Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Channel Estimation by Infinite Width Convolutional Networks

Mohammed Mallik, Guillaume Villemaud

TL;DR

This work tackles sparse-pilot channel estimation in OFDM by formulating it as kernel regression via an infinite-width convolutional neural tangent kernel (CNTK). The proposed Channel-CNTK leverages a CNTK derived from an infinitely wide CNN to impute the full time-frequency channel image $H \\in \\mathbb{C}^{M imes N}$ from sparse pilot data, without requiring a large training dataset. A Local Image Prior initialized from the pilot-based LS estimate $H^p_{LS}$ is used to encode spatial structure, enabling accurate and fast channel reconstruction with reduced computational resources. Empirical results on realistic MATLAB 5G TD-L channels show Channel-CNTK outperforming deep learning baselines in speed and NMSE across pilot densities and SNRs, highlighting its practicality for real-world deployment and potential extension to uplink, downlink, and MIMO settings.

Abstract

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.

Channel Estimation by Infinite Width Convolutional Networks

TL;DR

This work tackles sparse-pilot channel estimation in OFDM by formulating it as kernel regression via an infinite-width convolutional neural tangent kernel (CNTK). The proposed Channel-CNTK leverages a CNTK derived from an infinitely wide CNN to impute the full time-frequency channel image from sparse pilot data, without requiring a large training dataset. A Local Image Prior initialized from the pilot-based LS estimate is used to encode spatial structure, enabling accurate and fast channel reconstruction with reduced computational resources. Empirical results on realistic MATLAB 5G TD-L channels show Channel-CNTK outperforming deep learning baselines in speed and NMSE across pilot densities and SNRs, highlighting its practicality for real-world deployment and potential extension to uplink, downlink, and MIMO settings.

Abstract

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.

Paper Structure

This paper contains 15 sections, 7 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Methodology
  4. Inverse Problem Formulation
  5. Image of Channel Response Time–frequency Grid
  6. Neural Tangent Kernels
  7. CNN model architecture
  8. Estimating the Channel
  9. Numerical Results
  10. Evaluation Metric
  11. Implementation details and datasets
  12. Visual Analysis
  13. Quantitative Analysis and Impact of pilot Density
  14. Comparative analysis of time efficiency of the algorithms
  15. Conclusion

Figures (4)

  • Figure 1: An overview of the proposed Channel-CNTK method, which accurately and quickly estimates channel response by exploiting the width limits of neural networks. The main contribution lies in the computation of kernels.
  • Figure 2: Example of a sample of channel time-frequency response images. (a) The received signal $Y$, (b) transmitted symbols $X$, (c) channel response at pilot locations $H^p_{LS}$ (the target matrix which we want to impute), (d) perfect channel estimate $H_{perf}$, by MATLAB 5G toolbox 5gToolbox.
  • Figure 3: Estimated Channels by different methods. (a) and (b) shows the estimation by DNN and cGAN model, (c) and (d) shows the fuzzy and degraded channel estimate from KNN and linear, (e) showcases our Channel-CNTK estimation and (f) is the perfect channel estimation from MATLAB for comparison which was not used for estimation.
  • Figure 4: Performance of different methods with varying SNRs