Fast Converging Iterative Precoding for Massive MIMO Systems: An Accelerated Weighted Neumann Series-Steepest Descent Approach

Deng, Qian; Liang, Xiaopeng; Wang, Xianpeng; Huang, Mengxing; Dong, Chao; Zhang, Yufang

doi:10.1109/access.2020.2979371

Cited by 12 publications

(16 citation statements)

References 36 publications

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“…In [121], by exploiting the properties of the WNS al-gorithm, a weighted Neumann series-steepest descent (WNS-SD) iterative precoder is proposed to obtain a fast convergence while maintaining low-complexity. Also in [121], an accelerated weighted Neumann series-steepest descent (AWNS-SD) precodig algorithm is proposed. The AWNS-SD algorithm has a remarkable increase in the convergence rates while maintaining low-complexity and guaranteeing a wide range of convergence.…”

Section: ) Linear Precoder Based On the Matrix Inversion Approximationmentioning

confidence: 99%

“…The JI algorithm has lower performance and lower convergence rate than the GS and SOR algorithms [99], [121], [124]. Conversely, the JI algorithm enjoys parallelism and effective hardware implementation and has O(K 2 ) computational complexity which is lower than the complexity of the NSA, GS, and SOR algorithms [117], [121], [128].…”

Section: ) Linear Precoder Based On the Matrix Inversion Approximationmentioning

confidence: 99%

“…• The determination of the optimized coefficient is complicated and must be updated in each iteration [121].…”

Section: Tpementioning

confidence: 99%

“…• When M is not large enough, it shows the same computational complexity of the MMSE algorithm [121]. • It has a significant loss of performance in large massive MIMO systems [146].…”

Section: Nsamentioning

confidence: 99%

“…• It can accelerate the convergence rate with a high probability when the ratio of (M/N ) is small [121]. • It offers a high parallelism and low complexity [121].…”

Section: Wns-sdmentioning

confidence: 99%

See 4 more Smart Citations

Overview of Precoding Techniques for Massive MIMO

et al. 2021

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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.

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Section: ) Linear Precoder Based On the Matrix Inversion Approximationmentioning

confidence: 99%

Section: ) Linear Precoder Based On the Matrix Inversion Approximationmentioning

confidence: 99%

“…• The determination of the optimized coefficient is complicated and must be updated in each iteration [121].…”

Section: Tpementioning

confidence: 99%

“…• When M is not large enough, it shows the same computational complexity of the MMSE algorithm [121]. • It has a significant loss of performance in large massive MIMO systems [146].…”

Section: Nsamentioning

confidence: 99%

“…• It can accelerate the convergence rate with a high probability when the ratio of (M/N ) is small [121]. • It offers a high parallelism and low complexity [121].…”

Section: Wns-sdmentioning

confidence: 99%

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Overview of Precoding Techniques for Massive MIMO

et al. 2021

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Low‐complexity linear massive MIMO detection based on the improved BFGS method

2022

IET Communications

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Linear minimum mean square error (MMSE) detection achieves a good trade‐off between performance and complexity for massive multiple‐input multiple‐output (MIMO) systems. To avoid the high‐dimensional matrix inversion involved, MMSE detection can be transformed into an unconstrained optimization problem and then solved by efficient numerical algorithms in an iterative way. Three low‐complexity Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) quasi‐Newton methods are proposed to iteratively realize massive MIMO MMSE detection without matrix inversion. The complexity can be reduced from scriptOfalse(K3false)$\mathcal {O}(K^{3})$ to scriptOfalse(LK2false)$\mathcal {O}(LK^{2})$, where K and L denote the number of users and iterations, respectively. Leveraging the special properties of massive MIMO, the authors first explore a simplified BFGS method (named S‐BFGS) to alleviate the computational burden in the search direction. For lower complexity, BFGS method with the unit step size (named U‐BFGS) is presented subsequently. When the base station (BS)‐to‐user‐antenna ratio (BUAR) is large enough, the two proposed BFGS methods can be integrated (named U‐S‐BFGS) to further reduce complexity. In addition, an efficient initialization strategy is devised to accelerate convergence. Simulation results verify that the proposed detection scheme can achieve near‐MMSE performance with a small number of iterations L as low as 2 or 3.

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Low Complexity Linear Detectors for Massive MIMO: A Comparative Study

et al. 2021

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Massive multiple-input multiple-output (M-MIMO) is a significant pillar in fifth generation (5G) networks where a large number of antennas is deployed. It provides massive advantages to modern communication systems in data rate, spectral efficiency, number of users serviced simultaneously, energy efficiency, and quality of service (QoS). However, it requires advanced signal processing for data detection. The growing MIMO size leads to complicated scenarios, which makes the detector design a knotty problem. The problem is also becoming more complicated when high-order modulation schemes are exploited and more users are multiplexed. Therefore, it is not practical to employ the maximum likelihood (ML) detector despite the excellent performance. Linear detectors are alternative solutions and relatively simple. Unfortunately, they still need an exact matrix inversion computation, which bears to a significant high complexity. Therefore, several iterative methods are utilized to approximate or evade the matrix inversion rather than computing it. This paper studies the pros and cons of iterative matrix inversion methods where the number of computations and bit-error-rate (BER) are considered to compare between the methods. The comparison is conducted in several scenarios such as different ratio between the number of base station (BS) antennas and user terminal (UT) antennas (β), the number of iterations (n), and the relaxation parameter (ω). This paper also studies the impact of ω in the performance of Richardson (RI) and the successive over-relaxation (SOR) methods. Numerical results show that the conjugate gradient (CG) and optimized coordinate descent (OCD) methods exhibit the lowest complexity with an acceptable performance. In addition, the Gauss-Seidel (GS) method outperforms all other detectors with a trivial complexity increment. It is also noticed that the performance is not improved with every iteration. It is also shown that ω has a great impact and a significant role in achieving a satisfactory performance in both RI and SOR based detectors. From implementation point of view, detectors based on RI, OCD, and CG methods have achieved the highest hardware efficiency (HE) while Jacobi (JA) based detector has obtained the lowest HE. Recent research advances of detection methods are also presented in the open research direction with a potential impact of linear detection methods in initialization and pre-processing.

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Fast Converging Iterative Precoding for Massive MIMO Systems: An Accelerated Weighted Neumann Series-Steepest Descent Approach

Cited by 12 publications

References 36 publications

Overview of Precoding Techniques for Massive MIMO

Overview of Precoding Techniques for Massive MIMO

Low‐complexity linear massive MIMO detection based on the improved BFGS method

Low Complexity Linear Detectors for Massive MIMO: A Comparative Study

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