# Analytical Performance Evaluation of Massive MIMO Techniques for SC-FDE Modulations
## 1 Introduction  
With the constant increase in users' needs, in particular, the interconnection of all their communication devices, and its access to the Internet everywhere, the Fourth Generation (4G) of telecommunications has to be rethought. The Fifth Generation (5G) of telecommunications networks arises as a response to existing technology limitations. The 5G network is predicted to have an increase of 10 times in spectral efficiency and 1000 times of system capacity when compared to 4G. It is also expected that this technology is energy efficient [1]. According to the report published by [2], at the end of 2019, about 13 million subscribers to the 5G technology were already expected. In October 2019, right before the official launch of this technology, more than 10 million users have already been registered. Despite the 5G launch ramp, 4G will still be dominant and will reach its peak in 2022, and then it will become superseded by 5G technology. It is also expected that by 2025, 4G will cover around 90% of the world's population, and 5G will cover only 65% of the population but at half of the data traffic. Also, according to the same report, the providersof this technology are working on a second generation that intends to reduce power consumption, increase frequencies and implement more integrated designs. The migration to 5G implies new developments in the system design, changes in components and system architecture. One way to achieve these changes is to use massive Multiple Input Multiple Output (mMIMO) [3]. This architecture consists of the existence of multiple antennas in the receiver and transmitter. This implementation allows these systems to have a substantial increase in the data rate and an improvement, not only in energy efficiency, but also in reliability of the connections [1; 4]. Channel estimation is one of the limiting factors in this type of system. Another problem is related to the assignment of sequences of finite orthogonal pilots. When the sequences of pilots is reused, it increases the contamination of pilots and coherent interference [3]. With the mMIMO system, the Single-Carrier with Frequency-Domain Equalization (SC-FDE) can be used since this technique allows a lower envelope fluctuation, when compared with Orthogonal Frequency Division Multiplexing (OFDM) [5; 6; 7]. SC-FDE allows an efficient power amplification at the Mobile Terminal (MT). In the uplink transmission, the linear Frequency-Domain Equalization (FDE) can be replaced with an iterative FDE on the receiver, such as the Iterative Block Decision Feedback Equalization (IB-DFE) [8]. This replacement leads to an increase in the receiver performance [9]. In the mMIMO system, the number of antennas in the receiver and transmitter increases to tens or hundreds of antennas. This implies the use of large matrices, which is a serious problem in receivers based on the IB-DFE concept [10; 11], since this type of receiver requires matrix inversions for each subcarrier and each iteration implies intensive computational processing. Some iterative receivers that achieve similar performance do not require matrix inversions. These receivers can implement, e.g., Maximum Ratio Combining (MRC), which requires the calculation of the hermitian of the channel matrix, or the Equal Gain Combining (EGC) that only needs phase rotations [12; 13]. The main problems associated with these low complexity receivers are related to the high interference between different transmitted streams and the Inter-Symbol Interference (ISI). There are several studies regarding the different receivers that can be used with mMIMO systems [14; 15; 16; 17], where the performance achieved is compared with the Matched Filter Bound (MFB). Authors from in [18] propose a hybrid receiver that combines IB-DFE with MRC, achieving performance values similar to MFB in its second iteration. In this paper, the performance achieved by IB-DFE, MRC, the hybrid receiver and the correlation factor is presented and compared with the theoretical values for the same receiver.