# Hybrid Precoding Design for Wireless Fading Channels
## 1 Introduction
These methods have excellent SER performance because they use both channel state information and the current information data values of each user to obtain a precoding vector for each symbol interval, but they have the disadvantage of greatly increasing computational complexity. Recently, among non-linear precoding techniques, much research has been conducted on the SLP technique, which has relatively less computational complexity than the DPC technique [16; 17; 18; 19; 20]. This technique defines a constructive interference region (CIR) in which inter-user interference helps improve receiver performance and SER performance by designing the interference signal so that the received signal exists in the CIR and is as far away from the decision boundary as possible. However, this technique still has the disadvantage of requiring significantly more calculations than linear precoding techniques because the precoding result must be obtained for each symbol duration. In particular, the SLP technique has the disadvantage that when the number of users increases or the number of transmitter antennas increases, its computational complexity increases significantly, making it difficult to actually implement [21; 22; 23; 24; 25]. In this paper, we propose a hybrid precoding technique that simultaneously applies linear precoding and non-linear precoding to appropriately control the SER performance and computational complexity of the entire system. When the number of users for which the base station needs to transmit data is high and the hardware performance of the base station is not satisfactory, it becomes impossible for the base station to apply non-linear precoding to all user data due to computational complexity. In such cases, the proposed technique divides users into two groups, namely User Group 1 and User Group 2. Therefore, to reduce the computational complexity required for applying precoding to the transmitter for the data of users belonging to Group 1, linear precoding is applied, while non-linear precoding is applied to the data of users belonging to Group 2 to enhance SER performance. When applying the existing linear precoding technique and non-linear precoding technique as they are, interference occurs between received signals with different precoding schemes, leading to significantly degraded SER performance. To prevent interference between received signals when applying two different types of precoding, we propose the orthogonal MMSE (OMMSE) precoding scheme and the orthogonal SLP (OSLP) scheme by utilizing the null space of the channel matrix for each user group. The OMMSE precoding matrix is designed to be orthogonal to the channels of User Group 2, while the OSLP precoding vector is designed to be orthogonal to the channels of User Group 1. This ensures that the received signals for User Group 1 do not contain signals from User Group 2, and vice versa. Considering the drawback of decreased SER performance as the number of users in User Group 1 increases, we can adjust the number of users in User Group 1 while taking into account the performance of the transmitter hardware. Through computer simulation, the proposed hybrid precoding scheme shows better performance than the scheme that applies linear MMSE precoding to all users and has less computational complexity than the scheme that applies SLP to all users. We also show that SER performance and computational complexity can be controlled by adjusting the number of users applying the SLP scheme. Overall, the contributions of this paper can be summarized as follows:  
* For the first time, we addressed the problem of simultaneously applying two types of distinct precoding schemes to transmit data to multiple users. To the best of the authors' knowledge, there is no existing research that simultaneously applies linear precoding and non-linear precoding among the papers published to date.