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Sum-Rate Maximization for IRS-Assisted UAV OFDMA Communication Systems

Zhiqiang Wei, Yuanxin Cai, Zhuo Sun, Derrick Wing Kwan Ng, Jinhong Yuan, Mingyu Zhou, Lixin Sun

arXiv:2008.09939v2cs.IT

TL;DR

The paper studies joint UAV trajectory, IRS scheduling, and resource-allocation design for maximizing sum-rate in IRS-assisted UAV OFDMA systems. It introduces a parametric approximation and reports sum-rate improvement from IRS deployment, with beamforming gain, UAV maneuverability, and IRS size affecting performance.

  • Problem

    Efficiently scheduling users to be assisted by the IRS remains an open design problem in UAV OFDMA communication systems.

  • Method

    The paper jointly designs UAV trajectory, IRS scheduling, and resource allocation for sum-rate maximization, using a parametric approximation to improve tractability.

  • Results

    The results demonstrate system sum-rate improvement through deploying an IRS in UAV OFDMA communication systems.

  • Takeaways & Limitations

    IRS beamforming gain and UAV maneuverability are both vital for improving communication performance, while IRS size affects the UAV trajectory's use of available degrees of freedom.

Abstract

from arXiv · show

In this paper, we consider the application of intelligent reflecting surface (IRS) in unmanned aerial vehicle (UAV)-based orthogonal frequency division multiple access (OFDMA) communication systems, which exploits both the significant beamforming gain brought by the IRS and the high mobility of UAV for improving the system sum-rate. The joint design of UAV's trajectory, IRS scheduling, and communication resource allocation for the proposed system is formulated as a non-convex optimization problem to maximize the system sum-rate while taking into account the heterogeneous quality-of-service (QoS) requirement of each user. The existence of an IRS introduces both frequency-selectivity and spatial-selectivity in the fading of the composite channel from the UAV to ground users. To facilitate the design, we first derive the expression of the composite channels and propose a parametric approximation approach to establish an upper and a lower bound for the formulated problem. An alternating optimization algorithm is devised to handle the lower bound optimization problem and its performance is compared with the benchmark performance achieved by solving the upper bound problem. Simulation results unveil the small gap between the developed bounds and the promising sum-rate gain achieved by the deployment of an IRS in UAV-based communication systems.

I. INTRODUCTION

UAV communications offer mobility and trajectory-design flexibility, but limited service duration, weak links, and hardware constraints restrict performance. This paper combines UAV mobility with IRS beamforming in an OFDMA system and develops parametric bounds whose simulations show improved sum-rate.

  • UAV communication opportunities: UAV trajectory and resource allocation can adapt to propagation and traffic demands, providing additional design flexibility for wireless communication systems.
  • Motivation: Existing UAV communication systems remain constrained by limited service duration and users with weak communication links.
  • IRS technology: IRSs can shape wireless propagation through programmable control of reflected-signal amplitude and phase.
  • Research gap: Most prior IRS studies focus on terrestrial communications, and narrow-band UAV-IRS works do not directly extend to wideband systems.
  • Proposed system: The proposed IRS-assisted UAV OFDMA system exploits IRS beamforming gain and UAV mobility for multi-user communication, differing fundamentally from narrow-band IRS models.
  • Optimization approach: A parametric approximation based on cosine fading patterns establishes upper and lower bounds, with an alternating optimization design for the lower-bound problem.
  • Results: Simulations reveal a reducible gap between the parametric bounds and show that deploying an IRS can substantially improve UAV OFDMA system sum-rate.

II. SYSTEM MODEL

The system models a single IRS-assisted UAV serving ground users through OFDMA, with jointly designed trajectory, IRS scheduling, and resource allocation. The IRS is represented by passive reflection units with controllable phase shifts, while UAV motion and propagation impose operational constraints.

  • OFDMA is adopted for multi-user communication, and the system model includes resource allocation and IRS scheduling variables.
  • The considered system uses a single UAV as an aerial base station providing downlink communication to ground users.
  • The IRS is installed on a building wall and consists of Mc×Mr passive reflection units arranged as a uniform planar array.
  • Each reflection unit independently re-scatters the incident signal using an amplitude a ∈[0, 1] and a controllable phase shift φmr,mc.
  • The UAV trajectory is discretized into N equal time slots, with q[n] = [x[n], y[n], z[n]]^T denoting its three-dimensional position.
  • The model constrains UAV altitude and treats ground-user and IRS locations as fixed, while neglecting signals reflected by the IRS two or more times.

B. Channel Model for IRS-assisted UAV OFDMA Communication Systems

The channel model combines broadband OFDMA propagation with direct and IRS-reflected links, producing frequency-selective composite fading. Because scattering makes the channel non-deterministic, the paper designs phase control and UAV trajectory using predictable LoS components while acknowledging implementation and modeling limitations.

  • The total bandwidth B is divided into NF OFDMA subcarriers with spacing Δf = B/NF, motivating a broadband channel model.
  • The model assumes a simple LoS UAV-to-IRS channel and leaves height-dependent path loss and phase optimization coupled with UAV trajectory for future work.
  • The IRS array response is frequency-flat, but the propagation phase term depends on subcarrier index and introduces non-uniform phase across subcarriers.
  • Rician fading models the UAV-to-user and IRS-to-user links, including scattering components that make the composite channel non-deterministic.
  • The proposed phase control and trajectory design use deterministic LoS components because they change slowly and can be predicted from UAV and user locations.
  • The IRS-assisted composite channel contains direct and reflected propagation paths whose different delays create frequency-selective fading.
  • The offline design requires user locations and Rician factors in advance, reducing CSI-acquisition overhead, but LoS-based operation may cause outage in random fading.

C. Resource Allocation and IRS Allocation Design

The system uses OFDMA scheduling, transmit-power allocation, and IRS-user assignment to serve users while exploiting IRS beamforming. IRS phase alignment is restricted to one selected user per time slot, limiting multi-user gains but simplifying design.

  • OFDMA assigns different users exclusively to subcarriers, eliminating inter-user interference in achievable rates.
  • Transmit powers p_k,i[n] are nonnegative and jointly constrained by the UAV’s per-slot maximum transmission power.
  • Each IRS phase shift affects all users and subcarriers because every PRU reflects the whole broadband signal.This creates frequency-selective coupling unlike narrow-band, single-user IRS-assisted UAV models.
  • Binary variables s_k[n] indicate whether user k is the IRS-assisted user in time slot n.The IRS reflection matrix is aligned with one selected user in each slot.
  • Aligning the IRS to multiple users could improve system performance but complicates UAV trajectory design.

III. PHASE CONTROL AT IRS AND THE COMPOSITE CHANNEL GAIN

The paper designs IRS phases from LoS geometry, yielding full beamforming gain for the scheduled user while producing cosine-pattern frequency and spatial selectivity in composite channels. This structure motivates tractable channel approximations for joint trajectory and resource design.

  • LoS-based IRS phase control depends on UAV and user locations and can therefore be designed offline with reduced signaling overhead.The control is independent of LoS phase terms and has a flat frequency response.
  • When user k is scheduled for IRS assistance, the composite channel achieves the full IRS beamforming gain.For other users, the gain depends on the azimuth and elevation AoD differences from the scheduled user.
  • The composite channel power gain combines the direct LoS path, the UAV-IRS-user LoS path, and their fluctuation caused by superposition.
  • The channel model generalizes prior IRS and UAV models and remains applicable to reverse links because it does not depend on communication direction.Removing the IRS recovers the conventional UAV channel, while blocking the direct link retains the reflected-path component.
  • Different subcarrier phase shifts create frequency-selective fading even when all subcarriers experience the same delay.The resulting fading follows a periodic cosine pattern whose period depends on the delay spread between the direct and reflected links.
  • The same cosine dependence on propagation-distance difference produces spatial-selective fading as the UAV moves along its trajectory.
  • The accurate composite-channel expressions are intractable for joint trajectory and resource-allocation design.The proposed phase control improves performance but introduces frequency-selective fading with a periodic cosine pattern.

IV. PROBLEM FORMULATION

The paper formulates a QoS-constrained sum-rate maximization over UAV trajectory, OFDMA resources, and IRS scheduling, then replaces difficult cosine channel gains with parametric upper and lower bounds. The resulting models simplify trajectory optimization while retaining the channel’s selective fading structure.

  • IV. PROBLEM FORMULATION: The optimization maximizes system sum-rate through joint UAV trajectory, resource allocation, and IRS scheduling design.The formulation includes user rates, transmit powers, scheduling variables, and IRS allocation.
  • A. Sum-rate Maximization Problem Formulation: The problem is a non-convex mixed-integer optimization because of binary scheduling variables and the non-convex achievable-rate function.Additional constraints impose OFDMA orthogonality, per-slot power limits, speed, endpoints, and altitude bounds.
  • A. Sum-rate Maximization Problem Formulation: QoS constraints enforce each user’s minimum average data rate over the whole flight period.
  • A. Sum-rate Maximization Problem Formulation: IRS deployment introduces spatial- and frequency-selective cosine fading in the composite channel, a feature not studied in the cited literature.
  • B. Parametric Bounds for the Formulated Problem: The paper establishes upper and lower bounds by replacing composite channel gains with parametric approximations.For non-IRS users, bounds use peak and trough levels; for IRS users, the cosine pattern is quantized into four fading modes.
  • B. Parametric Bounds for the Formulated Problem: The parametric models yield optimization problems P_LB and P_UB that provide lower and upper bounds for the formulated problem.The construction uses one approximation parameter and four fading modes for an IRS-assisted user.
  • B. Parametric Bounds for the Formulated Problem: Within each fading mode, the approximated channel gain is frequency-flat and trajectory design becomes more tractable because distances leave the cosine function.

V. SOLUTION OF THE LOWER BOUND PROBLEM

The lower-bound problem is solved by alternating between resource-allocation and IRS-scheduling optimization and UAV-trajectory optimization until convergence.

  • The lower-bound problem P_LB is divided into two subproblems and solved alternately until convergence.
  • Subproblem 1 optimizes resource allocation and IRS scheduling given the UAV trajectory.
  • Subproblem 2 designs the UAV trajectory given the resource-allocation and IRS-scheduling strategy.

A. Subproblem 1: Resource Allocation and IRS Scheduling Design

Subproblem 1 addresses resource allocation and IRS scheduling by relaxing binary assignments, transforming coupled variables, and solving the resulting convex formulation through dual decomposition. The resulting policies retain binary scheduling and exhibit multi-level water-filling power allocation, with IRS-assisted links gaining favorable scaling.

  • Relaxation and integrality: The binary subcarrier-allocation and IRS-scheduling variables are relaxed to [0,1] as time-sharing factors, yet the relaxation is tight and optimal solutions remain binary.The feasible set becomes a polyhedron, so optimal allocation, time-sharing, and scheduling variables lie at vertices.
  • Convex reformulation: Auxiliary variables ˜p_k,k′,i[n] = t_k,k′,i[n]p_k,i[n] decouple time-sharing from power allocation, yielding a convex reformulation solvable through Lagrange dual decomposition.The method alternates inner optimization over primal variables with outer optimization over Lagrange multipliers.
  • Power allocation: The optimal power allocation follows a multi-level water-filling principle governed by multipliers for minimum-rate and sum-power constraints.A larger ν_k allocates more power to satisfy user k’s minimum rate, whereas a larger ϱ_n allocates less power in time slot n.
  • Scheduling structure: At most one user is assigned to each subcarrier in a time slot, while t_k,k′,i[n] jointly determines subcarrier allocation and IRS scheduling.The coupling constraints enforce t_k,k′,i[n] = 1 if and only if both corresponding allocation and IRS-scheduling variables equal one.
  • IRS-assisted links: When M_r and M_c become large, the IRS-assisted composite channel gain is significantly larger, and fixed-rate transmission can reduce UAV transmit power according to an inverse-area scaling law.The cited scaling is 1/M^(2r)M^(2c) relative to the system without IRS.

B. Subproblem 2: UAV Trajectory Design

Subproblem 2 optimizes the UAV trajectory for fixed resource allocation and IRS scheduling. Successive convex approximation produces feasible iterates converging to a stationary point, and alternating the two subproblems yields the overall joint design.

  • Trajectory constraints: The UAV trajectory is constrained through slack variables and mobility-related constraints, with optimality requiring equality for constraints C15 and C16.The equality follows because bringing the UAV closer to ground users and the IRS increases system sum-rate.
  • Trajectory optimization: For fixed resource allocation and IRS scheduling, the trajectory subproblem remains non-convex and is addressed with successive convex approximation.Each iteration constructs a lower-bound problem using a first-order Taylor expansion around a feasible solution.
  • Overall algorithm: The overall algorithm alternates resource allocation and IRS scheduling optimization with trajectory optimization, starting from a feasible trajectory.Termination occurs at the maximum iteration count or when sum-rate improvement falls below a predefined threshold.
  • Convergence: Solving the convexified trajectory problem generates feasible solutions that converge to a stationary point of the trajectory subproblem.The lower bound is tightened iteratively by updating the approximation point.

VI. SIMULATION RESULTS

The paper evaluates the proposed scheme through simulations.

  • Simulation evaluation: Simulation results evaluate the proposed scheme’s performance.The evaluation is conducted through the optimization subproblems and associated system sum-rate calculations.

A. Simulation Setup and Baselines

The simulations compare IRS-assisted UAV OFDMA against non-IRS and straight-line baselines while examining the composite channel’s frequency and spatial selectivity. The IRS increases the assisted user’s channel gain, whereas the lower-bound approximation has an optimal parameter near α = 0.14.

  • Simulation Setup and Baselines: The considered setup uses K = 3 users and IRS areas ranging from 1 to 25 m^2, with system geometry and ground-user and IRS locations illustrated in Fig. 3.The simulation parameters are summarized in Table II.
  • Simulation Setup and Baselines: The evaluation compares the proposed IRS-assisted UAV OFDMA design with a non-IRS baseline and an IRS-assisted straight-line trajectory baseline.The non-IRS baseline is obtained by setting s_k[n] = 0 for all users and time slots.
  • B. Frequency Selective Fading: The IRS-assisted composite channel exhibits frequency-selective fading with a periodic cosine pattern across subcarriers, while non-IRS-assisted users are almost frequency-flat.The frequency selectivity is attributed to the induced reflected path through the IRS.
  • B. Frequency Selective Fading: The IRS substantially increases the composite channel power gain of the assisted user through passive beamforming compared with non-IRS-assisted users.The reported comparison is illustrated for user 1 assisted throughout the UAV flight.

C. Parametric Bounds and The Optimal Approximation Parameter

The proposed parametric bounds closely track the original optimization while the optimized IRS-assisted design improves sum-rate through coordinated trajectory, IRS, and resource decisions.

  • Optimal approximation parameter: At α = 0.14, the upper- and lower-bound problems share the same optimal approximation parameter.This setting is used in subsequent simulations.
  • Parametric bounds: 0.35 bit/s/Hz separates the upper and lower bounds at α = 0.14, approximately 4.5% of the optimal lower-bound performance.The result indicates a small performance gap between the bounds.
  • Optimal approximation parameter: The average system sum-rate first increases and then decreases as α grows because extreme α values loosen the cosine-fading lower bound.The best approximation parameter in this setup is α = 0.14.
  • IRS size and performance: Increasing the number of PRUs yields a significant sum-rate gain over baseline 2 through the IRS’s energy-focusing and passive-beamforming capabilities.The gain from deploying the IRS can dominate the gain from UAV trajectory optimization.

F. Outages in Rician Fading Channels

Rician scattering can produce subcarrier- and user-level outages because rates designed from deterministic LoS components may exceed instantaneous achievable rates. The IRS-assisted design is less sensitive to this randomness than baseline 2, while higher Rician factors yield higher average outage rates.

  • Outage sources: Rician fading may reduce achievable rates below their LoS counterparts, creating subcarrier-level and subsequently user-level outages.A rate-control parameter η is introduced to obtain a conservative solution.
  • Outage-aware rate control: The design allocates ηR_k,i,LoS[n] after optimizing with LoS rates to reduce possible subcarrier-level outage under channel randomness.The outage rate is evaluated using Monte Carlo experiments.
  • Rician-factor effects: Higher Rician factors produce higher average system outage rates because the LoS-based design more closely approximates the Rician-fading design.The evaluation uses η = 0.8 with p_max = 35 dBm, M_r = M_c = 200, N = 500, and R_min,k = 0.8 bit/s/Hz.
  • Comparison under fading: The proposed scheme and baseline 1 suffer less channel-randomness loss than baseline 2.IRS phase control focuses energy on the LoS path and suppresses energy through scattering paths, making the composite channel more deterministic.
  • IRS deployment location: With fixed IRS height and boundary placement, the optimal horizontal location is (x_R, y_R) = (200, 500) m, near the area with high user density.The study restricts the IRS to the service-area boundary so it remains in sight of the UAV and ground users.
  • Conclusion: The paper jointly designs UAV trajectory, IRS scheduling, and resource allocation using parametric approximation and alternating optimization.The approach addresses frequency- and spatial-selective fading introduced by the IRS.
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