Infinite Limits of Convolutional Neural Network for Urban Electromagnetic Field Exposure Reconstruction

Electromagnetic field exposure (EMF) has grown to be a critical concern as a consequence of the ongoing installation of fifth-generation cellular networks (5G). The lack of measurements makes it difficult to accurately assess the EMF in a specific urban area, as Spectrum cartography (SC) relies on a set of measurements recorded by spatially distributed sensors for the generation of exposure maps. However, when the spatial sampling rate is limited, significant estimation errors occur. To overcome this issue, the exposure map estimation is addressed as a missing data imputation task. We compute a convolutional neural tangent kernel (CNTK) for an infinitely wide convolutional neural network whose training dynamics can be completely described by a closed-form formula. This CNTK is employed to impute the target matrix and estimate EMF exposure from few sensors sparsely located in an urban environment. Experimental results show that the kernel, even when only sparse sensor data are available, can produce accurate estimates. It is a promising solution for exposure map reconstruction that does not require large training sets. The proposed method is compared with other deep learning approaches and Gaussian Process regression.