Despite Maxwell's formulation of the electromagnetic wave laws over a century and a half ago, accurately modeling the transmission of RF signals within electrically complex environments continues to be a formidable challenge. This complexity arises from intricate interactions of RF signals with various obstacles, such as reflections and diffractions. Inspired by the effective utilization of neural networks in computer vision for representing optical fields, this paper introduces NeRF2, a novel neural radio-frequency radiance field. NeRF2 conceptualizes a continuous, volumetric scene function to interpret RF signal propagation. Uniquely, NeRF2, once trained with limited signal measurements, can predict the characteristics and reception of a signal at an arbitrary point, given the transmitter's location. Functioning as a physical-layer neural network, NeRF2 amalgamates learned statistical models with physical ray tracing to create synthetic datasets, tailored for the training needs of application-layer artificial neural networks (ANNs). This integration, termed "turbo-learning," combines authentic and synthetic datasets, significantly augmenting ANNs' training efficacy. Experimental results illustrate that turbo-learning can substantially improve performance, with an estimated 50% enhancement. The efficacy of NeRF2 is further underscored in its applications in indoor localization and 5G MIMO systems.
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