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The millimeter wave (mmWave) multiuser multiple-input multiple-output(MU-MIMO) systems with discrete lens arrays (DLA) have received great attentiondue to their simple hardware implementation and excellent performance. In thiswork, we investigate the joint design of beam selection and digital precodingmatrices for mmWave MU-MIMO systems with DLA to maximize the sum-rate subjectto the transmit power constraint and the constraints of the selection matrixstructure. The investigated non-convex problem with discrete variables andcoupled constraints is challenging to solve and an efficient framework of jointneural network (NN) design is proposed to tackle it. Specifically, the proposedframework consists of a deep reinforcement learning (DRL)-based NN and adeep-unfolding NN, which are employed to optimize the beam selection anddigital precoding matrices, respectively. As for the DRL-based NN, we formulatethe beam selection problem as a Markov decision process and a double deepQ-network algorithm is developed to solve it. The base station is considered tobe an agent, where the state, action, and reward function are carefullydesigned. Regarding the design of the digital precoding matrix, we develop aniterative weighted minimum mean-square error algorithm induced deep-unfoldingNN, which unfolds this algorithm into a layerwise structure with introducedtrainable parameters. Simulation results verify that this jointly trained NNremarkably outperforms the existing iterative algorithms with reducedcomplexity and stronger robustness.

Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO with Lens Arrays