LunarRF: A Terrain-Aware Propagation Engine and Pole-Wide 3GPP Surface Coverage Atlas of the Lunar South Pole

PREPRINT, 19 OCTOBER 2026

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LunarRF: A Terrain-Aware Propagation Engine and Pole-Wide 3GPP Surface Coverage Atlas of the Lunar South Pole Christopher J. Santorelli

1 and Alexander M. Wyglinski

2

1

arXiv:2610.34554v1 [cs.NI] 25 Oct 2026

2

Department of Computer Science, Worcester Polytechnic Institute, Worcester, MA 01609 USA Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609 USA

Abstract—Artemis surface operations will depend on 3GPP cellular links, yet no public product shows where such links are physically possible across the lunar south pole. We present LunarRF, a GPU system for terrain-aware surface coverage, and the pole-wide atlas produced with it. A footprint engine casts 8192 radial profiles from one of 11,827 candidate masts enumerated by stated rules on the orbit-adjusted LOLA elevation model, takes the viewshed, and evaluates ITU-R P.1812 Delta-Bullington propagation on every profile, continuous through the radio horizon. An order-independent resolver merges the footprints per 20 m cell, making the run shardable and resumable. The atlas covers the disc south of 80°S at 20 m for four SFCGrecommended surface bands and the IM-2 demonstration band, 1.8 to 25.375 GHz, under a stated link budget, storing per cell the best-server power and identity, redundancy count, line of sight and coverability. The engine is validated against a parabolicequation solver, ray tracing and analytic solutions. Swapping Deygout for Delta-Bullington, or adding terrain noise at the level of the published height-error map of the DEM, moves the coverable class on under 1 % of a mast’s disc in the mean. With every candidate active, 90.5 % of the disc is coverable at 1.8 GHz, 59 % at 5.855 GHz and 10 % at 25.375 GHz, or 84, 43 and 5 % after the measured 3–4 dB engine optimism. A mast covers about 90 % of its visible area within its budget-set range, and no band is terrain-limited. The nine current Artemis regions are 85–99 % coverable at 1.8 GHz and 22–85 % at 5.855 GHz. The atlas and candidate table are released with a DOI. Index Terms—3GPP, 5G mobile communication, Artemis, coverage planning, diffraction, digital elevation models, graphics processing units, lunar surface communications, radio propagation, site selection, terrain factors.

I. I NTRODUCTION HE Artemis campaign will place crews, rovers and infrastructure within a few degrees of the lunar south pole, where the terrain is among the most rugged on the Moon and the Sun never rises more than a few degrees above the horizon. This region is characterized by heavily cratered highland terrain, kilometer-scale reliefs, and steep slopes mantled in loose, fine-grained regolith with unique electromagnetic properties [1], while a maximum solar elevation of approximately 1.5° [2] casts long shadows that have the potential to obscure surface hazards. Surface operations will rely on robust and resilient wireless communication links

T

Corresponding author: C. J. Santorelli (cjsantorelli@wpi.edu).

between the lander, the Lunar Terrain Vehicle (LTV), astronauts conducting extravehicular activity (EVA) and unattended instruments distributed across the landing region. The Space Frequency Coordination Group (SFCG) has recommended specific frequency ranges for wireless systems deployed to the lunar surface in Recommendation SFCG 32-2R5 [3], which map onto 3GPP operating bands supporting both Long-Term Evolution (LTE) and 5G New Radio (NR) [4]. This atlas evaluates four of those bands together with the 1.8 GHz band of the IM-2 demonstration [4]. In March 2025, Nokia Bell Labs’ Lunar Surface Communications System (LSCS), the first LTE network on the Moon, reached Mons Mouton, one of the candidate Artemis III landing regions, aboard Athena, the Nova-C lander of Intuitive Machines’ IM-2 mission [5], [6]. Although the network powered on and exchanged telemetry data with Earth, the Athena lander came to rest on its side [6]. The rover and hopper it carried could not be deployed and no connection to the network was established [5], [6]. Linkbudget analysis for lunar surface networks requires the path loss between every transmitter and every location a receiver may occupy. As the Moon lacks an atmosphere, this path loss is governed almost entirely by free-space spreading, ground reflection, and terrain obstruction. The lunar terrain constrains wireless propagation through both the proximity of the horizon and the scale of its relief. Over a smooth sphere of radius 1737.4 km, a 4 m mast and a 1.5 m receiver have a combined radio horizon of only 6.0 km (3.7 km plus 2.3 km respectively), beyond which coverage depends on the elevation of the mast relative to the surrounding terrain. Crater rims and massifs further obstruct line of sight (LOS) over distances of tens of kilometers, making local topography, rather than transmitter range, the governing factor in coverage. The permanently shadowed regions (PSRs), which host the volatile deposits motivating polar exploration, illustrate this constraint in a counterintuitive way. Terrain that shields a crater floor from sunlight arriving at elevations below approximately 1.5° does not necessarily block a mast on the overlooking rim, since the mast views the floor from above rather than across the horizon. Consequently, 61 % of the PSR area within the study region is in LOS of at least one permitted site, and 59 % is reachable at 1.8 GHz (53 % at 2.58 GHz, Table VI). The terrain a smaller mast cannot serve lies instead

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on the shadowed inner flanks of craters and in small craters with no candidate site in view, and 69 % of this unserved area at 1.8 GHz lies outside permanent shadow (Section IV-B). Surface network coverage is therefore a geographic problem that must be resolved with a digital elevation model (DEM) prior to network design. However, there is no publicly available dataset or product which quantifies achievable network coverage across the polar region as a whole. Existing lunar propagation studies are limited to one or a few sites, with examples such as ray-traced path-loss modeling along a single crater rim, DEM-based coverage estimates for a small number of candidate sites, and deployment analyses which involve a few towers (Section II). This paper addresses that gap with a potential-coverage atlas of the lunar south polar region. Rather than optimizing mast placement, we enumerate every plausible mast site south of 80°S, compute the coverage footprint of each with a terrainaware propagation engine, and merge the footprints into polewide layers. For every 20 m cell, these layers indicate whether any candidate mast can serve it, the achievable link quality, the sites from which it is served, and the number of alternative sites available. The design of the atlas serves two purposes. Prior to a mission it provides planners with a screening product for assessing the coverage potential of candidate regions and an input for subsequent network-design studies. After landing, the data contained in this study can support an onboard or crew-operated tool that identifies, from the actual landing location, the nearest candidate mast site offering the greatest coverage. The principal contributions of this paper are summarized as follows: 1) A GPU atlas engine that combines a radial viewshed with ITU-R P.1812 Delta-Bullington propagation on every receiver, carrying the grazing ground reflection through its spherical-Earth term, with a link budget derived from stated noise and power assumptions in both link directions (Section III-C). 2) A candidate-site methodology with two classes, terrain high points anywhere on the disc and landable 1 km grid cells inside the Artemis candidate landing regions, that produces 11,827 sites from stated rules with no hand selection (Section III-B). 3) The atlas itself, with continuous best-server received power, best-server identity, redundancy count and coverable mask at 20 m for four SFCG-recommended surface bands and the IM-2 band, computed for all 11,827 sites on the WPI Turing cluster (Section III-D), with a compact 160 m release product and per-region 20 m windows. 4) Validation against a parabolic-equation solver on real terrain profiles and against NVIDIA Sionna RT ray tracing on canonical obstacles and real terrain, including the limitation of wedge-based first-order diffraction on DEM meshes, and quantified sensitivity of the coverage class to the diffraction model, the DEM product, DEM error and candidate density across latitude bands (Section IV-A). 5) Pole-wide and per-region results for the nine current

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Artemis candidate landing regions and three regions of the 2022 list, showing that within its free-space range a mast covers about 90 % of its visible area at every band, that the range shrinks from 22 km to 1.6 km across the bands while a 20 dB stronger budget reaches visible terrain 100 km away, that most of the permanently shadowed area is visible from the permitted rim sites, and that coverage is effectively single-server at 25.375 GHz (Section IV). 6) The finding that local-maximum site selection on the PDS LDEM_80S_20M product picks orbit-track artifacts of 20–257 m at about one site in ten. The atlas uses the orbit-adjusted PGDA product, on which no selected site is more than 20 m higher in the PDS product, and carries the height difference between the two products for every site. Four products, namely the full-resolution atlas, the compact 160 m release product, the per-region 20 m windows, and the 11,827-site candidate table, are publicly released under a DOI. The remainder of this paper is organized as follows. Section II reviews lunar surface propagation models, terrain-based lunar visibility products, ray tracing and terrestrial coverage prediction, and places the atlas among them. Section III describes the system in the order in which it runs. It covers the terrain, shadow, region and regolith inputs (Section III-A), the two classes of candidate mast sites and the rules that produce them (Section III-B), and the footprint engine with its link budget, viewshed and Delta-Bullington propagation (Section III-C). It closes with the computation (Section III-D), in which the tiling and resolver merge 11,827 footprints into one pole-wide atlas on the cluster and the exact statistics behind every reported figure are defined. Section IV opens with the validation of the engine against a parabolic-equation reference, ray tracing and analytic solutions and the sensitivity of the coverage class to the model and the DEM (Section IV-A). It then presents the pole-wide, per-mast and per-region results, together with the throughput, power-control and referencebudget studies, and closes with a discussion of the scope and limitations of the atlas (Section IV-H). Section V concludes and outlines future work. Fig. 1 previews the system at its simplest. Candidate masts are enumerated on the polar terrain, the footprint of each is computed against that terrain, and all footprints are merged into one pole-wide atlas. Section III defines it exactly. II. BACKGROUND AND R ELATED W ORK A. Lunar surface propagation models Early lunar channel studies adapted existing terrestrial models. Foore and Ida introduced a modified Longley–Rice Irregular Terrain Model (ITM) [7], adapted for the lunar radius and the absence of an atmosphere, to predict path loss over the lunar surface [8]. Hwu et al. studied lunar terrain effects on surface communications using computational electromagnetics, taking the dielectric characteristics of the regolith as input alongside terrain geometry and antenna placement [9]. Chizhik et al. developed the Analytic Propagation Approximation over variable terrain (APA), which approximates the intervening

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

all together

each mast

in view

candidate masts on the polar terrain

3

bent over hidden

what it can reach, terrain in the way

every footprint merged into the coverage atlas

Fig. 1. Candidate LunarRF mast sites are enumerated on the south-polar terrain (left). For each mast, the system computes what it can reach with the terrain in the way, the ground in view, the ground just behind a rim that diffraction still reaches, and the ground that is hidden (center). Every footprint is merged into one pole-wide coverage atlas, darker where several masts overlap (right). Fig. 2 names the inputs, the processing loop and the outputs of the system outlined here, while Fig. 3 details the operations inside the processing block.

terrain by a constrained parabola and computes signal strength via a modal (Airy function) solution. Intended for rapid lunar coverage prediction, APA was validated against over 3000 measured links in the desert terrain of Fuerteventura, Spain, achieving 8.5 dB RMS error [10]. The campaign itself was a Nokia Bell Labs lunar-analog measurement at 1.8 GHz with a 4 m transmit antenna, the band and mast height of the later IM-2 demonstration [4], [10]. Edwards et al. reported a NASA study in which LOLA topography of a 27.5 km square around the Shackleton connecting ridge was imported at 55 m resolution into Remcom’s Wireless InSite ray tracer [4]. Configured with lunar curvature, no atmosphere, and regolith electrical properties, the simulation mapped path loss and throughput for a 30 m lander-mounted base station and a 3.5 m LTV user. Edwards et al. also summarized the SFCG-recommended 3GPP bands and the Artemis EVA range limits (2 km walking, 10 km LTV-assisted), which this paper adopts along with the study’s representative link parameters. Wang and Wyglinski later proposed the Barren, Irregular, Chaotic Terrain Ring (BICTR) model, a stochastic ring-of-reflectors multipath channel model inspired by Jakes’ and existing two-ray models [11]. BICTR was validated against the NASA Desert RATS 2022 lunar-analog measurement campaign, where it predicted received power on average 7.52 dB and 9.90 dB closer to measurement than ITM [7] and ITWOM [12], respectively [11]. Although BICTR captures multipath and fading, it omits diffraction, the mechanism that dominates path loss behind terrain obstructions. Adebowale and Ostermann published a ray-traced path-loss model at 5.855 GHz for Shoemaker Rim F [13], and Pabari et al. modeled radio-frequency propagation for a wireless sensor network on Chandrayaan-1 Terrain Mapping Camera DEMs of four sample sites [14]. Qin et al. searched the illuminated south-polar region for a main communication tower and placed sub-stations with a genetic algorithm to maximize field strength within a 10 km radius, using a P.526-based terrain model [15]. These three works are the closest antecedents of the present work. Lordos et al. proposed autonomously deployable towers for communication into permanently shadowed regions [16], a concept that bears directly on the PSR result of Section IV-B. Our work quantifies what small masts on the illuminated uplands cannot reach, and such infrastructure represents one approach to extending coverage into these regions. These studies established the governing propagation physics, operational requirements, and

site-specific coverage at one or a few locations. No published study provides coverage analysis at the scale of the full polar region, nor a systematic enumeration of candidate deployment sites. The present work addresses both, contributing a polewide coverage atlas in which candidate sites are enumerated and ranked. B. Terrain-based lunar visibility products Mazarico et al. published pole-wide illumination and Earthvisibility maps computed by horizon analysis of the LOLA DEM [2], and Barker et al. released improved, orbit-adjusted south-polar elevation products with error estimates [17], [18]. Peña-Asensio et al. combined illumination, Earth visibility, PSR proximity, and geological criteria in a multi-criteria assessment of 1247 candidate locations across the thirteen 2022 Artemis III regions [19]. Whereas these products address whether a given point can view the Sun or the Earth, the present work applies the same terrain data to visibility of a surface base station, and incorporates the propagation physics that a line-of-sight test alone omits. C. Ray tracing Differentiable GPU ray tracers such as NVIDIA Sionna RT [20], the ray-tracing module of the Sionna library [21], offer path enumeration (reflection, first-order UTD wedge diffraction [22], scattering) on triangle meshes. We use Sionna RT as a cross-check of the atlas engine on line of sight and reflection (Section IV-A); it is not a diffraction reference for gentle terrain, because wedge diffraction on a faceted mesh of a smooth crest returns little or no energy, which is a limitation of wedge-based diffraction on DEM meshes rather than of the software. Parabolic-equation (PE) methods [23]– [25] are the standard numerical reference for propagation over irregular terrain with lossy ground, and serve that role in our work. D. Terrestrial coverage prediction The atlas engine follows the structure of terrestrial planning tools, combining a viewshed with a point-to-area propagation model in which a spherical-Earth term carries the grazing ground reflection on clear paths and a knife-edge construction carries the diffraction on obstructed ones. The model is

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adapted to the Moon through the lunar radius, the absence of an atmosphere, regolith electrical properties, and a spheredrop term applied to every profile. The Delta-Bullington model of ITU-R P.1812 [26] is the standard point-to-area diffraction method for terrestrial prediction up to 6 GHz. Its application at 25.375 GHz is an extrapolation beyond the recommendation’s stated 6 GHz limit. However, the components of the method retained here, namely the knife-edge diffraction integral and the spherical-surface term, are frequency-scaled physical constructions rather than empirical fits. Moreover, the terrestrial effects that motivate the stated range, namely clutter and atmospheric attenuation, are absent on the Moon. The Deygout [27], Bullington, and single knife-edge methods [28] belong to the same family of knife-edge diffraction models and are retained as alternatives, allowing the sensitivity of the coverage classification to the choice of method to be quantified. III. S YSTEM A RCHITECTURE This section presents the LunarRF system architecture in the execution order of Fig. 2. Section III-A describes the input datasets, Section III-B the frozen table of candidate mast sites that drives the processing loop, Section III-C the per-mast footprint engine, and Section III-D the resolver and run-management layer through which 11,827 footprints are consolidated into a single pole-wide atlas. The design separates per-mast computation from pole-wide accumulation so that the loop can be sharded, interrupted, and resumed without coordination. Fig. 3 expands the processing block of Fig. 2 into the operations of the engine and the resolver. The parameter values behind each operation are given in the text of this section, and the field names of the released files in the data release. The validation studies of Section IV-A read the same profiles and accumulators but never write to the store. A. Inputs: Terrain, Shadow, Regions and Regolith All inputs are obtained from public products. The exact URLs, sizes and SHA-256 checksums are recorded in the provenance file of the data release. Each raster is handled in the LOLA south polar stereographic frame, a sphere of radius R = 1737.4 km, scale k = 1 at the pole, central meridian 0°E along +y and 90°E along +x (PROJ string +proj=stere +lat_0=-90 +lon_0=0 +k=1 +R=1737400). The map scale factor k(φ) =

2 1 + sin |φ|

(1)

reaches 1.0077 at 80°S (0.8 %) and is neglected in distances. 1) Elevation: The atlas terrain is the orbit-adjusted LOLA product LDEM_80S_20MPP_ADJ from the NASA Planetary Geodynamics Data Archive (PGDA) [18]: 30,400 × 30,400 cells at 20 m, spanning ±304 km, heights in meters above the reference sphere. The same grid and transform are used by the PDS Geosciences Node product LDEM_80S_20M V2.1 (float32 kilometers relative to R) [29], which we keep as a comparison DEM for error propagation. The two products differ in a way that matters for site selection (Section III-B),

the PDS product carries smooth positive bumps of 20–257 m height and more than 140 m width along orbit tracks at about one in ten of its local maxima, the adjusted product does not. Each candidate site therefore carries ∆zPDS , its height in the PDS product minus its height in the PGDA product, as a persite measure of inter-product elevation disagreement. For validation at higher resolution we use the PGDA 5 m LOLA mosaic of 87°S–90°S [17]. There is no public 5 m LOLA product that exists north of 87°S. 2) Permanent shadow: Permanently shadowed regions are taken from the PGDA 20 m product LPSR_80S_20MPP_ADJ [18] on the atlas grid, with the LOLA EXTRAS averagevisibility and PSR maps at 120 m and 60 m [2], [29] used for figures. Masts are not sited in permanent shadow regions as a solar-powered lander or mast would not be placed there. PSR floors remain valid receiver locations and are reported as coverable when they have line of sight and margin because a rover or astronaut may operate there. 3) Landing regions: Two NASA lists define the regions of interest. The release of 19 August 2022 named thirteen candidate regions of roughly 15 km × 15 km [30]. The update of 28 October 2024 named nine, of which five were kept from 2022 and four added [31]. NASA’s February 2026 architecture update makes Artemis III a low-Earth-orbit rendezvous test and moves the first crewed landing to Artemis IV [32]. The nine regions were defined for Artemis III [33] and remain the only published reference set and we refer to them as the Artemis candidate landing regions. Region footprints are the extents of the 1 km Lunar Grid Reference System navigational grids published by the USGS for the nine 2024 regions [34] and, where public, for the 2022 regions [35]. The region polygons are reprojected from the USGS polar stereographic frame (false easting and northing 500 km, scale factor 0.994) into the LOLA frame. Twelve regions have a public footprint, the nine current regions plus Faustini Rim A, Connecting Ridge and Amundsen Rim from the 2022 list. The five 2022 regions without a public grid (Peak near Shackleton, Connecting Ridge Extension, de Gerlache Rim 1, de Gerlache–Kocher Massif, Leibnitz Beta Plateau) are kept in the configuration as unverified Gazetteer centers and are excluded from all figures and tables. The polygons of Peña-Asensio et al. [19] are the closest citable replacement and could be adopted in a future run. 4) Regolith: The ground enters the propagation model through its admittance in the spherical-Earth term of DeltaBullington (Section III-C4), with a relative permittivity εr = 3.7 and loss tangent tan δ = 0.01, within the range of the Apollo-sample measurements of Olhoeft and Strangway [1] for compacted regolith of density ≈2 g cm−3 ; tan δ = 0.1 is retained as a high-loss sensitivity case. Conductivity follows as σ = 2πf ε0 εr tan δ.

(2)

No small-scale roughness term is applied, although subcentimeter and sub-pixel roughness of the regolith is well characterized [36], [37]. The same values define the impedance ground of the parabolic-equation reference (Section IV-A1),

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

INPUT

PROCESSING

OUTPUT

Terrain LOLA 20 m elevation model, 80°S–90°S

Candidate mast sites 11,827 sites from published rules

Footprint engine one candidate mast at a time (GPU)

footprint

5

Resolver keeps the best per cell, counts the rest (CPU)

Atlas layers per band and 20 m cell: best power, best server, mast count, LOS, coverable

next mast

Per-mast coverage table Link budget radio parameters, five 3GPP bands

repeated for every candidate, in any order and on any number of workers; restartable

Run manifest

Fig. 2. The terrain, the candidate mast table and the link budget enter the level-0 LunarRF processing block as its three inputs. The block produces the atlas layers, the per-mast coverage table and the run manifest. Processing is a loop between two components with fully separate state. The footprint engine owns one mast at a time on the GPU, and the resolver owns the pole-wide accumulators on the CPU. The footprint is the only data that crosses between them. The resolver applies order-independent per-cell rules, so the candidate list can be sharded and run in parallel, and a run that stops continues from its manifest rather than from the start.

and roughness below the DEM resolution is among the omissions listed in Section IV-H. B. Candidate Mast Sites The atlas does not choose where masts go. It enumerates every place a mast could plausibly stand and computes the coverage of each. The union over candidates is the coverable map, the per-cell count is a measure of serving redundancy, and the per-candidate table lets a planner or an optimiser select a subset. Two classes of place are enumerated by rules that are all stated parameters (listed with the released run parameters). 1) Rules common to both classes: Sites are extracted per 40 km tile with a 10 km halo (Section III-D) such that every site sees its full neighborhood and no site is counted twice. Sites north of 80°S (DEM corners) and inside permanent shadow are dropped. Within a class, sites are thinned to a minimum spacing of 1 km by a greedy pass that keeps the highest-scoring site first, 1 km is the scale at which coverage is assessed. The spacing does not limit the density: the localmaximum, prominence, permanent-shadow and slope rules have already fixed which cells qualify, and re-extracting the whole pole with the same rules at 500 m admits only 7 % more sites, 12,683. The atlas itself was run at 500 m spacing on three test tiles (Section IV-A7). Sites within the ray radius (22 km) of a verified region footprint are processed first (priority 0, 4020 sites) such that a partial run already answers the landingregion questions. 2) Ridge class: where the terrain offers a high point: A cell qualifies if it is either (i) a local maximum, the highest cell of its 1 km × 1 km neighborhood, standing at least 50 m above the lowest cell of that neighborhood (prominence), or (ii) a ridge or rim cell: Laplacian mean curvature more negative than −0.006 m−1 after a two-pixel Gaussian smooth (a convexup crest), thinned to one cell wide; and in either case its local slope at 20 m is at most 12°, a mobility limit for a small lander or a rover-placed tripod rather than a landing limit. Surviving cells are ranked by height (with a 50 m bonus for true peaks), thinned to 1 km and capped at 150 per tile (the

cap binds on no tile: the largest count is 146, the median 46). The result is 10,499 ridge-class sites, 7119 of them in the 80°– 83°S band, which holds the most area and the densest field of local maxima. Rhe polar band is the more rugged in the sense that matters for coverage (larger relief and PSR area per unit area, Section IV-B). This class is deliberately not a landability screen: rims and peaks are often too steep for a lander at the 100 m scale. It answers the question “if a 4 m mast could be put on the best terrain, what could it see?” 3) Landing-site class: where a lander can stand: Sites of this class lie only inside the twelve verified USGS region footprints. For each region we take the centers of the 1 km grid cells aligned to the footprint (the USGS grid itself), keep a cell if its 100 m-scale slope is at most 5°, the flatness requirement of the Human Landing System [19], and drop cells in permanent shadow. The slope is computed on the DEM after smoothing with a 100 m box filter. No further thinning is applied. The result is 1328 sites. Mons Mouton Plateau, by far the largest region, contributes 766, and Peak near Cabeus B, the steepest, contributes four (Table I). The landable fraction of the grid cells ranges from 25 % at Slater Plain to 1 % at Peak near Cabeus B. In the base atlas both classes carry a 4 m mast, the height at which the IM-2 base station was carried on an upper panel of the Nova-C lander [38], so that the layers are directly comparable. Taller landing-site masts of 10 m and 30 m represent lander-mounted equipment on larger vehicles such as Blue Moon Mk 2 (about 16 m tall) and Starship HLS (52 m tall) [39], whose antenna mounting heights are unpublished, they form separate sensitivity sets, of which the 30 m case is the reference scenario of Section IV-G and the others are future work. 4) Criteria deliberately not used: The candidate table is defined by terrain alone, and no further selection should be inferred from it. Illumination and solar power at the site are intentionally excluded as a candidate in a poorly lit location remains a valid coverage question, and the LOLA averagevisibility maps allow that coupling to be introduced at a later stage. Earth visibility for direct-to-Earth backhaul is outside

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PROCESSING Resolver Footprint engine

per footprint, on the CPU

per candidate mast, on the GPU

Find the tiles the footprint overlaps footprint

DEM window square, side equal to the free-space range

terrain

Radial profiles and viewshed 8,192 rays; which cells are in view

profiles

Diffraction loss Delta-Bullington on every cell, once per band

loss

Received power free-space loss minus diffraction; thresholds applied later

Merge per cell best power and its mast, count of masts above threshold, line-of-sight flags

next mast

The terrain is sampled once per mast; the propagation model runs on the raw profiles,

Accumulators on disk, one per tile and layer

once per band. The result is the footprint: power, line-of-sight flag and range on every cell.

Run management A manifest records every finished mast, so a stopped run resumes where it left off. Shards run the candidate list in parallel and are merged exactly, because every merge rule is order-independent.

Fig. 3. The engine evaluates the terrain geometry once per mast on 8192 radial profiles. It evaluates the propagation loss once per band on those same profiles. The loss model therefore sees the raw, unsmoothed terrain. The footprint carries the received power, the line-of-sight flag and the range of every cell. Nothing is thresholded or cached inside the engine. The resolver merges each footprint into the per-tile accumulators without knowing which mast it is merging, which shard produced it, or in what order the footprints arrive. This independence allows the run to be sharded and resumed. Run management is shared by both halves. It is the only place that reads the manifest. The link budget, the diffraction model and the merge rules are given in Sections III-C and III-D. TABLE I C ANDIDATE SITES PER REGION (12 VERIFIED FOOTPRINTS ; NUMBERS AS IN F IG . 4). F OOTPRINTS ARE THE USGS NAVIGATIONAL - GRID EXTENTS , NOT NASA REGION POLYGONS ( HENCE THE 4579 KM 2 OF M ONS M OUTON P LATEAU ). L ANDING - SITE CLASS INSIDE THE FOOTPRINT, RIDGE CLASS INSIDE IT, AND RIDGE CLASS WITHIN 8 KM OF IT. M ONS M OUTON OVERLAPS M ONS M OUTON P LATEAU (138 KM 2 ) AND N OBILE R IM 1 (89 KM 2 ), AND N OBILE R IM 1 OVERLAPS THE P LATEAU (43 KM 2 ). P ER - REGION COUNTS ARE NOT ADDITIVE , THE LAST ROW GIVES THE UNIQUE TOTALS . B OLD MARKS THE HIGHEST VALUE IN EACH COLUMN AND ITALIC THE LOWEST. No.

Region

List

1 2 3 4 5 6 7 8 9 10 11 12

de Gerlache Rim 2 Haworth Malapert Massif Mons Mouton Nobile Rim 1 Nobile Rim 2 Peak near Cabeus B Slater Plain Mons Mouton Plateau Faustini Rim A Connecting Ridge Amundsen Rim

2024 2024 2024 2024 2024 2024 2024 2024 2024 2022 only 2022 only 2022 only

Area (km2 )

Landing-site

Ridge inside

Ridge ≤ 8 km

446 941 468 293 446 425 446 446 4,579 425 293 425

44 137 21 53 53 65 4 107 766 69 26 50

8 14 9 5 5 16 3 14 138 13 9 11

43 23 16 24 19 36 11 52 171 38 15 30

1328

10499

All candidates (unique)

the scope of a surface-to-surface atlas. The distance from a ridge site to any landing region, and the geological, resource or scientific value of a site, are planning considerations rather than propagation ones and belong to a subsequent siteselection step applied to the released table. Overlapping footprints are neither optimized nor de-duplicated, every candidate transmits in the envelope, and the selection of a minimal set is future work. Finally, regolith bearing strength, boulders and roughness below the 20 m DEM resolution cannot be assessed from the available terrain data and are omitted. 5) DEM artifacts and site selection: The two 20 m products derive from the same LOLA shots and differ only by the orbit adjustment. Their difference is not a terrain-error estimate (Section IV-A). However, it does reveal a selection effect of the candidate rules. The local-maximum detector preferentially selects cells whose height is raised by an artifact. The artifacts are concentrated in the candidate set far beyond their share of

the terrain. When the candidate rules of Section III-B were first applied to the PDS product (13,415 sites), the site-height difference ∆zPDS , PDS minus PGDA, was below 1 m RMS for the landing-site class but 16.5 m RMS for the ridge class and one-sided: 10.0 % of ridge candidates (8.6 % in the 80°– 83°S band, 14.9 % in 83°–86°S and 13.7 % in 86°–90°S) sat on features 20–257 m higher in the PDS product than in the adjusted product. Inspection of the largest cases shows smooth positive bumps more than 140 m across in the PDS DEM that are absent from the adjusted DEM; orbit-track errors rather than single-pixel spikes, which the detector selects precisely because they are local maxima. A mast placed on such a feature overstates its footprint. The atlas is therefore run on the adjusted product. In the final candidate set, detected on that product, no site is more than 20 m higher in the PDS DEM, so the artifacts are no longer selected; the ridge-class RMS difference falls to 3.8 m, and 77 sites (0.7 %) are more

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

7

Candidate mast sites and Artemis candidate landing regions 300

9

150

3 4

y (km, +y = 0°E)

6

5

2 7

12 1

0

10

11

8

−150

−300 −300

−150

0

150

300

x (km, +x = 90°E) ridge class (10,499) 1 de Gerlache Rim 2 7 Peak near Cabeus B

landing-site class (1,328) 2 Haworth 8 Slater Plain

|PDS − PGDA| > 20 m (77) 3 Malapert Massif 9 Mons Mouton Plateau

2024 region footprint 4 Mons Mouton 10 Faustini Rim A

2022-only footprint 5 Nobile Rim 1 11 Connecting Ridge

82°–88°S rings 6 Nobile Rim 2 12 Amundsen Rim

Fig. 4. Candidate mast sites are shown on the orbit-adjusted LOLA 20 m DEM in south polar stereographic projection, 80°S–90°S. Gray marks the 10,499 ridge-class sites, and magenta marks the 1328 landing-site-class sites. Orange rings mark the ridge sites whose height differs by more than 20 m between the PDS LDEM_80S_20M and the adjusted product (n = 77). All 77 are higher in the adjusted product (Section III-B5). Black outlines show the nine 2024 region footprints as solid lines and the 2022-only footprints as dashed lines, numbered beside each footprint.

than 20 m higher in the adjusted product than in the PDS product (Fig. 4). Every site carries ∆zPDS . The orbit-adjusted product exists because such errors were known; the point here is the degree to which peak-picking on the unadjusted product concentrates them. Cells where the two products differ by more than 20 m occupy 0.05 % of the pixels, and those where the PDS product is the higher 0.02 %, yet they carry one ridge site in ten, a concentration of several hundred times. The 77 adjusted-product-higher sites are inspected individually (hillshade, profiles, LOLA shot count and local-maximum status in each product) in the candidate-freeze record of the release. All 77 are kept in the run and 60 are flagged in the released table, because only 23 are 1 km local maxima in the adjusted product (none is in the PDS product) and 28 stand on cells with no LOLA shot, so that their heights rest on interpolation in both products. A companion test compares the LOLA shot count at candidate cells with that of all cells in the same latitude band, per detector, to check that neither the local-maximum nor the curvature rule prefers interpolated cells (Section IV-A6).

C. Propagation Engine and Link Budget 1) Link budget and thresholds: The base atlas uses a modest small-lander budget. A base-station can transmit power 30 dBm and user-equipment (UE) power 23 dBm (power class 3 [40]), isotropic (0 dBi) vertically polarized antennas at both ends, a 4 m mast and a 1.5 m receiver, an astronaut or rover-mounted antenna. Isotropic gains are used because the atlas is a site-potential envelope: a sector pattern implies a pointing decision and belongs to a deployment study. Noise is
N = kB Tant + T0 (F − 1) B (3) with a downlink carrier of B = 20 MHz, an assumed UE noise figure F = 7 dB and an assumed base-station noise figure of 3 dB, both better than the minimum receivers implied by the reference-sensitivity requirements of [40], [41], and an antenna temperature Tant = 150 K, an assumed value between the cold sky and the regolith brightness temperature. Polar regolith brightness temperatures are lower than equatorial values [42], [43], so 150 K overstates the noise rather than understating it; a 100 K change moves the thresholds by about 1 dB. The

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PREPRINT, 19 OCTOBER 2026

required SNR is 0 dB over the full 20 MHz carrier with no fading, implementation or body-loss margin, i.e. a detection edge rather than a service threshold because the stored layer is continuous received power, any stricter requirement can be applied at read time, and we report a 10 dB “data link” contour throughout. The stored layer can be re-thresholded only to stricter thresholds: cells beyond the ray radius of every candidate hold no value, so a stronger budget than the base case requires a new run (Section IV-G). The downlink threshold TDL = N + SNRreq is −94.4 dBm. The downlink received power at a cell at ground distance d from the mast is Prx (d, f ) = PBS + GBS + GUE − Lfs (d, f ) − Lt (d, f ), (4) where Lfs = 20 log10 (4πdf /c) is the free-space loss and Lt ≥ 0 the terrain excess loss of Section III-C4. The uplink is evaluated by reciprocity: the same path with the UE power, so that uplink received power is Prx + (PUE − PBS ) with (PUE − PBS ) = −7 dB, against a base-station threshold TUL = −105.2 dBm over a 5 MHz cell-edge uplink allocation. Coverage uses the more restrictive direction, i.e. a cell is coverable when  Prx ≥ Teff = max TDL , TUL − (PUE − PBS ) ; (5) with these values the link is downlink-limited and Teff = −94.4 dBm (a full-carrier uplink assumption would make it uplink-limited at −92.2 dBm). The ray radius is the free-space range to the effective threshold at the lowest carrier fmin , r=

c 10(PBS +GBS +GUE −Teff )/20 , 4πfmin

(6)

22.0 km at 1.8 GHz, capped at 100 km with the cap reported; the same radius is used for all bands of a run, and the freespace ranges at the other bands are 15.4 km, 10.9 km, 6.8 km and 1.6 km. Section IV-F shows that this range, not the terrain, is what limits the coverage at every band. The five carriers are four SFCG-recommended surface bands [3], [4] and the IM-2 demonstration band [4]. They are 1.8 GHz (3GPP Band 3, flown on IM-2 but outside the SFCG surface allocations and unlikely to receive long-term approval because of radio-astronomy concerns), 2.58 GHz (n7/38/41, SFCGb1 of [4], expected to carry primary near-term use), 3.65 GHz (n48/77/78), 5.855 GHz (the lower edge of n47) and 25.375 GHz (n258). 2) Terrain profile and viewshed: For each candidate the engine (Fig. 3, left) reads a square DEM window of halfwidth one pixel beyond the ray radius (2207 cells wide at 20 m) and casts Naz = 8192 azimuthal rays, a one-pixel arc at the radius, sampled at the pixel spacing. DEM heights z are radial heights above the sphere, so every profile receives the sphere drop before any horizon or diffraction test, z ′ (d) = z(d) −

d2 , 2R

(7)

the “Earth-curvature” equivalent, here 14 m at 7 km and 140 m at 22 km. With the mast antenna at height zm = z ′ (0) + hm , a receiver at distance dj along the ray is in geometric line of

in view, served hidden, served by diffraction mast horiz on r

ay

not served

served by diffraction over the crest

beyond the budget: not served

in view: served

deep shadow: not served surface curves away

Fig. 5. Receiver classes are sketched along one ray from a mast on schematic terrain. Receivers in geometric line of sight are served at near free-space power. Receivers hidden just behind a crest can still be served by diffraction over it, at reduced power. Receivers deep in shadow, or in view but beyond the range of the link budget, are not served. The engine makes this test on every ray and every cell of the window.

sight (LOS) when its antenna clears the running maximum of the terrain elevation angle,

atan2 z ′ (dj ) + hr − zm , dj > max atan2 z ′ (di ) − zm , di , i<j

(8) such that one cumulative-maximum pass along each ray gives the LOS state of every receiver and, as a by-product, the horizon-forming obstruction; the same pass gives the profile needed by the diffraction model. Figure 5 sketches the three receiver classes that result along one ray, and Fig. 6 shows them on real terrain for one candidate. All of this is a batched torch [44] computation on the GPU. The per-mast cost for all five carriers is 14–29 s on an NVIDIA A30 including the DEM read, and about 6 s per carrier on an RTX 5080 (Section III-D). 3) Obstructed receivers: Delta-Bullington: Every receiver, visible or not, is evaluated with the Delta-Bullington method of ITU-R P.1812 Annex 1 §4.3 [26],  Lt = Lbulla + max Lsph − Lbulls , 0 , (9) where Lbulla is Bullington diffraction on the actual profile with the recommendation’s empirical term, Lbulls the same on a smooth-Earth profile with least-squares effective antenna heights, and Lsph the first-term spherical-Earth diffraction, all with the lunar radius and the regolith surface admittance. The model is continuous through the radio horizon, which avoids a step at the LOS boundary. Deygout [27], Bullington [45] and single knife-edge (ITU-R P.526 [28]) are implemented as alternatives. Deygout edges are frequency-independent and √ are found once per profile and rescaled by f , so the multiband run costs little more than a single band. Sensitivity of the coverage class to the model choice is quantified in Section IV-A. 4) Visible receivers: the ground reflection: On visible receivers the deviation from free space is the ground reflection, and Delta-Bullington accounts for it: its spherical-Earth term, evaluated with least-squares effective antenna heights above the fitted profile, is the plane-Earth grazing two-ray loss. On flat ground the Delta-Bullington power reproduces the analytic

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

two-ray field with the Fresnel TM coefficient of the regolith to 0.85 dB RMS (−0.1 dB mean, 0.2–2.9 km, 1.8 GHz; an engine regression test), and on a 2° plane to within 1 dB. A separate two-ray term applied on top of Delta-Bullington on visible receivers, as an earlier version of the engine did, doublecounts the reflection at grazing incidence (10.5 dB below the two-ray field on flat ground, 18 dB at 2.5 km) and is not used. The atlas value is therefore Delta-Bullington on every receiver, visible or not, and the sole terrain-and-ground model of the engine is P.1812 Annex 1 §4.3 with the lunar radius and the regolith admittance. The parabolic-equation comparison of Section IV-A1 tests this model on real profiles, including sloped visible paths where the effective-height fit is an approximation. A second layer, the no-reflection layer, is exported alongside free space on visible receivers and Delta-Bullington in shadow. It is an upper bound on the atlas value that shows how much the ground reflection costs on clear paths, and it is the appropriate comparison for ray-tracing results that find no specular path on the decimated terrain (Section IV-A). 5) Products: At every 20 m cell and for every carrier k the atlas stores, in both layers, the best-server received power Prx , the maximum over all candidates whose footprint reaches the cell (float32, −999 dBm for cells outside every footprint). The identity of that candidate, whether that candidate is in geometric line of sight of the cell; and the number of candidates whose received power at the cell exceeds the threshold. Two bandindependent layers record the number of candidates with line of sight to the cell and the distance to the nearest of them. The coverable mask is Prx ≥ −94.4 dBm. As the stored quantity is received power, stricter thresholds and weaker budgets follow by re-thresholding the released layers; a stronger budget or a taller mast changes the ray radius and requires a new run of the engine (Section IV-G). Per candidate, the run records the covered area per band and layer, the LOS area of its disc, the LOS-and-covered area, the LOS area within each band’s own free-space range, and the covered fraction of the 2 km and 10 km EVA discs around it. D. Computation 1) Tiling and accumulation: The 608 km disc is divided into pole-centered 40 km tiles (16 × 16 index space, 208 tiles intersecting the 80°S disc), each with a 10 km halo used for candidate extraction. A mast’s footprint is computed on its own window, independent of tile edges; and merged by the resolver (Fig. 3, right) into per-tile accumulators for every tile it touches, at most nine. Per band the accumulators hold, for the atlas value and for the no-reflection layer alike, the best power, the best identity, the count of masts above threshold (m) and the line-of-sight flag of the best server with Prx (c) the received power of mast m at cell c that is undefined outside the mast’s ray disc and ℓ(m) (c) ∈ {0, 1} its LOS flag, (m) (m) P ⋆ (c) = max Prx (c), m⋆ (c) = arg max Prx (c), m m X  ⋆ (m) n(c) = Prx (c) ≥ Teff , ℓ⋆ (c) = ℓ(m ) (c); m

(10)

9

two further layers common to all P bands hold the number of masts in line of sight of the cell, m ℓ(m) (c), and the distance to the nearest visible candidate (running minimum). Every operation in (10) is associative and commutative, so footprints can be accumulated in any order and on any number of workers, and merging shards is exact. No per-candidate footprint is stored (one float32 layer for 11,827 footprints of five bands on 22072 windows would be 1.15 TB); a manifest keyed by a hash of the radio parameters, the engine version, the store schema and the candidate table records which candidates are done, and a run is resumable by re-issuing the same command. 2) Cluster run: The whole-pole run was executed on the WPI Turing cluster using Slurm scripts and NVIDIA A30 GPUs as a 16-task job array. Each task processed one shard of 739–740 candidates into its own accumulator directory, with at most two tasks running concurrently. The run reported here is the second pass over the same frozen candidate table, whose SHA-256 is recorded in every manifest together with the engine version and the store schema. The first pass computed the retired two-ray layer alongside the atlas value. The second computes the Delta-Bullington value with the extended store, which holds the count and identity for both layers, the bestserver line-of-sight flag, the line-of-sight count and the distance to the nearest visible candidate. Tasks completed in 2.5 h each, or 12 s per candidate for all five bands including DEM reads, and 40 GPU h in total. Each task flushes its manifest after every candidate and re-queues itself on a stall or at the wall-time signal, so an interrupted task resumes at the next candidate, outlined in the run management of Fig. 3. A CPUonly merge then absorbed the sixteen shard accumulators into a single atlas in 2.7 h. The merge refuses overlapping candidate sets and differing engine versions, such that counts cannot double and layers cannot mix. It wrote the release bundle of 1.7 GB: pole-wide block-maximum mosaics of every layer at 160 m, minimum-reduced for the nearest-candidate distance; 20 m windows around each verified region footprint with an 8 km margin; the candidate and coverage tables; and the run parameters and the manifest. The figures of this paper derive from that bundle. The pole-wide statistics derive from the 20 m accumulators (Section III-D3), and the full 20 m tiles are available from the authors on request. 3) Statistics and areas: All pole-wide statistics in this paper are computed exactly on the 20 m accumulators. The 160 m release mosaics are block maxima over 8×8 cells intended for display. They overstate coverable fractions by 2–8 percentage points depending on band, and no statistic in this paper is taken from them. Areas and fractions are given in map (polar stereographic) space unless stated otherwise. The projected disc is 290,345 km2 against a spherical cap of 288,100 km2 , and the release statistics give both. IV. R ESULTS This section begins with the validation of the engine against reference solutions and the quantification of its sensitivities (Section IV-A). The pole-wide results follow (Section IV-B), then the footprints of individual masts (Section IV-C) and the Artemis candidate landing regions (Section IV-D). Those

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PREPRINT, 19 OCTOBER 2026

-1000

(a)

(b)

Height (m)

A′

r = 22.0 km DEM window 2207 × 2207 cells of 20 m covered, line of sight covered, diffraction not covered

hori

zon

direct

diffracted

ray

-2000 -2500

Received power (dBm)

A

-1500

no LOS Delta-Bullington (atlas)

(c)

-50

free space

threshold

-100

-150

covered 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 Distance from mast along A–A′ (km)

20.0

Fig. 6. The base case of the atlas engine is shown for one candidate mast (candidate 6430, ridge class, 84.13°S, 131.66°W) at 1.8 GHz with the atlas link budget (30 dBm base station, isotropic antennas, 4 m mast, 1.5 m receiver, effective threshold −94.4 dBm, ray radius 22.0 km). Panel (a) gives a plan view of the 2207 × 2207-cell DEM window (20 m cells). Light gray marks the cells covered in line of sight (226.8 km2 ), dark gray marks the cells covered by diffraction (1.1 km2 ), and white marks the cells not covered. The mast covers 227.9 km2 and sees 324.3 km2 of the 1526 km2 disc. Panel (b) shows the terrain along A–A′ (azimuth 30°, chosen to cross the visible valley wall) with the sphere drop applied. It draws the horizon ray through the crest that shadows the valley, a direct ray to a visible receiver on the far wall, and a diffracted path over the far crest to a shadowed receiver. The strip marks receivers without line of sight. Panel (c) shows the received power along A–A′ . The curves are the atlas value (Delta-Bullington on every receiver), free space and the coverage threshold. The strip marks covered receivers. The far wall is covered in line of sight at 8.6–13.4 km, the valley floor is 25–35 dB below free space, and the only receivers covered without line of sight lie just beyond the near crest.

results are then placed in context through three shorter studies, the throughput implied by the stored SNR (Section IV-E), a power-only control that separates terrain from budget (Section IV-F) and a run under the NASA reference budget (Section IV-G). The section closes with a discussion of the scope and limitations of the atlas (Section IV-H).

A. Validation and Sensitivity The engine is checked against three independent references a full-wave split-step parabolic-equation solver on real terrain profiles, against an independent ray tracer (NVIDIA Sionna RT) on line of sight and reflection, and against analytic solutions on canonical geometries. The sensitivity of the coverage class, covered or not at the stated threshold, is then quantified with respect to the diffraction model, the DEM product, DEM noise and candidate density, on tiles drawn from every latitude band rather than on a single tile. 1) Parabolic-equation reference on real profiles: A twodimensional split-step Fourier parabolic-equation (SSPE) solver [23] is used as the reference for both diffraction and ground reflection. The solver is the wide-angle Feit–Fleck propagator [46], which is exact in vacuum for any range step, with a shift-map treatment of the terrain [24]. The field is kept in the frame of the current profile segment, where the ground is the flat plane ζ = 0, and each change of slope rotates the angular spectrum by the slope change. The ground is an impedance boundary of Leontovich type for vertical

polarization, ∂u + αu = 0, ∂ζ

√ ik εc − 1 α= , εc

(11)

and εc from the regolith permittivity and loss tangent of the atlas, implemented with the discrete mixed Fourier transform of Dockery and Kuttler [25]. The impedance boundary is essential because with εr = 3.7, the reflection coefficient is 0.85 at 2° grazing and 0.67 at 5°, angles that sloped ground produces routinely, and a perfectly conducting ground would therefore bias the comparison. The transverse step is λ/4, which is 4.2 cm at 1.8 GHz and 1.3 cm at 5.855 GHz, which places propagator’s Nyquist angle at 90° and no angular truncation is applied in the local frame. The range step is 5 m. The domain height is the relief of the profile plus 500 m, with a 300 m absorbing layer of quadratically rising imaginary index on top, so that energy is never absorbed where later terrain could intercept it. Lunar curvature enters through the earth-flattening index m − 1 = z/R, applied to the raw DEM heights; the sphere drop is thereby counted exactly once. The solver uses no knife-edge approximation and no separate reflection term. Its self-tests, all with the impedance ground unless stated, give an RMS error of 0.13 dB for P.526 knife-edge diffraction on a Dirichlet half-plane, 0.14 dB for the analytic two-ray field with the Fresnel TM coefficient on flat ground and 0.07 and 0.41 dB on planes tilted 8.5° and 20°, and 0.10 dB for the P.1812 spherical-earth loss over the smooth lunar sphere beyond the 6.0 km horizon.

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

The shift map is exact for reflection on a tilted plane but approximate for diffraction over a convex crest. Against the exact eigenfunction solution for a soft wedge illuminated by a line source, the PE is within 0.7 dB RMS for a crest with 2° faces, 0.3 dB at 5°, 2.3 dB at 7°, 9 dB at 10° and fails at 15° (PE too little loss). The slope limit of the treatment is therefore taken as 7° for segment slopes, considerably stricter than the 10°–15° often quoted, and every receiver of the real-profile comparison is labeled with the steepest segment between it and the mast; statistics are reported for all receivers and for those within the limit. Crests steeper than the limit are covered by the exact wedge solution directly. On the same crests Delta-Bullington differs from it by 4.1 dB (5° faces), 1.4 dB (7°), −4.3 dB (10°) and −11.0 dB (15°) in the mean, the sign changing as the equivalent knife edge under-predicts the creeping-wave loss of a rounded soft crest; a soft wedge is a bounding case, not regolith, and the numbers are quoted as such. The comparison runs the atlas engine and the SSPE solver on the same LOLA profiles. Four masts drawn from each latitude band and candidate class that has one (the 80°–82°S band holds no landing-site candidates: 20 masts), eight azimuths each (160 profiles), at 1.8 and 5.855 GHz, with the receiver at 1.5 m; the PE power is averaged over the receiver height ±0.5 m and over three mast-site heights spanning ±1.3 m, so that the comparison is not decided by an unknowable phase at a single geometry. Receivers within 200 m of the mast and receivers where the PE excess loss exceeds 200 dB (below the solver’s numerical floor) are excluded, which is why the shadowed counts differ slightly between the two bands. Figure 7 shows representative profiles and Table II the statistics, for 160 profiles and 31,369 visible and 143,146 shadowed receivers, of which 2835 and 2361 lie within the 7° slope limit. Two limits are used in reading Table II. On visible paths the shift map is exact for reflection on a tilted plane. The slope limit, which is a limit on the treatment of diffraction over a crest, therefore does not apply there, and the “visible, all” rows are the estimate for line-of-sight receivers. In shadow the limit applies, and it is taken at 5° rather than at the 7° of the wedge test. At 7° the PE’s own error against the exact wedge, 2.3 dB, exceeds the 1.4 dB by which Delta-Bullington differs from it there, and a comparison at that limit would judge the model with a reference no better than the model. At 5° the PE is within 0.3 dB of the exact solution and Delta-Bullington 4.1 dB from it. The 7° rows are kept in the table for reference. On visible receivers the PE field is 3.9 dB below DeltaBullington at 1.8 GHz (RMS 4.6 dB, 31,369 receivers) and 3.3 dB below at 5.855 GHz (RMS 4.1 dB), with the 5th–95th percentiles of the difference at −7.9 and 0.1 dB. The atlas value is therefore optimistic on clear paths by 3–4 dB. DeltaBullington’s effective-height treatment of the grazing reflection, exact on a plane, recovers only part of the destructive interference on the undulating real profiles, where the local grazing angle at the reflection point differs from the planefit angle. The retired two-ray layer sits 3.1 dB above the PE by the same measure, closer in the mean but for the wrong reason, because its double-counted reflection loss happens to

11

overlap the shortfall of the effective-height fit on these profiles, while on flat ground it is 10 dB in error (Section III-C4). Delta-Bullington is kept as the atlas value and the bias is propagated rather than ignored. The PE-corrected columns of Table V re-threshold every cell served in line of sight by the bias measured at its band, 3.9 dB at 1.8 GHz and 3.3 dB at 5.855 GHz, interpolated between and held constant above, which moves the coverable class of 6.7 and 13.1 % of the visible receivers on the profiles at the two bands and 6.7 and 16.5 percentage points of the disc (Table V). In shadow the sign reverses. Behind crests of 5° or less the PE field is 3.6 dB above Delta-Bullington at 1.8 GHz (RMS 7.9 dB, 519 receivers) and 3.5 dB above at 5.855 GHz (RMS 9.8 dB), the equivalent knife edge over-predicting the loss behind rounded crests, as the wedge test anticipated. The class flips on 7.9 and 7.5 % of those receivers, in the direction of more coverage than the atlas shows. Behind steeper crests the wedge test, not the PE, is the reference, and it says the opposite, namely that Delta-Bullington is optimistic by 4 to 11 dB behind 10°– 15° faces. For all shadowed receivers, most of them behind segments steeper than either limit, the PE exceeds DeltaBullington by 24 and 32 dB in the mean with RMS values of 37–45 dB. Those figures include the receivers on which the shift map itself fails and are quoted only to show why the limit is needed. Three findings follow. First, the atlas is slightly optimistic on the visible paths that carry 97 % of its coverage, and the PE-corrected fractions of Table V are the numbers to plan with where that matters. Second, on the few percent that rest on diffraction it is conservative behind gentle crests and optimistic behind steep ones, and Table VII gives the share of those cells within 5 and 10 dB of threshold, which is the share at risk. Third, since a 3 dB shift moves the freespace range by 30 %, the in-range covered-to-visible ratio of Table VIII is an upper estimate at the edge of the range. All three are statements about the engine, not about the atlas’ completeness, and the released line-of-sight flag makes the first a read-time correction, because a planner who wants the PE’s answer subtracts the bias from the atlas value on line-ofsight cells. 2) Ray tracing: line of sight and reflection: The engine was cross-checked against NVIDIA Sionna RT 2.1.0 (Mitsuba 3.9.1, CUDA variant) [20], [47] on canonical obstacles and on one real tile, T06_07, which contains the northern half of de Gerlache crater and the de Gerlache Rim 2 region. Sionna’s scene is a quadric-decimated triangle mesh of the tile (18 M to 2 M triangles, rims weighted) in a local frame with the sphere drop applied, a regolith RadioMaterial, isotropic antennas and a measurement mesh 1.5 m above the terrain; paths include line of sight, specular reflection and first-order UTD diffraction. On the tile’s visible cells Sionna’s LOS-only power equals free space to 0.003 dB, confirming the calibration of both engines. Sionna finds no specular ground path on the decimated real terrain, where free space minus Sionna-full is 0.002 dB on the visible profile receivers. Its full result therefore equals the atlas no-reflection layer on visible cells, and the difference between it and the atlas value is the grazing ground reflection that Delta-Bullington carries and a faceted mesh cannot. On

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TABLE II PARABOLIC - EQUATION REFERENCE MINUS THE ATLAS ENGINE ON REAL LOLA PROFILES ( D B), ON VISIBLE AND SHADOWED RECEIVERS , FOR ALL RECEIVERS AND FOR THOSE WHOSE STEEPEST INTERVENING SEGMENT IS AT MOST 5° OR 7°. A CLASS FLIP IS A RECEIVER WHOSE COVERABLE CLASS DIFFERS BETWEEN THE PE AND THE ATLAS VALUE . B OLD MARKS THE ROWS USED AS THE ESTIMATE . A LL VISIBLE RECEIVERS QUALIFY BECAUSE THE SHIFT MAP IS EXACT FOR REFLECTION ON A TILTED PLANE . S HADOWED RECEIVERS BEHIND SLOPES OF AT MOST 5° QUALIFY BECAUSE THERE THE PE IS WITHIN 0.3 D B OF THE EXACT WEDGE SOLUTION . Band

Receivers

1.800 GHz 1.800 GHz 1.800 GHz 1.800 GHz 1.800 GHz 5.855 GHz 5.855 GHz 5.855 GHz 5.855 GHz 5.855 GHz

visible, all visible, slopes ≤ 5◦ shadow, slopes ≤ 5◦ shadow, slopes ≤ 7◦ shadow, all visible, all visible, slopes ≤ 5◦ shadow, slopes ≤ 5◦ shadow, slopes ≤ 7◦ shadow, all

n

PE − DB mean

RMS

PE − (DB+two-ray) mean

class flips (%)

31,369 1,510 519 2,361 143,146 31,369 1,510 519 2,361 142,844

-3.86 -3.34 +3.57 +6.97 +24.08 -3.33 -3.26 +3.53 +9.08 +31.59

4.61 4.07 7.90 12.18 36.75 4.07 3.74 9.79 16.12 45.36

-3.13 -2.30 +3.57 +6.97 +24.08 -2.73 -2.11 +3.53 +9.08 +31.59

6.73 0.00 7.90 8.01 1.90 13.08 0.20 7.51 4.11 0.50

the visible cells of the tile that difference is the excess of the no-reflection layer over the atlas value, which amounts to 11 to 14 % of covered area for a single mast at 1.8 GHz (Section IV-B) and 1.6–2.5 percentage points of the pole-wide coverable fraction. The ground reflection itself is validated against the analytic two-ray solution on flat and tilted planes (Section III-C4) and against the PE field on real profiles (Section IV-A1), not against ray tracing. 3) Ray tracing: wedge diffraction on DEM meshes: On canonical obstacles, a 120 m crest 3 km from a 60 m mast with 46 receivers 0.5–5 km behind it at 1.8 GHz, Sionna reproduces P.526 knife-edge diffraction on a thin screen (0.23 dB mean, 1.71 dB RMS) and on a 60° wedge (0.18 dB, 1.70 dB), but returns no diffracted path for 31° wedges of either orientation or for a Gaussian ridge of 300 m width. This is the expected behavior of first-order wedge diffraction on a faceted mesh. The diffraction points lie on silhouette edges of the primitive a ray hits, and a smooth DEM crest decimated to facets has no such edge. On the real tile Sionna holds diffracted energy in fewer than 6 % of shadowed cells and, where it does, sits 41–57 dB below Delta-Bullington. Ray tracing is therefore not used as a diffraction reference on lunar terrain, and the PE solver takes that role. 4) Sensitivity to the diffraction model: Deygout, Bullington, single knife edge and Delta-Bullington were run on the same masts. On three radial profiles of T06_07 (a descending slope, a single ridge and a crater interior), Deygout predicts more shadow loss than Delta-Bullington by 7–17 dB on the slope and ridge profiles and by 30–38 dB deep inside the crater, where Deygout’s sub-path sum is known to over-count; the P.526 §4.2 rounded-obstacle formula exceeds Deygout by 4.9 dB on the Gaussian ridge. The coverage class is far less sensitive than the shadow power, shadowed cells are typically 10–100 dB below threshold and only 0.8 % of them lie within ±6 dB of it. Table III gives the class-flip and covered-area statistics for 40 masts drawn from the three latitude bands and both classes. Swapping Deygout for Delta-Bullington changes the class of 0.55–0.75 % of the 22 km disc at 1.8 GHz depending on latitude band (95th percentile over masts 1.2– 2.0 %; about 8 % of the covered union) and 0.07–0.13 % at 5.855 GHz, and reduces the covered area by 6–8 % and 2– 4 %. Plain Bullington, which has no spherical-earth term and

therefore no grazing reflection, moves the class of 1.4 % of the disc the other way and adds 22 % of covered area at 1.8 GHz: the reflection term matters more than the choice of knife-edge construction. The PE comparison above sits between the two, 3–4 dB below Delta-Bullington on visible paths and 3.6 dB above it in the shadow of gentle crests. 5) Sensitivity to the DEM: Two effects are separated, on masts stratified by the three latitude bands and both classes. The first is the product difference between the PDS LDEM_80S_20M and the orbit-adjusted PGDA DEM, which is not a random error but a correction of orbit-track residuals. Running the same 40 masts on both products, the LOS state flips for a mean of 0.8 % of the 22 km disc and the coverable class for 0.8 % at 1.8 GHz (95th percentile 2.3 %) and 0.2 % at 5.855 GHz, with a signed covered-area change of −5 % in the mean; the change is not uniform. The ridge-class masts of the 82°–85°S band lose 12 % of covered area (one of them half) because their site heights differ between the two products, instances of the artifact of Section III-B5, while the landingsite masts, which stand on flat ground, change by 3–4 %. The second is the residual error of the adjusted product itself. Barker et al. give the vertical accuracy of the adjusted product as about 1 m where LOLA tracks are dense and worse in the gaps between tracks [18]. We model it as correlated Gaussian noise with a 200 m correlation length (the cross-track gap scale) whose amplitude is the PGDA per-pixel heighterror map multiplied by 1.3, 3 or 10 (the first brings the map’s median amplitude to the 1.3 m RMS of the PDS–PGDA product difference, the last is a stress case), added to the DEM including the mast cell, and re-run six masts per latitude band and class (30 masts) with eight realizations each from fixed, recorded seeds. Because the sites were selected as local maxima, zero-mean noise lowers their prominence on average, so the result is reported as a signed change in covered area as well as a class-flip fraction. At the level of the published error map (×1.3) the class of 0.2–0.6 % of the disc changes at 1.8 GHz by latitude band (Table III; 95th percentile over masts up to 1 %) and 0.05–0.25 % at 5.855 GHz, and the covered area of a peak-picked site changes by −2.5 % in the outer band, −2.2 % in the middle band and 1.0 % in the polar band. At three times the map the flips are 0.6–1.7 % of the disc and the area change −11–2.5 %, and at ten times, 2.3–5.8 %

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

PE, impedance ground

Delta-Bullington (atlas value)

receiver in shadow

13

steepest segment > 5° (outside the PE limit) 2000 1000 0 1000 2000

120

terrain (m)

excess loss (dB)

80-82S/ridge, candidate 7759, 1.8 GHz 80 40 0

2000 1000 0 1000 2000

120

terrain (m)

excess loss (dB)

82-85S/landing_site, candidate 2805, 1.8 GHz 80 40 0

2000 1000 0 1000 2000

120

terrain (m)

excess loss (dB)

82-85S/ridge, candidate 8533, 1.8 GHz 80 40 0

2000 1000 0 1000 2000

120

terrain (m)

excess loss (dB)

85-90S/landing_site, candidate 2400, 1.8 GHz 80 40 0

2000 1000 0 1000 2000

120

terrain (m)

excess loss (dB)

85-90S/ridge, candidate 3274, 1.8 GHz 80 40 0 0

5

10

range (km)

15

20

Fig. 7. Excess loss is shown along real LOLA profiles. Orange marks the split-step parabolic-equation reference with the impedance ground, and blue marks Delta-Bullington, the atlas value. The terrain profile is shaded. The strip along the top marks receivers in shadow (gray) and receivers behind a segment steeper than 5° (hatched), the limit adopted for the shadow comparison. One profile is shown per latitude band and class at 1.8 GHz, in each case at the azimuth with the most receivers inside the slope limit. The retired two-ray layer is not drawn because it coincides with the atlas value at this scale.

and −47–0 %. The bias is largest in the outer band, where the track gaps are widest and the sites are lowest, and absent in the polar band, where the tracks converge and the error map is small. The pole-wide statement is then that the class of under one percent of cells depends on DEM error at the level of the published error map, with a systematic loss of covered area for peak-picked sites of 2–2.5 % north of 85°S and a small gain south of it. 6) Effective resolution of the DEM: The 20 m grid of the adjusted product is not its effective resolution everywhere.

The LOLA track spacing at 80°S is several hundred meters between orbits, and between tracks the DEM is interpolated. Only close to the pole, where the tracks converge, is every 20 m cell constrained by measurements. The PGDA release includes per-pixel shot-count, height-error and effectiveresolution maps [18], and the atlas should be read with them, because the LOS state and the diffraction loss of a cell in a track gap are those of the interpolated surface, which is smoother than the true one. Unresolved relief cuts both ways, since an unresolved knoll can hide a receiver or lift a mast, and

14

PREPRINT, 19 OCTOBER 2026

TABLE III S ENSITIVITY OF THE COVERAGE CLASS TO THE MODEL AND THE DEM, BY LATITUDE BAND . T HE ENTRIES ARE THE FRACTION OF THE 22 KM MAST DISC WHOSE CLASS CHANGES ( MEAN AND 95 TH PERCENTILE OVER MASTS , %) AND THE SIGNED CHANGE OF THE COVERED AREA ( MEAN , %) AT 1.8 AND 5.855 GH Z . T HE MODEL AND PRODUCT ROWS USE 40 MASTS . T HE NOISE ROWS USE 30 MASTS WITH EIGHT NOISE REALIZATIONS EACH . T HE B ULLINGTON ROW IS PLAIN B ULLINGTON WITHOUT THE SPHERICAL -E ARTH TERM . B OLD MARKS THE LARGEST VALUE IN EACH COLUMN AND , FOR THE SIGNED AREA CHANGE , THE LARGEST MAGNITUDE . 1.8 GHz Perturbation

Band

Deygout vs. DB

80-82S 82-85S 85-90S 80-82S 82-85S 85-90S 80-82S 82-85S 85-90S 80-82S 82-85S 85-90S 80-82S 82-85S 85-90S 80-82S 82-85S 85-90S

Bullington vs. DB

PDS vs. PGDA

DEM noise 1.3x 200m

DEM noise 3x 200m

DEM noise 10x 200m

5.855 GHz

flip mean

flip p95

∆area

flip mean

flip p95

∆area

0.75 0.66 0.55 1.74 1.44 1.29 0.60 1.13 0.50 0.64 0.43 0.22 1.67 1.13 0.56 5.83 3.48 2.29

1.15 1.40 2.02 2.60 3.15 4.05 1.30 4.71 1.30 0.85 0.95 0.86 2.18 3.01 2.24 9.19 9.13 9.26

-7.2 -6.2 -7.8 +24.7 +17.5 +25.3 -1.5 -8.1 -3.7 -2.5 -2.2 +1.0 -11.1 -8.2 +2.5 -46.7 -30.7 +0.1

0.13 0.08 0.07 0.27 0.17 0.17 0.20 0.28 0.18 0.25 0.09 0.05 0.64 0.24 0.11 1.78 0.76 0.40

0.26 0.19 0.14 0.50 0.39 0.29 0.33 1.23 0.48 0.35 0.20 0.11 0.80 0.54 0.28 2.60 1.74 0.99

-3.5 -2.2 -2.0 +11.0 +9.5 +13.5 -1.5 -7.0 -8.0 -4.1 -1.9 -0.2 -15.8 -7.5 -1.5 -53.7 -31.8 -9.8

the coverable fractions at the outer latitudes are therefore likely optimistic rather than bounded. The DEM-noise experiment above is the quantitative form of this caveat. Its amplitude is taken from the height-error map, so it is largest in the track gaps, and its 200 m correlation length represents the crosstrack gap rather than the along-track shot spacing. A second check asks whether the candidate rules themselves respond to the interpolation structure, by comparing the LOLA shot count at candidate cells with that of all cells in the same latitude band, per detector (local maximum and curvature ridge). The interpolation is extensive. 75 % of all 20 m cells in the 80°– 82°S band hold no LOLA shot, 67 % in 82°–85°S and 43 % in 85°–90°S. The candidate cells are measured far more often than the terrain around them. Their zero-shot share is 23, 21 and 12 % in the three bands, 0.27–0.31 of the base rate, with 0.95–1.5 shots per candidate cell against 0.30–0.93 per cell overall. The local-maximum detector, which supplies 95 % of the ridge class, prefers measured cells the most (ratio 0.26– 0.29), and the curvature-ridge detector less so (0.52–0.72). The preference is the expected one, since a peak that is measured is a peak that exists, and it means that the candidate sites are better constrained than the receivers around them. It also means the candidate table is not a sample of the interpolated surface, which is why the DEM-noise experiment perturbs the mast cell along with the terrain. 7) Candidate density: The ridge-class candidate set uses a 1 km minimum spacing (Section III-B). To test whether the pole-wide coverable fraction has converged with respect to that choice, the extraction and the atlas run were repeated on three tiles, one per latitude band at the band’s median candidate density (T01_08 at 81.4°S, T10_03 at 83.4°S and T08_11 at 86.5°S), with a 500 m spacing and a cap of 2000 sites per tile. A fourth tile, the roughest on which the 150-per-tile cap of the base set binds, was foreseen but does not exist, because no tile reaches the cap (the maximum is 146 on T12_08, the median 46), and the cap is therefore not a constraint of the released

table. Halving the spacing adds only 5–7 % to the candidate count on the three tiles (62 to 66, 82 to 86, 43 to 46), because the 1 km rule already admits nearly every local maximum that passes the prominence, permanent-shadow and slope rules. The spacing rule is not what limits the density; the terrain is. Table IV gives the result. The coverable fraction of the tile core changes by 0.2–0.8 percentage points at 1.8 GHz, by 0.3–2.9 at 5.855 GHz and by 0.2–0.5 at 25.375 GHz, always upward and with Jaccard indices of the coverable masks of 0.991– 0.998 at 1.8 GHz. The largest change, 4.6 points at 3.65 GHz on the polar tile, is one added site on a rim that overlooks a floor the base set reached only at the low bands. The mean serving count moves by less than 0.3. The pole-wide fractions are therefore converged with respect to the spacing rule to about one percentage point at the low bands and to a few points in the mid bands on rough polar tiles. At 25.375 GHz the fraction is a density statement in the sense that each added site adds its own 1.6 km disc. 8) Internal consistency of the pole-wide run: Four checks were made on the merged atlas. First, the run reproduces an earlier computation by a previous version of the engine, which stored two layers, Delta-Bullington with the retired two-ray term on top (its atlas value at the time) and Delta-Bullington alone on every receiver, visible or shadowed, which it labeled “no reflection” because the separate term was omitted and which is exactly the present atlas value. The comparison is between that second layer and the present one. On the pilot tile T06_07, on the 3.3 million cells (visible and shadowed) whose best server is the same mast in both runs, the received power agrees to 0.000 dB in the mean with no cell above 0.01 dB, and the pole-wide coverable, data-link and medianpower statistics of Table V computed from the earlier layer agree with the present ones to the last digit shown. Second, the free-space range at each band for the stated budget (22.0 km, 15.4, 10.9, 6.8 and 1.6 km) matches the ray radius recorded in the run and the halo widths seen around isolated masts

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

15

TABLE IV C ANDIDATE - DENSITY CONVERGENCE . T HE ENTRIES ARE THE CHANGE OF THE COVERABLE FRACTION OF THE TILE CORE WHEN THE MINIMUM SPACING IS HALVED FROM 1 KM TO 500 M , ON ONE TILE PER LATITUDE BAND AT THE MEDIAN CANDIDATE DENSITY OF THE BAND . T HE JACCARD COLUMN IS THE OVERLAP OF THE TWO COVERABLE MASKS AT 1.8 GH Z . B OLD MARKS THE LARGEST CHANGE PER BAND , AND ITALIC MARKS THE LOWEST OVERLAP. Tile

T01_08 T10_03 T08_11

n (1 km)

62 82 43

n (500 m)

66 86 46

∆ coverable (pp) at

Jaccard 1.8 GHz

1.8

2.58

3.65

5.855

25.375

+0.51 +0.16 +0.84

+0.58 +0.18 +1.93

+0.63 +0.24 +4.55

+0.78 +0.28 +2.91

+0.50 +0.19 +0.35

in the mosaics. Third, band-to-band steps of the median bestserver power over the region windows (3.0, 2.6, 3.3 and 3.9 dB at Amundsen Rim) track the free-space differences of 3.1, 3.0, 4.1 and 12.7 dB, with the shortfall at the higher bands expected because the best server switches to a nearer mast as distant ones drop below threshold. Fourth, no tile seams or shard-boundary discontinuities are visible in any layer, and the count layer contains no doubled bands, confirming the orderindependent merge. These checks establish the consistency of the run. the physics is validated in the preceding subsections. Throughout, “coverable” means best-server received power at or above the effective threshold of −94.4 dBm (SNR ≥ 0 dB) with every candidate active, and “data link” means 10 dB above it (−84.4 dBm). Both are properties of the potentialcoverage envelope, not of a deployed network. Cells within one pixel of a mast, where the near-field geometry is meaningless, are clipped to −30 dBm before statistics are taken. Every statistic in this section is computed on the 20 m accumulators of the atlas (Section III-D3). The 160 m mosaics of the release bundle are used only to render the pole-wide maps. Mapprojection and sphere-weighted fractions differ by at most 0.1 percentage points (last column of Table V), and all fractions are therefore reported in map space. B. The whole disc Figure 8 shows the best-server power at 1.8 GHz and 5.855 GHz over the whole disc, and Fig. 9 shows all five bands. Figure 10 shows the serving redundancy, Table V the pole-wide statistics and Fig. 11 their dependence on band and latitude. Every cell of the disc lies within the ray radius of at least one candidate, which makes the atlas complete in the sense that the uncoverable area is uncoverable because of terrain and budget. a) Reachability is near-universal at the low bands: At 1.8 GHz, 90.5 % of the disc is coverable, and 85.5 % at 2.58 GHz (Table V). The parabolic-equation reference of Section IV-A1 finds the engine 3–4 dB optimistic on visible paths, and re-thresholding the visible cells by that bias (the “PE-corrected” columns of Table V) gives 83.8 and 74.0 %, with the data-link fraction falling from 58.2 to 38.8 % at 1.8 GHz. The correction bites hardest where the margin is thinnest, since 36 % of the coverable cells at 1.8 GHz and 74 % at 5.855 GHz lie within 10 dB of threshold. Both sets of numbers are reported throughout. The corrected ones are the conservative planning figures, the atlas values are what the released layers hold, and the line-of-sight flag turns one into the other at read time. The uncoverable remainder, 27,549 km2

0.994 0.998 0.991

at 1.8 GHz, is concentrated on, but not confined to, the permanently shadowed terrain near the pole. Table VI gives the split. The LOLA PSR product [18] covers 20,829 km2 of the disc (7.2 %). Of that area 59.1 % is coverable at 1.8 GHz and 61.1 % is in line of sight of at least one candidate, which means that the permanently shadowed floors are, for the most part, visible from the permitted sites on their rims and are reached at the low bands. What shadows them from the Sun at grazing incidence does not shadow them from a mast on the rim above. Shackleton is the clearest case. 93.7 % of its 234 km2 PSR floor is in line of sight of a rim candidate and 92.0 % is coverable at 1.8 GHz, falling to 38.4 % at 3.65 GHz and 5.5 % at 5.855 GHz as the 8–12 km rim-to-floor paths drop out of the free-space range. The PSR that is not reached at 1.8 GHz, 41 % of it, is the part with no line of sight to any candidate, namely the smaller shadowed craters and the deeper parts of the large floors that the 12° slope rule keeps a 4 m mast away from. That part makes up 31 % of the uncoverable area. The other 69 % of the low-band holes lie outside permanent shadow, on the shadowed flanks and floors of illuminated craters and on the far sides of massifs. At 1.8 GHz, 81 % of the holes have no line of sight to any candidate and 19 % are visible from a candidate but below the budget. Only 0.4 % of the noLOS holes lie beyond the ray radius of their nearest candidate, which confirms the completeness of the atlas in the sense of Section IV-B. The statement is conditional on the siting rules. No candidate stands in permanent shadow or on ground steeper than 12°, and the atlas therefore says what a network of small masts on the illuminated uplands reaches. b) How much of the coverage rests on diffraction: Table VII separates the two ingredients of the coverage with the best-server line-of-sight flag of the atlas. 91.5 % of the disc is in line of sight of at least one candidate, and of those cells 98.1 % are coverable at 1.8 GHz, 64.5 % at 5.855 GHz and 10.9 % at 25.375 GHz: the second column is the part of the visible area that the budget reaches, and it is the column that varies with band. The last column is the part of the atlas that rests on the diffraction model: only 2.7 % of the coverable cells at 1.8 GHz are served by a mast that is not in line of sight, 0.9 % at 5.855 GHz and 0.3 % at 25.375 GHz. Diffraction decides the class of a few percent of the disc; the rest is geometry and budget. The last two columns say how much of that diffraction-dependent coverage is at risk: the share of the NLOS-served cells whose margin above threshold is less than 5 and 10 dB, which is the share that a diffraction model in error by that much would move. The parabolic-equation comparison of Section IV-A1 finds the engine conservative in

16

PREPRINT, 19 OCTOBER 2026

Best-server received power, all candidate masts active 300

(a) 1.8 GHz

(b) 5.855 GHz

9

150

9

3

3 4

2

y (km)

7

4 6

5

2

7

12

12

1

0

6

5 1

10

11

10

11

8

8

−150

−300 −300

−150

0

150

300

−300

−150

x (km) -94.4

0

150

300

x (km)

−90

−85

−80

−75

−70

−65

−60

Best-server received power (dBm); grey: below threshold 2024 regions 1 de Gerlache Rim 2 7 Peak near Cabeus B

2022-only regions 2 Haworth 8 Slater Plain

82°–88°S rings 3 Malapert Massif 9 Mons Mouton Plateau

4 Mons Mouton 10 Faustini Rim A

5 Nobile Rim 1 11 Connecting Ridge

6 Nobile Rim 2 12 Amundsen Rim

Fig. 8. Best-server received power is shown over the 80°S–90°S disc with every candidate mast active, (a) at 1.8 GHz and (b) at 5.855 GHz. The maps are 160 m block-maximum mosaics rendered at 640 m. Gray marks the cells below the −94.4 dBm threshold, which are not coverable. Black outlines show the nine 2024 Artemis candidate landing regions as solid lines and the three 2022-only regions with public footprints as dashed lines. Dotted rings mark 82°S to 88°S. Footprints are numbered, and the key below the map matches Table XI. At 1.8 GHz the uncoverable area is concentrated on, but not confined to, the large permanently shadowed crater floors near the pole (Table VI). At 5.855 GHz the plains between ridge clusters also fall below threshold. TABLE V P OLE - WIDE COVERAGE STATISTICS OF THE POTENTIAL - COVERAGE ENVELOPE . A LL 11,827 CANDIDATES ARE ACTIVE , THE PROJECTED DISC IS 290,345 KM 2 (288,100 KM 2 ON THE SPHERE ), AND EVERY CELL IS WITHIN THE RAY RADIUS OF AT LEAST ONE CANDIDATE . T HE STATISTICS ARE EXACT AT 20 M ON THE MAP BASIS , AND THE LAST COLUMN IS SPHERE - WEIGHTED . T HE PE- CORRECTED ENTRIES ARE THE SAME TWO FRACTIONS AFTER THE CELLS SERVED IN LINE OF SIGHT ARE RE - THRESHOLDED BY THE BIAS OF THE ATLAS VALUE MEASURED AGAINST THE PARABOLIC - EQUATION REFERENCE (3.9 D B AT 1.8 GH Z AND 3.7, 3.5, 3.3 AND 3.3 D B AT THE HIGHER BANDS , S ECTION IV-A1). T HE DATA - LINK ENTRIES USE A THRESHOLD 10 D B ABOVE THE BASE THRESHOLD . T HE NO - REFLECTION ENTRIES GIVE THE COVERABLE FRACTION OF THE NO - REFLECTION LAYER ( FREE SPACE ON VISIBLE CELLS , S ECTION III-C4). T HE MEAN - MASTS ENTRIES GIVE THE MEAN NUMBER OF CANDIDATES ABOVE THRESHOLD PER COVERABLE CELL . M EDIAN Prx AND S HANNON CAPACITY C = B log2 (1 + SNR) FOR B = 20 MHz ARE OVER COVERABLE CELLS . Band (GHz) 1.8 2.58 3.65 5.855 25.375

Coverable (%)

Data link (%)

90.5 85.5 76.7 59.1 10.0

58.2 43.1 29.4 15.5 1.6

PE-corrected cov. (%) data link (%) 83.8 74.0 61.7 42.6 5.4

38.8 26.3 16.9 8.5 1.0

No refl. (%)

≥ 2 masts (%)

Mean masts per cell

Median Prx (dBm)

Median C (Mbit/s)

Coverable, sphere (%)

92.1 87.5 79.2 61.5 10.5

82.8 73.6 59.1 35.8 1.4

10.3 6.5 4.2 2.6 1.2

-81.9 -84.4 -86.4 -88.4 -90.8

85 70 58 47 35

90.5 85.4 76.7 59.0 10.0

shadow behind gentle crests and optimistic by 4–11 dB behind crests steeper than 10°, so the at-risk share is the 61 % of the NLOS-served cells at 1.8 GHz that lie within 10 dB of threshold, 1.6 % of all coverable cells (0.8 % at 5.855 GHz); a diffraction model in error by 10 dB on those paths could move at most that much of the disc downward. c) Coverage falls with the free-space range at every band: The coverable fraction falls to 76.7 % at 3.65 GHz, 59.1 % at 5.855 GHz and 10.0 % at 25.375 GHz (PE-corrected 61.7, 42.6 and 5.4 %), and the data-link fraction falls faster, from 58.2 % at 1.8 GHz to 1.6 % (38.8 to 1.0 % corrected). The correction moves the 5.855 GHz data-link fraction most, from 15.5 to 8.5 %. In Fig. 8(b) the plains between the ridge

clusters have turned gray. They were covered at 1.8 GHz by grazing line-of-sight paths from masts 10–20 km away, at −92– −85 dBm, and 10 dB more free-space loss removes them. The mechanism is the same at every band, including 1.8 GHz. Within its free-space range a mast covers about 90 % of its visible area whatever the band (Table VIII), and the range itself shrinks from 22.0 km to 1.6 km. The power-only control of Section IV-F confirms that the 1.8 GHz coverage is not terrainlimited either, because with 20 dB more budget the same masts reach visible terrain tens of kilometers away. The cumulative distribution of Fig. 12 makes the same point. The curves are parallel, shifted by the free-space difference, and the threshold line cuts them at very different heights.

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

17

Best-server received power by band

300

300

(a) 1.8 GHz

300

(b) 2.58 GHz

9

9

3 2

2

7

1

300

300

−300 −300

300

(d) 5.855 GHz

300

Region key

4 2

7

12

5

6 12

1

0

10

11

10

11

8

8

0

-94.4

2022-only regions

3 6

300

−90

−300 −300

−85

300

2024 regions 9

1

−300 −300

0

below threshold (not coverable)

4

0

−300 −300

(e) 25.375 GHz

3 5

10

11

8

0

9

2

6 12

8

0

7

5 1

0

10

11

2

7

1

8

−300 −300

4 6

5

12

0

10

11

3 4

6

5

12

0

9

3 4

7

(c) 3.65 GHz

0

1 de Gerlache Rim 2

7 Peak near Cabeus B

2 Haworth

8 Slater Plain

3 Malapert Massif

9 Mons Mouton Plateau

4 Mons Mouton

10 Faustini Rim A

5 Nobile Rim 1

11 Connecting Ridge

6 Nobile Rim 2

12 Amundsen Rim

300

−80

−75

−70

−65

−60

Best-server received power (dBm); gray: below threshold Fig. 9. Best-server received power for all five bands, same rendering and region numbering as Fig. 8, with the symbols and the region key in the lower-right panel. The coverable area shrinks toward the candidate clusters as the free-space range falls from 22.0 km at 1.8 GHz to 1.6 km at 25.375 GHz. TABLE VI P ERMANENTLY SHADOWED AREA AND THE UNCOVERABLE REMAINDER , PER BAND ( EXACT, 20 M ). T HE PSR AREA IS TAKEN FROM THE LOLA PSR PRODUCT [18] WITHIN THE DISC (20,829 KM 2 , 7.2 %). T HE PSR LOS ENTRIES COUNT THE PSR CELLS IN LINE OF SIGHT OF A CANDIDATE . T HE NO -LOS ENTRIES COUNT THE UNCOVERABLE CELLS WITH NO LINE OF SIGHT TO ANY CANDIDATE , TOGETHER WITH THE SHARE OF THOSE WHOSE NEAREST CANDIDATE LIES BEYOND THE RAY RADIUS . Band (GHz)

PSR cov. (% PSR)

PSR data link (% PSR)

PSR LOS (% PSR)

Uncoverable (km2 )

PSR share (% of uncov.)

no LOS (% of uncov.)

of which beyond ray radius (%)

1.8 2.58 3.65 5.855 25.375

59.1 52.5 41.5 25.2 2.4

24.9 15.7 9.4 4.2 0.2

61.1 61.1 61.1 61.1 61.1

27,549 42,213 67,611 118,818 261,403

31 23 18 13 8

81 56 36 21 9

0 0 0 0 0

d) Redundancy collapses with frequency, and the millimeter-wave fraction is a density statement: The mean number of candidate sites able to serve a coverable cell falls from 10.3 at 1.8 GHz to 2.6 at 5.855 GHz and 1.2 at 25.375 GHz, and the fraction of the disc with at least two serving candidates from 82.8 % to 1.4 % (Table V, Fig. 11(a)). At 25.375 GHz essentially every coverable cell has exactly one

site that can reach it: the band is a line-of-sight, single-server resource within about 1.5 km of a mast, suitable for pointto-point links between mutually visible sites rather than for area coverage. Its pole-wide coverable fraction is therefore a statement about the candidate density (1 km spacing) rather than about the terrain: it grows with the number of candidates rather than converging as the spacing is refined, although

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PREPRINT, 19 OCTOBER 2026

Coverage redundancy: candidate masts per cell 300

(a) 1.8 GHz

(b) 5.855 GHz

9

150

9

3

3 4

2

y (km)

7

4 6

5

2

7

12

12

1

0

6

5 1

10

11

10

11

8

8

−150

−300 −300

−150

0

150

300

−300

−150

0

x (km) 1

2

150

300

x (km) 3

5

10

20

50

250

Candidate masts covering the cell (count); no fill: none 2024 regions 1 de Gerlache Rim 2 7 Peak near Cabeus B

2022-only regions 2 Haworth 8 Slater Plain

82°–88°S rings 3 Malapert Massif 9 Mons Mouton Plateau

4 Mons Mouton 10 Faustini Rim A

5 Nobile Rim 1 11 Connecting Ridge

6 Nobile Rim 2 12 Amundsen Rim

Fig. 10. Serving redundancy is shown as the number of candidate masts whose received power at the cell exceeds the threshold, (a) at 1.8 GHz and (b) at 5.855 GHz. Region outlines and numbering follow Fig. 8. The count depends on the candidate density (1 km spacing) and is a measure of siting flexibility, not of a network property. The floors of illuminated craters such as Amundsen (at about x = 170 km, y = 0) are seen by every rim site, while the plains between ridge clusters are served by one or two distant masts.

Pole-wide coverage by band and latitude (exact 20 m statistics) (a) 91

coverable (SNR ≥ 0 dB) coverable, PE-corrected data link (SNR ≥ 10 dB) ≥ 2 masts

85 77

80

59

60 40 20 0

10

1.8

2.58

3.65

5.855

25.375

Band (GHz)

100

Coverable (%), exact 20 m

Fraction of the 80°–90°S disc (%)

100

(b)

80 60 40

1.8 GHz 2.58 GHz

3.65 GHz 5.855 GHz

25.375 GHz

20 0

80–82S

82–85S

85–90S

Latitude band

Fig. 11. Panel (a) gives the coverable, PE-corrected coverable, data-link and redundant (≥ 2 masts) fractions of the disc per band, from the exact 20 m statistics of Table V. Panel (b) gives the coverable fraction by latitude band (80°–82°S, 82°–85°S, 85°–90°S, the scheme used throughout). Coverage falls toward the pole at every band as the relief and the PSR area grow (exact values in the text).

slowly: doubling the density adds 0.2–0.5 percentage points on the test tiles of Section IV-A7, as most of the added sites stand within 1.6 km of an existing one. Figure 10 shows where the flexibility lies at the low bands: illuminated crater floors ringed by rim candidates (Amundsen, and the large craters of the 80°–84°S band) are seen by dozens of sites, whereas the plains are single-server territory even at 1.8 GHz.

e) Latitude: Coverage falls toward the pole at every band (Fig. 11(b)): at 1.8 GHz from 92.9 % of the 80°–82°S band and 92.1 % of 82°–85°S to 84.5 % of the 85°–90°S band; at 5.855 GHz from 66.2 and 58.4 to 49.8 %; at 25.375 GHz from 11.4 and 9.7 to 8.3 %. The polar band combines the largest relief, the largest PSR floors (11.3 % of its area against 4.8 % of the outer band) and the fewest illuminated high points: its PSR is 37.8 % coverable at 1.8 GHz against 73 % in the two

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

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TABLE VII L INE - OF - SIGHT CONTENT OF THE COVERAGE , PER BAND ( EXACT, 20 M ). T HE FIRST ENTRIES GIVE , OF THE CELLS IN LINE OF SIGHT OF AT LEAST ONE CANDIDATE , THE FRACTION ABOVE THRESHOLD . T HE SERVED - WITHOUT-LOS ENTRIES COUNT THE COVERABLE CELLS WHOSE BEST SERVER IS NOT IN LINE OF SIGHT. T HE LAST TWO COLUMNS GIVE THE SHARE OF THOSE CELLS WHOSE MARGIN ABOVE THRESHOLD IS BELOW 5 AND 10 D B. T HAT SHARE IS THE PART OF THE DIFFRACTION - DEPENDENT COVERAGE THAT A MODEL ERROR OF THAT SIZE WOULD MOVE . Band (GHz)

LOS to ≥ 1 candidate (%)

LOS cells coverable (%)

Served without LOS (%)

91.5 91.5 91.5 91.5 91.5

98.1 93.0 83.6 64.5 10.9

2.7 2.0 1.4 0.9 0.3

1.8 2.58 3.65 5.855 25.375

Distribution of best-server power

60 40

1.8 GHz

20

2.58 GHz 3.65 GHz 5.855 GHz 25.375 GHz

0 −140 −130 −120 −110 −100 −90

threshold + 10 dB

80

threshold

Disc area with Prx ≥ P (%)

100

−80

−70

−60

−50

Best-server received power P (dBm)

Fig. 12. Fraction of the disc whose best-server power exceeds P , per band. The dashed line is the coverage threshold, the dotted line the 10 dB data-link margin.

outer bands, and 12.7 % of its area has no line of sight to any candidate against 5.8–6.3 %. The outer band holds the densest field of local maxima but the widest gaps between LOLA tracks (Section IV-A6). f) The ground reflection: The no-reflection layer (free space on visible cells) exceeds the atlas value by 1.6 percentage points of coverable fraction at 1.8 GHz, 2.4 at 5.855 GHz and 0.5 at 25.375 GHz (Table V): this is the cost of the grazing ground reflection that the spherical-Earth term of Delta-Bullington carries on clear paths, an upper bound by construction (Section III-C4). For a single mast the layer covers 11 to 14 % more area at 1.8 GHz (medians over the landing-site and ridge classes); the pole-wide difference is smaller because the best-server maximum over many masts is taken over the cells where each mast’s path is least grazing. C. Per-mast footprints Figure 13, Table IX and Table X summarize the coverage of individual sites. A median ridge-class site covers 228 km2 at 1.8 GHz (the best 972 km2 , 64 % of the 1526 km2 ray disc) and 39 km2 at 5.855 GHz; a median landing-site class site, which by construction stands on flat ground rather than a high point, covers 56 km2 and 19 km2 . The geometric line-of-sight area of a site is small, a median of 18 % of the ray disc for the ridge class (269 km2 ) and 4 % (62 km2 ) for the landingsite class. The ratio of covered area to line-of-sight area is informative only when both are measured within the same

of which margin < 5 / < 10 dB (%) 32 38 43 50 80

61 67 73 81 98

range: with LOS counted to the 22 km ray radius (Table X, retained for comparison) the ratio falls at the higher bands mostly because their free-space range is shorter. Table VIII therefore measures LOS and covered area within each band’s own free-space range (22.0, 15.4, 10.9, 6.8 and 1.6 km), and the result is the same at every band: a ridge-class mast covers a median 89 % of the terrain it sees within its range (10th– 90th percentiles 75–96 %) and a landing-site mast 93–94 % (76–113 %). The deficit is the grazing visible terrain near the edge of the range, where the ground reflection and the sphere drop take the last few decibels; the excess of a few landingsite masts is diffraction over low ground close to the mast, where the budget has margin to spare. Within the 2 km EVA disc, where every path is short, the covered fraction exceeds the visible fraction (59 against 40 % for the ridge class at 1.8 GHz); over the whole range it does not. The landing-site class keeps a slightly higher ratio because its visible area is compact and close to the mast. For EVA planning the relevant quantity is the covered fraction of the 2 km walking disc around a landing-site mast: a median of 49 % at 1.8 GHz and 35 % at 5.855 GHz with a 4 m mast, which is the strongest argument for taller lander-mounted equipment. D. The Artemis candidate landing regions Figure 14 shows the twelve regions with public footprints at 1.8 GHz at the native 20 m resolution, Fig. 15 two contrasting regions across all five bands, Table XI the per-region statistics and Fig. 16 their band dependence. Region statistics are exact (20 m) and refer to the footprint only, not the margin drawn around it. a) Low-band coverage of the regions is not the problem: At 1.8 GHz every current region is at least 85.4 % coverable (Peak near Cabeus B) and most exceed 93 %; Slater Plain (98.5 %) and Nobile Rim 2 (97.7 %) are almost entirely coverable, and 85 and 75 % of their footprints hold a data link. Of the 2022-only regions, Faustini Rim A is the least coverable of the twelve (82.1 %). The uncoverable cells inside the footprints are small shadowed craters and PSR patches. b) The regions separate at the higher bands: At 5.855 GHz the coverable fraction spans 22.4 % (Peak near Cabeus B) to 85.3 % (Slater Plain), and at 25.375 GHz 1.9 % to 45.0 %. The ordering is not explained by the number of candidates inside a footprint: Nobile Rim 1 and Mons Mouton have the same landing-site count (53) and the same ridge count (5) yet reach 37.0 and 60.8 % at 5.855 GHz, and Haworth, with the most landing-site candidates after the Plateau (137),

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PREPRINT, 19 OCTOBER 2026

TABLE VIII C OVERED AREA RELATIVE TO LINE - OF - SIGHT AREA , BOTH MEASURED WITHIN THE FREE - SPACE RANGE OF EACH BAND ( MEDIAN AND 10 TH –90 TH PERCENTILES OVER MASTS ). B OLD MARKS THE LARGER CLASS PER BAND . n

Class

landing-site ridge

1,328 10,499

Covered / LOS area, both within the band’s free-space range (median; 10th–90th pct.) 1.8 GHz (22.0 km)

2.58 GHz (15.4 km)

3.65 GHz (10.9 km)

5.855 GHz (6.8 km)

25.375 GHz (1.6 km)

0.94 (0.76–1.13) 0.89 (0.75–0.96)

0.93 (0.78–1.07) 0.89 (0.76–0.96)

0.93 (0.80–1.03) 0.89 (0.77–0.95)

0.93 (0.83–1.00) 0.90 (0.79–0.96)

0.94 (0.88–0.97) 0.93 (0.87–0.97)

TABLE IX P ER - MAST FOOTPRINT STATISTICS BY CANDIDATE CLASS . T HE ENTRIES ARE THE MEDIAN GEOMETRIC LINE - OF - SIGHT FRACTION OF THE RAY DISC , THE MEDIAN COVERED AREA , AND THE MEDIAN COVERED FRACTION OF THE 2 KM EVA DISC AROUND THE MAST. B OLD MARKS THE LARGER CLASS PER COLUMN . n

Class

landing-site ridge

1,328 10,499

Covered area per mast (km2 )

LOS frac.

2 km EVA disc covered

(median)

1.8 GHz median

5.855 GHz median

1.8 GHz

5.855 GHz

0.04 0.18

56.0 227.9

19.5 38.6

49% 59%

35% 42%

TABLE X C OVERED AREA OF A SINGLE MAST RELATIVE TO ITS GEOMETRIC LINE - OF - SIGHT AREA WITHIN THE 22 KM RAY DISC , PER BAND AND CLASS ( MEDIAN AND 10 TH –90 TH PERCENTILES OVER MASTS ). T HE LOS AREA IS COUNTED TO 22 KM AT EVERY BAND , SO THE FALL OF THE RATIO WITH FREQUENCY MOSTLY REFLECTS THE SHORTER FREE - SPACE RANGE . TABLE VIII REMOVES THAT DEPENDENCE . n

Class

landing-site ridge

LOS area

Covered area / LOS area (median; 10th–90th pct.)

median (km2 )

1.8 GHz

2.58 GHz

3.65 GHz

5.855 GHz

25.375 GHz

62 269

0.94 (0.76–1.13) 0.88 (0.74–0.96)

0.80 (0.41–1.04) 0.53 (0.31–0.81)

0.61 (0.19–0.99) 0.31 (0.14–0.63)

0.34 (0.09–0.91) 0.14 (0.05–0.37)

0.04 (0.01–0.23) 0.01 (0.00–0.03)

1,328 10,499

(a) ridge class, n = 10,499 100 80 60 40 20 0 10−1

1.8 GHz 2.58 GHz 3.65 GHz 5.855 GHz 25.375 GHz

100

101

102

103

Area covered by one mast (km²)

Masts with at least this area (%)

Masts with at least this area (%)

Area covered by a single mast (b) landing-site class, n = 1,328 100 80 60 40 20 0 10−1

100

101

102

103

Area covered by one mast (km²)

Fig. 13. Complementary cumulative distribution of the area covered by a single candidate mast, per band, for (a) the ridge class and (b) the landing-site class. The ray disc, π × (22.04 km)2 , is 1526 km2 .

sits in the middle at 67.6 %. What separates the regions at the higher bands is the geometry of the footprint relative to the nearest high ground, and the regions form a continuum from 22 to 85 % rather than two groups. The quantity that orders them is the fraction of the footprint in line of sight of a candidate within the 5.855 GHz free-space range of 6.8 km (Table XI, from the nearest-LOS-candidate layer of the atlas): it runs from 22.8 % at Peak near Cabeus B to 86.2 % at Slater Plain, and it equals the 5.855 GHz coverable fraction to within two percentage points in every one of the twelve regions, the difference being the 1.1–2.1 % of coverable cells served without line of sight. The higher-band coverage of a region

is, to this accuracy, its visible fraction within range; the nearidentity is a consequence of the small non-line-of-sight share rather than an independent correlation. Where a footprint is a plain or a crater floor overlooked by rim sites within a few kilometers (Slater Plain, Amundsen Rim, de Gerlache Rim 2, Nobile Rim 2, the Plateau), most of it is in line of sight of several masts at short range and stays above the budget when the range shrinks; where a footprint is itself the high ground, a massif or a rim crest with steep flanks (Malapert Massif, Nobile Rim 1, Peak near Cabeus B), the sites inside it see one another and the ground below but the flanks and the terrain behind them are shadowed, and the sites outside

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Received power in the Artemis candidate landing regions at 1.8 GHz (a) 1. de Gerlache Rim 2 [2024]

(b) 2. Haworth [2024]

40

(c) 3. Malapert Massif [2024]

140

110

135

35

y (km)

130

100

30

125

25 90

20 15

120 115

80

110

10 5

−60

−50

−40

−60

(d) 4. Mons Mouton [2024]

125

y (km)

−50

−40

−30

−20

120 115 110 105 70

125

110

120

105

115

100

110

95

105

90

100

85

80

−35

80

−40

75

−45

70

−50

65

−55

60

−60

55

−65 −190

−180

80

90

100

140

(h) 8. Slater Plain [2024]

85

−170

150 140 130 120 70

80

60

100

120

80 75

−5

70 65

−10

60

−15

−5

80

(l) 12. Amundsen Rim [2022 only]

0

10

0

170

160

5

5

160

170

(k) 11. Connecting Ridge [2022 only]

15

150

(i) 9. Mons Mouton Plateau [2024] 180

60

(j) 10. Faustini Rim A [2022 only]

10

80 70

(g) 7. Peak near Cabeus B [2024]

0

(f) 6. Nobile Rim 2 [2024]

95 60

y (km)

−10

(e) 5. Nobile Rim 1 [2024]

130

y (km)

105

70

55

−10

−20

−15

−25 50

60

x (km)

70

−90

80

50 45 −20

−85

−10

x (km)

0

−80

150

−75

160

x (km)

−70

170

−65

180

−60

Best-server received power at 1.8 GHz (dBm); grey: below threshold ridge-class site

landing-site class

PSR boundary

2024 footprint

2022-only footprint

Fig. 14. Best-server received power at 1.8 GHz is shown in each Artemis candidate landing region with a public USGS footprint (20 m resolution rendered at 40 m, 8 km margin around the footprint). Panel numbers follow Fig. 4 and Table XI. Black triangles mark the ridge-class sites, and white circles mark the landing-site class. The black box is the footprint, dashed for the 2022-only regions. Panels (a)–(i) are the nine 2024 regions, and panels (j)–(l) are the 2022-only regions.

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PREPRINT, 19 OCTOBER 2026

Band dependence at two contrasting regions 2.58 GHz

3.65 GHz

5.855 GHz

25.375 GHz

7. Peak near Cabeus B

6. Nobile Rim 2

1.8 GHz

−90

−85

−80

−75

−70

−65

−60

Best-server received power (dBm); grey: below threshold

Fig. 15. Band dependence is shown at two contrasting regions. Nobile Rim 2 (top, region 6) is 97.7 % coverable at 1.8 GHz and 32.0 % at 25.375 GHz. Peak near Cabeus B (bottom, region 7) is 85.4 % and 1.9 % at the same bands. Peak near Cabeus B is itself the high ground. Its steep flanks are shadowed from the sites on the massif and, at the higher bands, beyond the range of the sites below it (Section IV-D). TABLE XI P ER - REGION COVERAGE OF THE FOOTPRINT ( EXACT, 20 M ). N UMBERS FOLLOW F IG . 4. A REAS ARE PIXEL COUNTS OF THE FOOTPRINT ( THE TWO 17 KM SQUARES GIVE 292 KM 2 ). T HE LOS ≤ 6.8 KM ENTRIES GIVE THE FOOTPRINT FRACTION IN LINE OF SIGHT OF A CANDIDATE WITHIN THE 5.855 GH Z RANGE . T HE NLOS- SERVED ENTRIES COUNT THE COVERABLE CELLS WHOSE BEST SERVER IS NOT IN LINE OF SIGHT. B OLD MARKS THE HIGHEST VALUE IN EACH COLUMN AND ITALIC THE LOWEST. No.

1 2 3 4 5 6 7 8 9 10 11 12

Region

de Gerlache Rim 2 Haworth Malapert Massif Mons Mouton Nobile Rim 1 Nobile Rim 2 Peak near Cabeus B Slater Plain Mons Mouton Plateau Faustini Rim A Connecting Ridge Amundsen Rim

List

2024 2024 2024 2024 2024 2024 2024 2024 2024 2022 only 2022 only 2022 only

Area

LOS ≤ 6.8 km

NLOS-served

Masts/cell

25.375

(% footprint)

5.855 GHz (%)

1.8 GHz

18.6 26.1 8.2 25.6 15.5 32.0 1.9 45.0 30.4 31.7 19.9 25.0

76.3 68.9 39.5 61.5 37.4 76.2 22.8 86.2 71.9 62.0 63.9 83.4

1.3 2.1 1.5 1.8 1.9 1.1 1.3 1.2 1.3 2.1 1.7 1.3

17.4 11.7 7.2 31.9 7.6 19.3 11.4 14.6 19.7 12.5 7.5 11.2

Coverable (%) at

(km2 )

1.8

2.58

3.65

5.855

446 941 468 292 446 425 446 446 4579 425 292 425

96.5 89.4 91.8 93.2 93.3 97.7 85.4 98.5 94.3 82.1 93.6 95.0

95.4 82.3 84.0 71.1 78.4 96.1 76.3 97.3 89.5 73.2 86.9 93.2

93.9 76.2 62.0 63.9 57.4 88.6 51.5 91.0 82.4 66.2 74.0 89.8

74.6 67.6 38.5 60.8 37.0 74.9 22.4 85.3 70.8 60.5 62.9 82.0

the footprint that reached the flanks by diffraction at 1.8 GHz are beyond the higher-band range. Mons Mouton fits neither group: it falls from 93.2 to 71.1 % already at 2.58 GHz, the largest step of any region, yet has the highest redundancy (31.9 masts per coverable cell at 1.8 GHz). This is the signature of a footprint of two parts: one overlooked at short range by many sites on the surrounding plateau rim, the other lying below the scarp and reached at 1.8 GHz only by long grazing paths from the rim sites, which the next band already loses; its visible fraction within 6.8 km (61.5 %) is indeed close to its 5.855 GHz coverage. The data-link fraction at 1.8 GHz anticipates the higher-band ordering: 84.9 % at Slater Plain against 22.9 % at Peak near Cabeus B.

c) Redundancy differs by a factor of four between regions: The mean number of serving candidates per coverable cell at 1.8 GHz ranges from 7.2 (Malapert Massif) and 7.5–7.6 (Connecting Ridge, Nobile Rim 1) to 31.9 (Mons Mouton), the difference being the number of candidate sites on the surrounding high ground that overlook the footprint rather than the number inside it. In the low-redundancy regions the choice of mast site matters and a second mast buys real resilience; in Mons Mouton or the Plateau almost any rim site serves the whole footprint. The count scales with the candidate density (1 km spacing) and is a relative measure between regions. At 25.375 GHz every region has 1.2–2.1 serving candidates per cell.

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

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Coverable fraction of each landing region by band

Coverable footprint (%)

100

2022-only →

80

60

40

20

0 ch rla Ge e d

2 eR

e 1 2 n n t. A m sif rth sB to dg lai Ri im im im Pla as eu ou Ri wo rP en iR on eR eR g M e ab tM s l l t n t Ha i i r n i d s C a t b b ti ou pe Sl on un us nr ec No No M .M ala Fa Am nn Pk M M Co 1.8 GHz

2.58 GHz

3.65 GHz

5.855 GHz

25.375 GHz

Fig. 16. The coverable fraction of each region footprint is shown per band. The nine 2024 regions lie left of the dotted line, and the three 2022-only regions lie right of it.

E. Throughput implications The atlas gives SNR, not throughput; the Shannon bound
C = B log2 1+SNR , SNR = Prx −TDL +SNRreq (dB), (12) for the 20 MHz carrier is nevertheless a useful scale (Table V). The median coverable cell supports 85 Mbit/s at 1.8 GHz, 47 Mbit/s at 5.855 GHz and 35 Mbit/s at 25.375 GHz; practical LTE/NR radios reach 60–75 % of the bound with a single stream and are modulation-capped above about 20 dB SNR, so the practical figures are 50–75 Mbit/s near a mast per 20 MHz carrier, scaling with carrier width (the n78 allocation permits 100 MHz carriers) and MIMO order, and 5–10 Mbit/s at the coverage edge. The TDD split of the NASA representative scenario [4] applies to the TDD bands (n41, n48/77/78, n47, n258); Band 3 and n7 are FDD, where uplink and downlink have their own carriers and the uplink rate is set by the 5 MHz cell-edge allocation of the budget rather than by a time split. In either case the uplink, which carries EVA video, has the smaller share.

neighborhood: distant crater walls and massif flanks facing the mast are in line of sight across the intervening basins, and the base budget simply cannot reach them. Table XII gives the result. With 20 dB more budget the median covered area of a mast grows by a factor of 5.2 at 1.8 GHz, 8.3 at 2.58 GHz, 14 at 3.65 GHz, 24 at 5.855 GHz and 58 at 25.375 GHz, with no dependence on latitude band beyond the noise of 50 sites; the factors fall short of the free-space scaling (102 in area) only because the 100 km cap truncates the low bands and because the visible area grows more slowly than the range. The covered-to-visible ratio within the enlarged range is 1.11 at 1.8 GHz, 1.04 at 2.58 GHz and 0.96–0.99 above, against 0.89 at every band under the base budget (Table VIII): the ratio is a function of the margin at the edge of the range, not of the band, and exceeds one only when the budget has decibels to spare for diffraction over low obstacles near the mast. The conclusion is that no band is terrain-limited. At every band the covered area is the visible area within the free-space range, less about a tenth, and the range is set by the budget. The terrain enters through the visible fraction, which is what the atlas maps.

F. Power-only control: terrain or budget? Is the coverage at the lowest band terrain-limited, so that more budget would not help, or budget-limited like the higher bands? The control that decides the question is the base link budget plus 20 dB at both ends (base station 50 dBm, user equipment 43 dBm), with the same 4 m masts, the same 1.5 m receiver and the same terrain, run with a 100 km ray radius on 213 ridge sites, 50 from each of the two outer latitude bands and 113 from the polar band. With 20 dB more budget a 4 m mast serves cells out to the edge of the 100 km ray disc: on 72 of the sites the median distance from a covered cell to its serving mast is 37 km at 1.8 GHz, 26 % of the covered cells lie more than 50 km from their mast and the 99th percentile is 99 km, against a free-space range of 22 km in the base case. The terrain that a rim mast sees is not confined to its

G. A reference budget The base atlas deliberately uses a small-lander budget and the resulting coverable fractions at the higher bands are low. Because the stored layers hold no value beyond the ray radius of the base run, a stronger budget cannot be obtained by re-thresholding; it requires a second run. The reference run uses the representative NASA scenario [4] on the landing-site candidates only: base station 50 dBm on a 30 m lander tower, user equipment 23 dBm at 3.5 m (the Lunar Terrain Vehicle), noise figure 2.5 dB and a 20 MHz channel in both directions. The scenario is not the “20 dB stronger budget” it appears to be. The downlink gains 20 dB, but the link is bidirectional and the uplink, with the same 23 dBm handset transmitting into a 20 MHz rather than a 5 MHz allocation, loses 2.6 dB.

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PREPRINT, 19 OCTOBER 2026

TABLE XII P OWER - ONLY CONTROL . T HE ENTRIES ARE THE MEDIAN GROWTH OF THE COVERED AREA OF A MAST WHEN THE BUDGET IS RAISED BY 20 D B AT BOTH ENDS WITH NOTHING ELSE CHANGED (4 M MAST, 1.5 M RECEIVER , 100 KM RAY RADIUS ), ON 213 RIDGE SITES DRAWN FROM THE THREE LATITUDE BANDS . T HE VALUES IN PARENTHESES GIVE THE MEDIAN RATIO OF COVERED TO VISIBLE AREA WITHIN THE 20 D B FREE - SPACE RANGE ( CAPPED AT 100 KM ). B OLD MARKS THE LARGEST GROWTH PER BAND . Latitude band

Growth factor of the covered area (covered / visible within range) 1.8 GHz

2.58 GHz

3.65 GHz

5.855 GHz

25.375 GHz

80°–82°S (n = 50) 82°–85°S (n = 50) 85°–90°S (n = 113) all (n = 213)

5.7 (1.10) 4.8 (1.10) 5.2 (1.11) 5.2 (1.11)

8.0 (1.03) 7.6 (1.03) 8.4 (1.04) 8.3 (1.04)

14.1 (0.99) 13.0 (0.99) 14.2 (0.99) 14.1 (0.99)

27.2 (0.96) 23.2 (0.97) 25.2 (0.97) 24.5 (0.97)

56.2 (0.96) 53.5 (0.96) 61.7 (0.96) 57.7 (0.96)

In numbers: the scenario is run with its own noise parameters from Table 2 of [4], a noise figure of 2.5 dB at both ends and a noise temperature of 250 K, which the run takes as the antenna temperature (the base case uses 150 K, Section III-C1). The base-station noise is then k (Tant + T0 (F − 1)) B with T0 (F − 1) = 226 K, Tsys = 476 K and B = 20 MHz, i.e. N = −98.8 dBm; the 23 dBm uplink therefore closes at a path loss of 121.8 dB, against 124.4 dB for the downlink-limited base case (30 dBm − (−94.4 dBm)), and at that path loss the 50 dBm downlink delivers −71.8 dBm, the effective threshold stored with the run. With the base case’s 150 K instead, the noise would be −99.8 dBm, the threshold −72.8 dBm and the range 18.4 km; the conclusion that the scenario is uplinklimited and shorter-ranged than the base case does not depend on the choice. The free-space range at 1.8 GHz is 16.4 km, shorter than the 22 km of the base case. The run was first started with a 100 km ray radius, as for the control above; on 134 sites no covered cell lay more than 16.3 km from its tower at 1.8 GHz or 5.0 km at 5.855 GHz, and the run was completed at the scenario’s own range (16.4 km at 1.8 GHz on the effective threshold of −71.8 dBm in downlink terms). What the reference scenario buys is therefore the tower: 30 m instead of 4 m raises the visible fraction of the surrounding terrain, and the 3.5 m vehicle antenna raises it again. Table XIII compares the per-region fractions with the base atlas. The two columns are not the same experiment: the base atlas has every candidate active, including the ridge sites on the high ground around each footprint, whereas the reference scenario puts towers on the landable cells inside the footprints only, so the comparison asks what a lander-mounted tower does without the surrounding ridge sites. At 1.8 GHz the reference scenario covers less of every footprint than the base atlas (83 against 97 % at de Gerlache Rim 2, 87 against 99 % at Slater Plain), for two reasons that the table separates: the shorter range, and the absence of the ridge sites, which is the whole difference at the three footprints that are themselves the high ground (Malapert Massif 53 %, Nobile Rim 1 44 %, Peak near Cabeus B 14.5 %), where the landable cells lie below the crests that shadow them. At 5.855 GHz and 25.375 GHz, however, the towers inside the footprint reach almost the same fraction as the full base atlas (71 against 68 % at Haworth, 82 against 85 % at Slater Plain, 76 against 82 % at Amundsen Rim; 46 against 45 % at Slater Plain in the millimeter-wave band): at short range the 30 m tower and the 3.5 m vehicle antenna raise the visible fraction of the footprint by as much as the base atlas gains from its thousands of surrounding sites, and the

data-link fractions at 1.8 GHz are within a few points of the base case in the overlooked regions. The table also shows the margin argument of Section IV-F in a second form: in every region and under both budgets the 1.8 GHz data-link column equals the 5.855 GHz coverable column to within a point, because both are the same 10 dB step from the 1.8 GHz threshold, one taken in margin and the other in free-space loss. Three base-case conclusions survive the reference scenario unchanged: the 25.375 GHz band remains single-server (1.1– 2.3 serving towers per coverable cell); the regions keep their order, Slater Plain, Amundsen Rim and Nobile Rim 2 at the top and Peak near Cabeus B, Nobile Rim 1 and Malapert Massif at the bottom, because the order is set by the visible fraction (91 to 14.5 % of the footprint in line of sight of a tower); and the steep regions are poorly served, more so without the ridge sites. What changes is the share of coverage that rests on diffraction, which falls to 0.1–0.5 % of coverable cells at 5.855 GHz with the towers: a tall tower sees what a small mast has to diffract to. H. Discussion and Limitations a) What the atlas is: The atlas is an envelope. Every one of 11,827 candidates transmits at once, and a coverable cell therefore means “some permitted site could serve this cell with margin”, not “a deployed network does”. The count layer is the number of such sites and is a measure of siting flexibility that scales with the 1 km candidate spacing. Turning the envelope into a design (a minimal set of sites serving a region, a traverse or a set of instruments, with interference between co-channel cells) is a set-cover or reinforcement-learning problem for which the per-candidate table and the best-server identity layer are the inputs. We deliberately stop short of it here. b) What is robust and what is not: The coverable fraction at 1.8–2.58 GHz is insensitive to the diffraction model (0.6 % of the disc, 8 % of covered cells at the edge), to the noreflection alternative (1.6–2.0 percentage points) and to the DEM product and DEM noise at the level of the published error map (0.8 and 0.4 % of cells; Section IV-A5), because most shadowed cells sit 10–100 dB below threshold and the choices above act on shadowed cells. What the coverable fraction is sensitive to is the level of the visible-path power itself, which none of those choices touches. The 3–4 dB by which the atlas value exceeds the parabolic-equation reference on visible paths moves 6.7 percentage points of the disc at 1.8 GHz and 16.5 at 5.855 GHz, more at the higher bands

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

25

TABLE XIII P ER - REGION COVERABLE FRACTION OF THE FOOTPRINT ( EXACT, 20 M ). T HE FRACTIONS ARE GIVEN UNDER THE BASE ATLAS AND UNDER THE REFERENCE SCENARIO OF [4] ON THE LANDING - SITE CANDIDATES ONLY. T HE BASE ATLAS HAS EVERY CANDIDATE ACTIVE , WITH 4 M MASTS , A 30 D B M BASE STATION AND A 5 MH Z UPLINK . T HE REFERENCE SCENARIO USES A 30 M TOWER , 50 D B M , A 3.5 M USER AND A 20 MH Z UPLINK . I T IS UPLINK - LIMITED , WITH AN EFFECTIVE RANGE OF 16.4 KM AT 1.8 GH Z . T HE DL 1.8 ENTRIES GIVE THE DATA - LINK FRACTION AT 1.8 GH Z . T HE LOS ENTRIES GIVE THE FOOTPRINT FRACTION IN LINE OF SIGHT OF AT LEAST ONE ACTIVE CANDIDATE . B OLD MARKS THE HIGHEST VALUE IN EACH COLUMN AND ITALIC THE LOWEST. No.

Region

1 2 3 4 5 6 7 8 9 10 11 12

de Gerlache Rim 2 Haworth Malapert Massif Mons Mouton Nobile Rim 1 Nobile Rim 2 Peak near Cabeus B Slater Plain Mons Mouton Plateau Faustini Rim A Connecting Ridge Amundsen Rim

Base atlas, all candidates (%)

Reference scenario, landing-site towers (%)

1.8

DL 1.8

5.855

25.375

LOS

1.8

DL 1.8

5.855

25.375

LOS

96.5 89.4 91.8 93.2 93.3 97.7 85.4 98.5 94.3 82.1 93.6 95.0

75.3 67.1 39.0 60.4 37.4 74.7 22.9 84.9 70.8 59.7 62.7 81.8

74.6 67.6 38.5 60.8 37.0 74.9 22.4 85.3 70.8 60.5 62.9 82.0

18.6 26.1 8.2 25.6 15.5 32.0 1.9 45.0 30.4 31.7 19.9 25.0

96.0 90.4 91.0 92.4 93.6 97.7 86.7 98.8 94.1 86.3 93.2 95.0

82.9 85.7 53.4 81.3 43.9 90.4 14.5 86.7 82.9 78.5 75.2 90.8

57.0 70.7 32.0 62.2 34.1 71.0 8.1 81.7 68.7 61.2 62.7 76.8

57.3 70.9 31.9 62.3 34.1 70.7 7.8 82.0 68.6 61.5 63.1 76.5

20.8 30.3 9.3 27.9 16.4 31.3 1.8 45.9 32.4 34.2 21.1 25.1

84.4 86.4 54.0 82.2 45.1 90.3 14.5 86.6 83.4 80.5 74.0 91.4

because a larger share of their coverable cells lies within a few decibels of threshold. That is why the PE-corrected fractions are reported beside the atlas values, and why they, not the noreflection layer, are the companion to read with the atlas. The reference puts the truth below the atlas value on visible paths, and the free-space layer bounds it from the other side. The release includes the line-of-sight flag that makes the correction a read-time operation, and the no-reflection layer with count and identity for each. The 25.375 GHz coverable fraction is in addition a property of candidate density, since its free-space range (1.6 km) is comparable to the candidate spacing. The convergence test of Section IV-A7 bounds this dependence to about half a percentage point when the spacing is halved, because the siting rules admit few additional sites. c) Validation gap: The engine is validated against a parabolic-equation solver on real terrain profiles, against ray tracing on line of sight and reflection and against analytic solutions on the flat-ground reflection and the knife edge, but not against measurements on obstructed lunar-like paths, because no such measurements exist for the Moon and the terrestrial analog campaign we are aware of (NASA Desert RATS 2022 [48]) has been published only as images. The PE comparison is the strongest available check on the propagation model, and it is a check of one model against another on the same DEM, not against the true surface. Sub-cell roughness, boulders and the interpolated surface between LOLA tracks are absent from both, and the PE’s own terrain treatment is trusted only to 5° segment slopes, so on steeper crests the reference is the exact wedge solution rather than the PE. The 5 m PGDA mosaic of 87°–90°S [17] allows a further resolution test on the polar regions (Connecting Ridge, de Gerlache Rim 2, Slater Plain, Haworth) that has not been run. d) Assumptions that are not citable: Four inputs are stated assumptions rather than measurements, namely the antenna temperature (150 K, ±1 dB on the thresholds per 100 K), the receiver noise figures (7 and 3 dB, about 1 dB on the thresholds per decibel), the antenna mounting heights on the crewed landers (unpublished, the 4, 10 and 30 m cases bracket

them), and the density and composition behind the regolith permittivity. The five 2022 regions without a public footprint are excluded rather than reconstructed. e) Model omissions: The engine has no multipath or fading representation, no antenna patterns, no interference, no surface roughness below the DEM cell [36], [37], no lander body blockage, and no time dependence. It is a static, singleuser, best-server map. Plasma and dust effects are neglected, as is the 0.8 % map-scale variation across the disc. f) DEM artifacts: The orbit-track features in the PDS 20 m product are relevant beyond this work. Any algorithm that selects local maxima on LDEM_80S_20M (for communications relays, solar towers or Earth-visibility studies) will prefer them at a rate of about one in ten. The orbit-adjusted product does not select them. The 77 sites that are higher in the adjusted product are inspected individually in the release. All are kept in the run, and 60 are flagged in the released table because they are local maxima in neither product at the 1 km scale or stand on cells with no LOLA shot (36 % of the 77), which allows a user to exclude them. Where the PDS product must be used, the per-site height difference is an effective filter. g) Future work: The reference budget of Section IV-G shows that a 30 m lander tower with a vehicle-height user reaches, at 5.855 GHz and above, nearly the same fraction of an overlooked footprint as the full base atlas does with its thousands of surrounding sites, but cannot replace the ridge sites where the footprint is itself the high ground. It also shows that the representative scenario is uplink-limited, leaving its 20 dB of extra base-station power unused. The next step is a scenario with the uplink matched to it (a higher-power vehicle radio, or a narrower uplink allocation), a further run of the engine on the same terrain. Coupling the atlas to the LOLA illumination maps gives the solar-power constraint on mast sites, and coupling it to the Earth-visibility maps gives the backhaul constraint. The best-server identity layer supports a set-cover placement study, and the per-region 5 m runs and a measurement-validated channel model are the next steps toward link-level simulation.

26

PREPRINT, 19 OCTOBER 2026

V. C ONCLUSION AND F UTURE W ORK LunarRF is a GPU-based surface-coverage analysis system for terrain-aware propagation, built from two independent components, a Delta-Bullington footprint engine that computes the received-power footprint of one candidate mast at a time and an order-independent resolver that merges each footprint into the pole-wide best-server, identity, count and line-of-sight layers. With lunar data, the system has produced the first polewide potential-coverage atlas for 3GPP surface networks at the lunar south pole, 11,827 candidate sites on the orbit-adjusted LOLA 20 m DEM [18] at four SFCG-recommended surface bands and the IM-2 band [3], [4], computed in 40 GPU h. With 4 m masts and a 30 dBm budget, 90.5 % of the 80°–90°S disc is coverable at 1.8 GHz, 59.1 % at 5.855 GHz and 10.0 % at 25.375 GHz. A ridge-class mast covers a median 89 % of its visible terrain within a free-space range that falls from 22.0 to 1.6 km, which shows that the budget, not the terrain, limits coverage at every band. Of the permanently shadowed area, 59.1 % is coverable at 1.8 GHz from the permitted rim sites, and every current Artemis candidate region [31] is at least 85.4 % coverable at that band. Prior lunar propagation studies address one or a few sites [4], [13], [15]. The atlas gives mission planners a screening product for every candidate region and an input to network design, and after landing it identifies from the actual touchdown point the nearest permitted site with the greatest coverage. The finding that local-maximum selection on the unadjusted PDS DEM picks orbit-track artifacts at one ridge site in ten applies to any siting algorithm on that product, for relays, solar towers or Earth-visibility studies alike. The atlas is an envelope of what permitted sites could serve, not a deployed network, and its accuracy is bounded by the engine and the terrain rather than by the candidate set. Against a parabolic-equation reference on 160 real profiles the engine is 3.3–3.9 dB optimistic on visible paths, a bias the released line-of-sight flag applies at read time. No measurement on obstructed lunar-like paths exists to validate either model. Between LOLA tracks the DEM is interpolated, and outerlatitude fractions are therefore likely optimistic. The antenna temperature, lander mounting heights and regolith density are assumptions rather than measurements. Future work includes coupling the atlas to the LOLA illumination and Earth-visibility maps [2], set-cover mast placement on the best-server identity layer, per-region runs on the 5 m PGDA mosaic [17] and validating the propagation model against measurements on obstructed lunar-analog paths. DATA AVAILABILITY The atlas bundle (160 m pole mosaics, 20 m region windows, candidate and coverage tables, run parameters and manifest), the exact-statistics tables from which every figure and table in this paper is derived, and the validation records (parabolic-equation profiles, sensitivity, convergence and power-control results) are released under CC BY 4.0 at https://doi.org/10.5281/zenodo.23301640 (about 3 GB). The full 20 m tiles (60 GB) are available from the authors on request. The run manifest records the engine version, the

configuration hash and the SHA-256 of the candidate table so that the released layers are traceable to one run. ACKNOWLEDGMENT The whole-pole atlas was computed on the Turing highperformance computing cluster at Worcester Polytechnic Institute, operated by WPI Academic and Research Computing; the authors thank the ARC staff for their support. The Artemis candidate landing region lists follow the NASA releases of 19 August 2022 [30] and 28 October 2024 [31] (https: //www.nasa.gov/news-release/nasa-provides-update-on-a rtemis- iii- moon- landing- regions/); region footprints are the USGS navigational-grid data releases of M. T. McClernan [34], [35]. Elevation, illumination and permanent-shadow products are from the LRO LOLA team [2], [17], [18], [29] via the NASA Planetary Geodynamics Data Archive and the PDS Geosciences Node. The authors also thank Dr. Galahad Wernsing and Srivatsan Mukunthraj of the Wireless Innovation Laboratory, Worcester Polytechnic Institute, whose careful reading and constructive comments improved an early draft of this article. R EFERENCES [1] G. R. Olhoeft and D. W. Strangway, “Dielectric properties of the first 100 meters of the Moon,” Earth and Planetary Science Letters, vol. 24, no. 3, pp. 394–404, 1975. [2] E. Mazarico, G. A. Neumann, D. E. Smith, M. T. Zuber, and M. H. Torrence, “Illumination conditions of the lunar polar regions using LOLA topography,” Icarus, vol. 211, no. 2, pp. 1066–1081, 2011. [3] Space Frequency Coordination Group, “Communication and positioning, navigation, and timing frequency allocations and sharing in the lunar region,” SFCG, Tech. Rep. Recommendation SFCG 32-2R5, Jun. 2023. [4] B. L. Edwards, R. Wagner, M. Zemba, W. Millard, S. Braham, K. Gifford, and O. Somerlock, “3GPP mobile telecommunications technology on the Moon,” in Proc. IEEE Aerospace Conference, Big Sky, MT, USA, 2023, pp. 1–12, NTRS 20220015268. [5] Nokia, “Nokia and Intuitive Machines deliver first cellular network to the Moon; achieve some key mission objectives,” Press release, 10 March 2025, https://www.nokia.com/newsroom/nokia-and-intuitive-machine s-deliver-first-cellular-network-to-the-moon-achieve-some-key-missi on-objectives/, 2025. [6] NASA, “NASA receives some data before Intuitive Machines ends lunar mission,” Release 25-025, https://www.nasa.gov/news-release/nasa-rec eives-some-data-before-intuitive-machines-ends-lunar-mission/, Mar. 2025. [7] G. A. Hufford, A. G. Longley, and W. A. Kissick, “A guide to the use of the ITS irregular terrain model in the area prediction mode,” U.S. Department of Commerce, National Telecommunications and Information Administration, Boulder, CO, USA, Tech. Rep. NTIA Report 82-100, Apr. 1982. [8] L. Foore and N. Ida, “Path loss prediction over the lunar surface utilizing a modified Longley-Rice irregular terrain model,” NASA, Cleveland, OH, USA, Tech. Rep. NASA/TM-2007-214825 (E-16017), 2007, Presented at the Wireless for Space Workshop, Colorado Springs, CO; NTRS 20070025224. [9] S. Hwu, M. Upanavage, and C. Sham, “Lunar surface propagation modeling and effects on communications,” in Proc. 26th AIAA International Communications Satellite Systems Conference (ICSSC), San Diego, CA, USA, 2008, NTRS 20080015374. [10] D. Chizhik, J. Moilanen, S. Klein, L. Maestro, and R. A. Valenzuela, “Analytic propagation approximation over variable terrain and comparison to data,” in Proc. 14th European Conference on Antennas and Propagation (EuCAP), Copenhagen, Denmark, 2020. [11] H. Y. Wang and A. M. Wyglinski, “Barren, irregular, chaotic terrain ring model for lunar 5G applications,” IEEE Open J. Commun. Soc., vol. 6, pp. 9523–9533, 2025. [12] S. E. Shumate, “Longley-Rice and ITU-P.1546 combined: A new international terrain-specific propagation model,” in Proc. IEEE 72nd Veh. Technol. Conf. (VTC 2010-Fall), Ottawa, ON, Canada, 2010.

SANTORELLI AND WYGLINSKI: LUNARRF: A TERRAIN-AWARE PROPAGATION ENGINE AND 3GPP COVERAGE ATLAS OF THE LUNAR SOUTH POLE

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