Massive multiple-input multiple-output (MIMO) is playing a crucial role in the fifth generation (5G) and beyond 5G (B5G) communication systems. Unfortunately, the complexity of massive MIMO systems is tremendously increased when a large number of antennas and radio frequency chains (RF) are utilized. Therefore, a plethora of research efforts has been conducted to find the optimal precoding algorithm with lowest complexity. The main aim of this paper is to provide insights on such precoding algorithms to a generalist of wireless communications. The added value of this paper is that the classification of massive MIMO precoding algorithms is provided with easily distinguishable classes of precoding solutions. This paper covers linear precoding algorithms starting with precoders based on approximate matrix inversion methods such as the truncated polynomial expansion (TPE), the Neumann series approximation (NSA), the Newton iteration (NI), and the Chebyshev iteration (CI) algorithms. The paper also presents the fixed-point iteration-based linear precoding algorithms such as the Gauss-Seidel (GS) algorithm, the successive over relaxation (SOR) algorithm, the conjugate gradient (CG) algorithm, and the Jacobi iteration (JI) algorithm. In addition, the paper reviews the direct matrix decomposition based linear precoding algorithms such as the QR decomposition and Cholesky decomposition (CD). The non-linear precoders are also presented which include the dirty-paper coding (DPC), Tomlinson-Harashima (TH), vector perturbation (VP), and lattice reduction aided (LR) algorithms. Due to the necessity to deal with a high consuming power by the base station (BS) with a large number of antennas in massive MIMO systems, a special subsection is included to describe the characteristics of the peak-to-average power ratio precoding (PAPR) algorithms such as the constant envelope (CE) algorithm, approximate message passing (AMP), and quantized precoding (QP) algorithms. This paper also reviews the machine learning role in precoding techniques. Although many precoding techniques are essentially proposed for a small-scale MIMO, they have been exploited in massive MIMO networks. Therefore, this paper presents the application of small-scale MIMO precoding techniques for massive MIMO. This paper demonstrates the precoding schemes in promising multiple antenna technologies such as the cell-free massive MIMO (CF-M-MIMO), beamspace massive MIMO, and intelligent reflecting surfaces (IRSs). In-depth discussion on the pros and cons, performance-complexity profile, and implementation solidity is provided. This paper also provides a discussion on the channel estimation and energy efficiency. This paper also presents potential future directions in massive MIMO precoding algorithms.

Quadrature spatial modulation (QSM) was recently proposed to increase the spectral efficiency of spatial modulation. In QSM, the real and imaginary parts of a symbol are transmitted independently from different antennas. A new spatial modulation technique, termed signed quadrature spatial modulation (SQSM), is introduced in this paper. Unlike QSM, SQSM creates four dimensional spatial constellation, and hence results in higher dimension into _ in-phase and quadrature-phase dimensions. The ensuing constellation consists of four antenna indices, which are chosen independently in order to transmit the real and imaginary parts of the modulated symbols and their inverse. The performance of the proposed technique is compared to the most-recent SM techniques, namely, QSM, double SM, and improved QSM (IQSM). Numerical results demonstrate that SQSM provides significant performance gains (3-7dB), particularly when a large number of transmit antennas is used. This comes with a marginal increase in computational complexity compared to QSM and SM. Also, while IQSM can be competitive with SQSM in some cases, SQSM has a much lower computational complexity, e.g., 46% reduction in complexity in case of 16 transmit antennas and 16 bps/Hz.

Signed quadrature spatial modulation (SQSM) was recently introduced to enhance the throughput of spatial modulation (SM) in multiple-input multiple-output (MIMO) systems. This strategy involves independently transmitting the real and imaginary components of a symbol and its inverse from four independent antennas. In this paper, an extended SQSM (ESQSM) system is proposed. It combines $K$ SQSM constellations and transmits them from the same transmit-antenna set with the aim of realizing a $K$ -fold improvement in the spectral efficiency (SE). The proposed ESQSM employs the average power of the $K$ SQSM constellations as an additional dimension for transmission. Performance of the proposed ESQSM surpasses that of other state-of-art SM systems such as the QSM, DSM, IQSM SQSM, and EQSM by 13 dB, 11 dB, 10.55 dB, 10 dB, and 6.8 dB, respectively. In this paper, we also propose an efficient ESQSM with a multi-user (ESQSM-MU) system inspired by the ESQSM ability in increasing the SE. The proposed ESQSM-MU system offers a significant bit error rate (BER) improvement and a higher capacity (i.e., $5K$ -users) compared to the current non orthogonal multiple access-SM (NOMA-SM) and SM-assisted multi-antenna NOMA (SM-AMA-NOMA) systems. Moreover, an efficient low-complexity detector is introduced for the ESQSM signal detection, promising a 91.2% reduction in the computational complexity of ESQSM and ESQSM-MU systems relative to the maximum likelihood (ML) with a trivial loss in performance.