  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.
