uncertain-channel terms before reformulation.
- The sub-problem is first expressed for transmit-power optimization after fixing the other design variables.
- Infinitely many CSI uncertainties make the power problem intractable directly, so the special structure of uncertain channel terms is exploited.
- The worst-case uncertain-channel expressions are reduced using magnitude and phase representations of channel-related vectors.
- Coherent addition of the terms determines the maximizing phase alignment for the uncertainty-related expression.
- The DL and UL secrecy-rate terms take logarithmic differences involving legitimate-channel and eavesdropping-channel coefficients.
B. Solution to Sub-Problem 2
Sub-problem 2 addresses uncertain eavesdropping CSI and non-convex RIS phase constraints using the S-Procedure, SCA, SDR, and Gaussian randomization.
- The S-Procedure converts infinitely many uncertainty-dependent inequalities into linear matrix inequalities under a stated existence condition.Nonnegative multipliers η1[n] and η2[n] certify the relevant implications.
- Semidefinite relaxation replaces the non-convex unit-modulus RIS constraints with relaxed matrix constraints.The reformulated problem also uses trace expressions.
- SCA approximates the non-concave logarithmic objective using first-order Taylor expansions at given points.The resulting approximated problem is convex and can be solved by standard solvers such as CVX.
- The relaxed solution may not be rank one, so Gaussian randomization recovers the DL and UL beamforming vectors.
C. Solution to Sub-Problem 3
Sub-problem 3 addresses UAV trajectory optimization under uncertain wiretap channels and trajectory-dependent, nonlinear UAV–RIS channel components. The authors approximate the difficult terms using the previous iteration and apply SCA to obtain a convex reformulation.
- C. Solution to Sub-Problem 3: For fixed RIS phases, transmit powers, and auxiliary variables, sub-problem 3 is formulated in terms of the UAV trajectory.
- C. Solution to Sub-Problem 3: The worst-case wiretap-channel setup is computed using the UAV trajectory from the previous iteration.
- C. Solution to Sub-Problem 3: The UAV–RIS LoS channel is complex and nonlinear in trajectory variables, so the previous trajectory provides an approximation for the current iteration.
- C. Solution to Sub-Problem 3: SCA handles the non-convex feasible regions and the non-concave term −log2(1 + ζ[n]) through first-order Taylor expansions.
- C. Solution to Sub-Problem 3: The resulting problem is convex and can be solved using the CVX solver.
D. Overall Algorithm
The proposed solutions to the three sub-problems are combined into an iterative overall algorithm. Its dominant computational cost comes from solving sub-problems 2 and 3, while the algorithm is observed to converge quickly.
- D. Overall Algorithm: The overall algorithm combines the proposed solutions to the three sub-problems and uses εc for convergence accuracy and jmax for the iteration limit.
- D. Overall Algorithm: Interior-point solutions for sub-problems 2 and 3 dominate the computational complexity of Algorithm 1.
- D. Overall Algorithm: The proposed algorithm can quickly converge, as observed in Fig. 2.
IV. SIMULATION RESULTS
Simulations evaluate the proposed JO algorithm against non-robust, heuristic-trajectory, and no-passive-beamforming benchmarks. Results show rapid convergence, improved secrecy-rate performance, trajectory adaptations across algorithms and UL/DL weighting, and robustness to CSI uncertainty.
- Simulation setup: The JO algorithm is evaluated against JO/NPB, JO/HT, and JO/NR benchmark schemes.JO/NPB omits passive beamforming; JO/HT uses a heuristic trajectory; JO/NR assumes exact eavesdropping-channel CSI.
- Convergence: Around 10 iterations are sufficient for the proposed algorithm to quickly converge, while average worst-case secrecy rate increases with flight time T.The observation is reported for w = 0.5, δ2_a = 0.5, and P̄ = Ḡ = 20 dBm.
- Trajectory behavior: At T = 124 s, JO and JO/NR trajectories arc toward locations between the ground user and RIS, whereas JO/NPB uses a more direct path near the ground user and away from the eavesdropper.All algorithms initially fly at Vmax, hover, and then fly to the final location at Vmax; JO and JO/NR balance direct and reflecting channel gains.
- Secrecy-rate performance: The JO algorithm exceeds all benchmark schemes in average worst-case secrecy rate as T increases.Longer hovering improves the average worst-case secrecy rate because the hovering location balances legitimate-link enhancement and eavesdropping-link weakening.
- Robustness: Average worst-case secrecy rates decrease as wiretap-channel CSI uncertainty increases, but JO maintains better performance than the benchmark algorithms.Large uncertainty can impair RIS passive beamforming, while JO/NPB is less affected because it excludes passive beamforming.
- UL/DL weighting: Increasing w makes downlink communication more dominant and leads JO to balance legitimate and wiretap links, producing more decentralized first-half paths and more direct final paths.For w = 0.1, uplink communication dominates; for sufficiently large w, such as w = 0.9, the UAV favors direct paths to avoid information leakage.
V. CONCLUSION
The paper develops a CSI-robust RIS-assisted UAV physical-layer secure communication design that jointly optimizes trajectory, passive beamforming, and transmit power for average worst-case secrecy rate. An efficient AO-based algorithm using SCA, the S-Procedure, and SDR improves secrecy performance, while multi-user extensions remain future work.
- The proposed design jointly optimizes the UAV trajectory, RIS passive beamforming, and legitimate transmit power under imperfect wiretap-channel CSI.The objective is to maximize the average worst-case secrecy rate for joint downlink and uplink transmissions.
- The non-convex optimization problem is approximately solved using alternating optimization with SCA, the S-Procedure, and SDR.
- RIS assistance substantially improves secrecy-rate performance in the considered UAV communication system.
- The proposed algorithm remains robust to inaccurate estimates of the wiretap-channel CSI.
- For multiple users, orthogonal access can reuse the single-user scheme with scheduling, whereas non-orthogonal access requires interference cancellation and is left for future work.