Fast 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.