The zero-forcing (ZF) and minimum mean square error (MMSE) based detectors can approach optimal performance in the uplink of massive multiple-input multiple-output (MIMO) systems. However, they require inverting a matrix whose complexity is cubic in relation to the matrix dimension. This can lead to the high computational effort, especially in massive MIMO systems. To mitigate this, several iterative methods have been proposed in the literature. In this paper, we consider accelerated Chebyshev SOR (AC-SOR) and accelerated Chebyshev AOR (AC-AOR) algorithms, which improve the detection performance of conventional Successive Over-Relaxation (SOR) and Accelerated Over-Relaxation (AOR) methods, respectively. Additionally, we propose using a deep unfolding network (DUN) to optimize the parameters of the iterative AC-SOR and AC-AOR algorithms, leading to the AC-AORNet and AC-SORNet methods, respectively. The proposed DUN-based method leads to significant performance improvements compared to conventional iterative detectors for various massive MIMO channels. The results demonstrate that the AC-AORNet and AC-SORNet are effective, outperforming other state-of-the-art algorithms. Furthermore, they are highly effective, particularly for high-order modulations such as 256-QAM (Quadrature Amplitude Modulation). Moreover, the proposed AC-AORNet and AC-SORNet require almost the same number of computations as AC-AOR and AC-SOR methods, respectively, since the use of deep unfolding has a negligible impact on the system’s detection complexity. Furthermore, the proposed DUN features a fast and stable training scheme due to its smaller number of trainable parameters.

Massive multiple-input multiple-output (MIMO) systems are critical technologies for the next generation of networks. In this field of research, new forms of deployment are emerging, such as extremely large-scale MIMO (XL-MIMO), in which the antenna array at the base station (BS) is of extreme dimensions. As a result, spatial non-stationary features emerge as users view just a section of the antenna array, known as the visibility regions (VRs). The XL-MIMO systems can achieve higher spectral efficiency, improve cell coverage, and provide significantly higher data rates than standard MIMO systems. It is a promising technology for future sixth-generation (6G) networks. However, due to the large number of antennas, linear precoding algorithms such as Zero-Forcing (ZF) and regularized Zero-Forcing (RZF) methods suffer from unacceptable computational complexity, primarily due to the required matrix inversion. This work aims to develop low-complexity precoding techniques for the downlink XL-MIMO system. These low-complexity linear precoding methods are based on Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) techniques, which avoid calculating the complex matrix inversion and lead to stable linear precoding performance. To further enhance linear precoding performance, we incorporate the Chebyshev acceleration method with the SOR and GS methods, referred to as the Cheby-SOR and Cheby-GS methods. As these proposed methods require optimizing parameters, we create a deep unfolded network (DUN) to optimize the algorithm parameters. Our performance results demonstrate that the proposed method significantly reduces computational complexity from to $\mathcal {O}(K^{2})$ , where $K$ represents the number of users. Moreover, our approach outperforms the original algorithms, requiring only a few iterations to achieve the RZF bit error rate (BER) performance.

Computing a Gram matrix and a large-dimensional matrix inversion accounts for most of the signal detection complexity in massive MIMO systems. When massive MIMO schemes are combined with Single-Carrier with Frequency-Domain Equalization (SC-FDE), employing powerful iterative equalizers like the Iterative Block Decision-Feedback Equalizer (IB-DFE), the matrix inversion operations need to be computed for each iteration, which further increases the receiver complexity. To avoid the exact matrix inversions in IB-DFE receivers, an alternative structure of IB-DFE is proposed in this work. The proposed IB-DFE receiver allows to incorporate the conventional iterative methods such as Richardson iteration, Gauss-Seidel iteration, etc. to replace the exact matrix inversions in the IB-DFE receiver. In addition, this work proposes Chebyshev accelerated Richardson iteration to improve the convergence rate of the conventional Richardson method and incorporates it with proposed IB-DFE receiver. The simulation results show that the proposed approach can significantly reduce computational complexity compared to the state-of-the-art methodologies while still obtaining a bit error rate (BER) performance similar to that of the conventional receiver.