Stochastic Successive Convex Optimization for Two-Timescale Hybrid Precoding in Massive MIMO

Hybrid precoding, which consists of an RF precoder and a baseband precoder, is a popular precoding architecture for massive multiple-input multiple-output (MIMO) due to its low hardware cost and power consumption. In conventional hybrid precoding, both RF and baseband precoders are adaptive to the real-time channel state information. As a result, an individual RF precoder is required for each subcarrier in wideband systems, leading to high implementation cost. To overcome this issue, two-timescale hybrid precoding (THP), which adapts the RF precoder to the channel statistics, has been proposed. Since the channel statistics are approximately the same over different subcarriers, only a single RF precoder is required in THP. Despite the advantages of THP, there lacks a unified and efficient algorithm for its optimization due to the nonconvex and stochastic nature of the problem. Based on stochastic successive convex approximation (SSCA), we propose an online algorithmic framework called SSCA-THP for general THP optimization problems, in which the hybrid precoder is updated by solving a quadratic surrogate optimization problem whenever a new channel sample is obtained. Then, we prove the convergence of SSCA-THP to stationary points. Finally, we apply SSCA-THP to solve three important THP optimization problems and verify its advantages over existing solutions.