# Precoded Generalized Spatial Modulation for Downlink MIMO Transmissions in Beyond 5G Networks
## 1 Introduction
A few precoded schemes have been introduced for spatial modulations (SM) and GSM since then. A new precoder scheme for the downlink of MU-SM systems was proposed in [16], which exploits the channel status information (CSI) at the base station (BS). Here, a precoding matrix is computed, which allows the MU downlink system to be broken down into several independent single user SM systems. A precoded scheme designed for multi-user (MU) GSM systems was reported in [17], with the aim of eliminating all inter-user interference while maintaining the antenna selection features of GSM, which means that only some of the antennas are active, while the rest are silenced. Both proposals of [16; 17] are limited in terms of spectral efficiency, since the first one was only defined for SM, while the later was designed specifically for a version of GSM, where the \(M\)-quadrature amplitude modulations (M-QAM) symbols are the same in all active antennas. CSI is fundamental in channel estimation process in order to enable uplink and downlink transmissions in MIMO systems. However, the channel estimation for downlink transmissions on massive MIMO systems operating at frequency division duplexing (FDD) represents a very complex problem, since it is unfeasible for practical applications [18; 19]. Time Division Duplexing (TDD) represents an interesting solution that can be used as alternative in order to overcome the aforementioned problem in context of downlink transmission in FDD systems. Considering the use of TDD mode, it is possible to exploit the channel reciprocity, which allows the estimation of the downlink channel by the base station through the uplink channel information. In the uplink scenario, orthogonal pilot signals are sent from the users to the base station, and based on that, signals at the base station will estimate the CSI to the user equipment (UE). After accomplishing this task, the base station beamforms the downlink data towards the UE. Considering that there is a limited number of orthogonal pilots that can be reused between cells, a pilot contamination issue may appear and become a critical problem for massive MIMO channel estimation [20]. In order to overcome this issue and others, such as the increasing amount of required hardware and computational complexity cost due to use of large number of required antennas in those schemes, several channel estimation algorithms have been developed over last few years [21; 22; 23]. The success of the channel estimation process affects the performance of massive MIMO schemes [24] and, such as, should also be taken into account in the system evaluation. It is important to highlight that even though we will not cover in this paper, massive MIMO systems such as the GSM schemes addressed here are prone to several hardware impairments such as non-linear distortions from power amplifier, I/Q imbalance, sampling jitter, and finite-resolution quantization in analog digital converters (ADCs) [20]. To reduce the impact of these effects on the overall performance of the system, compensation algorithms can be developed to mitigate the impairments. Another issue that must be considered with the introduction of 5G and beyond is the extreme densification of the network, which requires an increase in the network capacity [25; 26]. Poor cell-edge coverage and throughput are the most limiting factors of 4G cellular radio access network (RAN). Some research has been dedicated to decrease inter-cell interference by base station coordination and coordinated beamforming [27; 28]. Coordinated multi-point (CoMP) transmission or reception is one of the key techniques in 5G that mitigates inter-cell interference (ICI) from neighboring cells, providing higher spectral efficiency and coverage. CoMP indeed extends the cell coverage area and improves cell edge throughput. Joint processing coordinated multipoint transmission (JP-CoMP) requires the clustering of neighboring cells and cooperative transmission within each cluster.