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Beam scheduling policy for communications and PNT services from LEO satellites

Alejandro Gonzalez-Garrido, Francesco Menzione, Ottavio M. Picchi, Carla Amatetti

arXiv:2608.28217v1eess.SP

TL;DR

The paper asks how LEO multibeam satellites should allocate beams and power between communications and PNT while giving communications full priority. It formulates this as a network-level beam-power problem and compares two scheduler policies, finding that in-beam ranging reaches the geometric availability ceiling while co-satellite sharing achieves lower availability without waveform redesign.

  • Problem

    Existing beam scheduling, LEO-PNT, and integrated communication-navigation studies do not formulate constellation-level allocation of shared beams and power under communication demand and PNT visibility requirements.

  • Method

    The paper derives structural bounds and compares two closed-form COM-priority scheduler policies using power-differentiated ranging beams: co-satellite sharing and in-beam ranging.

  • Results

    70.5% / 88.2% 95% availability area is achieved under co-satellite sharing for homogeneous / population-weighted traffic, while in-beam ranging reaches the 92.9% geometric ceiling.

  • Takeaways & Limitations

    Co-satellite sharing avoids signal modification but leaves an availability shortfall, whereas in-beam ranging removes that gap at the cost of waveform, payload-coherence, and receiver redesign.

Abstract

from arXiv · show

Future low Earth orbit (LEO) constellations are expected to provide positioning, navigation, and timing (PNT) as a native service alongside broadband, removing the GNSS dependency inherited by 5G non-terrestrial networks. This is known in the literature as fused PNT. This paper asks how a multibeam satellites in a LEO constellation should share their beams and power between a communication service (COM) and PNT in the scenario when communications keep full priority. Each beam on a satellite can provide a communication service, a PNT service or both (this under certain limitations). Then, the PNT service is evaluated by the share of area the reach $95\%$-of-time availability for a fixed maximum power available on each satellite. This paper present this PNT availability question as a beam-power budget, as the PNT beams do not need to transmit at the same power as the communication beams thanks to the processing gain on the receiver. Two satellite beam scheduler policies are compared: one where on a cell the beam serving COM demand is exclusive for COM, therefore the PNT service in this cell is provided by the other satellites in line of sight, it requires no signal modification and attains $70.5\%$ / $88.2\%$ availability under homogeneous/population-weighted traffic profiles; and a second policy, the COM beam can provide also PNT signals, this in-beam ranging embeds the ranging signal in the COM waveform, reaching the ceiling at the cost of waveform redesign. The availability gap between the two policies is concentrated on the thin-overlap equatorial belt.

A. State of the art

Prior work treats beam scheduling, LEO positioning, and integrated communication-navigation mainly as separate problems. This paper connects them through network-level beam and power allocation on a global cell grid.

  • State of the art: Beam-scheduling research optimizes communication-centric objectives such as capacity matching, delay, or interference, typically assigning broadband service to every active beam.Its performance is usually measured per beam or user rather than by a multi-satellite ground-cell condition for PNT.
  • State of the art: LEO-PNT studies establish navigation feasibility and receiver-side visibility requirements but generally treat constellation transmissions and payload resources as given.The geometric prerequisite is commonly Kmin ≥4 simultaneously line-of-sight satellites, rather than a schedulable network design variable.
  • State of the art: Integrated communication-navigation work addresses waveform and architecture coexistence, while constellation-level allocation of beams and power under live communication demand remains unformulated.Power backoff and receiver processing gains support coexistence, but the network decision of which cells receive PNT beams is still missing.
  • Gap and contribution: The paper models joint COM/PNT beam allocation, derives structural bounds, and proposes two closed-form scheduler policies with communications always prioritized.The policies are evaluated through regional and global service metrics across traffic profiles.
  • System model: The system uses an equal-area global hexagonal/pentagonal grid, with cells weighted by service region for performance metrics.Each beam is associated with one grid cell, and regional weights can alter COM or PNT priority.

B. Constellation Geometry

The constellation is represented as a Walker delta fleet propagated over time, with satellite positions and ground tracks defining the evolving geometry used for coverage analysis.

  • Constellation Geometry: The space segment is a Walker delta constellation with P orbital planes, Q satellites per plane, altitude h, inclination i, and phasing factor F.The total satellite count is S = PQ.
  • Constellation Geometry: Satellite orbital elements are propagated with SGP4 to obtain time-varying Earth-centred, Earth-fixed satellite positions and sub-satellite points.The sub-satellite point is the geodetic projection of each propagated satellite position onto Earth.
  • Constellation Geometry: The deployment figure combines the constellation arrangement with a single satellite’s 110-minute ground track.The ground track illustrates the time-varying spatial geometry generated by satellite motion.

C. Beam Model and Cell Association

Each satellite carries a fixed cluster of digitally steered spot beams mapped one-to-one to grid cells, while visibility and closest-satellite association determine service opportunities.

  • Beam Model and Cell Association: Each satellite generates Nb spot beams arranged as a centred cluster of nr rings around a nadir beam.The beam cluster defines the satellite footprint over the cell grid.
  • Beam Model and Cell Association: Beams are Earth-fixed at slot times, with each beam steered to one cell centre and each footprint Fs(t) containing the Nb nearest cells.The footprint is approximately circular and centred at nadir.
  • Beam Model and Cell Association: The footprint geometry is constrained by field of view and a minimum elevation mask, illustrated with a 20° edge-elevation example.The beam diameter and beam count are selected so the footprint edge remains above the terminal elevation requirement.
  • Beam Model and Cell Association: Visibility indicators define the satellites in view Vg(t) and their multiplicity mg(t) for each cell.These quantities provide the geometric basis for simultaneous PNT coverage.
  • Beam Model and Cell Association: The serving COM satellite is the closest visible satellite, which maximizes elevation angle and minimizes free-space path loss.Equal-distance ties are resolved by selecting the lowest satellite index.

D. Time Discretization

The model discretizes a full-day simulation into geometry-preserving slots and generates reproducible, persistent COM demand under homogeneous or population-weighted spatial profiles.

  • Time discretization: Each slot freezes satellite geometry and advances footprints by approximately one ground-grid cell.The slot duration is chosen so the discrete footprint sequence does not skip cells.
  • COM service: A demanding cell is served by the closest satellite when that satellite allocates one COM beam to it.The association rule permits only the closest satellite to carry the cell’s COM traffic.
  • Traffic dynamics: Traffic sessions arrive according to a Poisson process and terminate independently with geometrically distributed durations.The process is initialized in stationarity, making active demand Poisson-distributed with mean offered load.
  • Spatial profiles: Homogeneous traffic assigns equal load to every cell, while population-weighted traffic follows population density with a non-zero floor for sparsely populated cells.Both profiles share the same total offered load, enabling direct policy comparison.
  • Spatial profiles: Population-weighted demand concentrates traffic in heavily populated regions, producing a lower mean demand probability than the homogeneous profile at equal total load.The concentration creates heavily saturated cells that the scheduler must resolve.
  • Metrics: COM performance is measured over the full simulation by served demand and normalized throughput, with regional weights allowing operator-defined priorities.The normalized throughput approaches one when all COM traffic demand is served.

F. PNT model

The PNT model treats positioning as a synchronized one-way ranging broadcast requiring a minimum number of visible satellites, and evaluates persistent area availability under slot-level scheduling.

  • PNT service: PNT receivers estimate position and clock bias from synchronized pseudoranges transmitted by at least Kmin ≥4 simultaneous satellites.Signals share the cell through code division.
  • Service rule: A cell is PNT-served when at least Kmin distinct visible satellites can allocate a PNT beam to it.The model assumes line of sight and does not require extra beams for the user.
  • Performance metric: Per-cell availability is the fraction of simulation slots with valid PNT service, while system availability is the weighted area share meeting γ = 95% time availability.The 95% threshold follows navigation-service specifications.
  • Metric properties: The availability metric is bounded by constellation geometry and is stricter than time-averaged served area.A rotating footprint can serve much area on average while leaving each cell below the persistence target.
  • Regional evaluation: Regional weights can prioritize selected areas, while uniform weights recover plain area-share evaluation.Unless otherwise stated, results use uniform weights.
  • Scheduling scope: The scheduling analysis assumes independent per-slot power limits and develops closed-form policies for communications with full priority.No constraint couples beam-power decisions across time slots.

A. PNT availability metric analysis

PNT availability is constrained independently by constellation geometry and beam budget; relaxing the service rule to Kmin signals makes cost uniform and exposes further availability improvements.

  • Availability bounds: PNT availability is limited by a geometric ceiling and a beam-budget bound, identifying whether constellation visibility or resources are binding.The two mechanisms provide separate upper bounds for any scheduler.
  • Availability bounds: Cyclic rest rotation attains the beam-budget bound exactly when γK is an integer.Each compliant cell needs service in only ⌈γK⌉ slots.
  • Reference instance: For the reference constellation, the geometric ceiling is 92.9% of total coverage area, while the beam budget is lower.The reference uses a Walker 24 × 11 constellation with 264 satellites and Kmin = 4.
  • Service-rule alternatives: Using all visible satellites for each PNT cell sustains only 7,845 cells because cell beam cost varies with visibility from 4 to 14 beams.The mean cost is 5.31 beams per served slot.
  • Service-rule alternatives: Requiring only Kmin = 4 beams reduces a ±50° cell’s cost from 10–14 beams to 4.The uniform cost decouples service location from overlap geometry.
  • Availability improvements: Increasing beam capacity, reducing Kmin, widening PNT beams, or changing the availability denominator can raise the attainable area share.The inhabited-area denominator reaches a 96.0% ceiling under the stated scenario.
  • Scope boundary: A common COM/PNT spot-beam lattice excludes the conceptual GNSS-like alternative of broadcasting ranging signals on much wider beams without consuming spot beams.This is identified as a scope boundary of the analysis.

B. Power-differentiated ranging beams and the loaded satellite

Power-differentiated ranging treats PNT beams as cheaper than COM beams, allowing the loaded satellite’s PNT capacity to be analyzed through a power-versus-beam constraint and its saturation regimes.

  • Power differentiation: Processing gain allows PNT spot beams to use a fraction of COM power while preserving the required post-correlation C/N0.The policy models a PNT-to-COM power ratio X with PNT beams transmitted at 1/X of COM power.
  • Power budget: The per-satellite constraint is X P_x + P_y ≤ XNmax with integer X, combining COM power units and lower-power PNT beams.The formulation is retained in exact integer arithmetic.
  • Operating thresholds: Two PNT beams can be supported per COM-beam power with only −2.8 dB per-beam backoff.Serving mean homogeneous and population-weighted COM demand requires X ≥2.31 and X ≥2.02, respectively.
  • Loaded satellite: With n active COM beams, a satellite retains X(Nmax − n) power units and Nb − n physical beams for PNT.The smaller of these two resources determines PNT capacity.
  • Loaded satellite: Below X∗, capacity grows linearly with X; above X∗, the physical beam count binds and extra power provides no benefit.The threshold begins at X∗(0) = 3.65 and marginal load tolerance declines as X increases.
  • Loaded satellite: The scenario’s worst COM peaks are 60 and 88 beams for homogeneous and population-weighted traffic, matched exactly by X = 6 and X = 8.The population profile has lower total load but sharper megacity-pass peaks.

C. Two scheduling policies

The paper compares beam policies that preserve COM priority while allocating remaining satellite beam and power resources to PNT. Co-satellite sharing excludes the COM beam from PNT, whereas in-beam ranging embeds ranging in the COM waveform and removes the resulting geometric requirement.

  • Mode Exclusivity: Mode exclusivity forbids COM and PNT from sharing one satellite beam, although other visible satellites may provide PNT on a COM-served cell.A COM-served cell requires at least Kmin + 1 visible satellites, and no more than Kmin ranging beams are admitted.
  • Co-satellite sharing: Adaptive co-satellite sharing divides leftover satellite power among PNT beams, operating at the full-footprint threshold until the receiver-driven limit is reached.The policy uses X(n) as a load-dependent power ratio rather than a fixed design constant.
  • Co-satellite sharing: At Xmax = 10, the receiver-driven limit is 105 beams, exceeding the worst measured peak of 88 beams, so serving all serviceable COM demand and admissible ranging beams is feasible.In this regime, the serve-all policy is optimal because it simultaneously completes COM service and reaches the coexistence eligibility ceiling.
  • Mode Exclusivity: Two-tier ranging power assigns 1/Xhot power to PNT beams aimed at COM-served cells and 1/Xfree to beams on traffic-free cells.This separates interference protection for COM from the higher ranging power available on quiet cells.
  • In-beam ranging: Under mode exclusivity, cells with mg = Kmin exhaust the miss budget by geometry alone, so no beam allocation can recover them.This is a structural limitation of requiring Kmin ranging beams from satellites other than the COM server.
  • In-beam ranging: In-beam ranging embeds the ranging signal in the COM waveform, removing the +1 requirement so COM-served cells need only mg ≥ Kmin.The resulting eligibility condition matches that of traffic-free cells, and the availability ceiling becomes reachable on both traffic profiles.

IV. Simulation and Results

The evaluation toolchain is deterministic under fixed constellation, traffic-seed, and power-ratio parameters, making the reported figures reproducible from one configuration.

  • Implementation: The campaign generator, traffic replay, policy evaluation, and availability evaluation are deterministic given the constellation parameters, traffic seed, Xfree, and Xhot.The implementation therefore produces reproducible figures from a single configuration line.
  • Implementation: A single configuration line is sufficient to reproduce every figure in the evaluation.Reproducibility covers campaign generation through availability evaluation.
  • Implementation: The reproducibility claim depends on fixing both the traffic seed and the power parameters Xfree and Xhot.These inputs are listed alongside the constellation parameters as determinants of the toolchain output.

B. Scenario and coverage statistics

The simulation establishes the constellation’s geometric PNT ceiling and measures how COM demand reduces 95%-of-time availability under undifferentiated and power-differentiated operation. Co-satellite sharing reaches 70.5%/88.2% for homogeneous/population-weighted traffic, while in-beam ranging reaches the 92.9% ceiling.

  • Coverage statistics: 92.9% of the coverage area, or 19,865 cells, is the geometric ceiling for 95%-of-time PNT availability.The missing 7.1% consists of never-eligible polar cells and band-edge cells with excessive eligibility gaps.
  • Traffic profiles: The homogeneous profile keeps 33.0% of cells busy on average, while the population-weighted profile concentrates the same total load on 10.2% of cells.Mean and peak per-satellite COM loads are 26.1 / 8.2 and 60 / 88 beams for the two profiles.
  • Availability evaluation: At γ = 0.95, only 72 of 1,440 slots may miss PNT service.This availability target makes the impact of COM-served cells visible in the area metric.
  • Availability evaluation: Without power differentiation, 95%-of-time PNT availability collapses to 74.1% for the population-weighted profile.Only nearly empty ocean cells comply under this condition.
  • Co-satellite sharing: Co-satellite sharing with Xhot = 20 and Xfree = 5/6 is power-feasible at every satellite and slot and reaches its eligibility ceiling.Its remaining limitation is that COM-demand cells require mg ≥ Kmin + 1.
  • In-beam ranging: In-beam ranging removes the extra-satellite requirement and reaches the 92.9% ceiling for both traffic profiles.The policy makes the geometric ceiling attainable while preserving complete COM service.

D. Trade-off between the two solutions

The two policies both preserve full communication demand but trade implementation complexity against PNT availability. Co-satellite sharing requires no waveform redesign, while in-beam ranging reaches the geometric ceiling and recovers cells concentrated in the thin-overlap equatorial belt.

  • Trade-off: 88.2% vs 92.9% availability under population-weighted traffic makes co-satellite sharing deployable with current payloads while reserving waveform redesign for a later generation.Under uniformly loaded cells, the gap widens to 22.4% and the second solution becomes the difference between regional and near-global availability.
  • Common operating point: Both solutions serve complete COM demand with the same two-tier power discipline, and neither requires a beam scheduler at the nominal design point.The policies differ only in the coexistence rule on a COM-served cell.
  • Geographic trade-off: 4,789 homogeneous and 1,015 population-weighted cells recovered by in-beam ranging concentrate in the thin-overlap equatorial belt.The largest regional gains occur in Africa: +40.1% homogeneous and +36.6% population-weighted.
  • Scope boundary: The reference constellation imposes a 92.9% geometric ceiling, while the alternative Kmin = 3 raises that ceiling to 95.4%.The Kmin = 3 alternative cheapens every cell and merits a separate system-level study.
  • Co-satellite sharing: 70.5% / 88.2% availability is achieved by co-satellite sharing for homogeneous / population-weighted traffic profiles.The COM-serving satellite remains exclusive to communications, while other visible satellites provide PNT at a power backoff.
  • In-beam ranging: 92.9% availability is reached by in-beam ranging, matching the full geometric ceiling at the cost of waveform and receiver redesign.The COM waveform carries the PNT signal itself.
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