# Comparative Analysis of Data Detection Techniques for 5G Massive MIMO Systems
## 1 Introduction
information (CSI)/ channel impulse response (CIR) is required at the BS. In addition, the DL data are precoded to concentrate the spatial data-streams at the user's location [17]. In the UL, an efficient detector is required to estimate the transmitted signal where the main issue with utilizing a large number of antennas is the high detection complexity involved. The maximum likelihood (ML) detector is considered as an optimum detector; however, it is prohibitively complex due to an exhaustive search [18; 19]. Researchers have put tremendous efforts to achieve a satisfactory trade-off between the performance and computational complexity. A substantial literature in detection schemes for massive MIMO UL has appeared and comprehensive surveys are presented in [18; 20]. In [21], the computational complexity of linear detection mechanisms based on the QR, Cholesky, and LDL decomposition algorithms for different massive MIMO configurations is presented. Other detectors, such as the sphere decoding (SD), require the QR-decomposition which increases the computational complexity. Therefore, most existing detectors need a refinement to meet the implementation demands of a low computational complexity and high performance, in particular under complicated environments. The approximate message passing (AMP) and iterative matrix inversion methods are popular schemes to achieve a pleasant performance and partially release a burden of computational complexity. The first scheme, the AMP algorithm, was initially proposed for signal reconstruction and solving the selection problem and state evolution analysis in compressed sensing (CS) [22]. The AMP algorithm with a large system size is attractive in terms of realization and implementation. Therefore, the utilization of the AMP algorithm is extended for applications in linear estimation for massive MIMO systems, precoding, and multi-user detection [22]. The convergence rate of the AMP algorithm is good, but it is not guaranteed, especially in highly loaded systems. The damping principle is a solution to slow down the estimates and ease convergence. Another solution includes an appropriate initialization, which would affect the convergence rate and impact substantially both the performance and the complexity [23]. The second scheme of detection in massive MIMO includes free-matrix-inversion methods to estimate the received signal. In other words, such methods have inversion-less terms. Instead of matrix multiplications, matrix-vector products are utilized, and the diagonally dominant property of the equalization matrix is exploited. Therefore, a detector based on free matrix inversion methods often has a low computational complexity [24]. We notice that there is a significant room for fundamental research contributions in data detection for large-scale MIMO systems. In this paper, we propose efficient initialization methods of the AMP algorithm for base station (BS) detectors using free matrix inversion methods, namely, the successive over relaxation (SOR), the Gauss-Seidel (GS), and the Jacobi (JA). The diagonally dominant property of the equalization matrix, the SOR, the GS, and the JA methods will be exploited to compute the initial solution of the AMP-based detector. In other words, the SOR, the GS, and the JA are utilized to effectively initialize the AMP-based detector.