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Reconfigurable Intelligent Surface Assisted UAV Communication: Joint Trajectory Design and Passive Beamforming
Sixian Li, Bin Duo, Xiaojun Yuan, Ying-Chang Liang, Marco Di Renzo
TL;DR
Urban obstructions can degrade UAV communication links, motivating RIS assistance for improving propagation and achievable rate. The paper jointly designs UAV trajectory and RIS passive beamforming, deriving phase alignment for a fixed trajectory and optimizing trajectory with SCA; simulations show substantial gains over counterpart approaches.
Problem
Urban propagation environments can block the UAV-to-user LoS link, motivating a RIS-assisted system that improves communication quality.
Method
The paper jointly optimizes UAV trajectory and RIS passive beamforming, using a closed-form phase-shift solution followed by SCA-based trajectory optimization.
Results
The proposed joint trajectory-and-passive-beamforming algorithm significantly exceeds benchmark algorithms in average achievable rate.
Takeaways & Limitations
Joint optimization lets the ground user benefit from channel gains from both the UAV and RIS, producing the largest average achievable rate among the considered approaches.
Abstract
from arXiv · showhide
Thanks to the line-of-sight (LoS) transmission and flexibility, unmanned aerial vehicles (UAVs) effectively improve the throughput of wireless networks. Nevertheless, the LoS links are prone to severe deterioration by complex propagation environments, especially in urban areas. Reconfigurable intelligent surfaces (RISs), as a promising technique, can significantly improve the propagation environment and enhance communication quality by intelligently reflecting the received signals. Motivated by this, the joint UAV trajectory and RIS's passive beamforming design for a novel RIS-assisted UAV communication system is investigated to maximize the average achievable rate in this letter. To tackle the formulated non-convex problem, we divide it into two subproblems, namely, passive beamforming and trajectory optimization. We first derive a closed-form phase-shift solution for any given UAV trajectory to achieve the phase alignment of the received signals from different transmission paths. Then, with the optimal phase-shift solution, we obtain a suboptimal trajectory solution by using the successive convex approximation (SCA) method. Numerical results demonstrate that the proposed algorithm can considerably improve the average achievable rate of the system.
I. INTRODUCTION
The paper motivates RIS-assisted UAV communication for urban environments and models joint trajectory and passive beamforming to improve average achievable rate. It describes the system, channel assumptions, mobility constraints, and optimization objective.
- RIS-assisted communication: RIS elements induce controllable phase shifts that align signals from different paths, increasing received signal energy and achievable rate with low energy consumption.
- Motivation: UAVs provide flexible, low-cost communication through mobility and LoS transmission, but urban obstructions can severely degrade UAV-to-user links.
- System model: The system comprises a rotary-wing UAV, a ground user, and a building-mounted RIS, with the UAV following a discretized horizontal trajectory at fixed altitude.
- Constraints: The UAV obeys per-slot displacement and endpoint constraints, while the RIS uses continuously controllable element phase shifts within [0, 2π).The maximum horizontal displacement is D = vmaxδt, with initial and final locations fixed by q0 and qF.
- Channel model: The U-R link is modeled as LoS, the blocked U-G link as Rayleigh fading, and the R-G link as Rician fading because of its additional LoS path.
- Optimization objective: The communication objective is to maximize average achievable rate over N time slots through joint optimization of the UAV trajectory and RIS phase-shift matrices.
B. Problem Formulation
The problem formulation maximizes average achievable rate by jointly optimizing UAV trajectory and RIS phase shifts under mobility and phase-shift constraints. Although the constraints are convex, the objective is non-convex in both variable sets.
- Problem Formulation: The optimization variables are the UAV trajectory Q and RIS phase-shift matrices Φ across all N time slots.
- Problem Formulation: The objective maximizes average achievable rate subject to UAV mobility constraints and RIS phase-shift bounds 0 ≤ θ_i[n] < 2π.
- Problem Formulation: Despite convex constraints, the objective is non-convex with respect to Q and Φ, so the paper develops an efficient algorithm for a suboptimal solution.
III. PROPOSED ALGORITHM
The proposed algorithm decomposes the non-convex joint design into passive beamforming and UAV trajectory optimization, solving them through phase alignment and successive convex approximation.
- A. Optimal Φ for Given Q: Passive beamforming aligns signals from the U-G and U-R-G paths for any fixed UAV trajectory, maximizing received signal energy.The resulting phase-shift solution has a closed form and transforms the joint problem into trajectory optimization.
- B. Optimization of Q: The trajectory subproblem remains non-convex, so slack variables u and v are introduced to reformulate distance-related terms.The reformulation preserves the optimal solution because the distance constraints hold with equality at optimum.
- B. Optimization of Q: Lemma 1 establishes joint convexity of the relevant logarithmic slack term with respect to u[n] and v[n].This enables first-order Taylor expansions as global underestimators for convex approximation.
- C. Overall Algorithm: Algorithm 1 alternates trajectory and phase-shift updates, then refreshes the average achievable rate using the current solution.The iterations initialize Q, Φ, u, and v before repeatedly solving the trajectory and passive-beamforming subproblems.
- B. Optimization of Q: The approximated trajectory problem is convex and can be solved efficiently using standard solvers such as CVX.The successive convex approximation step produces the trajectory update used in the proposed algorithm.
C. Overall Algorithm
The overall algorithm iteratively updates the UAV trajectory and RIS phase shifts, with convergence controlled by an accuracy parameter.
- C. Overall Algorithm: The average achievable rate is guaranteed to be non-decreasing over the algorithm’s iterations.The iteration process alternates trajectory optimization, phase-shift updating, and rate evaluation.
- C. Overall Algorithm: The proposed algorithm has complexity O(KiteN^3.5), where Kite is the total number of iterations.The parameter ϵ controls convergence accuracy.
IV. NUMERICAL RESULTS
Simulations compare joint trajectory and passive-beamforming optimization with trajectory-only and heuristic benchmarks. The joint method achieves the strongest average achievable-rate performance.
- IV. NUMERICAL RESULTS: The evaluation compares JT&PB with T/NPB, HT/PB, and HT/NPB benchmark algorithms.The benchmarks respectively omit passive beamforming, use a heuristic trajectory with passive beamforming, or use a heuristic trajectory without passive beamforming.
- IV. NUMERICAL RESULTS: At T = 740 s, the three benchmark algorithms use the same hovering location above the ground user and identical trajectories.The heuristic trajectory flies to the user, hovers as long as possible, and then flies to qF at vmax.
- IV. NUMERICAL RESULTS: At T = 740 s, JT&PB follows an arc path and selects a different hovering location by balancing U-G and U-R-G channel gains.This trajectory differs from all benchmark trajectories.
- IV. NUMERICAL RESULTS: The JT&PB algorithm achieves considerable average achievable-rate improvement over all benchmark algorithms.Figure 3 reports average achievable rates versus T, with JT&PB significantly exceeding the other algorithms.
- IV. NUMERICAL RESULTS: Average achievable rates of the benchmark schemes increase with T because larger mission durations provide more time for transmission near hovering locations.The joint method obtains the largest average achievable rate by exploiting channel gains from both the UAV and RIS.
APPENDIX
The appendix proves convexity of a function by analyzing its first- and second-order partial derivatives and showing that its Hessian is positive definite.
- APPENDIX: The proof begins by deriving the first-order partial derivatives of f(x, y) with respect to x and y.These derivatives support the subsequent Hessian-based convexity argument.
- APPENDIX: The second-order partial derivatives are then derived to construct the Hessian matrix of f(x, y).The Hessian provides the criterion used to establish convexity.
- APPENDIX: Because the relevant cross-partial condition is positive, the Hessian matrix ∇2f is positive definite.Positive definiteness implies that f(x, y) is convex.
SUPPLEMENTARY INFORMATION
The supplementary proof establishes positivity properties for derivatives of f and concludes that its Hessian matrix is positive definite.
- The proof defines η using ln 2 and three positive terms involving x, y, and the path loss exponent κ.The supplied passage presents the definition in a truncated form.
- Under K1 > 0, K2 > 0, K3 > 0, x > 0, y > 0, and κ > 0, the proof analyzes the second derivatives of f.These positivity assumptions support the derivative-sign analysis.
- The proof concludes that ∂²f/∂y∂x > 0 and that the Hessian matrix ∇²f is positive definite.This conclusion follows after comparing the terms in equations (28) and (29) and noting the signs of the remaining terms.