# Hybrid Precoding Design for Subarray-Structure-Enabled mmWave URLLC System
## 1 Introduction  
Ultra-reliable low-latency communication (URLLC) is one of the most creative technologies in fifth generation (5G) communication, which is widely used in many fields such as industrial production, smart medical care, the internet of vehicles, electric power control, and so on [1, 2]. According to the third generation project of the URLLC, the latency of the transmission should be less than 1 ms, and the block error rate should be less than \(10^{-5}\)[3]. The rapid development of 5G has resulted in a significant increase in demand for spectrum resources, making them increasingly scarce and valuable.  
This scarcity has led researchers to explore new techniques for enhancing the capacity of cellular networks without increasing the cell density [4]. One such technique is the use of millimeter-wave (mmWave) communication, which has garnered significant attention due to its ability to provide large bandwidth and a high transmission rate of up to gigabit-per-second [5]. To overcome the fading of the mmWave channel, precoding technology can be employed. Compared with traditional all-digital precoding, hybrid precoding can effectively reduce the system hardware complexity and improve the communication performance due to the lower number of radio frequency (RF) links [6]. The existing hybrid architecture schemes can be divided into two categories: fully connected architecture and subarray-connected architecture [7]. Compared with the fully connected architecture, the number of phase shifters (PSs) in the subarray-connected architecture is much lower.  
In recent years, there has been a significant increase in research related to URLLC. Researchers have explored various approaches to optimize the design of the bandwidth,power allocation, beamforming, and other system parameters. One such approach was proposed in [8], which considered a multiuser URLLC scenario and aimed to optimize the maximum throughput of a downlink single-input single-output (SISO) and multiple-input multiple-output (MIMO) system. The proposed approach employed a path tracking algorithm to design the optimal digital precoding matrix, which could enhance the system capacity and improve the communication performance. A URLLC downlink MIMO communication model with the optimization objective of maximizing energy efficiency was adapted in [9], by constraining the block error rate and transmit power, and an iterative optimization algorithm was applied to design the all-digital precoding matrix. A hybrid precoding scheme for mmWave MIMO with a subarray-connected structure was designed in [10], which leveraged the Kronecker product to establish a coupled scheme of digital and analog precoders. The proposed scheme was shown to outperform traditional successive interference cancellation (SIC) algorithms in terms of performance, offering promising potential for enhancing the system capacity and communication performance in mmWave MIMO systems.  
It can be observed that current research on URLLC typically focuses on the design of all-digital precoders, and the research on designing hybrid precoders in the mmWave frequency band is more oriented towards traditional communication scenarios [11; 12]. As we can see, the research on the precoding design for a mmWave URLLC system is limited. Therefore, this paper investigates the precoding design for a subarray-structure-enabled mmWave URLLC system. The methods and results of this research can provide some reference for the practical application of technology in communication scenarios.  
In order to facilitate the analysis of the nonconvex optimization problem, we utilize the rate optimization algorithm and the hybrid precoder alternating minimization algorithm. The simulation results show that our algorithms can solve the new scenario optimization problem, and the hybrid precoder with a subarray structure performs better than a fully connected hybrid precoder and all-digital precoder.