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arxiv: 2605.18127 · v1 · pith:WGR3AD3Tnew · submitted 2026-05-18 · 📡 eess.SP

R²Net: 2D Deep Residual Learning with Height Embedding for 3D Radio Map Estimation

Huiting Rao , Junyuan Wang , Huiling Zhu , Cheng-Xiang Wang This is my paper

Pith reviewed 2026-05-20 00:49 UTC · model grok-4.3

classification 📡 eess.SP
keywords 3D radio map estimationheight embeddingresidual networkspathloss estimationindoor radio mapsoutdoor radio mapsdeep learning for wirelesssignal propagation
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The pith

Embedding height information into 2D images allows a residual network to estimate accurate 3D radio maps without 3D convolutions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that receiver height can be incorporated into 2D images to let a 2D residual network predict pathloss across three dimensions in wireless environments. It introduces the R²Net architecture with separate indoor and outdoor variants that target penetration losses and diffraction losses respectively. If correct, this would mean practitioners no longer need full 3D networks or detailed geometric simulators to generate usable radio maps at multiple heights. The approach directly supports applications such as cellular handover decisions that depend on height-specific signal strength. Experiments report gains in accuracy together with lower computational and storage costs plus faster inference than prior benchmarks.

Core claim

The authors first embed height information into 2D images and then apply a general 2D radio residual network called R²Net to perform 3D radio map estimation. They create R²Net-In to capture penetration loss in indoor settings and R²Net-Out to capture diffraction loss in outdoor settings. This produces radio maps that vary correctly with receiver height while delivering higher estimation accuracy, reduced computational and storage costs, and faster inference than existing methods.

What carries the argument

Height embedding into 2D images fed to the R²Net, a 2D residual network that models radio-specific loss mechanisms.

If this is right

  • 3D radio maps can be generated using only 2D network architectures and lower resource demands.
  • R²Net-In specifically improves modeling of indoor penetration losses while R²Net-Out improves modeling of outdoor diffraction losses.
  • Estimation accuracy, computational cost, storage cost, and inference speed all improve over prior state-of-the-art approaches.
  • A public 3D indoor radio map dataset supports training and benchmarking of height-aware models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar height-embedding steps could extend to other spatial prediction tasks such as coverage mapping at multiple frequencies.
  • Fast inference from the 2D design may support real-time radio map updates in environments with changing conditions.
  • The method could be tested on scenarios that include moving obstacles or multi-floor buildings to check robustness beyond the current dataset.

Load-bearing premise

Embedding height information into 2D images supplies enough detail for a 2D residual network to capture full three-dimensional radio propagation effects without explicit 3D operations or geometric modeling.

What would settle it

Direct comparison of R²Net pathloss predictions against measured values at multiple distinct receiver heights in a real indoor or outdoor site would show whether the 3D estimates match observed propagation behavior.

Figures

Figures reproduced from arXiv: 2605.18127 by Cheng-Xiang Wang, Huiling Zhu, Huiting Rao, Junyuan Wang.

Figure 1
Figure 1. Figure 1: Illustration of the input and the output of the propos [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of a typical U-Net that serves as the fou [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of ASPP. is necessary because the resolution of a feature map at the encoder could be higher than that at the decoder due to the loss of border pixels after convolution when the size of the input feature map is not divisible by the kernel size. C. ResNet ResNet [33] introduces a residual block to ease the training of very deep networks with affordable training time. A typical residual block is… view at source ↗
Figure 5
Figure 5. Figure 5: Images from sample No. 120 of 3DiRM3200, including (a [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: R2Net architecture. BatchNorm + ReLU BatchNorm + ReLU BatchNorm BatchNorm + ReLU BatchNorm + ReLU BatchNorm BatchNorm + ReLU BatchNorm + ReLU ReLU ReLU BatchNorm ReLU    Conv 1×1 Conv 1×1 Conv 1×1 Conv 1×1 Conv 1×1 Conv 1×1 Conv 1×1 Conv 3×3 Conv 3×3 Conv 3×3 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: R2Net-In architecture. the encoder and the decoder of R2Net, the number of pixels in a feature map at the encoder is ensured to be the same as that at the decoder, as a result of which, cropping used in the conventional U-Net is not needed in our R2Net. 5) Numbers of Channels: As the effect of an environmental object on the pathloss depends on its material, to distinguish different materials of objects, th… view at source ↗
Figure 9
Figure 9. Figure 9: Upsampling blocks for (a) R2Net-In and (b) R2Net-Out. stochastically “dropping out” neurons [44] to avoid overfitting, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: R2Net-Out architecture. 3)(%2XWOLWH 'HFRGHU &DVFDGHG UHVLGXDO EORFNV ,QSXW îî &DVFDGHG UHVLGXDO EORFNV $633 &RQFDW  &RQYî %DWFK1RUP 5H/8 0D[SRROLQJî 'URSRXW &RQYî %DWFK1RUP 5H/8 'URSRXW 2XWSXW îî &RQFDW  7UDQVSRVHG &RQYî 5H/8 (QFRGHU 'URSRXW *URXQG WUXWK 1HDUHVWQHLJKERU ,QWHUSRODWLRQ [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: R2Net-Outlite architecture. D. R2Net-Out for Outdoor Scenarios Based on the proposed R2Net architecture, R2Net-Out is designed to estimate outdoor radio maps, in which PFEB-Out concentrates on extracting abundant features of diffraction loss that dominants the outdoor pathloss. The detailed architecture is described below. 1) PFEB-Out: In outdoor scenarios, the main pathloss comes from the diffraction los… view at source ↗
Figure 12
Figure 12. Figure 12: Visualization of estimation results of R [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Visualization of estimation results of R [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Visualization of the effectiveness of the proposed [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
read the original abstract

Acquiring channel knowledge is required by many applications. For instance, handover in cellular networks is mainly decided based on the knowledge of pathloss. In contrast to traditional statistical distance-determined models that might provide misleading pathloss estimates, researchers started to explore deep learning methods recently to accurately estimate the radio map that characterizes the spatial distribution of pathloss according to the specific physical wireless propagation environment. However, existing works mainly focused on 2D radio map estimation by assuming that all receivers are at the same height. In fact, radio maps could be significantly different at different receiver heights, highlighting the importance of 3D radio map estimation. In this paper, we first propose a method to embed height information into 2D images, and then propose a general 2D radio residual network (R$^{2}$Net) for 3D radio map estimation. Since pathloss exhibits different characteristics in indoor and outdoor scenarios, we specifically propose R$^{2}$Net-In for indoor scenarios and R$^{2}$Net-Out for outdoor scenarios to better capture penetration loss and diffraction loss, respectively. Extensive experimental results show that our R$^{2}$Net significantly outperforms the state-of-the-art benchmarks in terms of estimation accuracy, computational and storage costs, and inference speed. In addition, due to the lack of publicly available 3D radio map datasets, a 3D indoor radio map dataset (3DiRM3200) is created, which took more than $1,000$ labour hours. The dataset and codes will be available at https://github.com/lighttime2023/3DiRM3200.git.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a height-embedding technique to convert 3D radio-map inputs into 2D tensors, then applies a residual network (R²Net) to estimate pathloss across multiple receiver heights. Separate variants are defined for indoor (R²Net-In, emphasizing penetration) and outdoor (R²Net-Out, emphasizing diffraction) scenarios. The authors release a new 3D indoor dataset (3DiRM3200) and report that R²Net outperforms prior benchmarks on accuracy, storage, compute, and inference speed.

Significance. If the central claims are substantiated, the work would demonstrate that a carefully designed 2D residual architecture with height embedding can deliver practical 3D radio maps at lower cost than explicit 3D models, which is relevant for network planning and handover applications. The public release of 3DiRM3200 and the associated code is a clear positive contribution that lowers the barrier for future 3D radio-map research.

major comments (2)
  1. [§3.2] §3.2 (Height Embedding): the formulation concatenates or tiles height scalars into 2D feature maps, yet provides no mechanism (ray-tracing prior, vertical consistency loss, or multi-height attention) that would allow subsequent 2D convolutions to enforce physically consistent diffraction or shadowing across heights; this is load-bearing for the claim that a purely 2D network suffices for full 3D estimation.
  2. [§4.3, Table 2] §4.3 and Table 2: the reported RMSE and inference-time gains are presented without error bars, without per-height breakdown, and without an ablation that isolates the height-embedding block; without these controls it is impossible to verify that the 2D architecture, rather than dataset-specific tuning, drives the claimed superiority over 3D baselines.
minor comments (2)
  1. [Abstract] The abstract states quantitative superiority but supplies no numerical values or baseline names; adding one sentence with key metrics would improve readability.
  2. [§3.1] Notation for the embedded height channel (e.g., H_e) is introduced without an explicit equation; a short definition in §3.1 would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below with clarifications and indicate the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Height Embedding): the formulation concatenates or tiles height scalars into 2D feature maps, yet provides no mechanism (ray-tracing prior, vertical consistency loss, or multi-height attention) that would allow subsequent 2D convolutions to enforce physically consistent diffraction or shadowing across heights; this is load-bearing for the claim that a purely 2D network suffices for full 3D estimation.

    Authors: We acknowledge that the current formulation does not include an explicit mechanism such as a vertical consistency loss or multi-height attention. The height embedding injects scalar height information by concatenation or tiling into the 2D feature maps, allowing the residual blocks to learn height-dependent features from the training data, which contains pathloss values across multiple receiver heights. This data-driven learning enables the network to capture effects like diffraction and shadowing implicitly. To better substantiate the claim, we will revise §3.2 to include a more detailed explanation of how the embedding facilitates vertical consistency and add qualitative visualizations of estimated radio maps at consecutive heights demonstrating physical plausibility. revision: partial

  2. Referee: [§4.3, Table 2] §4.3 and Table 2: the reported RMSE and inference-time gains are presented without error bars, without per-height breakdown, and without an ablation that isolates the height-embedding block; without these controls it is impossible to verify that the 2D architecture, rather than dataset-specific tuning, drives the claimed superiority over 3D baselines.

    Authors: We agree that the absence of error bars, per-height breakdowns, and an ablation isolating the height-embedding block limits the strength of the experimental claims. In the revised version, we will update §4.3 and Table 2 to include error bars (mean ± standard deviation over multiple runs), report RMSE results separately for each receiver height, and add an ablation study comparing the full model against a variant without the height-embedding module. These changes will help isolate the contribution of the proposed components. revision: yes

Circularity Check

0 steps flagged

No circularity: standard residual network training on height-embedded 2D inputs

full rationale

The paper proposes a height-embedding step into 2D images followed by application of a 2D residual network (R²Net) for 3D radio map estimation, with separate indoor/outdoor variants. No equations, derivations, or fitted parameters are shown that reduce the claimed estimation outputs to quantities defined by or fitted on the evaluation data itself. The central results rest on experimental comparisons to benchmarks using a newly created dataset, with no load-bearing self-citations or uniqueness theorems invoked to force the architecture. The approach is therefore self-contained as a standard deep-learning method applied to a new input representation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that height can be usefully encoded as additional channels or features within 2D image inputs for a residual network.

axioms (1)
  • domain assumption Height information can be effectively embedded into 2D image representations to capture 3D radio propagation variations.
    This premise is required for the proposed embedding step to enable 3D estimation from 2D processing.

pith-pipeline@v0.9.0 · 5843 in / 1218 out tokens · 60096 ms · 2026-05-20T00:49:15.982427+00:00 · methodology

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