# Deep Learning for Estimation and Pilot Signal Design in Few-Bit Massive MIMO Systems

arXiv: https://arxiv.org/abs/2107.11958 · HTML: https://mlsanity.com/paper/2107.11958/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 54 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Learning to Detect](https://mlsanity.com/paper/1805.07631/) (2018)
- [Adaptive Neural Signal Detection for Massive MIMO](https://mlsanity.com/paper/1906.04610/) (2019)
- [LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers](https://mlsanity.com/paper/2102.02993/) (2021)
- [Channel Estimation for One-Bit Multiuser Massive MIMO Using Conditional GAN](https://mlsanity.com/paper/2006.11435/) (2020)
- [Deep Learning for Massive MIMO with 1-Bit ADCs: When More Antennas Need Fewer Pilots](https://mlsanity.com/paper/1910.06960/) (2019)
- [SVM-based Channel Estimation and Data Detection for One-Bit Massive MIMO Systems](https://mlsanity.com/paper/2003.10678/) (2020)
- [Linear and Deep Neural Network-based Receivers for Massive MIMO Systems with One-Bit ADCs](https://mlsanity.com/paper/2008.03757/) (2020)
- [Deep Learning-Aided Tabu Search Detection for Large MIMO Systems](https://mlsanity.com/paper/1909.01683/) (2019)
- [Robust Data Detection for MIMO Systems with One-Bit ADCs: A Reinforcement Learning Approach](https://mlsanity.com/paper/1903.12546/) (2019)
- [Deep Learning based Channel Estimation for Massive MIMO with Mixed-Resolution ADCs](https://mlsanity.com/paper/1908.06245/) (2019)
- [Neural Network-Optimized Channel Estimator and Training Signal Design for MIMO Systems with Few-Bit ADCs](https://mlsanity.com/paper/2003.09007/) (2020)
- [Linearized Binary Regression](https://mlsanity.com/paper/1802.00430/) (2018)
- [Supervised and Semi-Supervised Learning for MIMO Blind Detection with Low-Resolution ADCs](https://mlsanity.com/paper/1906.04090/) (2019)
- [Two-Stage Learning for Uplink Channel Estimation in One-Bit Massive MIMO](https://mlsanity.com/paper/1911.12461/) (2019)
- [Dominant Channel Estimation via MIPS for Large-Scale Antenna Systems with One-Bit ADCs](https://mlsanity.com/paper/1808.06754/) (2018)
- [Channel Estimation for Spatially/Temporally Correlated Massive MIMO Systems with One-Bit ADCs](https://mlsanity.com/paper/1910.13243/) (2019)
- [Channel Estimation via Gradient Pursuit for MmWave Massive MIMO Systems with One-Bit ADCs](https://mlsanity.com/paper/1912.08524/) (2019)
- [A design framework for all-digital mmWave massive MIMO with per-antenna nonlinearities](https://mlsanity.com/paper/1912.11643/) (2019)
- [ADMM-Based One-Bit Quantized Signal Detection for Massive MIMO Systems with Hardware Impairments](https://mlsanity.com/paper/2002.01698/) (2020)
- [Algorithm and VLSI Design for 1-bit Data Detection in Massive MIMO-OFDM](https://mlsanity.com/paper/2009.02068/) (2020)

## Built on by (most cited first, 4 of 4)

- [Variational Bayes for Joint Channel Estimation and Data Detection in Few-Bit Massive MIMO Systems](https://mlsanity.com/paper/2212.01717/) (2022)
- [Knowledge and Data Dual-Driven Channel Estimation and Feedback for Ultra-Massive MIMO Systems under Hybrid Field Beam Squint Effect](https://mlsanity.com/paper/2403.12813/) (2024)
- [Deep-Learning-Based Channel Estimation for Distributed MIMO with 1-bit Radio-Over-Fiber Fronthaul](https://mlsanity.com/paper/2406.11325/) (2024)
- [MIMO Detection with Spatial Sigma-Delta ADCs: A Variational Bayesian Approach](https://mlsanity.com/paper/2410.03891/) (2024)

## Abstract (arXiv)

Estimation in few-bit MIMO systems is challenging, since the received signals are nonlinearly distorted by the low-resolution ADCs. In this paper, we propose a deep learning framework for channel estimation, data detection, and pilot signal design to address the nonlinearity in such systems. The proposed channel estimation and data detection networks are model-driven and have special structures that take advantage of the domain knowledge in the few-bit quantization process. While the first data detection network, namely B-DetNet, is based on a linearized model obtained from the Bussgang decomposition, the channel estimation network and the second data detection network, namely FBM-CENet and FBM-DetNet respectively, rely on the original quantized system model. To develop FBM-CENet and FBM-DetNet, the maximum-likelihood channel estimation and data detection problems are reformulated to overcome the vanishing gradient issue. An important feature of the proposed FBM-CENet structure is that the pilot matrix is integrated into its weight matrices of the channel estimator. Thus, training the proposed FBM-CENet enables a joint optimization of both the channel estimator at the base station and the pilot signal transmitted from the users. Simulation results show significant performance gain in estimation accuracy by the proposed deep learning framework.