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Optimal 3D-Trajectory Design and Resource Allocation for Solar-Powered UAV Communication Systems

Yan Sun, Dongfang Xu, Derrick Wing Kwan Ng, Linglong Dai, Robert Schober

arXiv:1808.00101v1cs.ITmath.OC

TL;DR

The paper addresses joint 3D trajectory and wireless resource allocation for sustainable solar-powered UAV communications under channel knowledge and energy constraints. It solves the offline problem optimally with monotonic optimization, develops online schemes, and finds that the UAV climbs for solar harvesting before descending to reduce communication path loss.

  • Problem

    The paper studies how to jointly design a solar-powered UAV’s 3D trajectory, power adaptation, and subcarrier allocation to maximize system sum throughput.

  • Method

    The paper solves the offline mixed-integer non-convex allocation problem using monotonic optimization and develops optimal and iterative suboptimal online schemes.

  • Results

    The proposed suboptimal online scheme closely approaches the offline scheme’s performance, while the optimal designs reveal altitude-dependent harvesting and communication behavior.

  • Takeaways & Limitations

    The solar-powered UAV first climbs to harvest sufficient solar energy, then descends to reduce communication-link path loss.

Abstract

from arXiv · show

In this paper, we investigate the resource allocation algorithm design for multicarrier solar-powered unmanned aerial vehicle (UAV) communication systems. In particular, the UAV is powered by solar energy enabling sustainable communication services to multiple ground users. We study the joint design of the three-dimensional (3D) aerial trajectory and the wireless resource allocation for maximization of the system sum throughput over a given time period. As a performance benchmark, we first consider an offline resource allocation design assuming non-causal knowledge of the channel gains. The algorithm design is formulated as a mixed-integer non-convex optimization problem taking into account the aerodynamic power consumption, solar energy harvesting, a finite energy storage capacity, and the quality-of-service (QoS) requirements of the users. Despite the non-convexity of the optimization problem, we solve it optimally by applying monotonic optimization to obtain the optimal 3D-trajectory and the optimal power and subcarrier allocation policy. Subsequently, we focus on online algorithm design which only requires real-time and statistical knowledge of the channel gains. The optimal online resource allocation algorithm is motivated by the offline scheme and entails a high computational complexity. Hence, we also propose a low-complexity iterative suboptimal online scheme based on successive convex approximation. Our results unveil the tradeoff between solar energy harvesting and power-efficient communication. In particular, the solar-powered UAV first climbs up to a high altitude to harvest a sufficient amount of solar energy and then descents again to a lower altitude to reduce the path loss of the communication links to the users it serves.

I. INTRODUCTION

The paper develops sustainable solar-powered UAV communication by jointly optimizing 3D trajectories and wireless resources under energy, aerodynamic, storage, and QoS constraints. It addresses limitations of battery-powered and prior solar-powered designs through optimal offline and practical online algorithms.

  • Motivation: Battery-powered UAV designs have constrained operation time and may require frequent returns to base for recharging, limiting stable and sustainable services.These constraints can create a system performance bottleneck.
  • Motivation: Solar-powered UAVs can harvest solar energy for long-endurance flight, but harvested energy depends on altitude and cloud conditions.Prototypes demonstrated continuous flight for 28 hours, while clouds reduce received solar energy flux.
  • Motivation: Higher altitude can increase solar harvesting but also causes more severe air-to-ground path loss, creating a tradeoff between energy harvesting and communication performance.This tradeoff is absent from conventional UAV communication systems.
  • Research gap: Earlier solar-powered resource allocation work used a constant aerodynamic power model, omitted QoS requirements, and optimized positioning rather than full 3D aerial trajectories.Constant aerodynamic consumption is invalid for realistic UAVs with non-constant speed because aerodynamic power depends significantly on flight velocity.
  • Contributions: The paper formulates offline joint trajectory and resource allocation as a finite-horizon combinatorial non-convex problem and solves it optimally using monotonic optimization.The formulation includes solar harvesting, aerodynamic power, energy-storage dynamics, and user QoS requirements.
  • Contributions: For online operation, the paper develops an optimal policy and a lower-complexity successive-convex-approximation scheme that closely approaches offline performance and improves average throughput over two baselines.The online designs use causal channel information, while the optimal online policy has high computational complexity.

II. NOTATION AND SYSTEM MODEL

The system models a solar-powered multicarrier UAV serving multiple ground users over discretized 3D trajectories, with wireless channels, solar harvesting, and aerodynamic flight dynamics represented across time slots.

  • System architecture: The MC-UAV system comprises one UAV-mounted transmitter and K downlink users, with the UAV equipped with solar panels and an onboard battery.The battery powers both communication services and flight operation.
  • Wireless model: The wideband channel divides bandwidth W into NF orthogonal subcarriers, each allocated to at most one user under the adopted multiple-access model.The framework can be extended to NOMA using a related allocation design.
  • Trajectory model: The operation period T is discretized into NT equal-length time slots, each lasting ΔT, with UAV positions treated as approximately constant within a slot.The trajectory is represented through discrete waypoints.
  • Wireless model: The UAV-to-user path loss follows ζ∥r[n] − r_k∥^-2, where r[n] gives the UAV’s 3D position and z[n] is its altitude.The channel coefficient captures shadowing and small-scale multipath fading.
  • Wireless model: The model includes AWGN, subcarrier transmit powers, channel gains, and slot-wise channel constancy when UAV displacement is sufficiently small.For the stated example, channel constancy requires displacement below half a carrier wavelength.
  • Energy model: Solar output is represented using actual power and a lower bound, while cloud attenuation affects harvested energy but is assumed negligible for RF signals below the stated carrier-frequency regime.Figure 2 illustrates the actual solar output and its lower bound.

C. Solar Energy Harvesting

The section models solar harvesting and aerodynamic consumption jointly, exposing a flight-planning tradeoff: higher altitude improves solar harvesting but worsens communication path loss.

  • Solar energy harvesting: Cloud attenuation reduces harvested solar energy, so solar-panel output depends on the optical absorption coefficient and the distance light travels through clouds.The attenuation is modeled through βc and dcloud.
  • Solar energy harvesting: Solar-panel output is modeled as a piecewise function of altitude, increasing exponentially inside clouds and becoming constant below or above the cloud.The nonsmooth output motivates adopting a lower bound for subsequent resource-allocation design.
  • Solar energy harvesting: The solar model uses harvesting efficiency η, panel area S, and average solar radiation intensity G to characterize electrical output power.Cloud-related parameters adjust the lower-bound approximation.
  • Altitude tradeoff: Higher altitude can increase solar harvesting but also increases communication path loss, creating a fundamental tradeoff in trajectory design.The paper identifies this tradeoff as central to solar-powered UAV operation.
  • Aerodynamic power consumption: Aerodynamic power combines induced power, vertical-flight power, and blade-drag profile power under a quasi-static slot-wise flight model.The velocity components are assumed constant during each time slot.
  • Aerodynamic power consumption: Climbing consumes more power than hovering or descending, while level flight consumes less power than hovering and drag power depends on horizontal velocity.Descending can yield power savings because gravity makes vertical-flight power negative.

III. OFFLINE TRAJECTORY AND RESOURCE ALLOCATION DESIGN

The offline design jointly optimizes the UAV’s 3D trajectory, transmit powers, and subcarrier allocation with non-causal channel knowledge, solving the resulting mixed-integer non-convex problem optimally through monotonic optimization.

  • Problem formulation: The offline formulation assumes non-causal channel-gain knowledge and maximizes system sum throughput over NT time slots.It jointly determines trajectory and wireless resource allocation.
  • Problem formulation: The optimization accounts for UAV energy evolution, aerodynamic consumption, finite battery capacity, mobility limits, transmit-power limits, and user QoS requirements.It also enforces initial and final battery-energy conditions and altitude constraints.
  • Problem formulation: Problem (10) is difficult because it combines a mixed-integer combinatorial objective, non-convex constraints, and binary subcarrier selection.The main non-convexities occur in constraints C1, C2, and C14, with C13 imposing binary selection.
  • Offline solution: Monotonic optimization provides an optimal offline trajectory and resource-allocation solution, whose performance serves as a benchmark for other offline and online schemes.The derived offline solution also supports online resource-allocation design.
  • Offline solution: For sufficiently large ξ, the optimal penalized formulation assigns each subcarrier exclusively to at most one user per time slot.Thus, no subcarrier is shared by multiple users, establishing equivalence with the original formulation.
  • Offline solution: Equivalent transformations convert the problem into canonical monotonic-optimization form with a normal-set and conormal-set feasible-region representation.The objective is monotonically increasing, and the feasible set is approached using sequential polyblock approximation.

IV. ONLINE TRAJECTORY AND RESOURCE ALLOCATION DESIGN

The online design uses only causal channel-state information, developing an optimal scheme and a lower-complexity iterative suboptimal scheme inspired by the offline solution.

  • Online design: The online trajectory and resource-allocation problem requires only causal knowledge of channel states.It is formulated as a non-convex optimization problem.
  • Online design: An optimal online resource-allocation algorithm is developed based on the structure of the offline solution.The optimal online scheme provides a reference for evaluating lower-complexity approaches.
  • Online design: A low-complexity suboptimal online scheme is proposed to balance performance and computational complexity.The scheme is iterative and has polynomial time complexity.

A. Achievable and Expected Data Rate

The online design uses exact current-slot rates from near-perfect CSI and expected future-slot rates when future CSI is unavailable. An upper bound on future expected rates is used for tractable optimization and is reported to be a good approximation in typical UAV channels.

  • Online allocation updates in every time slot using near-perfect current-slot CSI and expected rates for future slots without available CSI.The current rate is obtained after handshaking, while future rates are modeled statistically.
  • The current-slot achievable rate is computed exactly for the subcarrier assigned to each user.
  • The bound on the difference between the upper-bound and actual expected rates can be very small in UAV communication channels.The paper relates this bounded difference to the dominance of the LoS path in air-to-ground channels.
  • Future expected data rates are reformulated using an upper bound to facilitate tractable resource-allocation design.The bound is estimated using historical channel observations and reflects the small variance of channel power in the considered model.

B. Optimization Problem Formulation

The online problem updates trajectory and resource allocation each slot by maximizing current achievable throughput together with expected future throughput. It remains a difficult mixed-integer non-convex optimization problem with future QoS represented through upper-bound constraints.

  • At each time slot, the online formulation maximizes current achievable throughput plus expected throughput over future slots.The resulting trajectory and resource-allocation policy are updated in real time.
  • Constraints C14a and C14b represent minimum data-rate requirements for the current slot and expected-rate requirements for future slots.
  • Future users’ actual expected rates may be slightly lower than the minimum requirement because future CSI is unavailable.Current-slot minimum required rates are guaranteed because current CSI is known.
  • The formulation is a mixed-integer non-convex optimization problem that is very difficult to solve.Its constraints include the offline constraints together with online rate requirements.

C. Optimal Solution

The paper solves the online formulation optimally through monotonic optimization and develops a lower-complexity successive-convex-approximation scheme for the remaining non-convex program. The optimal scheme is globally optimal for its bound-based objective, while the iterative scheme converges locally in polynomial time.

  • Optimal Solution: The online problem is recast as a standard monotonic optimization problem using equivalent constraints and feasible sets.Sequential polyblock approximation is then applied to obtain its optimal solution.
  • Optimal Solution: The monotonic-optimization algorithm finds the globally optimal online trajectory and resource-allocation policy.Its objective maximizes current achievable rate together with the upper bound on future expected rate.
  • Optimal Solution: The optimal online algorithm has computational complexity that grows exponentially with the number of time slots and users.This growth is prohibitive for real-time UAV communication operation.
  • Suboptimal Solution: A computationally efficient suboptimal scheme finds a locally optimal policy with polynomial time complexity.It is proposed as a practical alternative and the optimal online scheme remains a quantitative benchmark.
  • Suboptimal Solution: Successive convex approximation replaces non-convex components with global underestimators and repeatedly solves convex lower-bound problems.The resulting sequence tightens the lower bound across iterations.

SYSTEM PARAMETERS

Simulations evaluate convergence, expected-throughput approximation, and trajectory behavior under specified UAV communication parameters. The online schemes approach the offline solution, while the suboptimal scheme converges faster and is less sensitive to problem size.

  • System Parameters: The simulations assume daytime operation over a cloud-covered service area, Rician fading with a 6 dB factor, and user QoS requirements of Rreq = 50 Mbits/s.
  • Convergence: The online optimal and suboptimal schemes converge to the optimal offline resource-allocation solution across the considered transmission periods and user counts.
  • Convergence: For T = 15 minutes and K = 1, the optimal and suboptimal online schemes converge in fewer than 430 and 20 iterations, respectively.
  • Convergence: For T = 30 minutes and K = 4, optimal schemes require more iterations because the search space grows exponentially with users and time slots.
  • Convergence: The suboptimal online scheme’s iteration count is less sensitive to transmission duration and user number, demonstrating practicality.
  • Expected Throughput: Actual expected throughput and its upper bound closely approach the performance of the optimal offline scheme.This supports the upper-bound approximation for the adopted typical system parameters.

B. Trajectory

The proposed trajectories jointly balance solar harvesting, communication path loss, and aerodynamic power consumption. Across offline and online designs, the UAV climbs above clouds to harvest energy, then descends or repositions to serve users efficiently.

  • The UAV first heads toward users or their centroid, then cruises near clustered users because level flight consumes less aerodynamic power than hovering.
  • Offline and online schemes produce very similar vertical trajectories, while the suboptimal online trajectory closely approaches the optimal online trajectory.The offline trajectory is more sophisticated because it uses non-causal channel-state information.
  • The UAV climbs above the clouds, remains there to harvest sufficient solar energy, and later descends to a lower altitude for lower-path-loss communication.The lower altitude improves system sum throughput by bringing the UAV closer to users.
  • Longer flight periods keep the UAV above clouds longer because additional energy is required, leaving less time for low-altitude communication.
  • The proposed schemes use maximum vertical velocity during climbs and descents, reduce speed to 0.1 m/s at the lowest altitude, and use maximum horizontal velocity for repositioning.Large horizontal velocity at low altitude can increase path-loss fluctuations and degrade throughput.
  • Stored energy rises above clouds when harvested solar power exceeds total consumption, then falls during descent until the required qend is reached.The proposed offline scheme transmits at maximum power Pmax throughout the considered period for the adopted parameters.

E. Average System Throughput versus Transmit Power

Average system throughput generally improves with transmit power, solar-panel size, and user count, but energy-harvesting demands and stricter QoS requirements constrain these gains. The proposed offline and online schemes outperform baselines, with offline optimization performing best.

  • Throughput increases monotonically with maximum transmit power, but gains diminish beyond 45 dBm as higher consumption requires additional battery energy.Higher transmit power improves users’ received SNR, while increased harvesting and storage demands reduce the marginal benefit.
  • Larger solar panels improve throughput because they harvest the required energy faster, allowing earlier descent and longer low-path-loss transmission.The proposed offline and online schemes achieve higher average throughput for larger solar-panel sizes.
  • The proposed offline and online schemes achieve higher average throughput than the baseline schemes through joint 3D-trajectory, power, and subcarrier optimization.Fixed horizontal coordinates increase aerodynamic power consumption, while random subcarrier allocation poorly utilizes system resources.
  • Throughput increases with the number of users for schemes exploiting multiuser diversity, whereas baseline scheme 2 remains independent of user count because it uses random subcarrier allocation.The proposed schemes grow faster with the number of users than baseline scheme 1.
  • The offline scheme outperforms the optimal online scheme, while the suboptimal online scheme closely approaches the optimal online scheme even for many users.The offline advantage is attributed to non-causal channel-gain knowledge.
  • Stricter QoS requirements reduce throughput because lower cruising altitude limits solar harvesting, prolongs high-altitude harvesting, and leaves less time for low-altitude communication.The maximum cruising altitude is reduced to alleviate propagation path loss and satisfy higher minimum data-rate requirements.

G. Average System Throughput versus Minimum Required Remaining Energy

Average system throughput decreases as the required remaining energy qend increases, because the UAV must harvest more solar energy and remain at high altitude longer. Smaller maximum storage capacity qmax also lowers throughput, while the proposed suboptimal online scheme approaches the optimal online scheme.

  • Effect of qend: Throughput decreases monotonically with qend for all considered schemes except baseline scheme 2.A larger qend requires the UAV to collect more solar energy over the operation period.
  • Effect of qend: Higher qend forces longer high-altitude flight, which degrades average system throughput.The UAV must remain at high altitude longer to harvest the additional required energy.
  • Effect of qmax: Smaller qmax reduces throughput because the UAV stores less energy and reaches full battery capacity sooner.After the battery is fully charged, the UAV can fly to a lower altitude.
  • Scheme comparison: The proposed suboptimal online scheme achieves performance similar to the optimal online scheme.The proposed offline scheme performs better than the online schemes because it uses non-causal channel-gain knowledge.
  • Scheme comparison: Baseline scheme 2 is insensitive to qend because its fixed altitude harvests sufficient energy to maintain the required remaining storage.Its remaining stored energy stays above qend for the considered altitude.
  • Overall comparison: The proposed offline and online schemes significantly improve system performance compared with the two baseline schemes.The resource allocation design jointly addresses trajectory, power adaptation, and subcarrier allocation for solar-powered MC-UAV communication.
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