scholarly journals MMSE turbo equalization using a low complexity series expansion to approximate the matrix inversion in frequency selective MIMO channels

2008 ◽  
Author(s):  
Nicolas Le Josse ◽  
Christophe Laot ◽  
Karine Amis
Keyword(s):  
Series Expansion ◽  
Low Complexity ◽  
Turbo Equalization ◽  
Matrix Inversion ◽  
Mimo Channels ◽  
The Matrix ◽  
Frequency Selective

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

2019 ◽  
Vol 8 (2S11) ◽  
pp. 2834-2840
Keyword(s):  
Conjugate Gradient ◽  
Massive Mimo ◽  
Mimo Systems ◽  
Mimo System ◽  
Low Complexity ◽  
Matrix Inversion ◽  
Gram Matrix ◽  
Linear Precoding ◽  
Inversion Algorithm ◽  
The Matrix

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.

scholarly journals Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 71 ◽  
Author(s):  
Mahmoud A. Albreem ◽  
Mohammed H. Alsharif ◽  
Sunghwan Kim
Keyword(s):  
Computational Complexity ◽  
Iterative Methods ◽  
Mimo Systems ◽  
Multiple Input Multiple Output ◽  
Low Complexity ◽  
Matrix Inversion ◽  
Multiple Input ◽  
The Matrix ◽  
Input Multiple Output ◽  
The Impact

In massive multiple-input multiple-output (M-MIMO) systems, a detector based on maximum likelihood (ML) algorithm attains optimum performance, but it exhaustively searches all possible solutions, hence, it has a very high complexity and realization is denied. Linear detectors are an alternative solution because of low complexity and simplicity in implementation. Unfortunately, they culminate in a matrix inversion that increases the computational complexity in high loaded systems. Therefore, several iterative methods have been proposed to approximate or avoid the matrix inversion, such as the Neuamnn series (NS), Newton iterations (NI), successive overrelaxation (SOR), Gauss–Siedel (GS), Jacobi (JA), and Richardson (RI) methods. However, a detector based on iterative methods requires a pre-processing and initialization where good initialization impresses the convergence, the performance, and the complexity. Most of the existing iterative linear detectors are using a diagonal matrix ( D ) in initialization because the equalization matrix is almost diagonal. This paper studies the impact of utilizing a stair matrix ( S ) instead of D in initializing the linear M-MIMO uplink (UL) detector. A comparison between iterative linear M-MIMO UL detectors with D and S is presented in performance and computational complexity. Numerical Results show that utilization of S achieves the target performance within few iterations, and, hence, the computational complexity is reduced. A detector based on the GS and S achieved a satisfactory bit-error-rate (BER) with the lowest complexity.

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