NOMA-Based Hybrid Satellite-UAV-Terrestrial Networks for Beyond 5G Maritime Internet of Things

I. INTRODUCTION

• 5G does not provide efficient sea coverage, while TBSs have limited reach and satellite links have low data rates and large transmission delays.The paper frames effective maritime network construction as an open problem.Source: §I · p. 1

A. Related Works

• Prior maritime studies did not address wide-sparsity maritime IoT with a corresponding on-demand coverage scheme, and full CSI can impose overhead.The paper also notes that practical NOMA-based hybrid coverage regimes remain lacking.Source: A. Related Works · p. 2

B. Main Contributions

• The paper establishes user-centric virtual clusters of TBSs and tethered UAVs, using NOMA for sparse maritime users and sharing spectrum with satellites.The satellite supports far-sea areas beyond nearshore coverage.Source: B. Main Contributions · p. 2
• The authors formulate large-scale-CSI-based ergodic sum-rate maximization with QoS and inter-segment interference constraints, then use max-min reformulation, an auxiliary function, and successive convex approximation.They report simulation evidence of interference mitigation, low algorithmic complexity, and potential coverage gains.Source: B. Main Contributions · p. 2

C. Organization and Notation

• The paper proceeds from the system model to joint power allocation, then presents simulations and conclusions.Sections II–V cover those topics, respectively.Source: C. Organization and Notation · p. 2
• Vectors and matrices use lower- and upper-case bold symbols; the notation also defines complex matrices, identity matrices, norms, conjugate transpose, determinants, and Gaussian expectations.The complex Gaussian distribution is denoted CN(0, σ^2).Source: C. Organization and Notation · pp. 2–3
• Fig. 1 depicts user-centric TBS–UAV virtual clusters, coastal ships paired with buoys, satellite-connected ocean-going ships, and interference across users, clusters, and network segments.Source: Figure 1 · p. 3

II. SYSTEM MODEL

• Tethered UAVs form dynamic virtual clusters with TBSs, serving nearshore users; NOMA pairs users, while satellites complement coverage farther offshore.Different user pairs within a cluster use orthogonal PRBs, and the model focuses on one PRB and its users.Source: §II · p. 3
• Each of K clusters serves two NOMA users through Tk TBSs and Uk UAVs, while J single-antenna satellite users share the same frequency.The cluster users have Mk antennas; TBSs and UAVs each have one antenna.Source: §II · p. 3
• The composite channel model includes small-scale fading and large-scale fading for links between users and cluster transmitters.The small-scale fading elements are i.i.d. CN(0, 1).Source: §II · p. 3
• TBS links use the Hata propagation model, while UAV links use a model accounting for line-of-sight and non-line-of-sight factors.The UAV channel model includes antenna gains and environment-related parameters.Source: §II · p. 3
• The optimization assumes only large-scale CSI is available to limit overhead, using position data obtainable from systems such as AIS.The paper distinguishes position-related large-scale fading from unpredictable small-scale fading.Source: §II · p. 4

A. Problem Formulation

• User 1 decodes and removes user 2’s message before decoding its own, while user 2 treats user 1’s signal as background noise.The model includes inter-cluster interference in user 1’s interference-plus-noise covariance.Source: A. Problem Formulation · p. 4
• NOMA feasibility requires user 1’s capacity for decoding user 2 to meet or exceed user 2’s own capacity.The paper assumes the users are separated by a large distance so this constraint can be guaranteed, consistent with maritime IoT sparsity.Source: A. Problem Formulation · p. 4
• The formulation imposes a minimum QoS rate for user 2 and caps leakage interference at satellite receivers.The authors neglect satellite-to-nearshore interference because they regard it as much smaller than inter-cluster and inter-user interference.Source: A. Problem Formulation · pp. 4–5
• The objective is to maximize nearshore ergodic sum rate based on large-scale CSI, subject to QoS, inter-segment interference, and practical power limits.The power limits include cluster budgets and maximum affordable TBS and UAV transmit powers.Source: A. Problem Formulation · p. 5
• Random matrix theory approximates the ergodic rate with a closed-form expression, removing expectation operations from the optimization.The approximation is derived asymptotically and is reported as accurate even with two or three antennas.Source: A. Problem Formulation · p. 5
• The resulting problem remains difficult because its objective and feasible set are non-convex, and the implicit parameter introduces additional complex non-linear constraints.The authors recast the problem and apply different schemes to handle the objective and QoS constraints.Source: A. Problem Formulation · p. 5

B. An Equivalent Max-Min Problem

• g_k,m(P, v_k,m) decreases before v*_k,m and increases afterward, making v*_k,m its minimum point.The section uses this monotonicity to express the minimum in optimization form.Source: B. An Equivalent Max-Min Problem · p. 5
• Based on (25), the original problem (P2) is recast as a max-min problem.Source: B. An Equivalent Max-Min Problem · p. 5
• A direct QoS-constraint transformation is rejected because it expands the optimization space without helping further simplification; the authors instead introduce an auxiliary function.Source: B. An Equivalent Max-Min Problem · p. 6

C. Simplification of the Non-Linear Constraint

• When M_k ⩾ T_k + U_k, f_k(P, z_k) increases with z_k, allowing the QoS constraint to be simplified.Slack variables t_k are introduced to define F_k(z_k, t_k), which is used to reformulate (P4) as (P5).Source: C. Simplification of the Non-Linear… · pp. 6–7
• The optimal solution to (P5) is also the optimal solution to (P2), and vice versa.The section uses this equivalence to justify working with the reformulated problem.Source: C. Simplification of the Non-Linear… · p. 7
• Introducing w variables transforms the quasi-convex function g(P, v) into a convex function G(P, w), while logarithmic rearrangement decouples variables in a constraint.The resulting problem (P5) is converted into (P6).Source: C. Simplification of the Non-Linear… · p. 7
• Successive convex approximation linearizes selected terms by first-order Taylor expansions and forms a convex subproblem for each iteration.The algorithm updates P, t, and z by solving (P7).Source: C. Simplification of the Non-Linear… · pp. 7–8
• Algorithm 1 is assured to converge, at least to a local optimum.Its stopping condition compares successive objective values against ϵ.Source: C. Simplification of the Non-Linear… · p. 8

IV. SIMULATION RESULTS AND DISCUSSIONS

• Above 75w, the scheme’s sum rate stops increasing, while the proposed scheme has not saturated in Fig. 3.The authors attribute the proposed scheme’s flexibility to large-scale CSI-based power allocation that balances useful signals and interference.Source: §IV · p. 8, Figure 3 · p. 9
• The proposed NOMA scheme remarkably outperforms the three OMA schemes in Fig. 4, at the cost of more complex receivers.The authors explain that SIC reduces inter-user interference and power-domain separation allows flexible resource assignment between paired users.Source: §IV · p. 8, Figure 4 · p. 9
• UAVs provide more than 50% rate improvement in the tested substitution, while a TBS-only case cannot meet user 2’s basic need.The authors attribute the gain to UAV height enabling high-quality LOS links and say UAV assistance enlarges nearshore coverage.Source: §IV · pp. 9–10
• Less than 6% performance degradation occurs as user 2’s rate requirement increases in the tested settings.The authors report that NOMA satisfies user 2’s basic QoS requirement while retaining system efficiency for high-rate connections to user 1.Source: §IV · p. 8, Figure 5 · p. 10
• Above −100dBm, relaxing the satellite-user interference constraint leaves the nearshore sum rate unchanged.At this point, the authors say the nearshore network and marine satellites can coexist without compromise.Source: §IV · p. 9, Figure 6 · p. 10
• Across 100 randomly generated topologies with Pmax = 50w, the iterative algorithm converges in fewer than 10 iterations in most cases.The authors cite this as evidence of potential for timely resource allocation in reality.Source: §IV · p. 10

• Tethered UAVs coordinate with TBSs in user-centric virtual clusters, where NOMA serves sparse maritime IoT users alongside spectrum sharing with marine satellites.Source: §V · p. 10
• Using large-scale CSI, the authors formulate ergodic sum-rate maximization and address its non-convex constraints through max-min reformulation, an auxiliary function, and iterative optimization subproblems.Source: §V · p. 10
• Simulations indicate the proposed hybrid network’s potential for maritime coverage enhancement.Source: §V · p. 10

APPENDIX A PROOF OF Theorem 1

• The introduced variable z_k corresponds to v*_2,k, and substituting the bound yields a new function f_k(P, z_k).Source: Appendix A · p. 11
• Under M_k ≥ T_k + U_k, f_k(P, z_k) increases with z_k, enabling an optimization-form representation of g_k,2(P, v*_k,2).Source: Appendix A · p. 11

APPENDIX B PROOF OF Lemma 1

• The proof establishes that the optimal solution to P5 is also optimal for P2, and vice versa.Source: Appendix B · p. 12

• Tangent-based approximations tighten constraints while keeping each iteration’s solution in the original problem’s feasible set.The proof applies convex and concave function tangents to construct the tighter constraints.Source: Appendix C · p. 12
• The algorithm is guaranteed to converge at least to a local optimum because its objective increases monotonically and the ergodic sum rate is upper-bounded.Source: Appendix C · p. 12