R$^{2}$Net: 2D Deep Residual Learning with Height Embedding for 3D Radio Map Estimation

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.

• The paper introduces R$^{2}$Net, leveraging 2D deep residual learning for scalable and efficient 3D radio map estimation with height embeddings.
• Employs a new 3DiRM3200 dataset for accurate radio maps using dominant path model simulations, optimizing prediction across height variations.
• R$^{2}$Net outperforms previous models in NMSE, SSIM, and PSNR metrics, demonstrating superior accuracy and efficiency in diverse environments.

R$^{2}$Net: 2D Deep Residual Learning with Height Embedding for 3D Radio Map Estimation

Problem Statement and Motivation

Pathloss estimation is fundamental for numerous wireless communication tasks, including handover, network planning, and localization. Conventional radio map construction relies on exhaustive site survey or time-consuming physical simulations, both of which face limitations in coverage and scalability. Existing learning-based approaches, especially those using deep learning and computer vision methods, have primarily focused on 2D radio map estimation, implicitly assuming height invariance or ignoring receiver height altogether. However, empirical and theoretical evidence indicates strong spatial and vertical variation in radio maps, particularly in indoor environments where object heights, transmitter heights, and receiver heights are comparable. This paper addresses the critical need for efficient, accurate, and scalable 3D radio map estimation incorporating object height information.

3DiRM3200 Dataset: Design and Methodology

The study introduces the 3DiRM3200 dataset, comprising 3,200 fully labeled 3D indoor radio maps across 200 building layouts (drawn from CubiCasa5K), each paired with furniture layouts and 16 transmitter locations per building. Radio maps are generated using dominant path model (DPM)-based physical simulations via WinProp, with a wavelength and propagation environment accurately configured for indoor wireless communication. Pathloss values are provided for every $(x, y, z)$ receiver location, spanning heights from 0.5 m to 2 m in 0.1 m increments, yielding 16 vertical slices per environment.

Height information is encoded into environmental images using a novel embedding scheme. For each pixel, height is normalized to $[0, 1]$ via a bias-corrected normalization, enabling the network to differentiate between zero-height objects and the absence of objects, overcoming ambiguity present in prior height normalization schemes [FadeNet 2020, Transformerradionet 2021]. This embedding underpins the transformation of the 3D estimation problem into a multi-channel 2D prediction task, with each channel representing a radio map at a specific receiver height.

R$^{2}$Net Architecture and Scenario-Specific Adaptations

The R$^{2}$Net architecture is grounded in the U-Net family, but integrates cascaded residual blocks, tailored pathloss feature enhancement blocks (PFEBs), and bespoke upsampling modules. The model is designed to maximize nonlinear feature extraction relevant to radio propagation, explicitly addressing penetration and diffraction losses.

• R$^{2}$Net-In (Indoor Scenarios): Emphasizes penetration loss, using dropout layers (dropout probability 0.3) across deep feature maps to enhance generalization and mitigate overfitting attributable to transmitter location and environment variation. The decoder employs nearest-neighbor interpolation for upsampling, compensating for information loss due to dropout.
• R$^{2}$Net-Out (Outdoor Scenarios): Prioritizes extraction of diffraction loss features arising from urban building diversity. PFEB-Out comprises five cascading residual blocks followed by atrous spatial pyramid pooling (ASPP) at multiple dilation rates ($6, 12, 18$), capturing multi-scale spatial information. Transposed convolutions are used for upsampling.
• R$^{2}$Net-Outlite: Designed for limited training sample regimes. Reduces the number of residual blocks, introduces additional dropout and pooling layers, and uses smaller channel counts and nearest-neighbor interpolation to deliver improved generalization and computational efficiency.

Height embedding and scenario-specific modifications ensure low computational burden and scalable inference, enabling a single model to generate radio maps across all receiver heights simultaneously.

Experimental Evaluation

Extensive experiments demonstrate the superiority of R$^{2}$Net-In and R$(x, y, z)$0Net-Out(Outlite) over prior art, both for indoor and outdoor environments.

3D Indoor Radio Maps

• Accuracy: R$(x, y, z)$1Net-In achieves NMSE = 0.0268 (vs RadioUNet: 0.0292), with SSIM = 0.8908 and PSNR = 29.65. The $(x, y, z)$2 confidence interval for NMSE is significantly narrower than competing methods, demonstrating robust estimation across diverse environments and transmitter locations.
• Efficiency: R$(x, y, z)$3Net-In reduces model size (8M params vs RadioUNet's 13M and FadeNet's 65M), MAC operations (6.5G vs FadeNet's 51.7G), and halves inference time per km$(x, y, z)$4 relative to the best prior method. Throughput is markedly higher.
• Ablation Studies: Dropout layers and residual blocks are essential for generalization and nonlinear feature extraction. Height embedding, while less critical indoors, still yields accuracy gains.

2D Outdoor Radio Maps (RadioMapSeer Dataset and Real-world Urban Measurements)

• Accuracy: R$(x, y, z)$5Net-Out achieves NMSE = 0.0046, SSIM = 0.9491, PSNR = 37.00, outperforming RadioUNet (0.0106) and other benchmarks. R$(x, y, z)$6Net-Outlite yields superior results when training data are scarce (NMSE = 0.0228 with only 5K radio maps).
• Efficiency: R$(x, y, z)$7Net-Outlite minimizes model complexity (4M params) and MACs (13.8G), with competitive inference times.
• Height Embedding Impact: Models using the proposed height embedding attain NMSE reductions of 16-34% and demonstrably better predictions for locations far from the transmitter.
• Real-World Validation: R$(x, y, z)$8Net variants surpass prior methods on the RSRPSet_urban dataset (NMSE = 0.1834 vs RadioUNet/Radiotrans/PPNet $(x, y, z)$9 0.3; SSIM $[0, 1]$0 0.527 vs 0.45).

Implications, Limitations, and Future Directions

The results establish that efficient 2D deep learning approaches—when supplemented with precise height embeddings—can accurately estimate complex 3D radio maps, overcoming the prohibitive cost and complexity of traditional 3D convolutional models. The practical implications include improved coverage prediction, handover management, and localization, especially in environments where vertical variation is significant.

The architecture's high generalization ability supports application in diverse propagation scenarios and transmitter/receiver placements, but WinProp-based dataset generation does not capture dynamic effects (mobility, weather). Fine-tuning or retraining on empirical data (as demonstrated with RSRPSet_urban) is necessary for deployment in real-world environments. Customization for rural or hybrid indoor-outdoor environments poses additional challenges, motivating future work on adaptive and environment-aware model enhancements.

Conclusion

R$[0, 1]$1Net sets a new benchmark for scalable, efficient, and accurate 3D radio map estimation. By transforming 3D prediction into a 2D residual learning task and embedding precise object height information, the model delivers superior accuracy, efficiency, and generalization. The creation of 3DiRM3200 addresses the pressing need for comprehensive 3D radio map datasets. Scenario-adaptive variants of R$[0, 1]$2Net (In, Out, Outlite) outperform prior approaches in both indoor and outdoor domains, with experimental results validating both theoretical claims and practical utility for future wireless network planning and operation (2605.18127). The methodology has substantial implications for AI-driven radio environment mapping and opens pathways for future research on dynamic and mixed propagation conditions.