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Cellular-Enabled UAV Communication: A Connectivity-Constrained Trajectory Optimization Perspective

Shuowen Zhang, Yong Zeng, Rui Zhang

arXiv:1805.07182v1cs.ITeess.SY

TL;DR

The paper addresses UAV communication in cellular networks and studies trajectory design for cellular-connected UAVs. It develops graph-based solution methods, including shortest-path formulations, while identifying interference and flight-speed considerations as future-work boundaries.

  • Problem

    Cellular-connected UAV trajectory design is presented as a relatively new communication problem within cellular UAV communications.

  • Method

    The proposed approach transforms two trajectory subproblems into shortest-path problems on constructed graphs, solvable with standard graph-theory algorithms.

  • Results

    The graph-based formulations enable the trajectory subproblems to be solved efficiently using off-the-shelf graph-theory algorithms.

  • Takeaways & Limitations

    Integrating UAVs into existing and future cellular networks is identified as an approach for meeting UAV communication requirements.

  • Takeaways & Limitations

    The paper leaves interference-aware trajectory optimization for future work and notes that minimum allowable flight speed may not always be optimal.

Abstract

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Integrating the unmanned aerial vehicles (UAVs) into the cellular network is envisioned to be a promising technology to significantly enhance the communication performance of both UAVs and existing terrestrial users. In this paper, we first provide an overview on the two main paradigms in cellular UAV communications, i.e., cellular-enabled UAV communication with UAVs as new aerial users served by the ground base stations (GBSs), and UAV-assisted cellular communication with UAVs as new aerial communication platforms serving the terrestrial users. Then, we focus on the former paradigm and study a new UAV trajectory design problem subject to practical communication connectivity constraints with the GBSs. Specifically, we consider a cellular-connected UAV in the mission of flying from an initial location to a final location, during which it needs to maintain reliable communication with the cellular network by associating with one GBS at each time instant. We aim to minimize the UAV's mission completion time by optimizing its trajectory, subject to a quality-of-connectivity constraint of the GBS-UAV link specified by a minimum receive signal-to-noise ratio target. To tackle this challenging non-convex problem, we first propose a graph connectivity based method to verify its feasibility. Next, by examining the GBS-UAV association sequence over time, we obtain useful structural results on the optimal UAV trajectory, based on which two efficient methods are proposed to find high-quality approximate trajectory solutions by leveraging graph theory and convex optimization techniques. The proposed methods are analytically shown to be capable of achieving a flexible trade-off between complexity and performance, and yielding a solution that is arbitrarily close to the optimal solution in polynomial time. Finally, we make concluding remarks and point out some promising directions for future work.

I. INTRODUCTION

The paper introduces cellular UAV communications as a way to improve UAV–ground connectivity and surveys two integration paradigms before motivating communication-aware trajectory design for cellular-connected UAVs.

  • Cellular-enabled UAV communication: Integrating UAVs into LTE/5G/B5G networks can enhance reliability, security, coverage, and throughput while supporting beyond-VLoS control links.The paper also highlights ubiquitous connectivity, high-capacity links, authentication, and potential business opportunities.
  • Research motivation: Communication-aware trajectory design is motivated by the need to maintain UAV communication requirements during mission-specific flight.The paper identifies this as a new and critical design problem within cellular-enabled UAV communication.
  • Two cellular UAV communication paradigms: Cellular UAV communications comprise UAVs served as aerial users by ground base stations and UAVs acting as aerial platforms for terrestrial users.The paper focuses its main research on the first paradigm.
  • Motivation: Direct UAV–ground links are limited in rate and reliability, vulnerable to interference and insecurity, and constrained to visual-line-of-sight operation.The paper connects these limitations with reported UAV crashes attributed to lost UAV–ground communication.

2) UAV-Assisted Cellular Communication:

UAV-assisted cellular communication uses UAVs as aerial communication platforms whose flexible 3D deployment and mobility can adapt cellular service to changing terrestrial demand.

  • Capabilities and benefits: UAVs can operate as quasi-stationary or mobile aerial base stations and relays, dynamically adjusting their locations to real-time traffic and user distributions.This flexibility supports swift network reconfiguration and more efficient communication over serving areas.
  • Applications: Typical applications include remote-area coverage, disaster-related service recovery, temporary-hotspot traffic offloading, aerial relaying, and IoT or machine-type communication.These use cases are illustrated in Fig. 2.
  • Design challenges: Quasi-stationary UAV deployment requires joint consideration of horizontal position, altitude, changing network topology, and wireless backhaul capacities.Unlike GBSs and fixed relays, UAV platforms generally rely on wireless backhauls whose capacities vary with mobility.
  • Design challenges: Mobile UAV trajectories should be designed to improve ground-user communication performance, potentially jointly with communication-resource allocation.Closer flight to high-rate users can shorten link distances, increase capacity, or reduce transmit power, while LoS channels create severe interference concerns.
  • Design challenges: Propulsion energy can dominate communication energy, making energy-efficient design crucial under UAV size, weight, and power constraints.The paper describes propulsion consumption as being on the order of kilowatts versus watts for communication energy.

B. Literature Review

Prior work spans aerial-user interference, UAV deployment, cooperative communication, and mobile relays, but communication-aware trajectory design for cellular-connected UAVs remains comparatively underdeveloped.

  • Cellular-enabled UAV communication: LTE studies report that increasing aerial-user altitude or population generally worsens aerial interference and reduces performance or spectral efficiency.Interference mitigation has been explored through antenna design, beamforming, cancellation, power control, and coordination.
  • Cellular-enabled UAV communication: Prior cellular-enabled UAV research also examined GBS antenna configuration, association rules, massive MIMO, and interference-aware path planning.These studies target coverage, coexistence, multi-UAV operation, or trade-offs involving energy, latency, and interference.
  • UAV-assisted cellular communication: UAV-assisted cellular research studied 3D deployment, coverage maximization, altitude and beamwidth optimization, cooperative transmission, and aerial-relay trajectories.The literature includes both single- and multi-UAV settings and several communication models.
  • Mobile UAV relays: Mobile-relay studies optimized trajectories for throughput, delay, routing, connectivity, or rate objectives under varied operational constraints.Some works jointly optimized trajectory with transmit power or packet size, while others derived closed-form headings or used reinforcement learning.
  • Research gap: The paper identifies limited prior work on communication-aware trajectory design for cellular-connected UAVs.It distinguishes this topic from related UAV-assisted and relay-trajectory studies, including work that generally did not jointly optimize relay trajectories with communication resources.

C. Main Contributions

The paper formulates a connectivity-constrained UAV trajectory problem for cellular communication and develops graph-based and convex-optimization methods for efficient approximate solutions.

  • Problem formulation: The paper studies a cellular-connected UAV flying between fixed initial and final locations while maintaining a minimum GBS-UAV SNR and minimizing mission completion time.The UAV associates with one GBS at each time instant, selecting the best available channel within coverage.
  • Problem formulation: The resulting optimization is non-convex, has infinitely many variables, and includes constraints on the UAV’s maximum speed and trajectory endpoints.Dedicated spectrum is assumed for the UAV, with interference from sufficiently distant users or UAVs neglected.
  • Feasibility checking: Feasibility is equivalent to connectivity between two specified vertices in a constructed graph, enabling efficient verification with graph-theoretic algorithms.The graph represents feasible sequential GBS-UAV associations during the mission.
  • Optimal structure: The optimal trajectory follows connected line segments at maximum speed, using the best-channel GBS within each segment.This structure transforms the original problem into finite-dimensional optimization over GBS association sequences and handover locations.
  • Approximate methods: Two graph-construction methods reduce the structured problem to shortest-path problems and produce approximate solutions arbitrarily close to optimal in polynomial time.The methods trade complexity against performance through bounding and approximation techniques.
  • Numerical evaluation: Numerical results show substantially lower complexity than exhaustive search, while outperforming straight flight in quality-of-connectivity and approaching exhaustive-search performance.The quality-of-connectivity gain over straight flight becomes more pronounced as GBS density increases.

D. Organization

The paper proceeds from system and problem formulation to feasibility analysis, structural characterization, efficient approximate methods, numerical evaluation, and conclusions with future directions.

  • Organization: Section II presents the system model and problem formulation.
  • Organization: Section III develops a graph-connectivity approach for checking feasibility.
  • Organization: Section IV derives structural properties of the optimal solution and proposes graph-theoretic methods for high-quality approximate trajectories.
  • Organization: Section V reports numerical results, while Section VI concludes and identifies promising future-work directions.
  • Notation: The paper defines notation for scalars, vectors, transposes, Euclidean norms, set cardinality, set unions, matrices, complex numbers, phase, imaginary units, distributions, expectations, and derivatives.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The paper formulates mission-time-minimizing trajectory optimization for a cellular-connected UAV that must preserve GBS connectivity throughout flight. It then develops graph-connectivity and convex-optimization methods to address feasibility and approximate solution construction.

  • II. SYSTEM MODEL AND PROBLEM FORMULATION: The system models a UAV flying at fixed altitude from a known initial location to a final location while communicating with cellular ground base stations.GBSs are assumed to share altitude HG, while the UAV remains at altitude H; the formulation can be extended to different GBS altitudes.
  • II. SYSTEM MODEL AND PROBLEM FORMULATION: At every time instant, the UAV associates with one GBS, using a LoS channel model with single omnidirectional antennas and perfectly compensated Doppler.The downlink model also applies to uplink transmission, and multiple antennas can be incorporated through a multiplicative beamforming gain.
  • II. SYSTEM MODEL AND PROBLEM FORMULATION: The selected GBS is the closest one because this maximizes received signal power, which determines the UAV receiver SNR and connectivity quality.The signal model includes the GBS transmission power, channel power gain, and receiver noise power.
  • II. SYSTEM MODEL AND PROBLEM FORMULATION: The optimization minimizes mission completion time T over the trajectory, subject to a minimum SNR target, known GBS locations, and maximum UAV speed.The SNR requirement is equivalently expressed through a maximum horizontal distance d̄ from the closest GBS; smaller d̄ imposes a stricter connectivity requirement.
  • II. SYSTEM MODEL AND PROBLEM FORMULATION: Problem (P1) is non-convex because each connectivity constraint is a pointwise minimum of convex functions, while the continuous trajectory creates infinitely many optimization variables.Consequently, obtaining the optimal solution is generally challenging.
  • II. SYSTEM MODEL AND PROBLEM FORMULATION: The proposed framework reformulates (P1) using graph theory, first checking feasibility through graph connectivity and then constructing approximate solutions with graph theory and convex optimization.The methods are designed to provide high-quality approximate trajectories with a flexible complexity-performance trade-off.
  • III. FEASIBILITY CHECK FOR PROBLEM (P1): A GRAPH CONNECTIVITY BASED APPROACH: Feasibility is characterized by a GBS-UAV association sequence whose first and last coverage areas contain the endpoints and whose consecutive coverage areas overlap.Each coverage area is a disk centered at a GBS with radius d̄.
  • III. FEASIBILITY CHECK FOR PROBLEM (P1): A GRAPH CONNECTIVITY BASED APPROACH: The feasibility test constructs an undirected weighted graph and declares (P1) feasible exactly when the initial and final UAV locations are connected in that graph.The graph represents GBS coverage and allowable transitions between consecutively associated GBSs.

IV. PROPOSED SOLUTION TO PROBLEM (P1): OPTIMAL STRUCTURE AND TWO GRAPH BASED METHODS

The section derives the optimal UAV trajectory structure from the GBS-UAV association sequence and proposes polynomial-complexity graph-theoretic and convex-optimization methods for approximate solutions.

  • A. Problem Reformulation Based on GBS-UAV Association Sequence: The optimal trajectory is determined by the GBS-UAV association sequence and the UAV locations where handovers occur.This reformulates the original trajectory problem as joint optimization over association sequences and handover locations.
  • A. Problem Reformulation Based on GBS-UAV Association Sequence: The resulting joint association and handover-location optimization remains non-convex and difficult to solve optimally.
  • IV. Proposed Solution to Problem (P1): Two approximate-solution methods use graph theory and convex optimization, require polynomial complexity in M, and achieve the optimal value within a bounded gap.The methods provide a flexible complexity-performance trade-off and can approach the optimum arbitrarily closely in polynomial time.
  • A. Problem Reformulation Based on GBS-UAV Association Sequence: Each handover location lies in the intersection of the coverage areas of the two consecutively associated GBSs.The feasible region is defined by horizontal-distance constraints to both GBSs.
  • B. Structural Property of Optimal UAV Trajectory: The optimal UAV path consists only of connected line segments flown at maximum speed, with one GBS associated along each segment.Segment endpoints are consecutive handover points, while the initial and final points are the mission endpoints.
  • B. Structural Property of Optimal UAV Trajectory: Using handover locations to represent the continuous trajectory significantly reduces the number of variables and yields an equivalent finite-dimensional problem.The reduced problem jointly optimizes the GBS-UAV association sequence and handover locations, after which the trajectory solution can be recovered.

C. Joint GBS-UAV Association and Handover Location Optimization

The joint optimization exploits structural properties of optimal GBS-UAV associations and handover locations to design efficient approximate trajectories. Two graph-based methods trade complexity against performance, with Method II approaching optimality as quantization increases.

  • Problem formulation: The problem is non-convex and combinatorial because the association sequence contains discrete variables, while its length is also an implicit variable.Exhaustive association-sequence search can require O(M!) complexity.
  • Method comparison: The two methods provide a flexible performance–complexity trade-off, and Method II can obtain an arbitrarily near-optimal solution with moderately increased complexity.The proposed approaches transform the design into graph-theoretic and convex-optimization subproblems.
  • Optimal structural properties: The optimal association sequence does not repeat any GBS, so the number of associated GBSs satisfies N ≤ M and the number of handovers is at most M − 1.This property reduces the relevant association search space.
  • Optimal structural properties: For each handover, an optimal location can be assumed to lie on the intersected coverage boundary between consecutive GBS coverage regions.These locations belong to the regions Ei defined by the corresponding GBS coverage boundary and overlap area.
  • Method I: Method I first selects an approximate association sequence through a shortest-path problem, then optimizes handover locations with convex optimization.The graph search has complexity O(M^2) over the constructed graph.
  • Method II: Method II jointly designs association and handover locations using a quantized graph, achieving arbitrarily high accuracy with sufficiently many quantization levels.Its performance gap approaches zero as Q goes to infinity, while complexity remains polynomial in Q.

D. Summary of Graph Theory Based Algorithms for Problem (P1)

The paper organizes feasibility checking and trajectory design within a unified graph-theoretic framework. Graphs encode connectivity and feasible trajectories, allowing the resulting shortest-path problems to be solved efficiently with standard algorithms.

  • Unified framework: The framework transforms the original problem into P3-I and P3-II using structural properties, bounding, and approximation techniques.P3-I replaces the objective with the upper bound in (40).
  • Graph construction: Graph vertices and edges represent communication connectivity constraints, while each path between designated vertices corresponds to a feasible UAV trajectory.This gives graph paths a direct feasible-solution interpretation.
  • Shortest-path solution: Both transformed problems become shortest-path problems between given vertices and can be solved efficiently using off-the-shelf graph-theory algorithms.The same framework also encompasses the graph-connectivity feasibility check for P1.
  • Unified framework: The feasibility-checking approach for P1 fits the same graph-theory-based design framework, although details are omitted.The paper presents this as a unified view of feasibility and trajectory design.

V. NUMERICAL RESULTS

The numerical evaluation places M GBSs uniformly at random in a D km × D km square and evaluates trajectory designs under fixed UAV, GBS, and speed settings.

  • Simulation setup: The experiments distribute M GBSs uniformly randomly in a D km × D km square region with density λ = M/D^2 GBSs/km^2.The region size is set to D = 10.
  • Simulation setup: The UAV altitude is H = 90 m, each GBS altitude is HG = 12.5 m, and the maximum UAV speed is Vmax = 50 m/s.These values define the principal geometric and mobility settings used in the evaluation.

A. Quality-of-Connectivity Performance

The proposed trajectory designs improve achievable connectivity over straight flight and approach optimal mission-time performance, with gains depending on GBS density, SNR target, and method settings.

  • Connectivity versus GBS density: Increasing GBS density improves SNR performance for both the proposed and straight-flight trajectory designs.More GBSs provide greater flexibility for improving connectivity.
  • Connectivity versus GBS density: 1.12 dB, 3 dB, and 3.65 dB median SNR gains over straight flight occur at GBS densities λ = 0.1, 0.8, and 1.6, respectively.The gain becomes more significant as GBS density increases.
  • Mission completion time: Method II with Q = 8 or Q = 16 achieves almost the same mission-completion-time performance as the optimal trajectory.Increasing quantization levels from Q = 8 to Q = 16 improves the proposed design's performance.
  • Mission completion time: Method I generally performs closely to optimal but requires 6.30% more mission completion time at SNR target ρ̄ = 17 dB.The loss is attributed to a possibly non-tight upper bound used to approximate the objective.
  • Overall comparison: The proposed methods generally achieve near-optimal performance and significantly outperform straight flight, while designs depend on connectivity requirements.The results validate trajectory optimization under the connectivity constraint.

VI. CONCLUDING REMARKS AND FUTURE WORK

The paper studies cellular-enabled UAV trajectory optimization under connectivity constraints and reports polynomial-complexity methods with arbitrarily small optimality gaps. It also identifies extensions involving altitude, cooperation, QoS, channel models, interference, and energy.

  • Paper focus: The paper focuses on a cellular-enabled UAV flying between endpoints while maintaining target connectivity through one GBS at each time instant.The trajectory minimizes mission completion time under a minimum received-SNR constraint.
  • Main contribution: The proposed framework checks feasibility and finds high-quality approximate trajectories for the formulated connectivity-constrained optimization problem.Its algorithms use graph-theoretic and optimization-based structure from the UAV-GBS association sequence.
  • Main contribution: The algorithms trade complexity against performance and approach the optimal solution with an arbitrarily small gap in polynomial complexity.Numerical results validate the efficacy of the proposed trajectory designs.
  • Future work: Future directions include cooperative CoMP association, alternative QoS requirements, non-LoS online trajectory optimization, interference management, and energy-aware design.The paper currently assumes one associated GBS, connectivity-based QoS, LoS channels, interference-free operation, and no energy constraints.
  • Future work: The LoS channel model supports offline design, while urban or lower-altitude non-LoS settings may require combined offline and online trajectory adjustment.Complete channel knowledge over all possible UAV locations may be unavailable in those settings.

APPENDIX A

Appendix A establishes equivalent trajectory formulations by representing feasible motion with connected line segments and GBS association intervals. It also bounds optimal association sequences by the number of GBSs.

  • Trajectory representation: A feasible continuous UAV trajectory can be represented by a finite path of connected line segments at constant altitude.The segment endpoints are discrete horizontal locations, with arbitrary speed satisfying the maximum-speed constraint.
  • Equivalent formulations: Any feasible trajectory can be mapped to a GBS-association sequence and interval durations satisfying the discrete formulation's constraints.The construction divides the mission interval into finitely many subintervals.
  • Equivalent formulations: The continuous and discrete-segment formulations have the same optimal value.The proof constructs feasible solutions in both directions without increasing the objective.
  • Association structure: The optimal association sequence contains no repeated GBS, so its length is bounded by N ≤ M.Removing repeated associations preserves feasibility while not increasing the objective.

APPENDIX E

Appendix E characterizes optimal waypoint placement on coverage boundaries and supports the approximation guarantees of the proposed quantized trajectory method.

  • Waypoint construction: For an optimal association sequence, intermediate waypoints can be shifted along adjacent segments to satisfy boundary-distance equalities.The construction uses α_i ∈ [0, 1] so each adjusted waypoint lies at distance d̄ from the associated GBS.
  • Waypoint construction: The waypoint construction preserves feasibility and does not increase the objective of Problem (P3).The proof derives the construction from Lemma 1 and the associated distance conditions.
  • Approximation analysis: The quantized solution is compared with the optimal solution through bounds on the objective gap.The analysis uses the triangle inequality, quantization properties, and the bound N⋆ ≤ M.
  • Approximation analysis: The approximation analysis explicitly relies on the non-repeated GBS-UAV association property.This property supplies the bound N⋆ ≤ M used in the final gap argument.
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