# DDPG-Driven Deep-Unfolding with Adaptive Depth for Channel Estimation with Sparse Bayesian Learning

arXiv: https://arxiv.org/abs/2201.08477 · HTML: https://mlsanity.com/paper/2201.08477/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 20 Jan 2022.

## Builds on (most cited first, 14 of 14)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems](https://mlsanity.com/paper/2006.08099/) (2020)
- [Tuning-free Plug-and-Play Proximal Algorithm for Inverse Imaging Problems](https://mlsanity.com/paper/2002.09611/) (2020)
- [Deep Reinforcement Learning for Dynamic Multichannel Access in Wireless Networks](https://mlsanity.com/paper/1802.06958/) (2018)
- [ViterbiNet: A Deep Learning Based Viterbi Algorithm for Symbol Detection](https://mlsanity.com/paper/1905.10750/) (2019)
- [Sharp Time--Data Tradeoffs for Linear Inverse Problems](https://mlsanity.com/paper/1507.04793/) (2015)
- [Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO with Lens Arrays](https://mlsanity.com/paper/2101.01336/) (2021)
- [FDD Massive MIMO Channel Estimation with Arbitrary 2D-Array Geometry](https://mlsanity.com/paper/1711.06548/) (2017)
- [Solving Sparse Linear Inverse Problems in Communication Systems: A Deep Learning Approach With Adaptive Depth](https://mlsanity.com/paper/2010.15376/) (2020)
- [Two-Timescale End-to-End Learning for Channel Acquisition and Hybrid Precoding](https://mlsanity.com/paper/2110.12059/) (2021)

## Built on by (most cited first, 2 of 2)

- [Multilinear Tensor Low-Rank Approximation for Policy-Gradient Methods in Reinforcement Learning](https://mlsanity.com/paper/2501.04879/) (2025)
- [Deep-Unfolding for Next-Generation Transceivers](https://mlsanity.com/paper/2305.08303/) (2023)

## Abstract (arXiv)

Deep-unfolding neural networks (NNs) have received great attention since they achieve satisfactory performance with relatively low complexity. Typically, these deep-unfolding NNs are restricted to a fixed-depth for all inputs. However, the optimal number of layers required for convergence changes with different inputs. In this paper, we first develop a framework of deep deterministic policy gradient (DDPG)-driven deep-unfolding with adaptive depth for different inputs, where the trainable parameters of deep-unfolding NN are learned by DDPG, rather than updated by the stochastic gradient descent algorithm directly. Specifically, the optimization variables, trainable parameters, and architecture of deep-unfolding NN are designed as the state, action, and state transition of DDPG, respectively. Then, this framework is employed to deal with the channel estimation problem in massive multiple-input multiple-output systems. Specifically, first of all we formulate the channel estimation problem with an off-grid basis and develop a sparse Bayesian learning (SBL)-based algorithm to solve it. Secondly, the SBL-based algorithm is unfolded into a layer-wise structure with a set of introduced trainable parameters. Thirdly, the proposed DDPG-driven deep-unfolding framework is employed to solve this channel estimation problem based on the unfolded structure of the SBL-based algorithm. To realize adaptive depth, we design the halting score to indicate when to stop, which is a function of the channel reconstruction error. Furthermore, the proposed framework is extended to realize the adaptive depth of the general deep neural networks (DNNs). Simulation results show that the proposed algorithm outperforms the conventional optimization algorithms and DNNs with fixed depth with much reduced number of layers.