Codebook-Based Downlink Beamforming with Imperfect CSI Using Model-Driven Deep Learning

Robust energy-efficient codebook (CB)-based down-link power allocation and precoding in MU-MISO wireless systems is considered. While model-based optimization algorithms for imperfect channel state information (CSI) scenarios often suffer from a high computational cost, deep learning (DL)-based methods with generic neural network architectures require large training data sets and lack the explainability for operation in critical systems. To address these problems, a computationally efficient model-aided DL approach that unrolls an optimization-based iterative algorithm for CB-based beamforming with a power minimization objective under quality of service (QoS) constraints is proposed. The key idea is to augment the QoS constraints with parametric functions that predict interference due to the CSI error. The model is trained end-to-end using a novel learning scheme with an adaptive loss function under approximated outage probability constraints, thereby considering different levels of CSI degradation. Experiments demonstrate the generalization of the proposed model over varying CSI error levels and the number of users.