In this paper, we propose a low-complexity widely-linear minimum mean square error (WL-MMSE) signal detection based on the Chebyshev polynomials accelerated symmetric successive over relaxation (SSORcheb) algorithm for uplink (UL) over-loaded large-scale multiple-input multiple-output (MIMO) systems. The technique of utilizing Chebyshev acceleration not only speeds up the convergence rate significantly, and maximizes the data throughput, but also reduces the cost. By utilizing the random matrix theory, we present good estimates for the Chebyshev acceleration parameters of the proposed signal detection in real large-scale MIMO systems. Simulation results demonstrate that the new WL-SSORcheb-MMSE detection not only outperforms the recently proposed linear iterative detection, and the optimal polynomial expansion (PE) WL-MMSE detection, but also achieves a performance close to the exact WL-MMSE detection. Additionally, the proposed detection offers superior sum rate and bit error rate (BER) performance compared to the precision MMSE detection with substantially fewer arithmetic operations in a short coherence time. Therefore, the proposed detection can satisfy the high-density and high-mobility requirements of some of the emerging wireless networks, such as, the high-mobility Internet of Things (IoT) networks.

In this paper, we propose an efficient regularized zero-forcing (RZF) precoding method that has lower hardware resource requirements and produces a shorter delay to the first transmitted symbol compared with truncated polynomial expansion (TPE) that is based on Neumann series in massive multiple-input multiple-output (MIMO) systems. The proposed precoding scheme, named matrix decomposition-polynomial expansion (MDPE), essentially applies a matrix decomposition algorithm based on polynomial expansion to significantly reduce full matrix multiplication computational complexity. Accordingly, it is suitable for real-time hardware implementations and high-mobility scenarios. Furthermore, the proposed method provides a simple expression that links the optimization coefficients to the ratio of BS/UTs antennas (β). This approach can speed-up the convergence to the matrix inverse by a matrix polynomial with small terms and further reduce computation costs. Simulation results show that the MDPE scheme can rapidly approximate the performance of the full precision RZF and optimal TPE algorithm, while adaptively selecting matrix polynomial terms in accordance with the different β and SNR situations. It thereby obtains a high average achievable rate of the UTs under power allocation.