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Hybrid Satellite-UAV-Terrestrial Networks for 6G Ubiquitous Coverage: A Maritime Communications Perspective

Yanmin Wang, Wei Feng, Jue Wang, Tony Q. S. Quek

arXiv:2104.12077v1cs.IT

TL;DR

The paper addresses limited-rate satellite links and incomplete offshore coverage from on-shore BSs by designing a hybrid satellite-UAV-terrestrial maritime network. It formulates energy-minimizing joint link scheduling and rate adaptation with QoS guarantees using predictable large-scale CSI, then solves the NP-hard problem through Min-Max transformation and iterative relaxation. Simulations report substantially reduced energy consumption and performance close to the optimal solution, with polynomial computation complexity.

  • Problem

    Existing maritime networks provide either limited satellite transmission rates or geographically restricted on-shore coverage, motivating deployable BSs for broader maritime coverage.

  • Method

    The paper orchestrates satellite, on-shore, UAV, and vessel links using large-scale CSI predicted from trajectories and shipping lanes, then applies Min-Max transformation and iterative relaxation to the resulting NP-hard MINLP.

  • Results

    83% lower network energy consumption than the fixed transmission scheme and 77% lower than the rate-adaptation-only scheme are achieved for α = 2/3, while performance remains close to the optimal solution.

  • Takeaways & Limitations

    The process-oriented scheme provides agile on-demand maritime coverage with reduced system overhead and polynomial computation complexity.

Abstract

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In the coming smart ocean era, reliable and efficient communications are crucial for promoting a variety of maritime activities. Current maritime communication networks (MCNs) mainly rely on marine satellites and on-shore base stations (BSs). The former generally provides limited transmission rate, while the latter lacks wide-area coverage capability. Due to these facts, the state-of-the-art MCN falls far behind terrestrial fifth-generation (5G) networks. To fill up the gap in the coming sixth-generation (6G) era, we explore the benefit of deployable BSs for maritime coverage enhancement. Both unmanned aerial vehicles (UAVs) and mobile vessels are used to configure deployable BSs. This leads to a hierarchical satellite-UAV-terrestrial network on the ocean. We address the joint link scheduling and rate adaptation problem for this hybrid network, to minimize the total energy consumption with quality of service (QoS) guarantees. Different from previous studies, we use only the large-scale channel state information (CSI), which is location-dependent and thus can be predicted through the position information of each UAV/vessel based on its specific trajectory/shipping lane. The problem is shown to be an NP-hard mixed integer nonlinear programming problem with a group of hidden non-linear equality constraints. We solve it suboptimally by using Min-Max transformation and iterative problem relaxation, leading to a process-oriented joint link scheduling and rate adaptation scheme. As observed by simulations, the scheme can provide agile on-demand coverage for all users with much reduced system overhead and a polynomial computation complexity. Moreover, it can achieve a prominent performance close to the optimal solution.

I. INTRODUCTION

The paper proposes integrating satellite, on-shore, UAV, and vessel infrastructures into a hybrid maritime network for energy-efficient, on-demand coverage. It formulates coordinated link scheduling and rate adaptation using predictable large-scale CSI under maritime deployment constraints.

  • Motivation: Existing maritime networks combine wide-coverage satellites with geographically limited on-shore BSs, leaving bandwidth, delay, and offshore coverage shortcomings.Satellites suffer long transmission distance and limited, expensive bandwidth, while on-shore BSs leave offshore coverage holes.
  • Motivation: Mobile UAVs and vessels can serve as deployable BSs, cooperating with fixed infrastructure to provide on-demand maritime services and extend coverage toward 6G requirements.This cooperation creates an irregular and dynamic satellite-UAV-terrestrial topology that complicates resource orchestration and backhaul coordination.
  • Framework: The proposed hierarchical framework uses satellites for global signaling, on-shore BSs for source data and backhaul, UAVs for blind-spot filling, and selected vessels for opportunistic relaying.Links among these components are orchestrated using UAV trajectories and vessel shipping lanes as extrinsic information.
  • Problem formulation: The paper formulates joint link scheduling and rate adaptation to minimize network energy consumption with QoS guarantees using only predictable, slowly varying large-scale CSI.The resulting optimization is an NP-hard MINLP with hidden nonlinear equality constraints.
  • Solution: An iterative relaxation, gradually approaching method, and Min-Max transformation produce a polynomial-complexity process-oriented suboptimal scheme.The scheme is designed for resource-limited practical applications and achieves performance close to the optimal solution in simulations.

III. JOINT LINK SCHEDULING AND RATE ADAPTATION

This section formulates joint link scheduling and rate adaptation as an NP-hard MINLP and develops a process-oriented suboptimal solution. The approach combines relaxation, gradual approximation, and Min-Max transformation with complexity analysis.

  • Problem formulation: The hybrid MCN optimization problem is an NP-hard mixed integer nonlinear programming problem.Its formulation includes hidden nonlinear equality constraints.
  • Solution approach: A process-oriented relaxation and gradually approaching method based on the gentlest ascent principle is introduced to solve the problem.The method is combined with a Min-Max transformation to derive the proposed scheme.
  • Solution approach: The resulting joint link scheduling and rate adaptation scheme is suboptimal and is accompanied by a detailed complexity analysis.The section presents the method as an efficient solution to the formulated optimization problem.

A. Problem Formulation

The hybrid network jointly schedules links and adapts rates to minimize total energy consumption while meeting vessel QoS and practical transmission constraints. The formulation uses large-scale CSI and includes causality, half-duplex, subcarrier, power, and UAV-energy considerations.

  • Network variables: Link scheduling activates or idles each transmitter-receiver link in each time slot, while large-scale fading is treated as identical across subcarriers.The scheduling indicator is binary, and subcarrier identifiers are omitted because each link has the same large-scale fading on different subcarriers.
  • Energy model: Transmission links use bounded powers, and total MCN energy is rewritten as a function of scheduling indicators and transmission rates.The transmit power on link i →j@t is bounded by transmitter i's maximum power, and the rate-dependent expression supports the optimization formulation.
  • Flow constraints: Data-forwarding causality requires transmissions in slot t + 1 not to exceed the data available at the end of slot t.Initial data volumes are specified at t = 1, and the formulation includes corresponding first-slot conditions.
  • QoS and operational constraints: The optimization enforces QoS guarantees for vessels and half-duplex restrictions on UAVs and vessels.Half-duplex constraints restrict simultaneous transmission and reception, while vessel QoS requirements are included in the formulation.
  • Energy limits: The objective minimizes total energy under link-quality-dependent rates, but extreme cases can violate UAV onboard-energy limits.An additional bound on active links transmitted by an energy-limited UAV can be added, although more elaborate energy-limit treatments remain future work.

B. Problem Analysis

The formulated problem is difficult because it is an NP-hard MINLP with hidden nonlinear equalities. The paper relaxes scheduling into rate variables, progressively shrinks the relaxed solution space, and uses a Min-Max transformation to obtain a polynomial-complexity solution close to the optimum.

  • Problem challenges: The original formulation is NP-hard and contains hidden nonlinear equality constraints linking auxiliary variables and transmission rates.These are the two main computational challenges identified for the optimization problem.
  • Relaxation and gradually approaching: Scheduling indicators can be merged into rates because inactive links must have zero rate, while active links must receive nonzero rate.After solving the relaxed problem, scheduling indicators are detached from rates, though relaxation may temporarily violate original scheduling constraints.
  • Relaxation and gradually approaching: The relaxed solution space is iteratively shrunk by identifying violated half-duplex and subcarrier constraints and selecting updates with the gentlest energy increase.Conflicting links are grouped across time slots, preserving the sequential structure of data streaming during coordinated updates.
  • Relaxation and gradually approaching: The process-oriented procedure repeatedly updates rates and scheduling across all time slots until the original constraints are satisfied.If violations remain, solution-space shrinking and variable updates are repeated; otherwise, the resulting variables solve the original formulation.
  • Min-Max transformation: The Min-Max transformation absorbs hidden nonlinear equalities by converting the relaxed problem into a convex-concave saddle-point problem with linear inequalities.The transformed objective is convex in rates and concave in auxiliary variables, with the latter constrained to z_i,j,t ≥ 1.
  • Solution properties: Polynomial-complexity computations obtain an optimal relaxed solution, while the complete process-oriented scheme achieves performance close to the optimal solution.The transformed problem's solution is a saddle point within the feasible convex set, and simulations illustrate the transformed objective in simplified scenarios.

C. Suboptimal Joint Link Scheduling and Rate Adaptation Scheme

The paper develops a suboptimal joint link scheduling and rate adaptation scheme by iteratively shrinking a relaxed solution space until the original constraints are satisfied.

  • The proposed scheme solves a suboptimal joint link scheduling and rate adaptation problem for the hybrid satellite-UAV-terrestrial MCN.
  • The algorithm first solves a Min-Max problem, detaches scheduling indicators from rate variables, and initializes iterative constraint sets.
  • For each of two processing stages, the algorithm identifies the latest active time slot and repeatedly solves constrained Min-Max problems.
  • The accumulated forced-to-zero constraints progressively shrink the relaxed solution space toward the original problem's feasible region.
  • The final Min-Max solution, obtained after the accumulated constraints are imposed, constitutes a solution to the original joint scheduling and rate adaptation problem.
  • The scheme converges within a maximum of [2(I + J) −N]T iterations, with s1 ≤ (I + J)T and s2 ≤[(I + J) −N]T.

D. Complexity Analysis

The complexity analysis bounds the iterative workload and shows that the proposed suboptimal scheme has polynomial complexity, substantially below exhaustive search in the considered scenarios.

  • The main computational cost comes from iteratively solving the Min-Max problems in (34).
  • The proposed scheme has polynomial complexity because each Min-Max problem can be solved with polynomial complexity.
  • Simulation results show that the number of solved problems N is less than 1/100 of the loose upper bound N̄ in the considered network scenarios.
  • Exhaustive search requires a maximum computation complexity of O(2(I+J)^2T), which rapidly becomes prohibitive as I + J and T grow.

IV. SIMULATION RESULTS AND DISCUSSIONS

The simulations model a hybrid maritime network in a 25km^2 area with shore, UAV, and vessel components under specified propagation and timing parameters.

  • The simulated MCN uses I = 1, J = 9, J′ = 8, T = 10, and N = 9 within a square area of 25km^2.
  • The on-shore BS is placed at the area's edge, while vessels sail along randomly generated straight shipping lanes.
  • Each time slot lasts Δτ = 30s and each subcarrier has bandwidth Bs = 1MHz.
  • The simulation sets the carrier frequency to fc = 2GHz, with BS, UAV, and vessel antenna heights of 50m, 100m, and 5m, respectively.

A. Performance of the Proposed Scheme

Across QoS guarantees, the proposed joint link scheduling and rate adaptation scheme reduces network energy consumption and uses relatively low computational effort. Its iterative implementation also converges quickly.

  • 83% and 77% lower energy consumption are achieved at α = 2/3 versus the fixed transmission and rate-adaptation-only schemes, respectively.The gains increase to 86% and 91% at α = 1/4.
  • The energy-efficiency gain increases as α decreases because vessels occupy fewer time slots to satisfy their QoS guarantees.The paper connects smaller α with greater opportunity to improve network energy efficiency.
  • N remains below 1% of the upper bound N̄ across all 10 randomly sampled topologies, indicating low computation complexity relative to the optimal scheme.For the considered network, the optimal scheme has maximum complexity O(2^((I+J)^2T)), while the proposed scheme solves substantially fewer problems.
  • The proposed scheme converges rather quickly for different α values and therefore different QoS guarantees.The convergence behavior is evaluated through the number of problems solved during the iterative implementation.

B. Comparison with the Optimal Solution

The paper compares the proposed scheme with an upper bound obtained from a relaxed Min-Max problem because exhaustive search for the optimal solution is prohibitively complex. The proposed scheme remains close to this super-optimal benchmark.

  • The comparison benchmark is efficiently obtained by solving the equivalent Min-Max problem after relaxing the original optimization problem.This avoids exhaustive search, whose complexity becomes prohibitive for larger networks.
  • About 10% is the performance gap between the proposed scheme and the super-optimal relaxed benchmark averaged over 10 randomly sampled topologies.Because the benchmark is super-optimal, the paper concludes that the gap to the true optimal solution must be even smaller.

C. Network Performance with and without UAVs

UAVs improve both energy consumption and coverage when combined with the proposed scheme. The coverage advantage is especially pronounced under more severe coverage conditions.

  • 78% lower energy consumption is achieved with UAV relaying at α = 2/3, compared with the network without UAV relaying.At α = 1/4, the reported reduction is 10%.
  • C1 denotes the UAV-aided MCN with the proposed scheme, whereas C2 uses fixed transmission and leaves the UAV idle.The comparison uses the minimum data volume received by vessels as the coverage indicator.
  • C1 achieves a noticeably larger minimum received data volume than C2 across the evaluated network topologies.The results average minimum received data volumes over 10 semi-random network topologies and vary the transmit powers of the shore BS, UAV, and vessels.
  • The average coverage gain of C1 over C2 is about 3.5 for ΔP = 0dB and 10 for ΔP = −10dB.The larger gain at −10dB indicates greater coverage-enhancement potential under more severe coverage problems.

V. CONCLUSIONS

The paper formulates and solves energy-aware link scheduling and rate adaptation for a hybrid maritime network using large-scale CSI. The resulting scheme provides agile on-demand coverage, polynomial complexity, and performance close to the optimal solution.

  • The proposed scheme orchestrates hierarchical links using slowly varying large-scale CSI derived from UAV trajectories and vessel shipping lanes.It targets total energy minimization with QoS guarantees for all users.
  • The NP-hard MINLP is addressed through Min-Max transformation, relaxation, and a gradually approaching method.These steps produce a process-oriented joint link scheduling and rate adaptation scheme.
  • The scheme converges quickly and has polynomial computation complexity.This makes the approach more suitable for practical resource-limited applications than the optimal solution, whose complexity is prohibitive.
  • The scheme provides agile on-demand coverage for all users while greatly reducing total energy consumption.
  • Its performance is prominent and close to the optimal solution.
  • Future work could incorporate UAV trajectory optimization, online dynamic adjustment, and more critical QoS requirements.

APPENDIX A PROOF OF THEOREM 1

The appendix establishes structural properties of the transformed objective and explains how iterative relaxation progressively enforces the original constraints. It also bounds the iteration process by tracking constraint violations and link removals.

  • Proof of Theorem 1: Equation (64) expresses total energy as a maximization over scheduling variables constrained by z_i,j,t ≥ 1.
  • Proof of Theorem 1: The transformed objective is convex in rate variables and concave in scheduling variables over the stated feasible domains.The proof invokes convexity of the exponential function and the relevant second-derivative result.
  • Proof of Theorem 1: Each iteration shrinks the relaxed problem's solution space according to the process-oriented rules.
  • Proof of Theorem 1: For x = 1, each iteration progressively transforms violated half-duplex constraints toward satisfaction.The worst-case iteration count assumes all such constraints are initially violated.
  • Proof of Theorem 1: After the first phase, at most I + J links remain active per time slot, so phase two removes at most (I + J − N)T extra active links.Each phase-two iteration can set additional active links idle to satisfy subcarrier constraints.
  • Proof of Theorem 1: The total iteration count is obtained by combining the bounds for the two iterative phases.
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