Low Complexity Zero Forcing Detector Based on Newton-Schultz Iterative Algorithm for Massive MIMO Systems

Negrete, Juan Carlos; Almeida, Celso de

doi:10.1109/tvt.2018.2874811

Cited by 24 publications

(21 citation statements)

References 23 publications

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“…We consider the imperfect CSI, which plays a highly important role in analyzing the performance of MIMO systems [8], [35]. Fig.3 depicts the effect of the channel estimation error on the performance of the proposed algorithms.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Recently, to avoid matrix inversion, low-complexity precoding and detection algorithms for massive MIMO systems have attracted great research interest for massive MIMO systems. In general, matrix inversion algorithms are primarily divided into four categories: direct inverse algorithms, polynomial series expansion algorithms, iterative algorithms and message passing algorithms [8]- [20]. The direct inverse algorithms, for example, Cholesky decomposition and Gauss-Jordan elimination [8], [9] can obtain the ''exact'' inversion, but their computational complexities reach up to O(N 3 ) orders of magnitude, where N denotes the dimension of the precoding matrix in massive MIMO systems.…”

Section: Introductionmentioning

confidence: 99%

“…In general, matrix inversion algorithms are primarily divided into four categories: direct inverse algorithms, polynomial series expansion algorithms, iterative algorithms and message passing algorithms [8]- [20]. The direct inverse algorithms, for example, Cholesky decomposition and Gauss-Jordan elimination [8], [9] can obtain the ''exact'' inversion, but their computational complexities reach up to O(N 3 ) orders of magnitude, where N denotes the dimension of the precoding matrix in massive MIMO systems. Another typical category is based on polynomial series expansion algorithms, for example, the Neumann series [10], [11] and truncated polynomial expansion (TPE) [12], [13].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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For massive multiple-input multiple-output (MIMO) systems, linear precoding is preferable to nonlinear precoding for better performance-complexity trade-off. However, linear precoding is still difficult to implement in practice for such large systems, because the precoding matrix involves the complicated matrix inversion that must be rapidly computed in real-time. In this paper, we use the large-scale property of massive MIMO systems, the excellent characteristics of the weighted Neumann series (WNS) matrix, and steepest descent (SD) method to devise a new iterative precoding for massive MIMO systems. First, by exploiting the characteristics of WNS iteration, we proposed a weighted Neumann series-steepest descent (WNS-SD) iterative algorithm to perform precoding with low-complexity, and the convergence condition is always met in underloaded scenarios. Second, by devising a novel first iterative step of the aforementioned WNS-SD iterative algorithm, we proposed an accelerated iterative algorithm, named the accelerated weighted Neumann series-steepest descent (AWNS-SD) algorithm. Furthermore, in the first iterative step of the AWNS-SD algorithm, we designed a promising preconditioning matrix for the SD algorithm based on the WNS matrix. Subsequently, via merger with the WNS iterative method, the AWNS-SD iterative precoding not only greatly improves the convergence rate of WNS-SD and other competitive precoding algorithms while maintaining low-complexity, but also guarantees a wide range of convergence. Finally, simulation results verify the validity of the theoretical analysis and show that without additional iteration steps, the proposed AWNS-SD precoding achieves near-optimal performance of the exact zero forcing (ZF) precoding in just one iterative step for typical massive MIMO system configurations. Furthermore, the diagonal matrix concept is applied to the preconditioning technique to further reduce the overall complexity. INDEX TERMS Massive MIMO, matrix inversion, iterative methods, convergence improvement, lowcomplexity.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…Nevertheless, we wish to conduct a brief numerical examination of imperfect CSI in general. The model we have adopted for imperfect CSI is given as [87], [88]:…”

Section: ) Effect Of Fronthaul Capacity On Ee and Sementioning

confidence: 99%

Energy-Efficient Resource Allocation in Single-RF Load-Modulated Massive MIMO HetNets

Ataeeshojai

Elliott

Krzymien

et al. 2020

IEEE Open J. Commun. Soc.

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Due to the dramatic increase in wireless data traffic and the associated increase in energy consumption, designing energy-efficient wireless networks with improved spectral efficiency is a pressing concern. The focus of this paper is the design of a green, highly energy-efficient cellular heterogeneous network (HetNet) by taking advantage of multiple-input-multiple-output (MIMO) structure and deployment of small cells. We consider the downlink of a two-tier HetNet, in which multiple-antenna small cells are coordinated to serve users. Even though the deployment of MIMO together with small cells improves the communication system's performance in terms of data rate and reliability, circuit energy consumption in such a network is a critical issue. To address this, an energy-efficient antenna selection and radio resource block assignment algorithm is proposed for the small cells, and a single radio-frequency (RF) chain structure is considered for the massive MIMO macro base station. Then, while coordinating transmissions between cells subject to user-centric clustering, an energy-efficient beamforming design and power allocation optimization problem with respect to the quality of service requirement of users, transmit power budget of base stations, and fronthaul capacity is formulated; the problem is solved using the Dinkelbach method. Simulation results demonstrate the performance potential of our proposed algorithm in terms of energy efficiency and spectral efficiency.

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“…In a multiuser M-MIMO scenario with low number of users and large number of antennas, linear detectors such as ZF and MF are known for providing near-optimal performance [4]. Some algorithms tries to explore the channel hardening feature of the M-MIMO system that results in a well-conditioned Gram matrix H H H [4], [5] approximating the matrix inversion operation using techniques such as Neumann series [6], the Gauss-Seidel algorithm [7], and variations considering Newton algorithm such as [8], [9], and Newton-Schultz [10]. However, in those scenarios, a very small number of users K limits the potential gains in spectral efficiency since the capacity is proportional to the minimum between K and base station antennas M , i.e., min(K , M ) [5] and, as the number of users increases, as in ultra-crowded heterogeneous machine type communication (mTC) and enhanced mobile broadband (eMBB) scenarios, the reliability and the performance of such detectors deteriorate [8], [11].…”

Section: Introductionmentioning

confidence: 99%

Linear, Quadratic, and Semidefinite Programming Massive MIMO Detectors: Reliability and Complexity

Fukuda

Abrão

2019

IEEE Access

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One of the downsides of the massive multiple-input-multiple-output (M-MIMO) system is its computational complexity. Considering that techniques and different algorithms proposed in the literature applied to conventional MIMO may not be well suited or readily applicable to M-MIMO systems, in this paper, the application of different formulations inside the convex optimization framework is investigated. This paper is divided into two parts. In the first part, linear programming, quadratic programming (QP), and semidefinite programming are explored in an M-MIMO environment with high-order modulation and under realistic channel conditions, i.e., considering spatial correlation, error in the channel estimation, as well as different system loading. The bit error rate is evaluated numerically through Monte Carlo simulations. In the second part, algorithms to solve the QP formulation are explored, and computational complexity in terms of floating-point operations (flops) is compared with linear detectors. Those algorithms have interesting aspects when applied to our specific problem (M-MIMO detection formulated as QP), such as the exploitation of the structure of the problem (simple constraints) and the improvement of the rate of convergence due to the well-conditioned Gram matrix (channel hardening). The number of iterations is higher when the number of users K becomes similar to the number of base station antennas M (i.e., K ≈ M) than the case K M ; the number of iterations increases slowly as the number of users K and base station antennas M increases while keeping a low system loading. The QP with projected algorithms presented better performance than minimum mean square error detector when K ≈ M and promising computational complexity for scenarios with increasing K and low system loading.

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Low Complexity Zero Forcing Detector Based on Newton-Schultz Iterative Algorithm for Massive MIMO Systems

Cited by 24 publications

References 23 publications

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

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

Energy-Efficient Resource Allocation in Single-RF Load-Modulated Massive MIMO HetNets

Linear, Quadratic, and Semidefinite Programming Massive MIMO Detectors: Reliability and Complexity

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