# Precoded Generalized Spatial Modulation for Downlink MIMO Transmissions in Beyond 5G Networks
## 1 Introduction  
Considering the technological advances over the last decades, the next generation of wireless communications is expected to follow this trend with a significant increase in system robustness (SR), spectral efficiency (SE) and energy efficiency (EE). In recent years, new emerging techniques have appeared in order to meet the increasingly challenging requirements of beyond fifth generation (B5G) communication systems, such as non-orthogonal multiple access (NOMA) schemes like Signaling Aided Sparse Code Multiple Access [1] or index modulations (IM). IM has received significant attention due to its ability to activate a subset of certain elements of communication resources, namely antennas, subcarriers, and slots [2, 3]. Generalized spatial modulation (GSM) constitutes a particular case of IM, which is suitable for large scale multiple input multiple output (MIMO) antennas schemes enabling greater EE with ease of implementation [4, 5]. Considering that the information is encoded in thecombination of active antennas and, also in the modulated symbols transmitted in the active antennas, GSM can also achieve a greater SE than single antenna communications. GSM can be considered as a compromise between conventional MIMO and simple radio frequency (RF) transmissions, since only a subset of the available transmission antennas is active for a certain period of time, thus reducing the number of RF chains required. Several detectors have been reported in the literature for single user scenarios. The authors of [6] proposed a minimal average square block error detector (OB-MMSE) that can achieve a close to optimal performance, while its required complexity is much lower when compared to other detectors. This detector uses an algorithm that sorts the possible transmit antenna combinations (TAC), followed by the detection in sequence of the possible signal vector for each TAC using block minimum mean square error (MMSE). A termination threshold must be applied in order to reduce the number of tested TACs. Although this detector is able to achieve near-optimal performance, it can incur in substantial complexity in large scenarios. A different GSM iterative detector is proposed in [7], which is based on dividing the problem of the maximum likelihood detection (MLD) into a sequence of simpler steps, such as the minimization of the unrestricted Euclidean distance, the projection of the elements onto the signal constellation and the projection onto the set of valid active antenna combinations. This approach allows a substantial complexity reduction when compared with the optimal MLD while still achieving near-optimal performance. Although the wide range of precoding schemes referred to in the literature for MIMO systems considering both uplink and downlink scenarios [8; 9; 10; 11; 12], there is a significant imbalance between the number of approaches aimed at those scenarios for GSM-based schemes. In fact, there are very few studies that have extended the use of GSM to downlink MU [13]. Despite describing a system for scalable video broadcast communications in [3], the proposed scheme also considered the use of GSM for multiple users. However, the removal of inter-user interference is made at the receiver, which demands a large number of antennas at the users. A better suited alternative for dedicated links relies on removing inter-user interference at the transmitter through a precoder. This approach is often applied for conventional MU-MIMO as presented in [14], where the authors describe a precoder that accomplishes block diagonalization (BD) of the equivalent channel matrix. The proposed BD precoding guarantees zero inter-user interference and can be thought of as a generalization of channel inversion. Despite the similarity of the approach proposed by the authors in [15], their method cannot only provide improved bit error rate (BER) and throughput performances, but also additional diversity gain by adopting a partial nulling technique for the generalized block diagonalization (GBD).