Densification Converses for Walker Constellations With Explicit Constants and Reuse Scaling Laws
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866913065929277440 |
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| author | Khalesi, Ali Baccelli, François |
| author_facet | Khalesi, Ali Baccelli, François |
| contents | We establish densification converses for Walker LEO constellations under nearest-visible association in the full-frequency-reuse setting. Performance is evaluated under the invariant (stationary) measure induced by the constellation/Earth dynamics on the user--constellation ``phase state.'' A key Walker-specific feature, absent from unbounded planar models, is that association is restricted to a bounded visible cap determined by Earth geometry. Under power-law path-loss, a two-level antenna-gain model, i.i.d.\ nonnegative fading with unit mean and finite second moment, and nonzero noise, we prove that increasing the total satellite count $N=N_oN_s$ forces the aggregate interference to grow at least linearly in $N$, while the useful signal remains uniformly bounded above. Consequently, the downlink SINR coverage probability at any fixed threshold and the ergodic spectral efficiency both vanish as $N\to\infty$. The key technical ingredient is a deterministic visibility-annulus block lemma, uniform over all sufficiently large constellations and all "phase states", showing that a fixed fraction of visible satellites lies in a distance annulus strictly inside the horizon; this yields explicit finite-$N$ collapse bounds. In particular, we derive nonasymptotic $O(1/N)$ upper bounds on both coverage and ergodic spectral efficiency. Finally, in the case of frequency reuse through independent thinning, with activity probability $q$, we show that avoiding densification collapse necessarily requires $qN=O(1)$, equivalently a reuse factor $Ω(N)$, and we obtain a corresponding explicit $O(1/(qN))$ upper bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Densification Converses for Walker Constellations With Explicit Constants and Reuse Scaling Laws Khalesi, Ali Baccelli, François Information Theory We establish densification converses for Walker LEO constellations under nearest-visible association in the full-frequency-reuse setting. Performance is evaluated under the invariant (stationary) measure induced by the constellation/Earth dynamics on the user--constellation ``phase state.'' A key Walker-specific feature, absent from unbounded planar models, is that association is restricted to a bounded visible cap determined by Earth geometry. Under power-law path-loss, a two-level antenna-gain model, i.i.d.\ nonnegative fading with unit mean and finite second moment, and nonzero noise, we prove that increasing the total satellite count $N=N_oN_s$ forces the aggregate interference to grow at least linearly in $N$, while the useful signal remains uniformly bounded above. Consequently, the downlink SINR coverage probability at any fixed threshold and the ergodic spectral efficiency both vanish as $N\to\infty$. The key technical ingredient is a deterministic visibility-annulus block lemma, uniform over all sufficiently large constellations and all "phase states", showing that a fixed fraction of visible satellites lies in a distance annulus strictly inside the horizon; this yields explicit finite-$N$ collapse bounds. In particular, we derive nonasymptotic $O(1/N)$ upper bounds on both coverage and ergodic spectral efficiency. Finally, in the case of frequency reuse through independent thinning, with activity probability $q$, we show that avoiding densification collapse necessarily requires $qN=O(1)$, equivalently a reuse factor $Ω(N)$, and we obtain a corresponding explicit $O(1/(qN))$ upper bound. |
| title | Densification Converses for Walker Constellations With Explicit Constants and Reuse Scaling Laws |
| topic | Information Theory |
| url | https://arxiv.org/abs/2604.24656 |