  In the paper we study a deep learning based method to solve the multicell
power control problem for sum rate maximization subject to per-user rate
constraints and per-base station (BS) power constraints. The core difficulty of
this problem is how to ensure that the learned power control results by the
deep neural network (DNN) satisfy the per-user rate constraints. To tackle the
difficulty, we propose to cascade a projection block after a traditional DNN,
which projects the infeasible power control results onto the constraint set.
The projection block is designed based on a geometrical interpretation of the
constraints, which is of low complexity, meeting the real-time requirement of
online applications. Explicit-form expression of the backpropagated gradient is
derived for the proposed projection block, with which the DNN can be trained to
directly maximize the sum rate via unsupervised learning. We also develop a
heuristic implementation of the projection block to reduce the size of DNN.
Simulation results demonstrate the advantages of the proposed method over
existing deep learning and numerical optimization~methods, and show the
robustness of the proposed method with the model mismatch between training and
testing~datasets.
