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Robust Trajectory and Transmit Power Design for Secure UAV Communications
Miao Cui, Guangchi Zhang, Qingqing Wu, Derrick Wing Kwan Ng
TL;DR
Secure UAV-ground communication is challenging because line-of-sight broadcasting exposes information and eavesdropper locations are imperfectly known. The paper jointly designs robust trajectory and transmit power, using an iterative suboptimal algorithm, and reports significantly improved average worst-case secrecy rates over non-robust benchmarks.
Problem
Imperfect knowledge of multiple eavesdroppers’ locations makes secure UAV-ground communication require robust secrecy-rate optimization rather than idealized perfect-location design.
Method
The paper jointly designs UAV trajectory and transmit power by applying block coordinate descent, the S-Procedure, and successive convex optimization.
Results
The proposed robust joint design significantly improves average worst-case secrecy rate compared with benchmark schemes that assume perfect locations or ignore eavesdroppers.
Takeaways & Limitations
Accounting for eavesdropper-location uncertainty improves worst-case secrecy-rate performance in the considered UAV communication system.
Abstract
from arXiv · showhide
Unmanned aerial vehicles (UAVs) are anticipated to be widely deployed in future wireless communications, due to their advantages of high mobility and easy deployment. However, the broadcast nature of air-to-ground line-of-sight wireless chan- nels brings a new challenge to the information security of UAV- ground communication. This paper tackles such a challenge in the physical layer by exploiting the mobility of UAV via its trajectory design. We consider a UAV-ground communication system with multiple potential eavesdroppers on the ground, where the information on the locations of the eavesdroppers is imperfect. We formulate an optimization problem which maximizes the average worst-case secrecy rate of the system by jointly designing the robust trajectory and transmit power of the UAV over a given flight duration. The non-convexity of the optimization problem and the imperfect location information of the eavesdroppers make the problem difficult to be solved optimally. We propose an iterative suboptimal algorithm to solve this problem efficiently by applying the block coordinate descent method, S-procedure, and successive convex optimization method. Simulation results show that the proposed algorithm can improve the average worst-case secrecy rate significantly, as compared to two other benchmark algorithms without robust design.
I. INTRODUCTION
The paper addresses secure UAV-ground communication when multiple eavesdropper locations are imperfectly known. It jointly designs a robust UAV trajectory and transmit power to maximize average worst-case secrecy rate.
- Motivation: Physical layer security exploits UAV mobility by jointly optimizing trajectory and communication resources for secure wireless communication.UAV-ground links commonly have line-of-sight channels, while the broadcast nature of these links creates information-security challenges.
- Problem: Perfect eavesdropper-location knowledge is overly optimistic because silent eavesdroppers can cause location-estimation errors.Prior secure UAV designs assumed perfectly known eavesdropper locations, unlike the practical setting considered here.
- Problem: The system contains multiple ground eavesdroppers whose exact locations are unknown, while only approximate regions are available.The objective is to maximize average worst-case secrecy rate over a fixed flight duration under mobility and average and peak power constraints.
- Approach: The proposed efficient suboptimal algorithm combines block coordinate descent, the S-Procedure, and successive convex optimization.These methods address the problem’s non-convexity and semi-infinite constraints.
- Results: The robust algorithm significantly improves average worst-case secrecy rate compared with benchmarks assuming perfect location information or ignoring eavesdroppers.The comparison supports the value of explicitly accounting for location uncertainty.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The model represents uncertain ground eavesdropper locations, constant-altitude UAV motion, line-of-sight channels, and constrained transmit power. The resulting robust secrecy-rate maximization is difficult because of non-smoothness, non-concavity, and infinitely many uncertainty realizations.
- Uncertainty model: Each eavesdropper’s actual coordinates equal its estimated coordinates plus bounded estimation errors.The uncertainty set is a continuous circular region centered at the estimated location with radius Q_k.
- UAV mobility: The UAV flies at constant altitude H, and its trajectory is discretized into N sufficiently small time slots.Initial and final locations are fixed, with mobility constrained by the maximum speed v_max.
- Channel model: Alice-to-Bob and Alice-to-Eve channels are modeled as line-of-sight links.The LoS model is reported as a good practical approximation even at a moderate altitude such as 85 m.
- Power constraints: Transmit power is constrained by average and peak limits, with the average limit assumed smaller than the peak limit.P[n] denotes Alice’s transmit power in slot n, while P̄ and P_peak denote the corresponding average and peak limits.
- Problem formulation: The optimization jointly chooses UAV trajectory and transmit power to maximize average worst-case secrecy rate under mobility and power constraints.The objective compares the legitimate rate with the worst eavesdropper rate over the uncertainty sets, using the nonnegative-part operator.
- Problem formulation: Problem (10) is hard because its objective is non-smooth and non-jointly concave, while uncertainty creates infinitely many constraints.The paper therefore proceeds with an iterative computationally efficient suboptimal method.
III. PROPOSED ALGORITHM FOR PROBLEM (10)
The algorithm first removes objective non-smoothness through an equivalent formulation, then applies block coordinate descent to alternate transmit-power and trajectory optimization.
- Equivalent reformulation: Lemma 1 replaces the original non-smooth secrecy-rate problem with an equivalent optimization problem having the same optimal solution.The equivalence is established by zeroing transmit power in slots whose secrecy-rate difference is negative.
- Equivalent reformulation: The algorithm’s reformulation preserves feasibility and equality of the two problems’ optimal objective values.The proof constructs a feasible solution to the reformulated problem from an optimal solution of the original problem.
- Block coordinate descent: The reformulated problem remains non-convex but separates naturally into trajectory and transmit-power variable blocks.This structure enables iterative block coordinate descent.
- Block coordinate descent: Sub-problem 1 optimizes transmit power for a fixed trajectory, while sub-problem 2 optimizes trajectory for fixed transmit power.The two sub-problems are solved iteratively to address the reformulated problem.
A. Solution to Sub-Problem 1
Sub-problem 1 optimizes transmit power for a fixed UAV trajectory, using the secrecy-rate formulation and a bisection-determined parameter to satisfy average-power constraints.
- A. Solution to Sub-Problem 1: For fixed trajectory coordinates (x, y), sub-problem 1 optimizes the UAV transmit powers P over the time slots.The sub-problem is derived from the joint trajectory-and-power formulation.
- A. Solution to Sub-Problem 1: The paper notes that the transformed problem is equivalent when both formulations share the same optimal solution.
- A. Solution to Sub-Problem 1: The parameter λ ≥ 0 ensures that the average-power constraint is satisfied at the optimal solution and is determined by bisection search.
B. Solution to Sub-Problem 2
Sub-problem 2 optimizes the UAV trajectory for fixed transmit power by replacing infinitely many uncertainty constraints with tractable semidefinite constraints and iteratively convexifying the problem.
- B. Solution to Sub-Problem 2: With transmit power fixed, the trajectory sub-problem is reformulated using slack variables and retains non-convex objective and constraint terms.The variables u and t support the reformulation, while logarithmic and squared-coordinate terms remain non-convex.
- B. Solution to Sub-Problem 2: The continuous eavesdropper-location constraints are converted into equivalent constraints through the S-Procedure and nonnegative slack variables ξ_k.
- B. Solution to Sub-Problem 2: First-order Taylor expansions around a feasible point produce approximations for the logarithmic and quadratic terms.
- B. Solution to Sub-Problem 2: The resulting semidefinite programming problem can be solved optimally using an interior-point method.
- B. Solution to Sub-Problem 2: Algorithm 1 alternates trajectory optimization and power optimization after initialization, repeating until the fractional objective increase falls below ε.
- B. Solution to Sub-Problem 2: The approximation uses lower bounds that preserve feasibility and yield a nondecreasing objective value relative to the previous feasible point.
C. Overall Algorithm
The overall algorithm alternates the power and trajectory updates until convergence, producing a suboptimal solution with polynomial-time subproblem solutions.
- C. Overall Algorithm: Algorithm 1 solves problems (12) and (27) alternately and iteratively until convergence.
- C. Overall Algorithm: Because the objective value is nondecreasing and the optimal value is finite, the algorithm is guaranteed to converge to a suboptimal solution.
- C. Overall Algorithm: The method can obtain its solution in polynomial time, with complexity depending on the iteration number Nite.
IV. SIMULATION RESULTS
Simulations compare robust joint design with non-robust and best-effort benchmarks under uncertain eavesdropper locations. The robust method changes its trajectory to manage uncertainty and achieves the strongest secrecy-rate performance.
- IV. SIMULATION RESULTS: The simulations compare robust joint trajectory-and-power design against non-robust joint design and best-effort trajectory design with equal transmit power.
- IV. SIMULATION RESULTS: When flight duration is small, robust and non-robust trajectories are similar because limited time restricts trajectory flexibility.
- IV. SIMULATION RESULTS: At sufficiently large flight duration, the robust algorithm places its hovering point left of Bob, unlike the non-robust algorithm, which hovers directly above Bob.
- IV. SIMULATION RESULTS: The robust trajectory moves closer to Eve 1 and farther from Eve 2 to balance the legitimate link and both eavesdropping links under worst-case uncertainty.
- IV. SIMULATION RESULTS: Average worst-case secrecy rates increase with flight duration and average power, while the robust algorithm significantly outperforms both benchmark algorithms.
- IV. SIMULATION RESULTS: At high average power, secrecy rates saturate because the maximization becomes independent of transmit power and depends only on the UAV trajectory.
V. CONCLUSION
The paper addresses secure UAV communication with uncertain eavesdropper locations through robust joint trajectory and transmit-power design. The proposed algorithm improves worst-case secrecy-rate performance over benchmarks that ignore location uncertainty.
- The system handles imperfect knowledge of eavesdropper locations in a practical secure UAV communication scenario.
- A robust joint design optimizes the UAV trajectory and transmit power to maximize average worst-case secrecy rate.
- The design respects the UAV’s mobility constraints together with average and peak transmit-power constraints.
- The proposed algorithm improves worst-case secrecy-rate performance significantly compared with two benchmarks that do not consider eavesdropper-location uncertainties.