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Satellite Swarms for Direct-to-Cell Networks: A Distribution-Performance Trade-off Analysis

Xavier Artiga, Marius Caus, Ana I. Pérez-Neira, Yerassyl Akhmetkaziyev, Malte Schellmann

arXiv:2609.01380v1eess.SP

TL;DR

This paper examines how distributed satellite swarms can exploit larger apertures for direct-to-cell networks beyond prior uniform-user analyses. Simulations compare swarm configurations and show that highly distributed apertures improve performance most strongly for dense hotspot users, while practical constraints limit near-term scalability.

  • Problem

    Evidence remains limited on communication performance across distributed swarm configurations, especially with positioning and synchronization errors and nonuniform user distributions.

  • Method

    The study simulates monolithic arrays and formation-flying satellite swarms with centrally controlled planar apertures across multiple antenna-distribution configurations.

  • Results

    The most distributed configuration consistently outperformed others under ideal conditions, with gains moderate for uniform users but significantly larger for users concentrated in hotspots.

  • Takeaways & Limitations

    Large distributed apertures show substantial performance potential for dense hotspot service, motivating research on scalable synchronization, positioning, and data distribution.

  • Takeaways & Limitations

    Hundreds- or thousands-satellite swarms remain impractical with current technology and require joint evaluation of performance, impairments, deployment, formation flying, and cost.

Abstract

from arXiv · show

This work investigates 2D distributed satellite swarm configurations for direct-to-cell (D2C) applications. Unlike previous studies, which primarily considered swarms as deployment alternatives to monolithic arrays, this paper focuses on exploiting the increased spatial resolution enabled by large distributed apertures. Simulation results show that, for the considered scenarios, increasing the level of antenna distribution across satellite platforms enlarges the effective aperture and improves the system sum rate under ideal operating conditions. While gains are moderate for uniformly distributed users, they become particularly pronounced in scenarios including hotspot with high user densities. The results further show that user scheduling strategies do not invalidate the superiority of highly distributed configurations, as these architectures provide a more balanced rate distribution across the coverage area, including hotspot regions. In addition, the paper analyzes several key implementation challenges associated with large distributed swarms, including errors in inter-satellite relative positioning, synchronization impairments, and limited beamforming and user-position update rates. Although within the range of swarm configurations and scenarios considered in this work, performance gains continue to increase with aperture size, these practical constraints may restrict swarm sizes in the medium term. Nevertheless, the observed performance gains strongly motivate further research into scalable synchronization, positioning and data distribution techniques for future large-scale satellite swarms.

I. INTRODUCTION … II. System model

The paper examines distributed satellite swarms for direct-to-cell connectivity, comparing antenna-distribution architectures and system-model assumptions to identify communication-performance trade-offs under practical impairments. It addresses limitations of handheld-device link budgets and gaps in prior swarm evaluations through a fixed-EIRP comparison spanning monolithic arrays, FoAs, and fully distributed swarms.

  • I. INTRODUCTION: D2C broadband connectivity remains challenging because handheld-device antenna limitations create an extremely constrained link budget, while existing systems mainly support low-data-rate applications.The introduction describes emergency messaging and basic text communications as examples of current low-data-rate D2C uses.
  • I. INTRODUCTION: Distributed satellite approaches use coordinated smaller spacecraft instead of one large complex satellite, offering potential scalability improvements for future D2C systems,.The paper contrasts this paradigm with lower-altitude, higher-power strategies and large deployable antennas,.
  • A. Related work: Prior work distinguishes widely separated coordinated satellites from close-formation swarms forming large distributed apertures, with synchronization, interference alignment, and grating-lobe challenges –,.For close formations, FoA architectures use a few satellites equipped with large antenna arrays, whose radiation patterns can partially mitigate grating lobes,,,.
  • A. Related work: The paper identifies missing fair cost–performance comparisons and calls for sensitivity analysis covering synchronization, satellite position and attitude, and user-position estimation errors.These issues must be assessed from the communications perspective before detailed aerospace cost optimization.
  • B. Novel Contributions: The paper compares monolithic satellites, FoAs with different antennas per satellite, and fully distributed single-antenna swarms under fixed EIRP, addressing a previously unreported fair comparison.The study asks which level of antenna distribution provides the highest communication performance under realistic user distributions, scheduling policies, and beamforming impairments.
  • B. Novel Contributions: Its contributions include multicarrier and OFDM modeling, realistic user distributions and scheduling, and analysis of inter-satellite spacing in relation to hotspot size.The contribution list notes that prior studies use restricted hotspot, scheduling, or user-distribution assumptions [7],,.
  • C. Paper Organization: The paper proceeds from an error-free system model through radiation-pattern theory, beamforming, user distributions and scheduling, imperfect-position phase errors, and performance evaluation.The organization explicitly separates these modeling and evaluation stages across Sections II–VI.
  • II. System model: The system model considers either a monolithic satellite or Ns formation-flying satellite nodes cooperatively synthesizing K beams toward ground users with a planar array of N radiating elements.Formation-flying inter-node distances are on the order of meters, and antenna elements lie within a circle of radius R.

A. Transmitter · B. Satellite channel model

The model transmits simultaneously scheduled users through precoded pulse-shaped signals and represents each user–antenna path with delay, Doppler, gain, and Rician fading. Its assumptions preserve spatial signatures and average channel power while allowing instantaneous SINR fluctuations.

  • A. Transmitter: The transmitter schedules K users on the same time–frequency resources, weighting each intended symbol with an antenna coefficient before pulse shaping.Square-root raised-cosine pulses provide spectral confinement and perfect reconstruction over the symbol period Ts.
  • B. Satellite channel model: Each user–antenna channel is modeled over an interval of constant user direction using a gain, differential delay, and Doppler-dependent impulse response.The differential delay is defined relative to the coordinate-system origin and the corresponding radiating element.
  • B. Satellite channel model: For monolithic satellites or closely spaced nodes, path Doppler shifts are treated as nearly identical and constant across bandwidth when BW ≪ fc, following.This approximation relies on the carrier frequency being significantly higher than the signal bandwidth.
  • B. Satellite channel model: The channel coefficient combines deterministic line-of-sight propagation with statistically modeled diffuse multipath through a Rician formulation.The model identifies KR as the Rician factor, An as the large-scale amplitude, and ϕn as the deterministic propagation phase.
  • B. Satellite channel model: Large-scale channel amplitude depends on terminal and element antenna gains, path loss, and other implementation or propagation losses.Clear-sky path loss uses carrier frequency and slant range, whose relation to departure angle is described in.
  • B. Satellite channel model: Correlated diffuse fading preserves each user’s spatial signature and beamforming trade-offs, while increasing instantaneous SINR variance without changing average channel power.The NLoS component introduces random received-power fluctuations but does not alter beam patterns or the analyzed beamwidth, sidelobe, and aperture-size trade-offs.

C. Receiver

The receiver model combines Gaussian thermal noise with autonomous Doppler compensation, matched filtering, and sampling. Non-negligible differential delays additionally introduce inter-symbol and inter-user interference.

  • Receiver: Receiver noise is modeled as zero-mean white Gaussian noise with variance σ2 = KBTBW, determined by Boltzmann constant, bandwidth, and equivalent noise temperature.The equivalent noise temperature is defined from antenna temperature, noise factor, and reference temperature.
  • Receiver: The UE uses known satellite/swarm trajectory and user location to autonomously compensate Doppler frequency shifts in accordance with 3GPP requirements.The noise stochastic model remains unchanged after frequency correction.
  • Receiver: Matched filtering followed by sampling every Ts seconds recovers the transmitted-symbol sequence for subsequent discrete-time reception modeling.Under Nyquist orthogonal transmission, the sampled noise is modeled as independent, identically distributed complex Gaussian variables.
  • Receiver: Differential delays between satellites impair received symbols through both inter-symbol interference (ISI) and inter-user interference (IUI).The delay difference is explicitly modeled as non-negligible.

D. Narrowband conditions

Under narrowband conditions, negligible intersymbol interference enables an analytically tractable input-output model. When this condition fails, true-time-delay compensation or multicarrier modulation can mitigate intersymbol interference, with OFDM requiring fewer subcarriers in the example considered.

  • D. Narrowband conditions: Neglecting ISI yields a more analytically tractable narrowband model when the maximum differential delay is significantly below the symbol period.The model can be used without significant modeling error under this condition.
  • D. Narrowband conditions: True Time Delay pre-compensation aligns desired signals at the receiver, but interference mitigation remains difficult because many interfering components arrive asynchronously.The approach uses adjustable time offsets on antenna elements for each user.
  • D. Narrowband conditions: Multicarrier modulation satisfies the narrowband condition per subcarrier when sufficiently many subcarriers increase the effective symbol period.Frequency-separated carriers with guard bands avoid inter-carrier interference and are compatible with DVB-S2 bandwidth partitioning.
  • D. Narrowband conditions: Nsc = 40 OFDM subcarriers satisfy the narrowband assumption in the numerical example, versus Nsc = 51 for the general multicarrier condition.The example uses R = 30 m, BW = 20 MHz, θmax = 44.4° and α = 0.1; OFDM is therefore less stringent in this case.

E. OFDM · F. Performance Metrics

The OFDM formulation performs signal processing independently on each subcarrier, with frequency-dependent channels evaluated across the band. Performance is characterized through subcarrier SINR, Shannon user rates with scheduling factors, and system sum rate under equal per-subcarrier power allocation.

  • E. OFDM: OFDM processing is performed on a per-subcarrier basis, defining each user’s demodulated signal separately for every subcarrier.
  • E. OFDM: The OFDM signal model incorporates the channel response and additive noise for each user–subcarrier pair.
  • E. OFDM: For an even number of subcarriers, indices span the centered OFDM grid, while the channel vector is evaluated at each subcarrier frequency fq = fc + q BW.
  • F. Performance Metrics: Performance evaluation computes SINR separately at each subcarrier under the OFDM assumption.
  • F. Performance Metrics: Equal power allocation across subcarriers scales each subcarrier beamformer’s power by the number of subcarriers relative to the full-band beamformer.
  • F. Performance Metrics: User rates follow Shannon’s formulation with scheduling factor fsch,k, and the resulting system sum rate aggregates performance across scheduled users.

III. Swarm model · A. Theoretical background

The theoretical background links distributed-aperture beam resolution and sidelobe behavior to user SINR and sum-rate performance. A hard-core random-array model predicts angle-dependent sidelobe suppression near the main beam, while its accuracy and analytical scope are limited for finite layouts and peak-SLL prediction.

  • A. Theoretical background: System sum-rate depends on user SINR, which is mainly constrained by inter-beam interference from adjacent-beam main lobes and motivates reuse, interference-aware precoding, and minimum-distance scheduling.A general analytical SINR or sum-rate expression would require restrictive assumptions about user distributions and scheduling strategies.
  • A. Theoretical background: For sufficiently uniform satellite distributions, beam characteristics are governed mainly by effective aperture diameter, while distributing elements across satellites creates a beamwidth–sidelobe trade-off.Periodic layouts can produce severe grating lobes because inter-element spacings exceed the wavelength; randomizing satellite positions mitigates this effect but can alter sidelobe distribution and level.
  • A. Theoretical background: The swarm radiation pattern combines the individual element pattern, satellite-subarray factor, and random array factor of distributed satellite centroids.For the considered square subarray, the peak sidelobe level is approximately −13.26 dB in the two principal planes.
  • A. Theoretical background: The structure factor makes random-array sidelobe statistics angle dependent by incorporating spatial correlations caused by the minimum-distance constraint.This differs from classical random-array theory, where the incoherent contribution is spatially uniform.
  • A. Theoretical background: A hard-core point-process model predicts a low-energy spatial-spectrum region around the origin, where the incoherent random-array contribution is suppressed.The suppression follows from the Bessel-function term remaining positive before its first zero and being subtracted from unity in the structure factor.
  • A. Theoretical background: The hard-core analytical prediction may lose accuracy for finite arrays or layouts departing from the ideal spatial model, and it does not yet provide a closed-form expected peak-SLL prediction.Peak-sidelobe modeling is left for future work because existing statistical approaches do not directly relate expected peak SLL to physical array parameters.
  • A. Theoretical background: Outside the low-frequency region, the structure factor converges to unity and the analytical model reduces to the classical result of Lo.Thus, the minimum-distance effect is predicted to be localized around the main beam rather than persistent across all spatial frequencies.
  • A. Theoretical background: Distributed swarms can improve hotspot performance because larger apertures narrow beams, spatially separate dense users, and reduce nearby-beam interference through a low-sidelobe region.For relatively uniform users, sidelobe-limited interference may remain weak compared with thermal noise, yielding only modest SINR and sum-rate differences across array configurations.

B. Evaluated swarm configurations

The study evaluates monolithic, four-satellite, and highly distributed swarm apertures with fixed total radiating elements. Increasing aperture reduces beamwidth, while distribution changes sidelobe levels and spatial structure.

  • Evaluated swarm configurations: The evaluated architectures use N radiating elements distributed across Ns satellite nodes, with square subarrays, near-half-wavelength element spacing, and cos2(θk) element patterns.The three principal cases are Ns = 1, Ns = 4, and Ns ≫ 4, with highly distributed satellites randomly placed within a diameter-D circle subject to minimum separation.
  • Evaluated swarm configurations: Larger apertures reduce half-power beamwidth, enabling more aggressive spatial reuse, but increasing subarray size raises sidelobe levels.These effects reflect increased subarray gain and fewer satellite nodes in the distributed configurations.
  • Evaluated swarm configurations: Randomized satellite geometries spread grating-lobe energy across the sidelobe region, whereas the four-satellite arrangement produces distinct grating lobes.The comparison uses configurations with N = 1600 radiating elements and is illustrated by the evaluated radiation patterns.
  • Evaluated swarm configurations: The single-antenna-per-satellite configuration achieves both the lowest sidelobe levels and the widest low-sidelobe region around the main beam.For minimum feasible swarm diameter, the predicted low-sidelobe region agrees with the D = 60 m, Ns = 1600 and D = 32 m, Ns = 400 configurations; smaller swarms suffer boundary effects.

IV. Beamforming design

The beamforming design uses location-based CSI acquisition because FDD operation prevents reciprocity and exhaustive reference-signal transmission is infeasible for large antenna or beam counts. It compares a conventional MRT-like beamformer with MMSE, using estimated geometry and double normalization to satisfy per-antenna power constraints.

  • CSI acquisition: Location-based CSI acquisition is assumed, with users periodically reporting their positions after random access because reciprocity and exhaustive reference signaling are impractical.Random access is particularly challenging because swarm beams are narrow relative to the overall field of view, and its design is outside the section’s scope.
  • Beamformer design: The conventional beamformer uses only the conjugate LOS phase component with equal per-user power, rather than instantaneous channel amplitudes, and is retained as MRT for comparison,,.This approximation is motivated by unavailable instantaneous amplitude variations and a high Rician K-factor.
  • Beamformer design: The MMSE beamformer is constructed from an estimated LOS geometry matrix whose elements depend on estimated user and antenna positions.The estimated matrix accounts for deterministic magnitudes and phases associated with user–satellite geometry.
  • Power constraints: Double normalization by rows and columns enforces per-antenna power constraints and outperforms alternative approaches under the low-SNR conditions considered.The normalization is applied to the MMSE-related expressions using the estimated channel geometry.

V. User distribution and scheduling

Performance across distributed swarm configurations depends on both their radiation patterns and the distribution of simultaneously served users, motivating analysis of user distributions and scheduling algorithms.

  • The section examines how simultaneously served-user distributions and scheduling algorithms affect performance alongside the swarm radiation patterns discussed in Section III.

A. User distribution · B. User scheduling · VI. Positioning and synchronization errors

The study evaluates uniform, hotspot, and clustered user distributions alongside unscheduled and TDMA scheduling under equal-demand assumptions. It models distributed-aperture impairments through synchronization, antenna-relative-position, and user-position uncertainties, including their spatial and temporal assumptions.

  • A. User distribution: Three user distributions are considered: uniform coverage, a single hotspot, and clustered users with a hotspot component and residual users across the coverage.Users are distributed in geodetic coordinates, and user height is fixed at sea level; the first two scenarios identify trends, while clustered users simplify realistic scenarios.
  • A. User distribution: The uniform and single-hotspot scenarios distribute users in geodetic coordinates, producing larger densities at coverage edges in the uniform case.The hotspot is bounded by |θk| ≤ θhsmax around a central position within the overall coverage region.
  • B. User scheduling: Scheduling compares simultaneous service of all users with TDMA groups designed to keep outage probability arbitrarily low.User groups are formed using a minimum-distance criterion.
  • B. User scheduling: Because all users are assumed to have equal demand, TDMA groups are served sequentially in round-robin order and each user’s scheduling factor reflects its group participation.This assumption isolates the impact of different swarm configurations rather than demand heterogeneity.
  • VI. Positioning and synchronization errors: Distributed apertures face synchronization, precise relative-antenna-position, and precise user-position knowledge challenges that affect beamforming performance.Synchronization is more difficult than within a monolithic aperture, while antenna positions are not physically fixed as they are in monolithic apertures.
  • B. User scheduling: Minimum-distance scheduling projects angular coordinates into the u-v plane, computes pairwise distances, forms groups under distance and size constraints, and equalizes group sizes.Remaining users are allocated across groups, with reassignment continuing until no changes are possible or group sizes differ by at most one user.
  • VI. Positioning and synchronization errors: The error model assumes independent impairments, planar swarm position uncertainties, normally distributed synchronization phase errors, and shared errors across antennas collocated on one satellite.User-position errors depend on update rates from users and satellites; intrinsic positioning accuracy is assumed well below the half-power beamwidth, and these rate effects are analyzed in Section VII.

VII. Numerical evaluation

The numerical evaluation uses a 600-km LEO satellite serving S-Band users under a 40° minimum elevation angle and 20-MHz bandwidth, evaluating array configurations across four user-distribution scenarios.

  • Evaluation setup: The evaluation considers a 600-km LEO orbit, a 40° minimum elevation angle, S-Band operation, and 20-MHz bandwidth.The simulation parameters are summarized in Table 3 unless otherwise stated.
  • Evaluation setup: The baseline simulation assumes 1-m minimum inter-satellite spacing to enable direct comparison with relevant prior works.The passage notes that prior literature assumes spacings ranging from 100 m to around 1 m, while formation experiments demonstrated accurate positioning at 2–3 m distances.
  • Evaluation setup: The numerical analysis evaluates the array configurations summarized in Table 2 across four user-distribution scenarios detailed in Table 4.

A. Baseline results · B. Impact of scheduling

The study shows that larger antenna distribution and aperture can improve sum rate, while scheduling preserves these gains and enables more balanced capacity allocation, including hotspot regions.

  • A. Baseline results: Baseline Monte Carlo simulations compare MRT and MMSE beamformers across antenna formations, user counts, and uniform or hotspot user distributions under idealized conditions.The idealized setup assumes no scheduling with perfect synchronization and positioning, isolating radiation-pattern trade-offs such as beamwidth and sidelobe levels.
  • A. Baseline results: A lower Rician factor of K_R = 10 dB degrades sum rate relative to K_R = 60 dB for both uniform-user and single-hotspot scenarios.The comparison uses MMSE beamforming and the two extreme configurations: a monolithic array and a 1600-satellite single-antenna swarm.
  • A. Baseline results: For a fixed hotspot size, enlarging the aperture by increasing inter-satellite spacing improves sum rate until saturation, despite narrower beams and higher sidelobe levels.The example considers 100 satellites serving 50 users while increasing aperture diameter beyond the minimum-distance configuration.
  • A. Baseline results: Reducing hotspot size decreases sum rate because inter-beam interference grows, whereas baseline evaluations vary users across uniform and single-hotspot distributions.The hotspot is positioned between boresight and coverage edge, with θ_hsmax = 10° in the baseline hotspot evaluation.
  • B. Impact of scheduling: In clustered scenarios, scheduling is evaluated against different antenna configurations using MRT, with separate results reported for clustered scenarios 1 and 2.The more challenging clustered scenario 1 is used for the scheduling-algorithm comparison and user-rate distribution analysis.
  • B. Impact of scheduling: The scheduling algorithm prevents users within one main beam from sharing a slot, reducing outage probability and making residual interference depend mainly on sidelobe distribution.Narrower beams also require fewer scheduling slots to serve all users, increasing the scheduling factor f_sch.
  • B. Impact of scheduling: Scheduling improves sum rate for all evaluated antenna configurations, while the 1600-satellite swarm continues serving hotspots and distributes capacity more evenly across coverage.The scheduling comparison uses MRT in clustered scenario 1; the rate-distribution comparison contrasts a monolithic array with a 1600-satellite single-antenna swarm.

C. Impact of position and synchronization errors · VIII. Conclusions

Practical synchronization, positioning, and update-rate impairments constrain the gains of highly distributed satellite swarms, despite their strong ideal-condition performance, especially for hotspot users. The conclusions frame large swarms as a long-term objective requiring scalable implementation and cost-per-bit analysis.

  • C. Impact of position and synchronization errors: The impairment analysis evaluates relative-position and synchronization errors using smaller and larger random swarms with uniformly distributed users to balance error effects across coverage.Figures 12 and 13 report sum rate versus relative-position and synchronization-error standard deviations for 301 uniformly distributed users.
  • C. Impact of position and synchronization errors: Synchronization phase errors with σs ≤20° can limit sum-rate degradation to below 10% in the considered configurations.The study reports that error sensitivity does not increase with greater distribution, larger apertures, or the beamformer, excluding monolithic arrays.
  • C. Impact of position and synchronization errors: User-position ageing is assessed in a worst-case 10° hotspot centered at θhsc = 0°, using MRT, 300 users, speeds up to 350 km/h, and a pure LoS channel.The setup isolates mobility effects by avoiding direct GNSS position errors and complex fading during user movement.
  • C. Impact of position and synchronization errors: Beamforming updates are required every 50 ms with 5 s user-position ageing and every 120 ms without ageing for a 1600-satellite single-antenna swarm.The assumption is that SINR fluctuations up to 1 dB within 10 ms are tolerable for a given MCS; larger fluctuations may affect BLER.
  • VIII. Conclusions: Under ideal synchronization and satellite-user positioning, single-antenna satellites consistently outperform less distributed architectures, with gains especially pronounced for hotspot users.The comparison uses configurations with identical antenna-element counts and EIRP; improvements are moderate for uniformly distributed users.
  • VIII. Conclusions: Large distributed swarms require coherent beamforming updates on the order of a few tens of milliseconds, compatible with current 5G frame durations but restrictive for longer intervals.Longer update intervals require reducing the effective aperture, trading capacity for link stability.
  • VIII. Conclusions: Although hundreds- or thousands-satellite distributed swarms remain impractical, the paper presents them as a long-term research objective requiring cost-per-bit analysis across performance, impairments, deployment, and formation flying.The main contribution is to demonstrate the potential of distributed architectures while identifying the implementation conditions that determine their practicality.
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