Hybrid Precoding Optimization for mmWave Massive MIMO with Finite Blocklength

Hybrid digital-analog precoding is a pivotal transmission technique to balance communication performance and hardware costs associated with radio frequency (RF) chains in millimeter wave (mmWave) massive multiple-input multipleoutput (MIMO). However, most existing designs utilize Shannon rate and assume an infinite blocklength, which is impractical for emerging finite blocklength (FBL) applications, such as massive machine-type communications. To fill in this gap, this paper investigates hybrid precoding optimization in the FBL regime. The aim is to maximize the weighted sumrate (WSR), while fulfilling the transmit power budget at the base station (BS) and users' minimum rate requirements. The formulated optimization problem is highly challenging to solve, particularly due to the complex and nonconcave FBL rate function and the intricate coupling between analog and digital precoders. To tackle these issues, we propose a computationally efficient solution based on the penalty dual decomposition (PDD) method, which is guaranteed to converge to the Karush-KuhnTucker (KKT) solutions under mild conditions. Simulation results demonstrate that our proposed hybrid precoding design significantly outperforms several baseline schemes, especially those ignoring the impact of blocklength and adopting Shannon rate as the performance metric.