# NeRF2: Neural Radio-Frequency Radiance Fields

arXiv: https://arxiv.org/abs/2305.06118 · HTML: https://mlsanity.com/paper/2305.06118/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 72 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Urban Radiance Fields](https://mlsanity.com/paper/2111.14643/) (2021)
- [LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping](https://mlsanity.com/paper/2007.00258/) (2020)
- [mD-Track: Leveraging Multi-Dimensionality in Passive Indoor Wi-Fi Tracking](https://mlsanity.com/paper/1812.03103/) (2018)
- [Deep Learning for UL/DL Channel Calibration in Generic Massive MIMO Systems](https://mlsanity.com/paper/1903.02875/) (2019)
- [Dead on Arrival: An Empirical Study of The Bluetooth 5.1 Positioning System](https://mlsanity.com/paper/1909.08063/) (2019)
- [Towards Flexible Wireless Charging for Medical Implants Using Distributed Antenna System](https://mlsanity.com/paper/2001.07644/) (2020)
- [End-to-end Wireless Path Deployment with Intelligent Surfaces Using Interpretable Neural Networks](https://mlsanity.com/paper/2010.10351/) (2020)

## Built on by (most cited first, 30 of 57)

- [DART: Implicit Doppler Tomography for Radar Novel View Synthesis](https://mlsanity.com/paper/2403.03896/) (2024)
- [A Scalable and Generalizable Pathloss Map Prediction](https://mlsanity.com/paper/2312.03950/) (2023)
- [Physics-informed Generalizable Wireless Channel Modeling with Segmentation and Deep Learning: Fundamentals, Methodologies, and Challenges](https://mlsanity.com/paper/2401.01288/) (2024)
- [Radar Fields: An Extension of Radiance Fields to SAR](https://mlsanity.com/paper/2312.12961/) (2023)
- [Differentiable and Learnable Wireless Simulation with Geometric Transformers](https://mlsanity.com/paper/2406.14995/) (2024)
- [RMTransformer: Accurate Radio Map Construction and Coverage Prediction](https://mlsanity.com/paper/2501.05190/) (2025)
- [Empowering Wireless Network Applications with Deep Learning-based Radio Propagation Models](https://mlsanity.com/paper/2408.12193/) (2024)
- [Data Can Speak for Itself: Quality-guided Utilization of Wireless Synthetic Data](https://mlsanity.com/paper/2506.23174/) (2025)
- [Bridging Visual and Wireless Sensing via a Unified Radiation Field for 3D Radio Map Construction](https://mlsanity.com/paper/2601.19216/) (2026)
- [Spatial Channel State Information Prediction with Generative AI: Towards Holographic Communication and Digital Radio Twin](https://mlsanity.com/paper/2401.08023/) (2024)
- [RetailOpt: Opt-In, Easy-to-Deploy Trajectory Estimation from Smartphone Motion Data and Retail Facility Information](https://mlsanity.com/paper/2404.12548/) (2024)
- [Model-based learning for multi-antenna multi-frequency location-to-channel mapping](https://mlsanity.com/paper/2407.07719/) (2024)
- [Neural Reflectance Fields for Radio-Frequency Ray Tracing](https://mlsanity.com/paper/2501.02458/) (2025)
- [Generalizable Radio-Frequency Radiance Fields for Spatial Spectrum Synthesis](https://mlsanity.com/paper/2502.05708/) (2025)
- [Radio Propagation Modelling: To Differentiate or To Deep Learn, That Is The Question](https://mlsanity.com/paper/2509.19337/) (2025)
- [Environment-Aware Channel Inference via Cross-Modal Flow: From Multimodal Sensing to Wireless Channels](https://mlsanity.com/paper/2512.04966/) (2025)
- [RadioFormer: A Multiple-Granularity Radio Map Estimation Transformer with 1textpertenthousand Spatial Sampling](https://mlsanity.com/paper/2504.19161/) (2025)
- [Wideband RF Radiance Field Modeling Using Frequency-embedded 3D Gaussian Splatting](https://mlsanity.com/paper/2505.20714/) (2025)
- [Can NeRFs See without Cameras?](https://mlsanity.com/paper/2505.22441/) (2025)
- [RadarSim: Simulating Single-Chip Radar via Multimodal Neural Fields](https://mlsanity.com/paper/2605.26328/) (2026)
- [SANDWICH: Towards an Offline, Differentiable, Fully-Trainable Wireless Neural Ray-Tracing Surrogate](https://mlsanity.com/paper/2411.08767/) (2024)
- [Rasterizing Wireless Radiance Field via Deformable 2D Gaussian Splatting](https://mlsanity.com/paper/2506.12787/) (2025)
- [Bayesian-Driven Graph Reasoning for Active Radio Map Construction](https://mlsanity.com/paper/2508.09142/) (2025)
- [RF-PGS: Fully-structured Spatial Wireless Channel Representation with Planar Gaussian Splatting](https://mlsanity.com/paper/2508.16849/) (2025)
- [Generative AI Meets Wireless Sensing: Towards Wireless Foundation Model](https://mlsanity.com/paper/2509.15258/) (2025)
- [GSpaRC: Gaussian Splatting for Real-time Reconstruction of RF Channels](https://mlsanity.com/paper/2511.22793/) (2025)
- [An Efficient and Explainable KAN Framework for Wireless Radiation Field Prediction](https://mlsanity.com/paper/2601.11656/) (2026)
- [Physics-Informed Neural Networks with Architectural Physics Embedding for Large-Scale Wave Field Reconstruction](https://mlsanity.com/paper/2603.02231/) (2026)
- [GeoGS-CE: Learning Delay--Beam Channel Priors with 3D Gaussians for High-Mobility Scenarios](https://mlsanity.com/paper/2605.16094/) (2026)
- [Point-Cloud-Assistant Localized Statistical Channel Prediction by Tangent Gaussian Splatting](https://mlsanity.com/paper/2606.18734/) (2026)

## Abstract (arXiv)

Although Maxwell discovered the physical laws of electromagnetic waves 160 years ago, how to precisely model the propagation of an RF signal in an electrically large and complex environment remains a long-standing problem. The difficulty is in the complex interactions between the RF signal and the obstacles (e.g., reflection, diffraction, etc.). Inspired by the great success of using a neural network to describe the optical field in computer vision, we propose a neural radio-frequency radiance field, NeRF2, which represents a continuous volumetric scene function that makes sense of an RF signal's propagation. Particularly, after training with a few signal measurements, NeRF2 can tell how/what signal is received at any position when it knows the position of a transmitter. As a physical-layer neural network, NeRF2 can take advantage of the learned statistic model plus the physical model of ray tracing to generate a synthetic dataset that meets the training demands of application-layer artificial neural networks (ANNs). Thus, we can boost the performance of ANNs by the proposed turbo-learning, which mixes the true and synthetic datasets to intensify the training. Our experiment results show that turbo-learning can enhance performance with an approximate 50% increase. We also demonstrate the power of NeRF2 in the field of indoor localization and 5G MIMO.