# Precoding for RIS-Assisted Multi-User MIMO-DQSM Transmission Systems
## 1 Introduction  
Massive multiple-input multiple-output (MIMO) in combination with leading-edge technologies, methodologies, and architectures are poised to be a cornerstone technology for the next-generation wireless systems and networks. The capabilities and performance of future massive MIMO systems will be enhanced through the incorporation of reconfigurable intelligent surface (RIS), artificial intelligence (AI), Terahertz (THz) communications, and cell-free architectures [1]. In particular, RIS-assisted systems have been recently proposed as one of the key enabling technologies for beyond 5G/6G wireless communication networks to support a massive number of users at a high data rate, low latency, and secure transmissions with both spectral and energy efficiency [2; 3; 4]. A RIS is a surface of electromagnetic metamaterial that can control the phase, amplitude, frequency, and/or polarisation of the impinging signals in a nearly passive way without the need for radio-frequency (RF) operations [5; 6]. For example, the RIS can be designed to coherently combine the signals in the reception. In this way, the RIS changes the destructive effect of the multipath fading channel into a controllable channel that exploits diversity gains to improve the performance of the system. As a result, the overall energy of the transmitted signals can be used more efficiently. Since the RIS does not amplify the signals, RF chains are not required and thermal noise is not added during reflections [7; 8; 9]. RIS-assisted systems can be further improved if intelligent omni-surface (IOS) are considered. IOS-based systems can achieve full-dimensional wireless communications by enabling the simultaneous reflection andrefraction of the surface, and thus users on both sides can be served [10]. Due to the system's complexity, the analysis is typically limited to single-antenna users and single Tx antenna systems [11]. In particular, some frameworks for the implementation of RIS-assisted multi-user (MU) downlink transmission systems have been recently proposed [12; 13; 14; 15; 16]. In these previous works, the design of the system is mainly focused on the optimization problem for the joint design of the beamforming matrix at the base station (BS) and the phase shift vector at the RIS. As a result, the design of the system leads to a non-convex optimization problem. When full MIMO systems are considered, the main drawback of the systems is the high complexity of the optimization algorithms which require intensive signal processing and frequent actualization of the channel state information (CSI) at the RIS. This approach can be a challenge mainly for the future massive MIMO (mMIMO) systems [2]. Additionally, the practical implementation of RIS-assisted MU-MIMO systems can be complicated considering that the RIS could be located at remote places. Recently, linear precoding has been used to simplify the complexity of RIS-assisted transmission systems [17]. The precoding strategy can be effective to reduce the overloaded RIS while allowing to eliminate interference [18]. Inspired by the above, this paper presents two precoding strategies for the transmission of double quadrature spatial 2 modulation (DQSM) signals in a RIS-assisted MU-MIMO scenario. In the first strategy, the proposed system uses two precoding stages at the BS. The first precoding stage applies the optimal amplitudes and phases required to pre-cancel the MU interference (MUI) in the second hop (from the RIS to the users). The second precoder is designed to pre-cancel the interference in the first hop (from the BS to the RIS). This strategy guarantees that the RIS reflects the signals with the appropriate amplitude and phase, producing an interference-free signal at the receivers. A second strategy, that combines the two precoding blocks in just one, is also presented. The two proposed strategies are evaluated considering a correlated fading channel and two different configurations. The overall system performance is improved by incorporating a DQSM transmission scheme [19].