Modified Conjugate Gradient Algorithms for Gram Matrix Inversion of Massive MIMO Downlink Linear Precoding

This paper deals with various low complexity algorithms for higher order matrix inversion involved in massive MIMO system precoder design. The performance of massive MIMO systems is optimized by the process of precoding which is divided into linear and nonlinear. Nonlinear precoding techniques are most complex precoding techniques irrespective of its performance. Hence, linear precoding is generally preferred in which the complexity is mainly contributed by matrix inversion algorithm. To solve this issue, Krylov subspace algorithm such as Conjugate Gradient (CG) was considered to be the best choice of replacement for exact matrix inversions. But CG enforces a condition that the matrix needs to be Symmetric Positive Definite (SPD). If the matrix to be inverted is asymmetric then CG fails to converge. Hence in this paper, a novel approach for the low complexity inversion of asymmetric matrices is proposed by applying two different versions of CG algorithms- Conjugate Gradient Squared (CGS) and Bi-conjugate Gradient (Bi-CG). The convergence behavior and BER performance of these two algorithms are compared with the existing CG algorithm. The results show that these two algorithms outperform CG in terms of convergence speed and relative residue.

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Conjugate Gradient Method Based Linear Precoding with Low-Complexity for Massive MIMO Systems

2018 IEEE 4th International Conference on Computer and Communications (ICCC) ◽

10.1109/compcomm.2018.8780818 ◽

2018 ◽

Author(s):

Xu Qiao ◽

Yao Zhang ◽

Longxiang Yang

Keyword(s):

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Massive Mimo ◽

Mimo Systems ◽

Low Complexity ◽

Linear Precoding

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An Efficient Precoding Algorithm for mmWave Massive MIMO Systems

Symmetry ◽

10.3390/sym11091099 ◽

2019 ◽

Vol 11 (9) ◽

pp. 1099 ◽

Cited By ~ 3

Author(s):

Imran Khan ◽

Shagufta Henna ◽

Nasreen Anjum ◽

Aduwati Sali ◽

Jonathan Rodrigues ◽

...

Keyword(s):

Massive Mimo ◽

Mimo Systems ◽

Matching Pursuit ◽

Mimo System ◽

Multiple Input Multiple Output ◽

Low Complexity ◽

Global Optimum ◽

Vital Role ◽

Matrix Inversion ◽

Inner Product

Symmetrical precoding and algorithms play a vital role in the field of wireless communications and cellular networks. This paper proposed a low-complexity hybrid precoding algorithm for mmWave massive multiple-input multiple-output (MIMO) systems. The traditional orthogonal matching pursuit (OMP) has a large complexity, as it requires matrix inversion and known candidate matrices. Therefore, we propose a bird swarm algorithm (BSA) based matrix-inversion bypass (MIB) OMP (BSAMIBOMP) algorithm which has the feature to quickly search the BSA global optimum value. It only directly finds the array response vector multiplied by the residual inner product, so it does not require the candidate’s matrices. Moreover, it deploys the Banachiewicz–Schur generalized inverse of the partitioned matrix to decompose the high-dimensional matrix into low-dimensional in order to avoid the need for a matrix inversion operation. The simulation results show that the proposed algorithm effectively improves the bit error rate (BER), spectral efficiency (SE), complexity, and energy efficiency of the mmWave massive MIMO system as compared with the existing OMP hybrid and SDRAltMin algorithm without any matrix inversion and known candidate matrix information requirement.

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A Low Complexity Precoding Algorithm Based on Parallel Conjugate Gradient for Massive MIMO Systems

IEEE Access ◽

10.1109/access.2018.2870861 ◽

2018 ◽

Vol 6 ◽

pp. 54010-54017 ◽

Cited By ~ 2

Author(s):

Geng Chen ◽

Qingtian Zeng ◽

Xiaomei Xue ◽

ZhengQuan Li

Keyword(s):

Conjugate Gradient ◽

Massive Mimo ◽

Mimo Systems ◽

Low Complexity

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A Low-Complexity Linear Precoding Algorithm Based on Jacobi Method for Massive MIMO Systems

2018 IEEE 87th Vehicular Technology Conference (VTC Spring) ◽

10.1109/vtcspring.2018.8417575 ◽

2018 ◽

Cited By ~ 3

Author(s):

Juan Minango ◽

Celso de Almeida

Keyword(s):

Massive Mimo ◽

Mimo Systems ◽

Low Complexity ◽

Jacobi Method ◽

Linear Precoding

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PCA-Aided Linear Precoding in Massive MIMO Systems with Imperfect CSI

Wireless Communications and Mobile Computing ◽

10.1155/2020/3425952 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Van-Khoi Dinh ◽

Minh-Tuan Le ◽

Vu-Duc Ngo ◽

Chi-Hieu Ta

Keyword(s):

Principal Component Analysis ◽

Computational Complexity ◽

Massive Mimo ◽

Mimo Systems ◽

Minimum Mean Square Error ◽

Principal Component ◽

Low Complexity ◽

Component Analysis ◽

Linear Precoding ◽

Block Diagonalization

In this paper, a low-complexity linear precoding algorithm based on the principal component analysis technique in combination with the conventional linear precoders, called Principal Component Analysis Linear Precoder (PCA-LP), is proposed for massive MIMO systems. The proposed precoder consists of two components: the first one minimizes the interferences among neighboring users and the second one improves the system performance by utilizing the Principal Component Analysis (PCA) technique. Numerical and simulation results show that the proposed precoder has remarkably lower computational complexity than its low-complexity lattice reduction-aided regularized block diagonalization using zero forcing precoding (LC-RBD-LR-ZF) and lower computational complexity than the PCA-aided Minimum Mean Square Error combination with Block Diagonalization (PCA-MMSE-BD) counterparts while its bit error rate (BER) performance is comparable to those of the LC-RBD-LR-ZF and PCA-MMSE-BD ones.

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