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Improvement of the Global Connectivity using Integrated Satellite-Airborne-Terrestrial Networks with Resource Optimization

Ahmad Alsharoa, Mohamed-Slim Alouini

arXiv:1912.03828v1cs.NI

TL;DR

Terrestrial networks may not support growing demand or remote areas, while satellite-ground links face path loss and delay. The paper optimizes associations, power, and HAP locations in an integrated network; at 400 users, its proposed scheme improves average rate throughput over two benchmark solutions.

  • Problem

    Terrestrial infrastructure can be infeasible in remote areas, while satellite-ground links face high path loss and added delay.

    Source: A. Background · p. 2

  • Method

    The framework optimizes associations and power in a short-term stage and HAP locations in a long-term stage.

    Source: C. Contributions · p. 5, §VII · p. 23

  • Results

    At U = 400, the proposed solution enhances average rate throughput by at least 39% versus optimized associations with uniform power and 88% versus random associations with uniform power.

    Source: §VI · p. 21

  • Takeaways & Limitations

    The simulations illustrate the proposed framework’s impact on user throughput while accounting for back-haul limitations.

    Source: §VII · pp. 23–24

    The authors identify the back-haul bottleneck as a limitation and propose considering a free-space optical gateway-to-HAP link, which would add optimization parameters such as line-of-sight angles.

    Source: §VII · p. 24

Abstract

from arXiv · show

In this paper, we propose a novel wireless scheme that integrates satellite, airborne, and terrestrial networks aiming to support ground users. More specifically, we study the enhancement of the achievable users' throughput assisted with terrestrial base stations, high altitude platforms (HAPs), and satellite station. The goal is to optimize the resource allocations and the HAPs locations in order to maximize the users' throughput. In this context, we propose to solve the optimization problem in two stages; first a short-term stage and then a long-term stage. In the short-term stage, we start by proposing a near optimal solution and low complexity solution to solve the associations and power allocations. In the first solution, we formulate and solve a binary linear optimization problem to find the best associations and then using Taylor expansion approximation to optimally determine the power allocations. While in the second solution, we propose a low complexity approach based on frequency partitioning technique to solve the associations and power allocations. One the other hand, in the long-term stage, we optimize the locations of the HAPs by proposing an efficient algorithm based on a recursive shrink-and-realign process. Finally, selected numerical results show the advantages provided by our proposed optimization scheme.

I. INTRODUCTION

The introduction motivates integrating terrestrial, airborne, and satellite networks to support connectivity where terrestrial infrastructure or satellite links are limited. It presents a resource-optimization framework that jointly considers associations, power, and HAP locations, with short- and long-term solution stages.

A. Background

  • Terrestrial networks may struggle with growing wireless demand, and terrestrial infrastructure can be infeasible in remote areas.The introduction motivates integrating high-altitude stations with terrestrial networks to provide global connectivity.Source: A. Background · p. 2
  • HAPs are presented as an aerial complement to terrestrial and satellite networks because they can improve satellite-ground links and offer broad coverage and rapid deployment.The cited background contrasts HAP coverage radii of about 30 km with about 1,000 m for terrestrial base stations.Source: A. Background · p. 3, B. Related Works · p. 3

B. Related Works

  • The paper identifies a gap in integrated satellite-airborne-terrestrial resource management: prior HAP throughput studies did not consider HAP back-haul links.Prior integration work considered HAP relaying for satellite links or network-function offloading, while the cited throughput work omitted back-hauling.Source: B. Related Works · p. 4, C. Contributions · p. 5

C. Contributions

  • The framework maximizes ground-user downlink throughput by optimizing front-haul and back-haul associations, base-station power, and HAP locations under resource and back-haul constraints.It is intended to support users where terrestrial base stations are overloaded or where users lie outside their coverage.Source: C. Contributions · pp. 4–5
  • The short-term stage optimizes associations and power with fixed HAP locations, while the long-term stage relocates HAPs using average user distributions.The short-term variables can be optimized more frequently than the long-term location variables.Source: C. Contributions · p. 5
  • Two short-term solutions are proposed: alternating association optimization and Taylor-approximation power allocation, and a lower-complexity frequency-partitioning approach.HAP locations are optimized with a low-complexity heuristic based on a recursive shrink-and-realign process.Source: C. Contributions · p. 5

D. Paper Organization

This material outlines the paper’s structure and models a three-tier downlink network with OFDMA resource blocks. Its assumptions specify user association, interference, and the channel-coordinate representation.

D. Paper Organization

  • The paper proceeds from the system model and problem formulation to short-term association and power solutions, long-term HAP placement, simulation results, and conclusion.The corresponding sections are II through VII.Source: D. Paper Organization · p. 6

II. SYSTEM MODEL

  • The modeled network has one satellite station, L HAPs, M terrestrial base stations, W gateway feeder stations, and U ground users.The gateways provide back-haul links in the model.Source: §II · p. 6

A. Assumptions

  • The model uses OFDMA resource blocks and assumes each user is served by at most one base station on one resource block.It assumes orthogonal resource blocks prevent intra-cell downlink interference, while nearby terrestrial base stations can cause inter-cell interference; space- and air-tier interference is ignored.Source: A. Assumptions · pp. 6–8

B. Channel Model

  • The channel model represents user and base-station locations in a three-dimensional coordinate system, with the prime symbol denoting transpose.Base stations include terrestrial stations, HAPs, and the satellite station.Source: B. Channel Model · p. 8

1) Front-hauling Channel Model:

The front-haul channel model combines distance-dependent propagation with environmental attenuation and fading. It assigns different fading models to terrestrial, air, and space links.

1) Front-hauling Channel Model:

  • Front-haul channel gain includes propagation and path loss, environmental attenuation, and a fading term.The base-station-to-user distance and tier carrier frequency are identified as model inputs.Source: 1) Front-hauling Channel Model · p. 8
  • The channel fading assumptions differ by tier: terrestrial links use Rayleigh fading, HAP links use Rician fading, and satellite links use shadowed Rician fading.The satellite shadowed-Rician model is parameterized by average line-of-sight and multipath powers and a Nakagami parameter.Source: 1) Front-hauling Channel Model · p. 8
  • The model assumes fast fading is approximately constant across subcarriers within a resource block and independently identically distributed across resource blocks.HAP Rician fading uses a Rician factor.Source: 1) Front-hauling Channel Model · p. 8

2) Back-hauling Channel Model:

The model specifies back-haul channel assumptions, front-haul and back-haul association rules, and downlink rate expressions. Associations and resource blocks are constrained to limit interference and respect each HAP’s back-haul link.

2) Back-hauling Channel Model:

  • Back-haul links from gateways to HAPs and from the satellite station to HAPs use a Rician-fading channel model.The Rician factor depends on whether the link is the main or alternative back-haul link.Source: 2) Back-hauling Channel Model · p. 9

C. Front-hauling Association

  • Each user can associate with at most one base station on one resource block, while a base station can serve multiple users on distinct resource blocks.The distinct-resource-block rule is used to mitigate intra-cell interference.Source: C. Front-hauling Association · pp. 9–10

D. Back-hauling Association

  • Each HAP is associated with exactly one gateway or the satellite station, subject to a maximum number of HAPs per station.The selected back-haul link depends on user distribution and back-haul link quality.Source: D. Back-hauling Association · p. 10

E. Downlink Data Rates

  • The downlink rate model includes allocated transmit power, noise, and terrestrial inter-cell interference, while space- and air-tier inter-cell interference is ignored.The model attributes the latter assumption to different antennas, beams, and frequency sets; back-haul rate depends on station bandwidth and transmit power.Source: E. Downlink Data Rates · pp. 10–11

III. PROBLEM FORMULATION

The formulation maximizes ground-user downlink rate utility by jointly optimizing associations, base-station power, and HAP locations under resource constraints. It compares sum-rate and max-min utility objectives and divides the solution into short- and long-term stages.

III. PROBLEM FORMULATION

  • The optimizer maximizes ground-user downlink rate utility by selecting associations, base-station transmit powers, and HAP locations, with satellite or HAP service considered when TBS capacity or coverage is insufficient.Which network elements are used depends on user locations, user demand, and TBS availability.Source: §III · p. 11
  • The formulation assumes perfect fiber backhaul for TBSs and feeder links for the satellite, while constraining BS peak power, HAP backhaul, user association, and HAP backhaul associations.The constraints also prevent intra-cell interference between users associated with the same BS.Source: §III · p. 12

A. Utility Selection

  • The paper characterizes two different utility metrics for use in the optimization problem given in (12)–(18).Source: A. Utility Selection · p. 12
  • Max-sum utility promotes users with favorable channel gains and interference conditions, allocating them better resources but leaving users with poor conditions very low data rates.This metric is equivalent to the sum of users’ FH data rates.Source: 1) Max-Sum Utility (MSU) · pp. 12–13
  • Max-min utility seeks to maximize the minimum user utility and gives greater priority to lower-rate users, leading to more fairness.The formulation introduces R_min as the minimum user rate.Source: 2) Max-Min Utility (MMU) · p. 13
  • The problem is a mixed integer non-linear program, so the paper divides its solution into short-term association and power allocation and long-term HAP-location optimization.The short-term stage offers near-optimal and low-complexity solutions.Source: 2) Max-Min Utility (MMU) · p. 13

IV. SHORT-TERM STAGE

The short-term stage holds HAP locations fixed and addresses front-haul and backhaul associations and base-station transmit powers. It proposes a near-optimal Taylor-approximation solution and a low-complexity frequency-partitioning heuristic.

IV. SHORT-TERM STAGE

  • The short-term stage first solves front-haul and backhaul associations using uniform power distributions, with HAP locations fixed.It then optimizes BS transmit powers for those associations using a Taylor-expansion approximation.Source: §IV · p. 13
  • The near-optimal solution uses Taylor-expansion approximation, while the low-complexity heuristic uses frequency partitioning and omits inter-cell interference among TBSs.Omitting that interference allows the heuristic to solve the problem quickly.Source: §IV · p. 13

A. Near Optimal Solution

The near-optimal approach alternates between association and power decisions, using binary linear optimization for associations and successive convex approximation for power allocation. It approximates a HAP backhaul constraint to obtain a convex power-allocation problem.

A. Near Optimal Solution

  • With transmit powers fixed, the association variables form a binary linear optimization problem after the non-linear utility term is rewritten.The resulting linear problem can be solved with off-the-shelf software such as the Gurobi/CVX interface.Source: A. Near Optimal Solution · p. 14
  • The association and power variables are optimized iteratively by linearizing the utility with respect to associations and approximating the utility and backhaul constraint for power optimization.The stated non-convex terms include constraints (12) and (14).Source: A. Near Optimal Solution · p. 14
  • The power-allocation objective combines the rates for the satellite, HAP, and TBS links, and is made concave in transmit powers for optimization.The paper identifies the second and third terms as concave and applies approximation to the first term.Source: 1) Approximation of The Objective… · p. 15
  • With associations fixed, the power-allocation objective contains a convex term that is lower-bounded by its first-order Taylor expansion at each local point in successive convex approximation.The resulting objective is concave in transmit powers, and the iterative procedure solves the approximated problem using an interior-point method.Source: 1) Approximation of The Objective… · pp. 15–16
  • The HAP backhaul constraint is approximated by requiring each associated user’s HAP data rate to be below the average backhaul constraint.This approximation makes the power-allocation problem convex for fixed associations and HAP locations, with zero duality gap in the stated OFDMA setting.Source: 1) Approximation of The Objective… · p. 16

B. Low Complexity Solution

The low-complexity solution partitions users into cell-center and cell-edge groups, assigning center users to TBSs and serving edge users through HAPs or the satellite. This simplifies association to a linear assignment problem.

B. Low Complexity Solution

  • The frequency-partitioning technique restricts TBS associations to center users and serves edge users through HAPs or the satellite.The method assumes negligible inter-cell interference among center users using the same ground-tier frequency bands.Source: B. Low Complexity Solution · p. 16, Figure 3 · p. 17
  • The resulting association problem is a linear assignment in front-haul and backhaul variables, solved by the Hungarian algorithm with stated complexity (MNM + LNL + N0)^3.The passage gives this complexity for the assignment solution.Source: B. Low Complexity Solution · p. 17
  • With the backhaul constraint approximated, power allocation becomes a convex optimization problem that can be solved through its dual problem.This is the power-allocation step following the assignment solution.Source: B. Low Complexity Solution · p. 17

V. LONG-TERM STAGE

The long-term stage optimizes HAP locations with a recursive shrink-and-realign process, evaluating candidate combinations by the average users served within HAP coverage. It uses average network statistics and throughput rather than instantaneous throughput.

V. LONG-TERM STAGE

  • The non-convex location problem is addressed with a low-complexity SR algorithm focused on average channel statistics and average, not instantaneous, user throughput.The authors describe the algorithm as simple to implement, quick to converge, and near optimal.Source: §V · p. 17
  • Candidate HAP-location combinations are evaluated using average BS associations and transmit powers to maximize the number of average users within HAP coverage.Users associated with terrestrial base stations are excluded from this HAP-user count.Source: §V · pp. 17–18
  • The SR process halves the candidate-circle radius around each local solution until the sample space falls below a threshold or no improvement is possible.The search starts with circles around current HAP locations and selects local combinations with the most average users associated with HAPs.Source: §V · pp. 17–18
  • Fig. 4 illustrates the search with two HAPs, T=4, and Imax=3; compare how candidate circles shrink around local solutions.The radius is halved at each recursive iteration.Source: §V · p. 18, Figure 4 · p. 18

VI. SIMULATION RESULTS

Simulations show the proposed solutions improve average user throughput over benchmark approaches, with HAP placement adapting to user density and network links. The results also expose a fairness trade-off between utility choices and throughput ceilings imposed by backhaul constraints.

  • Simulations use a 180 km × 180 km area with five HAPs at 18 km and user clusters spanning regions with different terrestrial infrastructure availability.Source: §VI · pp. 18–19
  • At low user counts the approximate and low-complexity solutions perform almost equally, but their gap grows at higher counts because frequency partitioning constrains HAP placement.The paper describes that gap as acceptable given HAPs' large coverage areas.Source: §VI · p. 20
  • Fig. 5 shows HAP placement adapting to high- and low-density users while improving FH and BH links; users outside HAP and TBS coverage are associated with the satellite.Source: §VI · pp. 19–20, Figure 5 · p. 21
  • MSU yields the highest average data rate, while MMU maximizes the minimum rate and gives users nearly equal rates, resulting in greater fairness.Source: §VI · pp. 21–22, Table III · p. 23
  • At U = 400, the proposed solution improves average rate throughput by at least 39% over association optimization with uniform power and 88% over random associations with uniform power.Source: §VI · p. 21, Figure 6 · p. 22
  • For HAP users, average rate rises with backhaul bandwidth until the backhaul rate constraint imposes a cutoff; increasing HAP peak power also reaches a backhaul-limited plateau.Source: §VI · pp. 22–23
  • The shrink-and-realign algorithm converges in around 8–13 iterations for both MSU and MMU utilities.Source: §VI · p. 23

VII. CONCLUSION

The paper proposes an optimization framework integrating terrestrial base stations, HAPs, and a satellite station to improve ground-user throughput under backhaul limitations. Simulations illustrate the approach’s behavior and significant impacts on throughput.

VII. CONCLUSION

  • The framework optimizes front-hauling and back-hauling associations, base-station transmit powers, and HAP locations to maximize users’ throughput.It integrates terrestrial base stations, HAPs, and a satellite station while considering backhaul limitations.Source: §VII · p. 23
  • Figure 7 presents average data rate of HAP users versus backhaul bandwidth.Source: Figure 7 · p. 24
  • Simulation results illustrate the approach’s behavior and significant impacts on users’ throughput.Source: §VII · p. 24
  • A future free-space optical link between the gateway and HAPs is proposed to mitigate the backhaul bottleneck, with added complexity from optimizing line-of-sight angles.Source: §VII · p. 24

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