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Hybrid Offline-Online Design for UAV-Enabled Data Harvesting in Probabilistic LoS Channel

Changsheng You, Rui Zhang

arXiv:1907.06181v2cs.ITcs.NI

TL;DR

The paper studies max-min data collection for UAV-enabled WSNs in urban environments with probabilistic building blockage and incomplete channel knowledge. It combines a generalized-logistic probabilistic LoS model with hybrid offline-online optimization, using statistical CSI to plan a 3D path and real-time CSI to adapt speed and scheduling. The paper reports simulation evidence for the effectiveness of this hybrid design and identifies joint offline-online trajectory and scheduling insights.

  • Problem

    Urban blockage and incomplete UAV-SN CSI make jointly optimizing a UAV’s 3D trajectory and SN scheduling for minimum average collection rate difficult.

  • Method

    The paper constructs a Manhattan-city probabilistic LoS model and uses hybrid offline-online optimization that combines statistical and real-time CSI.

  • Results

    Simulation results demonstrate the effectiveness of the proposed hybrid design and reveal insights into joint offline-online 3D trajectory and communication-scheduling optimization.

  • Takeaways & Limitations

    The design separates offline path planning from online speed and scheduling adaptation while leveraging instantaneous channel states and accumulated SN data.

  • Takeaways & Limitations

    The subsequent UAV trajectory design uses limited CSI obtained from previous operations.

Abstract

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This paper considers an unmanned aerial vehicle (UAV)-enabled wireless sensor network (WSN) in urban areas, where a UAV is deployed to collect data from distributed sensor nodes (SNs) within a given duration. To characterize the occasional building blockage between the UAV and SNs, we construct the probabilistic line-of-sight (LoS) channel model for a Manhattan-type city by using the combined simulation and data regression method, which is shown in the form of a generalized logistic function of the UAV-SN elevation angle. We assume that only the knowledge of SNs' locations and the probabilistic LoS channel model is known a priori, while the UAV can obtain the instantaneous LoS/Non-LoS channel state information (CSI) with the SNs in real time along its flight. Our objective is to maximize the minimum (average) data collection rate from all the SNs for the UAV. To this end, we formulate a new rate maximization problem by jointly optimizing the UAV three-dimensional (3D) trajectory and transmission scheduling of SNs. Although the optimal solution is intractable due to the lack of the complete UAV-SNs CSI, we propose in this paper a novel and general design method, called hybrid offline-online optimization, to obtain a suboptimal solution to it, by leveraging both the statistical and real-time CSI. Essentially, our proposed method decouples the joint design of UAV trajectory and communication scheduling into two phases: namely, an offline phase that determines the UAV path prior to its flight based on the probabilistic LoS channel model, followed by an online phase that adaptively adjusts the UAV flying speeds along the offline optimized path as well as communication scheduling based on the instantaneous UAV-SNs CSI and SNs' individual amounts of data received accumulatively.

I. INTRODUCTION

The paper addresses UAV-enabled data harvesting in urban WSNs, where building blockage makes simplified LoS-dominant models and purely offline designs inadequate. It proposes a hybrid 3D trajectory and scheduling design that combines probabilistic channel statistics with real-time CSI.

  • Motivation: Urban building blockage can make simplified LoS-dominant channel models inaccurate because they omit location-dependent multipath fading and shadowing.Probabilistic LoS models represent LoS/NLoS occurrence statistically as a function of elevation angle.
  • Motivation: Existing offline policies may lose rate performance because they cannot adapt to real-time, location-dependent channel variation under random blockage.Prior probabilistic-LoS approaches still used deterministic expected gains without channel-aware online adaptation.
  • Problem formulation: The objective is to maximize the minimum average data collection rate by jointly designing the UAV’s 3D trajectory and SN transmission scheduling.The formulation targets all SNs rather than a single node.
  • Proposed approach: The proposed method constructs a Manhattan-city probabilistic LoS model as a generalized logistic function of UAV-SN elevation angle.This model captures the statistical occurrence of LoS and NLoS states while avoiding exhaustive channel measurements.
  • Proposed approach: Hybrid offline-online optimization uses statistical CSI offline and real-time CSI online to adapt the UAV path and communication scheduling.The approach decouples the design and dynamically schedules SNs with favorable channels.
  • Insights and implementation: The 3D trajectory exploits vertical degrees of freedom to balance elevation-angle and distance effects, while online adaptation improves minimum-rate performance.The online linear program is solved with low complexity at the UAV in real time, supporting practical implementation.

II. SYSTEM MODEL

The system models a rotary-wing UAV collecting data from ground sensor nodes over a discretized mission, with constrained 3D motion between predetermined initial and final locations. The trajectory is represented by waypoints and line segments subject to speed, altitude, and time-slot constraints.

  • A rotary-wing UAV collects data from K ground sensor nodes during a duration T0.
  • The mission horizon is divided into N equal time slots of length δ = T0/N.
  • UAV trajectory model: Predetermined initial and final locations constrain the UAV trajectory, while horizontal and vertical speeds are independently bounded.
  • UAV trajectory model: The UAV trajectory is approximated by an (N+1)-point 3D sequence of horizontal locations and altitudes.
  • Trajectory constraints: Maximum horizontal and vertical travel distances per slot are Sxy,max = Vxy,maxδ and Sz,max = Vz,maxδ.
  • Trajectory constraints: The UAV must remain within an altitude range and avoid buildings, while increasing N further raises trajectory-design complexity.

B. UAV-SN Channel Model

The channel model represents random building blockage through probabilistic LoS and NLoS states whose probabilities depend on UAV–SN elevation angle. A Manhattan-type city simulation followed by regression yields a generalized logistic LoS model for the environment-specific channel statistics.

  • LoS probability depends on the UAV–SN elevation angle and is modeled statistically when complete CSI is unavailable.
  • The UAV–SN channel state is binary, with ck,n = 1 and ck,n = 0 denoting LoS and NLoS states.
  • The conventional logistic model can be inaccurate because it assumes simplified building arrangements such as evenly spaced buildings.
  • Probabilistic LoS model: A combined Manhattan-city simulation and data-regression procedure produces a generalized logistic approximation of LoS probability.
  • Probabilistic LoS model: The generalized logistic model uses environment-dependent constants B1, B2, B3, and B4, with B3 + B4 = 1.
  • Channel gain: The resulting large-scale channel gain accounts for distance, path loss, shadowing, and the additional attenuation associated with NLoS propagation.

C. Data Collection Model

Data collection jointly involves binary SN scheduling and real-time channel-dependent rates, while the UAV adapts its motion and scheduling using instantaneous CSI. The proposed hybrid design separates statistically informed path planning from low-complexity online adaptation.

  • Data collection: Energy-harvesting SNs transmit at maximum power when scheduled and remain silent otherwise.
  • Data collection: At most one SN is scheduled in each time slot through binary variables ak,n.
  • Data collection: The achievable rate depends on the real-time LoS/NLoS channel state and the corresponding channel gain.
  • Problem formulation: The optimal joint trajectory-and-scheduling solution is difficult because complete UAV–SN CSI is unavailable across the 3D region.
  • Hybrid design: Offline optimization uses the probabilistic LoS model to generate a path that maximizes minimum expected rates across SNs.
  • Hybrid design: Online optimization fixes the offline waypoints, then adjusts flying speeds and communication scheduling using instantaneous CSI.
  • Hybrid design: The method decouples path optimization from real-time speed and scheduling adaptation, enabling low-complexity online implementation.

IV. PROPOSED OFFLINE DESIGN

The offline design maximizes the minimum expected collection rate under the probabilistic LoS model, but the resulting optimization remains difficult because expected rates are highly nonlinear and scheduling is binary. A lower-bound approximation provides an achievable and more accurate formulation for trajectory design.

  • Offline design: The offline phase designs a 3D UAV trajectory and scheduling policy to maximize the minimum expected rate from all SNs.
  • Problem transformation: The transformed problem remains difficult because its expected-rate objective is non-concave and its scheduling constraints are binary and non-convex.
  • Problem transformation: Expected rate is highly complicated because it depends jointly on LoS/NLoS rates and the LoS probability.
  • Expected-rate approximation: Replacing expected channel gain with its average can maximize an upper bound rather than the expected rate, with a non-negligible gap between LoS and NLoS strengths.
  • Expected-rate approximation: Because LoS rates are much larger than NLoS rates, the design uses a lower-bound approximation that accounts for the expected LoS-state rate.
  • Illustrative evaluation: For the illustrative parameters, the exact expected rate is 2.93 bps/Hz, while the new approximation gives 2.92 bps/Hz.
  • Illustrative evaluation: The conventional approximation gives 4.87 bps/Hz and therefore overestimates the expected rate in the illustrative case.

B. Proposed Algorithm for Problem (P3)

The proposed algorithm addresses coupled trajectory, scheduling, non-convex rate, elevation-angle, and integer constraints through relaxation, successive convexification, and iterative block optimization.

  • The joint design is challenging because trajectory variables appear in non-convex rate and elevation-angle constraints, alongside integer scheduling variables.
  • Integer scheduling constraints are relaxed, and the elevation-angle constraints are further relaxed without changing the optimal solution of the intermediate problem.
  • Block coordinate descent alternately optimizes communication scheduling and the UAV’s horizontal and vertical trajectories to obtain a suboptimal solution.
  • For fixed feasible trajectories, the scheduling subproblem is a standard linear program that can be solved efficiently, with continuous scheduling reconstructible as binary scheduling without compromising performance.
  • Successive convex approximation replaces non-convex rate constraints with lower bounds, yielding a convex problem whose objective is a lower bound on the original subproblem.
  • The offline design can extend to fixed-wing UAVs by adding minimum horizontal and vertical speed constraints.

3) UAV Vertical Trajectory Optimization:

The online phase keeps the offline path fixed while optimizing segment durations and transmission scheduling using instantaneous CSI and accumulated data, producing an adaptive linear program.

  • The hybrid method always converges to a suboptimal solution, with offline complexity O((N+KN)^3.5 log^2(1/ϵ)) and decreasing online complexity along the path.
  • The hybrid method adapts UAV flying speeds along the offline path and communication scheduling using real-time UAV–SN CSI and accumulated received data.
  • Online optimization uses common travel durations for horizontal and vertical motion on each line segment, thereby converting speed optimization into duration optimization.
  • The online policy allocates transmission time τ_k,n to each SN and computes received data as τ_k,nr_k,n while tracking cumulative data across segments.
  • At each waypoint, the policy re-optimizes remaining travel and communication durations subject to speed, remaining-time, and scheduling constraints.
  • Because online optimization is an LP over remaining segments, it is suitable for real-time implementation by the UAV.
  • Scheduling favors segments with high instantaneous or expected rates while balancing the SNs’ individual average rates.
  • The online policy exploits channel macro-diversity by scheduling transmissions during favorable channel states and shortening travel through segments dominated by NLoS states.

VI. SIMULATION RESULTS

Simulations evaluate the hybrid offline-online design and its optimized three-dimensional trajectories and adaptive scheduling in a randomized urban WSN setting.

  • The simulations assess the proposed hybrid offline-online design, including offline and online UAV trajectories and adaptive communication scheduling.
  • Unless otherwise stated, results use 100?

A. Offline Phase

Offline experiments show that probabilistic-LoS trajectory design uses horizontal and vertical motion to balance blockage, elevation angle, distance, and available flight time.

  • The iterative algorithm’s max-min expected rate quickly converges after around 10 iterations for all flight durations.
  • The probabilistic-LoS expected rate increases monotonically with flight duration as more time is spent hovering above SNs at low altitude.
  • The PLB scheme uses vertical trajectory freedom to enlarge elevation angles moderately, balancing angle and distance more effectively than PLA.
  • At T0 = 10.6 s, PLB and PLLA move closer to SNs 1 and 2 than LB, while remaining farther from SN 4.
  • With short flight duration, the UAV flies relatively high to maintain elevation angles and increase LoS probabilities; with longer duration, it descends and approaches SNs.
  • At T0 = 25.6 s, the UAV can hover above each SN at minimum altitude, maximizing elevation angle and minimizing path loss.
  • PLLA outperforms LB, while PLB further improves rates by using vertical motion to reduce blockage; the gain diminishes as flight duration increases.

B. Online Phase

The online phase adapts communication scheduling and, in the proposed JA scheme, UAV flying speeds along a fixed offline path using instantaneous CSI. JA improves max-min rates over simpler online schemes, with computation remaining practically affordable.

  • Online scheme design: The online schemes compare fixed-path scheduling and joint optimization of communication scheduling and UAV flying speeds, with OJA providing a non-causal-CSI upper bound.The proposed JA scheme jointly optimizes speeds and scheduling, whereas ACS updates only scheduling; OJA assumes perfect non-causal CSI.
  • Rate versus flight duration: Expected max-min rate increases with flight duration before saturating, while ACS’s gain over PLB diminishes for long durations.With long durations, rates are dominated by periods when the UAV flies nearly above each SN, making scheduling adaptation less effective.
  • Rate versus flight duration: JA sustains rate gains for long flight durations by allocating more time to line segments with relatively higher achievable rates.It adjusts traveling durations online according to instantaneous CSI while following the offline path.
  • Per-SN rate comparison: JA improves the max-min rate over ACS by adapting travel duration and scheduling to instantaneous CSI, while OJA achieves the largest rate using non-causal CSI.For the illustrated realization, ACS slightly improves the bottleneck SN’s average rate, whereas JA further improves the max-min rate.
  • Computational complexity: JA takes slightly longer than ACS because it jointly optimizes speeds and scheduling, but both schemes require computation on the order of a second per line segment.JA’s running time decreases along the path as the number of optimization variables falls, and the reported time is practically affordable.
  • Effect of the number of SNs: Expected max-min rates decrease as the number of SNs increases, while flying-UAV schemes significantly outperform static UAV placement.The static benchmark can be severely limited by an NLoS channel at its optimized location; flight exploits time-varying channel states.

VII. CONCLUSIONS

The paper develops a hybrid offline-online design for UAV data harvesting under probabilistic LoS channels, using statistical information before flight and instantaneous CSI during flight. Simulations demonstrate the design’s effectiveness, while the conclusion identifies broader channel models, repeated operations, and multiple UAVs as open extensions.

  • Channel modeling: The channel model is constructed for a Manhattan-type city and represented as a generalized logistic function of UAV-SN elevation angle.The model is part of the paper’s probabilistic LoS characterization for urban blockage.
  • Problem and assumptions: The problem maximizes the minimum average data collection rate across SNs by jointly optimizing the UAV’s 3D trajectory and communication scheduling.Before flight, only SN locations and the probabilistic LoS model are known; instantaneous UAV-SN CSI becomes available during flight.
  • Proposed design: The hybrid offline-online optimization method obtains a suboptimal solution by leveraging both statistical and real-time CSI.It first determines the UAV path offline, then jointly adjusts flying speeds and communication scheduling online along that path.
  • Conclusions: Simulation results demonstrate the effectiveness of the proposed hybrid design and provide insights into joint offline-online 3D trajectory and communication-scheduling optimization.
  • Limitations and future work: The study is limited to one adopted probabilistic LoS channel model and a single data collection operation, with extensions to other models and repeated operations left open.The conclusion also identifies multiple-UAV cooperation and efficient optimal design under complete CSI as directions for further investigation.

APPENDIX

The appendix supports the probabilistic LoS model through randomized Manhattan-city simulations and derives convexity properties used in the optimization analysis. It also records specific sampling ranges for elevation, altitude, and city realizations.

  • Probabilistic LoS model: The LoS probability is estimated from simulated LoS/NLoS states across randomly generated Manhattan-type cities with distributed buildings and sensor nodes.Buildings use random heights following a Rayleigh distribution, and SNs are generated on unoccupied areas.
  • Simulation settings: The simulations vary elevation angles from 5° to 90° and azimuth angles from 0° to 360° while accounting for UAV horizontal location.UAV altitude is varied from 30 m to 300 m in 30 m steps to characterize altitude effects on LoS probability.
  • Convexity analysis: The analysis establishes that ξ(x, y) is convex, which leads to convexity of ψ(x, y) and supports the subsequent successive-convex-approximation derivation.The appendix then applies a first-order lower bound at a reference point for the transformed function.
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