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Common Throughput Maximization in UAV-Enabled OFDMA Systems with Delay Consideration
Qingqing Wu, Rui Zhang
TL;DR
The paper addresses whether UAV mobility can improve communication under heterogeneous delay requirements. It jointly optimizes UAV trajectory and OFDMA allocation, finding that stricter MRR constraints reduce max-min throughput and mobility gains.
Problem
Whether UAV mobility provides performance gain when users have heterogeneous, delay-constrained communication requirements remains unknown.
Method
The paper jointly optimizes UAV trajectory and OFDMA resource allocation using a parameter-assisted block coordinate descent method and an MRR formulation.
Results
Max-min throughput generally decreases with users’ MRRs, while throughput gains from UAV mobility become less significant as user delay requirements increase.
Takeaways & Limitations
The results reveal a throughput-delay tradeoff in UAV-enabled communications and support the effectiveness of the proposed designs.
Takeaways & Limitations
The coordinate descent method may fail to update the UAV trajectory when solving the formulated problem.
Abstract
from arXiv · showhide
The use of unmanned aerial vehicles (UAVs) as communication platforms is of great practical significance in future wireless networks, especially for on-demand deployment in temporary events and emergency situations. Although prior works have shown the performance improvement by exploiting the UAV's mobility, they mainly focus on delay-tolerant applications. As delay requirements fundamentally limit the UAV's mobility, it remains unknown whether the UAV is able to provide any performance gain in delay-constrained communication scenarios. Motivated by this, we study in this paper a UAV-enabled orthogonal frequency division multiple access (OFDMA) network where a UAV is dispatched as a mobile base station (BS) to serve a group of users on the ground. We consider a minimum-rate ratio (MRR) for each user, defined as the minimum instantaneous rate required over the average achievable throughput, to flexibly adjust the percentage of its delay-constrained data traffic. Under a given set of constraints on the users' MRRs, we aim to maximize the minimum average throughput of all users by jointly optimizing the UAV trajectory and OFDMA resource allocation. First, we show that the max-min throughput in general decreases as the users' MRR constraints become more stringent, which reveals a fundamental throughput-delay tradeoff in UAV-enabled communications. Next, we propose an iterative parameter-assisted block coordinate descent method to optimize the UAV trajectory and OFDMA resource allocation alternately, by applying the successive convex optimization and the Lagrange duality, respectively. Furthermore, an efficient and systematic UAV trajectory initialization scheme is proposed based on a simple circular trajectory. Finally, simulation results are provided to verify our theoretical findings and demonstrate the effectiveness of our proposed designs.
I. INTRODUCTION
UAV-enabled communications offer flexible, mobile deployment, but trajectory design must balance throughput gains against user delay requirements. This paper formulates a joint UAV trajectory and OFDMA resource-allocation problem with MRR constraints and develops methods to solve it.
- Motivation: UAVs provide flexible three-dimensional deployment and can improve communication links through controlled mobility, especially when ground infrastructure is insufficient.Their airborne role is particularly relevant to temporary events and emergencies.
- Related work: Prior trajectory designs either omit mobility, restrict UAV communication to stop points, or assume predetermined trajectories, limiting mobility optimization.These limitations motivate joint trajectory and adaptive communication design.
- Research gap: UAV mobility can increase throughput, but the gain comes at the cost of user communication delay because users may wait for the next flight period.Prior work mainly leaves instantaneous rates unguaranteed, motivating delay-aware analysis.
- Problem formulation: The paper introduces MRR constraints and jointly optimizes UAV trajectory and OFDMA resource allocation to maximize the minimum average throughput of ground users.MRR represents the minimum instantaneous rate required relative to average achievable throughput.
- Main findings: The system max-min throughput is non-increasing with users’ MRRs, so stricter delay constraints reduce the throughput gain of mobile UAVs over static UAVs.This establishes a throughput-delay tradeoff in UAV-enabled communications.
- Solution approach: A parameter-assisted block coordinate descent algorithm alternates resource allocation and trajectory optimization, complemented by successive convex optimization and circular-trajectory initialization.The proposed design addresses ineffective trajectory updates that can occur with conventional block coordinate descent under MRR constraints.
A. System Model
The system models a UAV as a mobile aerial base station serving ground users through OFDMA over a periodically repeated, speed-limited trajectory. It supports mixed delay-constrained and delay-tolerant traffic using per-user minimum-rate ratios.
- System architecture: The UAV serves a group of ground users as an aerial base station using OFDMA resource allocation.Users receive fractions of bandwidth and transmit power, enabling simultaneous communication during the UAV flight period.
- UAV mobility: The UAV follows a horizontal trajectory at fixed altitude H, returns to its initial location after period T, and obeys maximum speed Vmax.The trajectory is discretized into N equally spaced time slots, with Smax = Vmaxδt limiting movement per slot.
- Channel model: Channel quality mainly depends on UAV-user distance under a free-space path-loss model, with receiver Doppler effects assumed perfectly compensated.The air-to-ground links are treated as predominantly line-of-sight, supporting the distance-based simplification.
- OFDMA resources: The model approximates bandwidth fractions as continuous variables between 0 and 1 and constrains their sum across users in each time slot.This approximation applies when the number of OFDMA subcarriers is sufficiently large.
- Delay model: Each user’s MRR θk specifies the fraction of average throughput that must be supported in every time slot, while the remainder is delay-tolerant.θk = 0 represents entirely delay-tolerant service, whereas θk = 1 represents entirely delay-constrained service.
B. Problem Formulation
The paper formulates max-min average-throughput optimization under users’ MRR constraints, jointly selecting OFDMA allocation and UAV trajectory. It proves that stricter MRR requirements generally reduce the optimal objective value.
- Optimization objective: The objective maximizes the minimum average throughput across users by jointly optimizing bandwidth allocation, power allocation, and UAV trajectory.The MRR constraints apply to all users while the design variables include A, P, and Q.
- Problem structure: The resulting problem is non-convex because rate and throughput constraints are not jointly concave in allocation and trajectory variables.Even with fixed trajectory, the MRR constraint remains non-convex because average throughput appears on its left-hand side.
- Reformulation: The reformulated problem generally has an equivalent optimum when all users achieve equal average throughput.Otherwise, resources can be shifted toward a lower-throughput user without violating total bandwidth and power constraints.
- Throughput-delay tradeoff: The maximum objective value is element-wise non-increasing with respect to the users’ MRRs.Thus, increasing any user’s required minimum-rate ratio cannot improve the optimized max-min throughput.
- Throughput-delay tradeoff: Stricter MRR requirements restrict the UAV’s ability to approach individual users while maintaining rates for users elsewhere, lowering max-min average throughput.The paper identifies this mobility restriction as the mechanism behind the throughput-delay tradeoff.
III. PROPOSED SOLUTION
The proposed solution alternates between OFDMA resource allocation and UAV trajectory optimization using block coordinate descent. Each subproblem is solved with a method suited to its structure.
- III. PROPOSED SOLUTION: The algorithm alternately optimizes bandwidth and power allocation for a fixed trajectory and the UAV trajectory for fixed resource allocation.The alternating process continues until convergence is achieved.
A. Joint Bandwidth and Power Allocation
For fixed trajectory, the paper solves bandwidth and power allocation through Lagrange duality and convex subproblems. The resulting algorithm has total complexity O(K^4N^4).
- Convexity and duality: The fixed-trajectory bandwidth and power allocation subproblem is convex because its rate expression is jointly concave in αk[n] and pk[n].This permits the use of strong duality and convex optimization tools.
- Dual decomposition: Lagrange duality decomposes the allocation problem into one η subproblem and KN independent user-time-slot subproblems.The dual variables are updated using subgradients and a constrained ellipsoid method.
- Resource allocation: The optimal power allocation has a multi-level water-filling structure, while bandwidth allocation is obtained from a linear program.Power is derived from KKT conditions, and the resulting bandwidth problem is solved over αk[n].
- Primal recovery: The dual-optimal maximizers are not unique, so additional steps are required to construct a primal-feasible optimal allocation.In particular, η⋆ and A⋆ maximizing the Lagrangian need not be unique, and the resulting allocation cannot be taken directly as the primal optimum.
- Dual optimization: The dual function is convex but generally non-differentiable, so the constrained ellipsoid method updates dual variables toward the optimum.The paper reports global convergence for this dual-variable update procedure.
- Complexity: O(K^4N^4) is the total computational complexity of Algorithm 1.The dominant contribution comes from the ellipsoid-based dual optimization steps.
B. UAV Trajectory Optimization
The UAV trajectory subproblem is non-convex, so the design replaces selected constraints with Taylor-based lower bounds to obtain a tractable convex approximation and lower-bound solution.
- For fixed bandwidth and power allocation, the method optimizes the UAV trajectory separately.
- The trajectory subproblem is generally non-convex because key constraint left-hand sides are not concave in the UAV position.
- Successive convex optimization uses first-order Taylor expansions as global under-estimators at a given local trajectory point.
- The Taylor-based replacements produce convex quadratic constraints and a linear constraint, yielding a QCQP solvable in polynomial complexity by standard convex solvers.
- The approximated problem’s optimal objective value is a lower bound on the corresponding original trajectory problem.
C. Overall Algorithm Design
The paper develops a parameter-assisted block coordinate descent algorithm that alternates resource allocation and trajectory optimization while gradually tightening temporary MRRs.
- The algorithm alternately solves the resource-allocation and trajectory subproblems with the other variable block fixed.
- Direct block coordinate descent can update the UAV trajectory ineffectively because MRR constraints restrict simultaneous distance reduction to users.
- The proposed parameter-assisted method introduces temporary MRRs above the target values and decreases them gradually during iterations.
- Relaxing the temporary MRR constraints permits more effective trajectory updates while eventually reaching the target MRRs and preserving feasibility.
- The objective is non-decreasing and bounded above, so the algorithm converges to a feasible solution, although the solution is generally suboptimal.
- Simulations compare the proposed algorithm with benchmark schemes to validate its effectiveness.
D. UAV Initial Trajectory and Users’ MRR Initialization
The initialization scheme uses a circular UAV trajectory centered at the users’ geometry center, with its radius and initial MRRs adapted to the target MRR constraints.
- The proposed circular initialization scheme includes the no-MRR case as a special case.
- The initial circle center is set to the geometry center of all ground users.
- As MRR targets increase, the covered trajectory area and initial circle radius decrease; with all targets equal to one, the radius is zero.
- The initialization selects the no-MRR radius using user coverage and the UAV speed constraint, then constructs the sampled circular trajectory.
- The radius formula yields the no-MRR radius when θk = 0 for all users and zero when θk = 1 for all users.
- Users without MRR constraints receive initial MRR zero, whereas users with positive targets receive initial MRRs selected to mitigate ineffective trajectory updates.
IV. NUMERICAL RESULTS
Numerical experiments validate the joint OFDMA resource-allocation and UAV-trajectory design, as well as the throughput-delay tradeoff, in a four-user UAV-enabled system.
- The numerical results evaluate the proposed joint OFDMA resource allocation and UAV trajectory design and the fundamental throughput-delay tradeoff.
- The simulation system contains K = 4 ground users located in a horizontal plane.
- The UAV flies at fixed altitude H = 500 m with total bandwidth B = 10 MHz.
- Unless otherwise specified, the simulations use Pmax = 0.1 W, Vmax = 50 m/s, T = 270 s, and N = 540.
- Trajectories are sampled every 4 s, with sampled points marked by triangles.
A. UAV Trajectory and Max-min Throughput versus Homogeneous MRRs
Under homogeneous MRR constraints, stricter instantaneous-rate requirements progressively restrict UAV mobility and reduce max-min throughput, while mobility gains depend on available delay tolerance and flight time.
- Trajectory behavior: As homogeneous MRR increases, the optimized UAV trajectory shrinks from broad paths toward a fixed point and becomes more restricted around users.The trajectory changes from sequential user visits at θ = 0 toward a fixed point at θ = 1.
- Throughput effects: Meeting MRR constraints consumes power and bandwidth, becoming a throughput bottleneck that worsens with larger MRR or inter-user distance.
- Trajectory behavior: The UAV trajectories are symmetric across users when all users share the same MRR constraint and average throughput.
- Throughput effects: Max-min average throughput decreases with MRR for mobile trajectories, confirming a fundamental throughput-delay tradeoff.
- Trajectory comparisons: At small MRR, the proposed trajectory outperforms circular and static trajectories, whereas fly-and-hover is close initially but loses throughput at large MRR.Fly-and-hover becomes inefficient because its time-varying channels are highly asymmetric under stringent MRR requirements.
B. UAV Trajectory and Max-min Throughput versus Heterogeneous MRRs
With heterogeneous MRRs, the UAV adapts its trajectory toward users with more stringent requirements, producing asymmetric paths and a less pronounced throughput decrease when only some users’ MRRs increase.
- Trajectory adaptation: As users 3 and 4 receive larger equal MRRs, the optimized UAV trajectory moves closer to them to satisfy their stricter minimum-rate requirements.
- Trajectory adaptation: Different MRR priorities produce asymmetric trajectories, unlike the symmetric trajectory obtained under homogeneous constraints.
- Trajectory adaptation: Users 1 and 2 have worse air-to-ground channels along the trajectory, so the UAV slows or hovers near them to preserve equal average throughput.
- Throughput effects: As θ3 = θ4 increases with θ1 = θ2 = 0.4 fixed, max-min average throughput decreases gradually but less significantly than when all users’ MRRs increase.
- Problem and design: The study jointly optimizes UAV trajectory and OFDMA resource allocation for users with heterogeneous communication-delay requirements.
- Optimization method: The proposed parameter-assisted block coordinate descent approach addresses the difficulty of directly applying conventional block coordinate descent, which may fail to update the trajectory.