# Over-the-Air Design of GAN Training for mmWave MIMO Channel Estimation

arXiv: https://arxiv.org/abs/2205.12445 · HTML: https://mlsanity.com/paper/2205.12445/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 61 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Model Pruning Enables Efficient Federated Learning on Edge Devices](https://mlsanity.com/paper/1909.12326/) (2019)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Generative Models for Effective ML on Private, Decentralized Datasets](https://mlsanity.com/paper/1911.06679/) (2019)
- [Convolutional Neural Networks at Constrained Time Cost](https://mlsanity.com/paper/1412.1710/) (2014)
- [Adaptive Quantization of Model Updates for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2102.04487/) (2021)
- [MD-GAN: Multi-Discriminator Generative Adversarial Networks for Distributed Datasets](https://mlsanity.com/paper/1811.03850/) (2018)
- [High Dimensional Channel Estimation Using Deep Generative Networks](https://mlsanity.com/paper/2006.13494/) (2020)
- [Robust Compressed Sensing using Generative Models](https://mlsanity.com/paper/2006.09461/) (2020)
- [Task-Aware Compressed Sensing with Generative Adversarial Networks](https://mlsanity.com/paper/1802.01284/) (2018)
- [Wideband Channel Estimation with A Generative Adversarial Network](https://mlsanity.com/paper/2012.12063/) (2020)
- [MEGAN: Mixture of Experts of Generative Adversarial Networks for Multimodal Image Generation](https://mlsanity.com/paper/1805.02481/) (2018)
- [Physical Layer Communications System Design Over-the-Air Using Adversarial Networks](https://mlsanity.com/paper/1803.03145/) (2018)
- [WGAN-based Autoencoder Training Over-the-air](https://mlsanity.com/paper/2003.02744/) (2020)
- [MIMO-GAN: Generative MIMO Channel Modeling](https://mlsanity.com/paper/2203.08588/) (2022)
- [Initial Access in 5G mm-Wave Cellular Networks](https://mlsanity.com/paper/1602.07731/) (2016)
- [Robust One-Bit Recovery via ReLU Generative Networks: Near-Optimal Statistical Rate and Global Landscape Analysis](https://mlsanity.com/paper/1908.05368/) (2019)
- [Score-Based Generative Models for Robust Channel Estimation](https://mlsanity.com/paper/2111.08177/) (2021)
- [DeepWiPHY: Deep Learning-based Receiver Design and Dataset for IEEE 802.11ax Systems](https://mlsanity.com/paper/2010.09268/) (2020)

## Built on by (most cited first, 5 of 5)

- [Generative Diffusion Models for High Dimensional Channel Estimation](https://mlsanity.com/paper/2408.10501/) (2024)
- [Generating High Dimensional User-Specific Wireless Channels using Diffusion Models](https://mlsanity.com/paper/2409.03924/) (2024)
- [Leveraging Variational Autoencoders for Parameterized MMSE Estimation](https://mlsanity.com/paper/2307.05352/) (2023)
- [A Comprehensive Survey on Network Traffic Synthesis: From Statistical Models to Deep Learning](https://mlsanity.com/paper/2507.01976/) (2025)
- [On optimal solutions of classical and sliced Wasserstein GANs with non-Gaussian data](https://mlsanity.com/paper/2509.06505/) (2025)

## Abstract (arXiv)

Future wireless systems are trending towards higher carrier frequencies that offer larger communication bandwidth but necessitate the use of large antenna arrays. Existing signal processing techniques for channel estimation do not scale well to this "high-dimensional" regime in terms of performance and pilot overhead. Meanwhile, training deep learning based approaches for channel estimation requires large labeled datasets mapping pilot measurements to clean channel realizations, which can only be generated offline using simulated channels. In this paper, we develop a novel unsupervised over-the-air (OTA) algorithm that utilizes noisy received pilot measurements to train a deep generative model to output beamspace MIMO channel realizations. Our approach leverages Generative Adversarial Networks (GAN), while using a conditional input to distinguish between Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) channel realizations. We also present a federated implementation of the OTA algorithm that distributes the GAN training over multiple users and greatly reduces the user side computation. We then formulate channel estimation from a limited number of pilot measurements as an inverse problem and reconstruct the channel by optimizing the input vector of the trained generative model. Our proposed approach significantly outperforms Orthogonal Matching Pursuit on both LOS and NLOS channel models, and EM-GM-AMP -- an Approximate Message Passing algorithm -- on LOS channel models, while achieving comparable performance on NLOS channel models in terms of the normalized channel reconstruction error. More importantly, our proposed framework has the potential to be trained online using real noisy pilot measurements, is not restricted to a specific channel model and can even be utilized for a federated OTA design of a dataset generator from noisy data.