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Ultra-dense LEO: Integrating Terrestrial-Satellite Networks into 5G and Beyond for Data Offloading

Boya Di, Hongliang Zhang, Lingyang Song, Yonghui Li, Geoffrey Ye Li

arXiv:1811.05101v1cs.NI

TL;DR

The paper addresses challenges from limited small-cell backhaul capacity by proposing an ultra-dense LEO-based integrated terrestrial-satellite network. It formulates joint sum-rate and user-access optimization and solves decomposed subproblems with low-complexity matching algorithms, yielding conclusions about LSC access and satellite deployment.

  • Problem

    Limited backhaul capacity in small cells creates new challenges in complex environments.

  • Method

    The paper proposes an ultra-dense LEO-based integrated terrestrial-satellite network and decomposes the optimization into subproblems solved with two low-complexity matching algorithms.

  • Results

    The conclusions encourage arranging more users to access LSCs as traffic grows and identify an optimal number of visible LEO satellites for TSTs.

  • Takeaways & Limitations

    LEO-based backhaul offers a new way to extend traditional networks while jointly optimizing LSC backhaul capacity and user access.

Abstract

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In this paper, we propose a terrestrial-satellite network (TSN) architecture to integrate the ultra-dense low earth orbit (LEO) networks and the terrestrial networks to achieve efficient data offloading. In TSN, each ground user can access the network over C-band via a macro cell, a traditional small cell, or a LEO-backhauled small cell (LSC). Each LSC is then scheduled to upload the received data via multiple satellites over Ka-band. We aim to maximize the sum data rate and the number of accessed users while satisfying the varying backhaul capacity constraints jointly determined by the LEO satellite based backhaul links. The optimization problem is then decomposed into two closely connected subproblems and solved by our proposed matching algorithms. Simulation results show that the integrated network significantly outperforms the non-integrated ones in terms of the sum data rate. The influence of the traffic load and LEO constellation on the system performance is also discussed.

I. INTRODUCTION

The paper integrates ultra-dense LEO satellite networks with terrestrial networks for traffic offloading, jointly optimizing user access, terrestrial resources, and dynamically varying satellite backhaul capacity.

  • The proposed architecture lets users access macro cells, traditional small cells, or LEO-based small cells, whose traffic is uploaded through terrestrial or LEO backhaul.Each LSC can connect to multiple satellites simultaneously over Ka-band.
  • The optimization jointly maximizes users’ sum rate and the number of accessed users subject to each cell’s backhaul capacity constraint.Satellite selection and resource allocation also maximize each LSC’s backhaul capacity.
  • Existing studies commonly assume ideal or fixed backhaul capacity, whereas this paper considers capacity dynamically determined by satellite selection and Ka-band allocation.
  • The coupled optimization is decomposed into terrestrial scheduling and satellite backhaul-capacity subproblems connected by iteratively varying Lagrangian multipliers.The two subproblems are converted into matching problems with externalities.
  • The paper develops a modified Gale-Shapley algorithm for terrestrial scheduling and a swap-matching algorithm with power control and gradient-based pruning for satellite backhaul.The satellite algorithm captures angle-sensitive effects.
  • Simulation results show that the integrated UD-LEO scheme significantly outperforms traditional non-integrated networks in performance.Traffic load and different LEO constellations influence the user scheduling strategy.

II. SYSTEM MODEL

The system model combines macro cells, traditional small cells, and LEO-backhauled small cells to serve uplink users, with LEO links providing dynamically constrained backhaul.

  • A. Scenario Description: Users access the network through a macro cell, a traditional small cell, or a LEO-based small cell.The macro cell has large backhaul capacity, traditional small cells have limited capacity, and LSCs use Ka-band backhaul.
  • A. Scenario Description: Each LSC sends user data from its terrestrial-satellite terminal to LEO satellites, which forward it to an earth gateway or another TST-equipped node.
  • A. Scenario Description: Multiple satellites are visible over the service area at each time slot, supporting seamless mobile-user coverage.
  • A. Scenario Description: Each TST can connect to multiple satellites simultaneously through independent antenna apertures, increasing LSC backhaul capacity.
  • A. Scenario Description: The architecture assumes satellites act as remote radio heads without onboard processing, with access control located at the macro BS.
  • B. Transmission Model for Terrestrial Communications: The model represents user coverage with a binary matrix A and user association and subchannel allocation with a binary matrix X.A indicates whether a user lies within a cell’s coverage; X indicates service by a base station over a subchannel.
  • B. Transmission Model for Terrestrial Communications: Cell data rates must not exceed their backhaul capacities, with terrestrial-cell capacities fixed for the macro cell and traditional small cells.

C. Transmission model for LEO-based Backhaul

The transmission model represents LEO backhaul through satellite associations, Ka-band subchannel allocation, interference-aware channels, antenna gains, angular separation, propagation delay, traffic load, and equivalent capacity.

  • The LEO backhaul capacity is constrained by traffic load and the capacities of the associated TST–satellite links, with total capacity defined separately from TST-to-satellite links.The associated-satellite set N_m determines which satellite links contribute to a TST’s backhaul.
  • Satellite positions, altitudes, and speeds are known per time slot, and a quasi-static model treats satellite positions as unchanged within each slot.The approach uses pre-planned orbits and semi-persistent scheduling to update LEO backhaul links periodically.
  • Each TST associates with satellites over Ka-band subchannels using a binary matrix B, where b_m,n,q=1 denotes an active TST–satellite–subchannel link.The model also includes the received signal, transmit power, transmitted signal, channel gain, and inter-satellite co-channel interference.
  • The channel model incorporates large-scale fading, shadowed-Rician fading, antenna gains, off-axis gains, angular separation, and additive white Gaussian noise.Antenna gain and satellite geometry are illustrated in Fig. 2.
  • Each TST–satellite link has propagation delay, and its achievable rate is used to compute an equivalent backhaul capacity dependent on link capacity, traffic load, and round-trip delay.The round-trip delay is calculated as T_trip,n=2H_n/c, where H_n is satellite altitude and c is the speed of light.

III. PROBLEM FORMULATION AND DECOMPOSITION

The paper formulates joint terrestrial offloading and LEO-backhaul resource allocation to maximize sum rate and accessed users under angular, association, power, and capacity constraints, then decomposes the problem using Lagrangian multipliers.

  • III. PROBLEM FORMULATION AND DECOMPOSITION: The optimization jointly maximizes the sum rate and number of accessed users by optimizing terrestrial offloading, TST–satellite association, and resource allocation.The objectives address both network throughput and expanded user coverage.
  • A. Angular constraints for LEO backhaul: Satellites serving the same TST cannot share a subchannel when their angular separation is within the threshold θ_th, preventing transmission failure.The constraint uses elevation-angle differences from the angle matrix Θ.
  • B. Problem Formulation: The formulation assigns binary user–cell–subchannel and TST–satellite–subchannel variables while restricting each user to one reachable cell and one subchannel.Orthogonal frequency-resource use within each cell is enforced, and each user can access only one cell.
  • B. Problem Formulation: The constraints couple terrestrial cell data rates to backhaul capacities, limit satellite-subchannel assignments and simultaneous satellite links, and bound TST backhaul transmit power.Each satellite subchannel is assigned to at most one TST, while each TST uses at most N_r satellite links simultaneously.
  • C. Lagrangian Dual Decomposition: Lagrangian dual decomposition separates the coupled original problem into terrestrial traffic offloading and LEO-based backhaul capacity optimization subproblems.For fixed multipliers, the Lagrangian terms depend separately on terrestrial association variables and backhaul association and power variables.
  • C. Lagrangian Dual Decomposition: The optimization iteratively solves the terrestrial traffic offloading and LEO-backhaul problems for given multipliers, then updates the multipliers until the change in δ falls below ε.The multiplier update uses a decreasing exponential function of the iteration index t.
  • C. Lagrangian Dual Decomposition: Because binary variables make cell data rates discontinuous, the Lagrangian dual method does not guarantee constraint satisfaction, so user scheduling is adjusted after optimization.For violated capacity constraints, users are removed in increasing order of their user–base-station link data rates.

IV. ALGORITHM DESIGN FOR TERRESTRIAL DATA OFFLOADING

The terrestrial offloading problem is recast as a matching problem with externalities, then addressed using modified preference relations and propose-and-reject operations.

  • Problem formulation: The TTO problem is a three-dimensional integer program with a non-convex objective, motivating a low-complexity matching-based solution.Users, BSs, and subchannels form the three dimensions, while co-channel interference creates interdependencies among users.
  • Matching formulation: Users, BSs, and subchannels are modeled as three player sets in a multivariate matching process with interference-driven externalities.A BS-subchannel unit is created by pairing each BS with each subchannel, and users are matched to these units.
  • Matching formulation: A one-to-one matching between users and BS-subchannel units naturally satisfies the user-association and subchannel-allocation constraints.Matching user j to unit (m, k) means associating that user with BS m over subchannel k.
  • Propose-and-reject operation: The modified matching process alternates proposals and rejection decisions by BS-subchannel units, subchannels, and users.Users retain the highest-utility proposal, while subchannels retain the candidate pair providing the highest positive utility.

3) Algorithm Description:

TUASA initializes user-BS-subchannel matches and iteratively applies propose-and-reject operations, guaranteeing maximum user access while improving sum rate and converging finitely.

  • Algorithm Description: TUASA initializes each subchannel with the best feasible combination of one user and one BS, then iterates propose-and-reject operations.The process continues while unmatched users remain or matched BS-subchannel units still seek proposals.
  • Algorithm Description: The propose-and-reject operation guarantees the maximum number of accessed users while improving the sum rate.A user is compulsorily served whenever an unmatched BS-subchannel unit can satisfy the coverage condition.
  • Algorithm Description: TUASA is guaranteed to converge to a final matching after a limited number of iterations.This convergence guarantee is established in Appendix A.
  • Stability and convergence: Co-channel interference makes preferences non-substitutable, so traditional blocking-pair and stability concepts cannot be directly applied.The paper therefore introduces a stricter blocking-pair concept for its matching analysis.
  • Stability and convergence: When ρ2 = 0, the analysis uses group stability; when ρ2 ≠ 0, the final matching reaches an equilibrium against utility-improving individual-rational blocking pairs.Under ρ2 ≠ 0, improving one new pair cannot occur without compromising other matched BS-subchannel units.

3) Computational Complexity:

The LBCO problem introduces multi-connectivity, angle-sensitive interference, and power-control challenges beyond TTO, motivating SMPC and its structured swap cases.

  • Computational Complexity: The terrestrial-to-LEO association problem is converted into a many-to-one matching problem with externalities, and SMPC adds continuous power control.TSTs can match multiple satellite-subchannel units, while each satellite-subchannel unit matches at most one TST.
  • Computational Complexity: LBCO lacks transmit-power adjustment during propose-and-reject operations, and constructing complete preference lists over power levels is difficult.The angularly sensitive setting also prevents Algorithm 1 from guaranteeing group stability.
  • Computational Complexity: Angular sensitivity makes satellite reassignment alter interference through different off-axis antenna gains, creating dynamic interactions across subchannels.These interactions mean most existing matching algorithms and TUASA are no longer suitable for the LBCO problem.
  • Computational Complexity: SMPC evaluates five swap types, including cases with virtual or identical nodes, and allocates power by solving the corresponding control problem.Power may need to be redistributed across multiple links or subchannels during a swap.
  • Computational Complexity: A swap is approved only when feasibility constraints remain satisfied and the involved subchannels’ total utility increases.The procedure prunes candidate swaps to reduce repeated utility optimization and comparison.

1) Convergence:

SMPC repeatedly executes feasible, utility-improving swaps until none remains, producing a swap-stable matching and guaranteeing convergence under bounded weighted capacity.

  • Convergence: Each approved swap matching increases the utility of the whole system, while limited resources impose an upper bound on weighted capacity.Consequently, the total utility cannot increase indefinitely.
  • Convergence: SMPC is guaranteed to converge because approved swaps monotonically improve bounded total utility.The convergence claim follows from the finite improvement process described for the algorithm.
  • Convergence: The final matching is swap-stable when no feasible and approved swap can further improve total utility.Algorithm 2 stops when no approved swap matching remains.
  • Convergence: When TSTs are geographically close enough to share coordinates, the final matching is also an equilibrium when ρ2 = 0.This is presented as a proved remark about Algorithm 2’s equilibrium behavior.

3) Complexity:

The paper analyzes the matching algorithms’ complexity and evaluates the integrated network under varied simulation settings, traffic loads, and LEO configurations.

  • Complexity: The worst case contains NQ(M−M′) type-1 or type-2 swap matchings, plus additional type-3, type-4, and type-5 possibilities.The type-3 count is Nr(Nr−1)(M−M′)/2, while type-4 and type-5 counts depend on Nr, M−M′, and NQ.
  • Complexity: Pruning substantially reduces the number of traversed swap matchings in practice.The reduction is evaluated through the swap-operation C.D.F. in Fig. 3(b).
  • Complexity: O(M) for random matching and O(M^2) for greedy matching provide reference complexity baselines.
  • Complexity: The proposed SMPC algorithm converges faster as the number of TSTs grows, especially when pruning is applied.This behavior reflects the algorithm’s low computational complexity with effective pruning.
  • Simulation results: The LITS scheme’s sum rate is close to ideal-backhaul performance and exceeds both TTH and NITS schemes.The comparison is shown against user density in Fig. 4(a).
  • Simulation results: Total backhaul capacity increases with satellite count but exhibits diminishing returns, while smaller projected areas can eventually reduce capacity through inter-satellite interference.Multi-connectivity raises capacity as Nr grows, but excessive satellite angular proximity can make interference dominant.
  • Simulation results: Backhaul selection depends on traffic load: TSCs have lower delay at low load, whereas LEO backhaul gains an advantage at high load.The LEO-based advantage emerges when transmission delay outweighs round-trip-time effects.
  • Simulation results: As per-user generated data increases, a larger proportion of users is scheduled to access LSCs.The paper links this scheduling shift to increased equivalent backhaul capacity and lower delay.

VII. CONCLUSION

The paper proposes an integrated terrestrial-satellite architecture that jointly optimizes user access and LSC backhaul capacity through two matching-based subproblems. It concludes that traffic load should guide terrestrial-versus-LEO access, while satellite deployment has an optimum for backhaul capacity.

  • VII. CONCLUSION: The proposed architecture integrates LEO-based backhaul with terrestrial networks to extend traditional network capabilities.
  • VII. CONCLUSION: The optimization maximizes sum rate and accessed users subject to jointly optimized backhaul capacities for LSCs.
  • VII. CONCLUSION: The intractable optimization is decomposed into two connected subproblems and solved as two low-complexity matching problems.
  • VII. CONCLUSION: TSC access is favored at low traffic load because it provides lower propagation delay.
  • VII. CONCLUSION: For a fixed number of visible LEO satellites, an optimal deployment exists for maximizing total backhaul capacity.

APPENDIX A

Appendix A establishes convergence and stability properties for the matching algorithms, then outlines solution methods for the continuous subproblems and swap-matching complexity.

  • Matching convergence: The coverage matrix limits potential users per BS, making each BS-subchannel unit’s preference list complete and transparent.These conditions support the matching-process convergence argument.
  • Matching convergence: The TUASA iterations terminate when every matched BS-subchannel unit has no available choices remaining in its preference list.The argument relies on shrinking remaining choice sets as proposals and rejections proceed.
  • Continuous subproblems: PC1 is solved by dividing it into two PC3-type problems with one continuous variable and searching their extreme and boundary points.The boundary points are 0 and P_T; the best solution is then selected to obtain the PC1 optimum.
  • Continuous subproblems: PC2 is formulated as a difference-of-convex objective over a convex closed constraint set and solved with a classic difference-of-convex algorithm.The reformulation uses p = (p1, p2), with interference and noise included in I′.
  • Swap-matching complexity: The swap-matching analysis bounds the number of type-1 through type-5 swaps using M, M′, N, Q, and each TST’s link count N_r.Type-3 swaps total N_r(N_r − 1)(M − M′)/2, while type-4 and type-5 counts use a maximum-based bound.
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