Tree-Coding-Aided Adaptive-Cross-Entropy Algorithm for Hybrid Precoding With Low-Resolution Analog Phase Shifters

This paper considers the hybrid precoder design in millimeter wave (mmWave) multi-input multi-output (MIMO) systems with low-resolution analog phase shifters. Aiming at reducing the complexities of the near-optimal algorithms, we propose a low-complexity multi-user hybrid precoding scheme based on tree-coding-aided adaptive-cross-entroy (TC-ACE) algorithm. By defining some discrete variables for the analog precoders and combiners, the problem of hybrid precoding is transformed into a cross-entroy (CE) optimization problem, which can be solved by iteratively updating the probability distributions of the predefined discrete variables. In order to derive the closed-form expression of the probability distributions, tree-coding is used to encode each entry of the analog precoders and combiners with a binary number. Through iterations, optimal analog precoders and combiners will be obtained when its probabilities are sufficiently high. Simulation results show that when the number of users exceeds a certain value, the proposed scheme outperforms the alternating minimization algorithm and coordinate descent method in terms of both the sum-rate and complexity.