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

TL;DR

This paper introduces a DDPG-driven deep-unfolding neural network with adaptive depth for channel estimation in MIMO systems, improving performance and reducing complexity by dynamically adjusting the number of layers based on input.

Contribution

It proposes a novel framework combining deep-unfolding with reinforcement learning to adaptively determine network depth, specifically applied to channel estimation with sparse Bayesian learning.

Findings

Outperforms fixed-depth DNNs and traditional algorithms in accuracy.

Reduces the number of layers needed for convergence.

Demonstrates effective adaptive depth control in simulations.

Abstract

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.