# High Dimensional Channel Estimation Using Deep Generative Networks

arXiv: https://arxiv.org/abs/2006.13494 · HTML: https://mlsanity.com/paper/2006.13494/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2020.

## Built on by (most cited first, 30 of 35)

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization](https://mlsanity.com/paper/2308.05384/) (2023)
- [MIMO Channel Estimation using Score-Based Generative Models](https://mlsanity.com/paper/2204.07122/) (2022)
- [Generative Diffusion Models for High Dimensional Channel Estimation](https://mlsanity.com/paper/2408.10501/) (2024)
- [Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation](https://mlsanity.com/paper/2403.03545/) (2024)
- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [Generating High Dimensional User-Specific Wireless Channels using Diffusion Models](https://mlsanity.com/paper/2409.03924/) (2024)
- [Generative Diffusion Models for Wireless Networks: Fundamental, Architecture, and State-of-the-Art](https://mlsanity.com/paper/2507.16733/) (2025)
- [Applications of Generative AI (GAI) for Mobile and Wireless Networking: A Survey](https://mlsanity.com/paper/2405.20024/) (2024)
- [Score-Based Generative Models for Robust Channel Estimation](https://mlsanity.com/paper/2111.08177/) (2021)
- [Leveraging Variational Autoencoders for Parameterized MMSE Estimation](https://mlsanity.com/paper/2307.05352/) (2023)
- [Over-the-Air Design of GAN Training for mmWave MIMO Channel Estimation](https://mlsanity.com/paper/2205.12445/) (2022)
- [Channel Estimation for Quantized Systems based on Conditionally Gaussian Latent Models](https://mlsanity.com/paper/2309.04014/) (2023)
- [Diffusion Models for Accurate Channel Distribution Generation](https://mlsanity.com/paper/2309.10505/) (2023)
- [Successive Interference Cancellation-aided Diffusion Models for Joint Channel Estimation and Data Detection in Low Rank Channel Scenarios](https://mlsanity.com/paper/2501.11229/) (2025)
- [Generative Diffusion Receivers: Achieving Pilot-Efficient MIMO-OFDM Communications](https://mlsanity.com/paper/2506.18419/) (2025)
- [End-to-End Autoencoder Communications with Optimized Interference Suppression](https://mlsanity.com/paper/2201.01388/) (2021)
- [Blind Estimation of a Doubly Selective OFDM Channel: A Deep Learning Algorithm and Theory](https://mlsanity.com/paper/2206.07483/) (2022)
- [Enhancements in Score-based Channel Estimation for Real-Time Wireless Systems](https://mlsanity.com/paper/2509.07839/) (2025)
- [An Encoder-Decoder Network for Beamforming over Sparse Large-Scale MIMO Channels](https://mlsanity.com/paper/2510.02355/) (2025)
- [Transfer Learning Capabilities of Untrained Neural Networks for MIMO CSI Recreation](https://mlsanity.com/paper/2111.07858/) (2021)
- [Outage Performance and Novel Loss Function for an ML-Assisted Resource Allocation: An Exact Analytical Framework](https://mlsanity.com/paper/2305.09739/) (2023)
- [Channel Fingerprint Construction for Massive MIMO: A Deep Conditional Generative Approach](https://mlsanity.com/paper/2505.07893/) (2025)
- [To Trust or Not to Trust: On Calibration in ML-based Resource Allocation for Wireless Networks](https://mlsanity.com/paper/2507.17494/) (2025)
- [Non-Identical Diffusion Models in MIMO-OFDM Channel Generation](https://mlsanity.com/paper/2509.01641/) (2025)
- [EVT-Based Generative AI for Tail-Aware Channel Estimation](https://mlsanity.com/paper/2604.25008/) (2026)
- [Gan-Based Joint Activity Detection and Channel Estimation For Grant-free Random Access](https://mlsanity.com/paper/2204.01731/) (2022)
- [A Comparative Study of Deep Learning and Iterative Algorithms for Joint Channel Estimation and Signal Detection in OFDM Systems](https://mlsanity.com/paper/2303.03678/) (2023)
- [Enhancing Channel Estimation in Quantized Systems with a Generative Prior](https://mlsanity.com/paper/2405.03542/) (2024)
- [MCRB for Parameter Estimation from One-Bit Quantized and Oversampled Measurements](https://mlsanity.com/paper/2503.22860/) (2025)

## Abstract (arXiv)

This paper presents a novel compressed sensing (CS) approach to high dimensional wireless channel estimation by optimizing the input to a deep generative network. Channel estimation using generative networks relies on the assumption that the reconstructed channel lies in the range of a generative model. Channel reconstruction using generative priors outperforms conventional CS techniques and requires fewer pilots. It also eliminates the need of a priori knowledge of the sparsifying basis, instead using the structure captured by the deep generative model as a prior. Using this prior, we also perform channel estimation from one-bit quantized pilot measurements, and propose a novel optimization objective function that attempts to maximize the correlation between the received signal and the generator's channel estimate while minimizing the rank of the channel estimate. Our approach significantly outperforms sparse signal recovery methods such as Orthogonal Matching Pursuit (OMP) and Approximate Message Passing (AMP) algorithms such as EM-GM-AMP for narrowband mmWave channel reconstruction, and its execution time is not noticeably affected by the increase in the number of received pilot symbols.