Channel Estimation by Infinite Width Convolutional Networks

In wireless communications, estimation of channels in OFDM systems spans frequency and time, which relies on sparse collections of pilot data, posing an ill-posed inverse problem. Moreover, deep learning estimators require large amounts of training data, computational resources, and true channels to produce accurate channel estimates, which are not realistic. To address this, a convolutional neural tangent kernel (CNTK) is derived from an infinitely wide convolutional network whose training dynamics can be expressed by a closed-form equation. This CNTK is used to impute the target matrix and estimate the missing channel response using only the known values available at pilot locations. This is a promising solution for channel estimation that does not require a large training set. Numerical results on realistic channel datasets demonstrate that our strategy accurately estimates the channels without a large dataset and significantly outperforms deep learning methods in terms of speed, accuracy, and computational resources.

GLIP: Electromagnetic Field Exposure Map Completion by Deep Generative Networks

In Spectrum cartography (SC), the generation of exposure maps for radio frequency electromagnetic fields (RF-EMF) spans dimensions of frequency, space, and time, which relies on a sparse collection of sensor data, posing a challenging ill-posed inverse problem. Cartography methods based on models integrate designed priors, such as sparsity and low-rank structures, to refine the solution of this inverse problem. In our previous work, EMF exposure map reconstruction was achieved by Generative Adversarial Networks (GANs) where physical laws or structural constraints were employed as a prior, but they require a large amount of labeled data or simulated full maps for training to produce efficient results. In this paper, we present a method to reconstruct EMF exposure maps using only the generator network in GANs which does not require explicit training, thus overcoming the limitations of GANs, such as using reference full exposure maps. This approach uses a prior from sensor data as Local Image Prior (LIP) captured by deep convolutional generative networks independent of learning the network parameters from images in an urban environment. Experimental results show that, even when only sparse sensor data are available, our method can produce accurate estimates.