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Maritime Coverage Enhancement Using UAVs Coordinated with Hybrid Satellite-Terrestrial Networks

Xiangling Li, Wei Feng, Yunfei Chen, Cheng-Xiang Wang, Ning Ge

arXiv:1904.02602v1cs.IT

TL;DR

The paper addresses how to coordinate UAVs with satellite and terrestrial systems for maritime coverage enhancement. It jointly optimizes UAV trajectory and transmit power under network and energy constraints using large-scale CSI, and simulations show that UAVs fit well with existing systems and provide performance gains.

  • Problem

    Coordinating UAVs with satellites and terrestrial networks for hybrid maritime coverage remains an open issue.

  • Method

    The paper jointly optimizes the UAV trajectory and transmit power under kinematic, interference, backhaul, and energy constraints using problem decomposition, successive convex optimization, and bisection.

  • Results

    Simulation results show that UAVs fit well with existing satellite and terrestrial systems, with performance gains from joint trajectory and transmit-power optimization using only large-scale CSI.

  • Takeaways & Limitations

    UAVs can provide on-demand coverage enhancement while coordinating spectrum use with satellites and using terrestrial systems for backhaul.

Abstract

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Due to its agile maneuverability, unmanned aerial vehicles (UAVs) have shown great promise for ondemand communications. In practice, UAV-aided aerial base stations are not separate. Instead, they rely on existing satellites/terrestrial systems for spectrum sharing and efficient backhaul. In this case, how to coordinate satellites, UAVs and terrestrial systems is still an open issue. In this paper, we deploy UAVs for coverage enhancement of a hybrid satellite-terrestrial maritime communication network. Under the typical composite channel model including both large-scale and small-scale fading, the UAV trajectory and in-flight transmit power are jointly optimized, subject to constraints on UAV kinematics, tolerable interference, backhaul, and the total energy of UAV for communications. Different from existing studies, only the location-dependent large-scale channel state information (CSI) is assumed available, because it is difficult to obtain the small-scale CSI before takeoff in practice, and the ship positions can be obtained via the dedicated maritime Automatic Identification System. The optimization problem is non-convex. We solve it by problem decomposition, successive convex optimization and bisection searching tools. Simulation results demonstrate that the UAV fits well with existing satellite and terrestrial systems, using the proposed optimization framework.

I. INTRODUCTION

Maritime wireless demand is growing, but satellite and terrestrial coverage face rate, cost, and range limitations. The paper investigates coordinating UAVs with existing maritime satellite-terrestrial systems using trajectory and transmit-power optimization based on large-scale CSI.

  • Hybrid satellite-terrestrial networks improve maritime coverage, but satellite transmission rates remain limited by long distances and restricted onboard payloads.
  • Achieving global broadband satellite coverage with state-of-the-art technology remains challenging at an affordable cost.
  • UAVs offer agile aerial base stations that can adapt their locations to communication demands and extend line-of-sight transmission.
  • Existing research largely studies UAV-only or UAV-terrestrial systems, leaving coordination among UAVs, satellites, and terrestrial networks open.
  • Because small-scale CSI is difficult to obtain before takeoff, the optimization assumes location-dependent large-scale CSI available from historical or measured data.
  • The proposed maritime model shares spectrum with satellites, uses terrestrial base stations for backhaul, and adapts UAV trajectories to mobile ships.
  • The paper jointly optimizes UAV trajectory and transmit power under kinematic, backhaul, interference, and communication-energy constraints.
  • Simulation results indicate that UAVs fit existing satellite and terrestrial systems, with performance gains from jointly optimizing trajectory and transmit power using only large-scale CSI.

II. SYSTEM MODEL

The system combines satellites, UAVs, and terrestrial base stations to enhance maritime broadband coverage, especially for ships underserved by satellite or coastal terrestrial links. UAV trajectory and power must account for mobile ships, composite fading, interference, and available backhaul.

  • A hybrid maritime network coordinates satellites, UAVs, and TBSs to provide broadband services for mobile ships.
  • UAVs provide on-demand broadband to fill coverage holes affecting low-end ships without high-gain satellite antennas.
  • UAVs share spectrum with satellites, so trajectory and transmit power are adjusted to mitigate interference while supporting wireless backhaul through TBSs or satellites.
  • UAV trajectories must adapt to ship mobility while maintaining a minimum achievable rate during travel time T0.
  • The channel model includes location-dependent path loss and Rician small-scale fading, with ship positions obtainable from historical or pre-measured shipping-route data.

III. UAV-AIDED COVERAGE ENHANCEMENT

The paper formulates UAV trajectory and in-flight transmit-power optimization and solves the resulting problem with an iterative algorithm.

  • The coverage-enhancement formulation jointly optimizes UAV trajectory and in-flight transmit power.
  • An iterative algorithm is provided to solve the optimization problem.

A. Problem Formulation

The problem maximizes the minimum ergodic rate over time while enforcing association, interference, backhaul, kinematic, altitude, and communication-energy constraints.

  • Interference-temperature constraints limit UAV interference toward satellite-served users sharing the spectrum.
  • UAV-to-user throughput is bounded by the TBS-to-UAV backhaul rate, while satellite backhaul uses a constant upper bound during short travel times.
  • The formulation constrains fixed-wing UAV velocity, acceleration, altitude, and line-of-sight-related height limits.
  • The objective maximizes the minimum ergodic achievable rate across T time slots by optimizing UAV power, position, velocity, and acceleration.
  • Communication energy is limited by an allowable budget E0 during the service interval, while sufficient flight fuel is assumed for the trip.

B. An Iterative Solution

The non-convex optimization is handled by analyzing rate and constraint curvature, applying Taylor approximations and successive convex optimization, then decoupling coupled trajectory and power variables for iterative solution.

  • The expectation over Rician fading makes the original optimization difficult, motivating transformations of rate-related constraints.
  • Theorem 1 establishes that the ergodic achievable rate is strictly concave and monotonically increasing.
  • First- and second-order Taylor approximations linearize selected convex functions, enabling successive convex optimization iterations.
  • Theorem 2 makes the curvature of f1(ca,t) conditional on whether Bs,tPs,t is below or above Bi,tPa,t.
  • Because trajectory, power, and auxiliary variables are coupled through multiplication, the method decouples the problem into two iteratively solved subproblems.

1) Optimization of transmit power:

The transmit-power subproblem is formulated with the stated constraints and solved as a linear program using CVX.

  • The optimization problem is solved subject to constraints (13), (14), (31), (38), and (39).
  • The resulting problem in (42) is a linear program.
  • CVX is used to solve the linear program.

2) Optimization of three-dimensional coordinates, velocities and accelerations:

The coordinate, velocity, acceleration, and auxiliary-variable optimization is decomposed into convex subproblems and solved iteratively using successive convex optimization and bisection.

  • Optimization procedure: Problem (41) is solved iteratively using successive convex optimization.
  • Optimization procedure: Bisection decouples Q_l and c_l when solving problem (43).
  • Optimization procedure: The problem in (43) is decomposed into convex problems by fixing Q_l.
  • Bounds: The lower bound of Q_1 is set to 0, while its upper bound is determined from the shortest UAV–mobile-user distance z_min.

IV. SIMULATION RESULTS AND DISCUSSION

Simulations validate the proposed algorithm in a maritime scenario where a UAV serves a moving user alongside satellite-served and interfered users.

  • The simulation validates the performance of the proposed algorithm.
  • Scenario: The user path is uniformly sampled at T = 10 positions, and the UAV follows its optimized trajectory.
  • Interference setting: Satellite-served and UAV-interfered users are randomly placed, with M_t = 1 because nearby satellite users are most affected by UAV interference.
  • Parameters: The system uses a 5 GHz carrier frequency and the path-loss shadowing term has standard deviation 0.1.
  • Evaluation: Small-scale fading is randomly generated for 1000 rounds to obtain ergodic achievable rates.

A. Performance Comparison among Different Algorithms

The proposed joint trajectory and transmit-power optimization outperforms comparison algorithms under large-scale CSI, while interference, energy, backhaul, and power constraints determine performance in different regimes.

  • A. Performance Comparison among Different Algorithms: The proposed algorithm jointly optimizes the whole UAV trajectory and transmit power using only large-scale CSI.
  • A. Performance Comparison among Different Algorithms: When P_max ≤ 30 dBm, performance is mainly determined by backhaul and maximum transmit power.
  • A. Performance Comparison among Different Algorithms: When P_max ≥ 30 dBm, performance is mainly determined by backhaul and total communication energy.
  • A. Performance Comparison among Different Algorithms: Reducing the Rician factor K yields much better performance for the proposed algorithm than for existing algorithms.
  • A. Performance Comparison among Different Algorithms: When P_max ≥ 36 dBm and I_0 = −55 dBm, the proposed algorithm has the best performance among the compared algorithms.
  • A. Performance Comparison among Different Algorithms: Joint optimization of the whole trajectory and transmit power with interference constraints improves the minimum ergodic achievable rate.
  • B. Discussion on the Impact of Key Parameters: When the energy constraint is tight, performance is determined by E_0; after increasing E_0, a tight interference constraint makes performance determined by I_0.
  • B. Discussion on the Impact of Key Parameters: The optimized trajectory bends to satisfy interference constraints, while UAV transmit power satisfies maximum-power and total-energy constraints.

C. Convergence Performance of the Proposed Algorithm

The proposed algorithm converges within 21 iterations under the tested maritime network settings. The paper coordinates UAVs with existing satellite and terrestrial systems by jointly optimizing trajectory and transmit power using only large-scale CSI.

  • C. Convergence Performance of the Proposed Algorithm: The maximum number of iterations is smaller than 21, so the algorithm converges within 21 iterations.The experiment varies transmit-power, interference-temperature, and total-energy settings across randomly generated scenes.
  • C. Convergence Performance of the Proposed Algorithm: UAVs are deployed for on-demand satellite-terrestrial maritime communications and coordinated with existing systems for spectrum sharing and efficient backhaul.
  • C. Convergence Performance of the Proposed Algorithm: The UAV trajectory and transmit power are jointly optimized subject to kinematic, interference, backhaul, and communication-energy constraints.The optimization assumes that only large-scale CSI is available, using ship positions obtained through maritime AIS.
  • C. Convergence Performance of the Proposed Algorithm: The non-convex optimization problem is solved through problem decomposition, successive convex optimization, and bisection searching.Simulation results show that the UAV fits well with existing satellite and terrestrial systems.

APPENDIX A PROOF OF THEOREM 1

The appendix establishes properties of the average rate function used in the theorem. It derives the fading distribution and shows that the rate is increasing and strictly concave, then applies a first-order Taylor bound.

  • APPENDIX A PROOF OF THEOREM 1: The channel variable b_a,i,t follows a non-central chi-square probability density function with two degrees of freedom.The derivation uses g_a,i,t ∈ C^N(0,1).
  • APPENDIX A PROOF OF THEOREM 1: The rate expression R_a,i,t uses the zeroth-order modified Bessel function of the first kind in its probability-density formulation.
  • APPENDIX A PROOF OF THEOREM 1: Because a_a,i,t ≥ 0 and f_ba,i,t(γ) > 0, the first derivative of R_a,i,t is positive and the second derivative is negative.Therefore, R_a,i,t is increasing and strictly concave.
  • APPENDIX A PROOF OF THEOREM 1: The proof uses a first-order Taylor expansion to obtain a global lower bound for the relevant convex function.The resulting inequalities are combined with constraints in (9), (29), and (30) to prove the lemma.
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