Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks
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 solu...
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MDPI AG
2020-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/1/71 |
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| author | Mahmoud A. Albreem Mohammed H. Alsharif Sunghwan Kim |
| author_facet | Mahmoud A. Albreem Mohammed H. Alsharif Sunghwan Kim |
| author_sort | Mahmoud A. Albreem |
| collection | DOAJ |
| description | 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 (<inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">D</mi> </semantics> </math> </inline-formula>) in initialization because the equalization matrix is almost diagonal. This paper studies the impact of utilizing a stair matrix (<inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula>) instead of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">D</mi> </semantics> </math> </inline-formula> in initializing the linear M-MIMO uplink (UL) detector. A comparison between iterative linear M-MIMO UL detectors with <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">D</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula> is presented in performance and computational complexity. Numerical Results show that utilization of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula> achieves the target performance within few iterations, and, hence, the computational complexity is reduced. A detector based on the GS and <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula> achieved a satisfactory bit-error-rate (BER) with the lowest complexity. |
| first_indexed | 2024-12-10T06:51:05Z |
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| id | doaj.art-2e135ef24e5e47fca38be4795c2d1c27 |
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| spelling | doaj.art-2e135ef24e5e47fca38be4795c2d1c272022-12-22T01:58:32ZengMDPI AGSymmetry2073-89942020-01-011217110.3390/sym12010071sym12010071Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless NetworksMahmoud A. Albreem0Mohammed H. Alsharif1Sunghwan Kim2Department of Electronics and Communications Engineering, A’Sharqiyah University, Ibra 400, OmanDepartment of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, 209 Neugdong-ro, Gwangjin-gu, Seoul 05006, KoreaSchool of Electrical Engineering, University of Ulsan, Ulsan 44610, KoreaIn 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 (<inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">D</mi> </semantics> </math> </inline-formula>) in initialization because the equalization matrix is almost diagonal. This paper studies the impact of utilizing a stair matrix (<inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula>) instead of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">D</mi> </semantics> </math> </inline-formula> in initializing the linear M-MIMO uplink (UL) detector. A comparison between iterative linear M-MIMO UL detectors with <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">D</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula> is presented in performance and computational complexity. Numerical Results show that utilization of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula> achieves the target performance within few iterations, and, hence, the computational complexity is reduced. A detector based on the GS and <inline-formula> <math display="inline"> <semantics> <mi mathvariant="bold">S</mi> </semantics> </math> </inline-formula> achieved a satisfactory bit-error-rate (BER) with the lowest complexity.https://www.mdpi.com/2073-8994/12/1/71massive mimoneumann seriesnewton iterationsuccessive overrelaxationgauss–seideljacobirichardsondiagonal matrixstair matrix |
| spellingShingle | Mahmoud A. Albreem Mohammed H. Alsharif Sunghwan Kim Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks Symmetry massive mimo neumann series newton iteration successive overrelaxation gauss–seidel jacobi richardson diagonal matrix stair matrix |
| title | Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks |
| title_full | Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks |
| title_fullStr | Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks |
| title_full_unstemmed | Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks |
| title_short | Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks |
| title_sort | impact of stair and diagonal matrices in iterative linear massive mimo uplink detectors for 5g wireless networks |
| topic | massive mimo neumann series newton iteration successive overrelaxation gauss–seidel jacobi richardson diagonal matrix stair matrix |
| url | https://www.mdpi.com/2073-8994/12/1/71 |
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