# LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers

arXiv: https://arxiv.org/abs/2102.02993 · HTML: https://mlsanity.com/paper/2102.02993/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 62 references that are in the map.
- First posted on arXiv 5 Feb 2021.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [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)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [What Will 5G Be?](https://mlsanity.com/paper/1405.2957/) (2014)
- [ViterbiNet: A Deep Learning Based Viterbi Algorithm for Symbol Detection](https://mlsanity.com/paper/1905.10750/) (2019)
- [DeepSIC: Deep Soft Interference Cancellation for Multiuser MIMO Detection](https://mlsanity.com/paper/2002.03214/) (2020)
- [Deep Task-Based Quantization](https://mlsanity.com/paper/1908.06845/) (2019)
- [Dynamic Metasurface Antennas for 6G Extreme Massive MIMO Communications](https://mlsanity.com/paper/2006.07838/) (2020)
- [Data-Driven Symbol Detection via Model-Based Machine Learning](https://mlsanity.com/paper/2002.07806/) (2020)
- [Deep Signal Recovery with One-Bit Quantization](https://mlsanity.com/paper/1812.00797/) (2018)
- [Data-Driven Factor Graphs for Deep Symbol Detection](https://mlsanity.com/paper/2002.00758/) (2020)
- [Multilevel MIMO Detection with Deep Learning](https://mlsanity.com/paper/1812.01571/) (2018)
- [Trainable Projected Gradient Detector for Massive Overloaded MIMO Channels: Data-driven Tuning Approach](https://mlsanity.com/paper/1812.10044/) (2018)
- [Deep Learning for Massive MIMO with 1-Bit ADCs: When More Antennas Need Fewer Pilots](https://mlsanity.com/paper/1910.06960/) (2019)
- [One-Bit Radar Processing with Time-Varying Sampling Thresholds](https://mlsanity.com/paper/1911.10170/) (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)
- [Task-Based Analog-to-Digital Converters](https://mlsanity.com/paper/2009.14088/) (2020)
- [BiLiMO: Bit-Limited MIMO Radar via Task-Based Quantization](https://mlsanity.com/paper/2010.00195/) (2020)
- [Unfolded Algorithms for Deep Phase Retrieval](https://mlsanity.com/paper/2012.11102/) (2020)
- [Autoencoder-Based Error Correction Coding for One-Bit Quantization](https://mlsanity.com/paper/1909.12120/) (2019)
- [UPR: A Model-Driven Architecture for Deep Phase Retrieval](https://mlsanity.com/paper/2003.04396/) (2020)
- [RF Chain Reduction for MIMO Systems: A Hardware Prototype](https://mlsanity.com/paper/1905.05315/) (2019)
- [Massive MIMO Channel Estimation with Low-Resolution Spatial Sigma-Delta ADCs](https://mlsanity.com/paper/2005.07752/) (2020)
- [Detection Algorithms for Communication Systems Using Deep Learning](https://mlsanity.com/paper/1705.08044/) (2017)
- [One-Bit OFDM Receivers via Deep Learning](https://mlsanity.com/paper/1811.00971/) (2018)
- [One-bit LFMCW Radar: Spectrum Analysis and Target Detection](https://mlsanity.com/paper/1905.09440/) (2019)

## Built on by (most cited first, 11 of 11)

- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)
- [Deep Learning for Estimation and Pilot Signal Design in Few-Bit Massive MIMO Systems](https://mlsanity.com/paper/2107.11958/) (2021)
- [Design and Analysis of Hardware-limited Non-uniform Task-based Quantizers](https://mlsanity.com/paper/2208.07525/) (2022)
- [Variational Bayes for Joint Channel Estimation and Data Detection in Few-Bit Massive MIMO Systems](https://mlsanity.com/paper/2212.01717/) (2022)
- [Limited Communications Distributed Optimization via Deep Unfolded Distributed ADMM](https://mlsanity.com/paper/2309.14353/) (2023)
- [Learning minimal volume uncertainty ellipsoids](https://mlsanity.com/paper/2405.02441/) (2024)
- [One-Bit Compressive Sensing: Can We Go Deep and Blind?](https://mlsanity.com/paper/2203.11278/) (2022)
- [Deep Learning Meets Adaptive Filtering: A Stein's Unbiased Risk Estimator Approach](https://mlsanity.com/paper/2307.16708/) (2023)
- [MIMO Detection with Spatial Sigma-Delta ADCs: A Variational Bayesian Approach](https://mlsanity.com/paper/2410.03891/) (2024)

## Abstract (arXiv)

The need to recover high-dimensional signals from their noisy low-resolution quantized measurements is widely encountered in communications and sensing. In this paper, we focus on the extreme case of one-bit quantizers, and propose a deep detector entitled LoRD-Net for recovering information symbols from one-bit measurements. Our method is a model-aware data-driven architecture based on deep unfolding of first-order optimization iterations. LoRD-Net has a task-based architecture dedicated to recovering the underlying signal of interest from the one-bit noisy measurements without requiring prior knowledge of the channel matrix through which the one-bit measurements are obtained. The proposed deep detector has much fewer parameters compared to black-box deep networks due to the incorporation of domain-knowledge in the design of its architecture, allowing it to operate in a data-driven fashion while benefiting from the flexibility, versatility, and reliability of model-based optimization methods. LoRD-Net operates in a blind fashion, which requires addressing both the non-linear nature of the data-acquisition system as well as identifying a proper optimization objective for signal recovery. Accordingly, we propose a two-stage training method for LoRD-Net, in which the first stage is dedicated to identifying the proper form of the optimization process to unfold, while the latter trains the resulting model in an end-to-end manner. We numerically evaluate the proposed receiver architecture for one-bit signal recovery in wireless communications and demonstrate that the proposed hybrid methodology outperforms both data-driven and model-based state-of-the-art methods, while utilizing small datasets, on the order of merely ~ 500 samples, for training.