# Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems

arXiv: https://arxiv.org/abs/2006.08099 · HTML: https://mlsanity.com/paper/2006.08099/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 30 of 44)

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- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Data-Driven Deep Learning Based Hybrid Beamforming for Aerial Massive MIMO-OFDM Systems with Implicit CSI](https://mlsanity.com/paper/2201.06778/) (2022)
- [Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO with Lens Arrays](https://mlsanity.com/paper/2101.01336/) (2021)
- [Neural Calibration for Scalable Beamforming in FDD Massive MIMO with Implicit Channel Estimation](https://mlsanity.com/paper/2108.01529/) (2021)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [Algorithm Unrolling for Massive Access via Deep Neural Network with Theoretical Guarantee](https://mlsanity.com/paper/2106.10426/) (2021)
- [Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networks](https://mlsanity.com/paper/2201.11799/) (2022)
- [Privacy-Preserving Decentralized Inference with Graph Neural Networks in Wireless Networks](https://mlsanity.com/paper/2208.06963/) (2022)
- [Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling](https://mlsanity.com/paper/2105.01853/) (2021)
- [Learn to Communicate with Neural Calibration: Scalability and Generalization](https://mlsanity.com/paper/2110.00272/) (2021)
- [Deep Learning-Based Rate-Splitting Multiple Access for Reconfigurable Intelligent Surface-Aided Tera-Hertz Massive MIMO](https://mlsanity.com/paper/2209.08456/) (2022)
- [Optimization Guarantees of Unfolded ISTA and ADMM Networks With Smooth Soft-Thresholding](https://mlsanity.com/paper/2309.06195/) (2023)
- [Deep Joint Semantic Coding and Beamforming for Near-Space Airship-Borne Massive MIMO Network](https://mlsanity.com/paper/2405.19889/) (2024)
- [Two-Timescale End-to-End Learning for Channel Acquisition and Hybrid Precoding](https://mlsanity.com/paper/2110.12059/) (2021)
- [A Model-based GNN for Learning Precoding](https://mlsanity.com/paper/2212.00860/) (2022)
- [Generative Diffusion Receivers: Achieving Pilot-Efficient MIMO-OFDM Communications](https://mlsanity.com/paper/2506.18419/) (2025)
- [Stability Analysis of Unfolded WMMSE for Power Allocation](https://mlsanity.com/paper/2110.07471/) (2021)
- [DDPG-Driven Deep-Unfolding with Adaptive Depth for Channel Estimation with Sparse Bayesian Learning](https://mlsanity.com/paper/2201.08477/) (2022)
- [Deep Learning for Multi-User MIMO Systems: Joint Design of Pilot, Limited Feedback, and Precoding](https://mlsanity.com/paper/2209.10332/) (2022)
- [Distributed-Training-and-Execution Multi-Agent Reinforcement Learning for Power Control in HetNet](https://mlsanity.com/paper/2212.07967/) (2022)
- [Generalization analysis of an unfolding network for analysis-based Compressed Sensing](https://mlsanity.com/paper/2303.05582/) (2023)
- [A Semi-amortized Lifted Learning-to-Optimize Masked (SALLO-M) Transformer Model for Scalable and Generalizable Beamforming](https://mlsanity.com/paper/2510.13077/) (2025)
- [Photothermal-SR-Net: A Customized Deep Unfolding Neural Network for Photothermal Super Resolution Imaging](https://mlsanity.com/paper/2104.10563/) (2021)
- [Augmented Deep Unfolding for Downlink Beamforming in Multi-cell Massive MIMO With Limited Feedback](https://mlsanity.com/paper/2209.01436/) (2022)

## Abstract (arXiv)

Optimization theory assisted algorithms have received great attention for precoding design in multiuser multiple-input multiple-output (MU-MIMO) systems. Although the resultant optimization algorithms are able to provide excellent performance, they generally require considerable computational complexity, which gets in the way of their practical application in real-time systems. In this work, in order to address this issue, we first propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed in matrix form to better solve the problems in communication systems. Then, we implement the proposed deepunfolding framework to solve the sum-rate maximization problem for precoding design in MU-MIMO systems. An efficient IAIDNN based on the structure of the classic weighted minimum mean-square error (WMMSE) iterative algorithm is developed. Specifically, the iterative WMMSE algorithm is unfolded into a layer-wise structure, where a number of trainable parameters are introduced to replace the highcomplexity operations in the forward propagation. To train the network, a generalized chain rule of the IAIDNN is proposed to depict the recurrence relation of gradients between two adjacent layers in the back propagation. Moreover, we discuss the computational complexity and generalization ability of the proposed scheme. Simulation results show that the proposed IAIDNN efficiently achieves the performance of the iterative WMMSE algorithm with reduced computational complexity.