# A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview

**H**) as

**n**is the additive noise. The column vectors of

**H**are assumed to be asymptotically orthogonal. Equation (2) is mostly used in detection approaches, where the channel state information (CSI) is supposed to be perfect at the BS with good synchronization. It is noteworthy that if the instantaneous values of $\mathbf{H}$ elements are known from the channel estimation, the detection of $\mathbf{x}$ belongs to the family of coherent detection. On the other hand, if the instantaneous channel state estimation is averted, the detection of $\mathbf{x}$ is said to be a noncoherent scheme. It should be noted that noncoherent detectors have high computational complexity and an enormous performance loss compared to the coherent detectors because of a degradation in the power efficiency. In M-MIMO detector, the transmitted vector $\mathbf{x}$ is retrieved from the received vector $\mathbf{y}$. The ML sequence detection (MLSD) obtains the optimum solution but it exhaustively searches all possible signals as

#### 2.1. MF-Based Detector

#### 2.2. ZF-Based Detector

#### 2.3. MMSE-Based Detector

**I**is the identity matrix. In MMSE detector, the signal is estimated as

**H**are asymptotically orthogonal, thus, the MMSE detector achieves near-optimal performance.

## 3. Matrix Inversion Methods

#### 3.1. Neumann Series

**D**is the main diagonal entries and

**E**is the non-diagonal elements [53,54]. The Gram matrix inversion can be approximated as

#### 3.2. Gauss-Seidel

**D**,

**L**and

**U**are the diagonal elements, the strictly lower triangular entries, and the strictly upper triangular entries, respectively. GS iterative method can estimate the signal ($\widehat{\mathbf{x}}$) as

#### 3.3. Successive Overrelaxation

#### 3.4. Jacobi Method

#### 3.5. Conjugate-Gradient Method

**A**, i.e.,

#### 3.6. Richardson Method

**H**[64]. The signal is estimated as

#### 3.7. Optimized Coordinate Descent Method

## 4. Complexity Analysis

## 5. Results and Discussion

## 6. Conclusions and Future Directions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2015–2020. White Paper. 2016, pp. 1–39. Available online: https://www.cisco.com/c/dam/m/en_in/innovation/enterprise/assets/mobile-white-paper-c11-520862.pdf (accessed on 27 March 2020).
- Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2016–2021. White Paper. 2017, pp. 1–35. Available online: https://www.ramonmillan.com/documentos/bibliografia/VisualNetworkingIndexGlobalMobileDataTrafficForecastUpdate2016_Cisco.pdf (accessed on 27 March 2020).
- Cisco, V.N.I. Cisco Visual Networking Index: Forecast and Trends, 2017–2022. White Paper. 2018, pp. 1–38. Available online: https://www.ericsson.com/en/press-releases/2018/11/5g-estimated-to-reach-1.5-billion-subscriptions-in-2024--ericsson-mobility-report (accessed on 27 March 2020).
- 5G estimated to reach 1.5 billion subscriptions in 2024-Ericsson Mobility Report. Report 2018. Available online: https://newsroom.cisco.com/press-release-content?type=webcontent&articleId=1955935 (accessed on 27 March 2020).
- Mohammed, S.L.; Alsharif, M.H.; Gharghan, S.K.; Khan, I.; Albreem, M. Robust Hybrid Beamforming Scheme for Millimeter-Wave Massive-MIMO 5G Wireless Networks. Symmetry
**2019**, 11, 1424. [Google Scholar] [CrossRef] [Green Version] - Björnson, E.; Larsson, E.G.; Marzetta, T.L. Massive MIMO: ten myths and one critical question. IEEE Commun. Mag.
**2016**, 54, 114–123. [Google Scholar] [CrossRef] [Green Version] - Verenzuela, D.; Björnson, E.; Wang, X.; Arnold, M.; ten Brink, S. Massive-MIMO Iterative Channel Estimation and Decoding (MICED) in the Uplink. IEEE Trans. Commun.
**2020**, 68, 854–870. [Google Scholar] [CrossRef] [Green Version] - Huang, P.; Rajan, D.; Camp, J. An Autoregressive Doppler Spread Estimator for Fading Channels. IEEE Wirel. Commun. Lett.
**2013**, 2, 655–658. [Google Scholar] [CrossRef] - Goldsmith, A. The road ahead for wireless technology: dreams and challenges. In Proceedings of the MobiHoc ’15: Proceedings of the 16th ACM International Symposium on Mobile Ad Hoc Networking and Computing, New York, NY, USA, June 2015. [Google Scholar]
- Yang, T.; Jiang, J.; Liu, P.; Huang, Q.; Gong, J.; Zhou, Y.; Uhlig, S. Elastic sketch: Adaptive and fast network-wide measurements. In Proceedings of the SIGCOMM ’18: Proceedings of the 2018 Conference of the ACM Special Interest Group on Data Communication, New York, NY, USA, 20–25 August 2018. [Google Scholar]
- Hasan, W.B.; Harris, P.; Doufexi, A.; Beach, M. Impact of User Number on Massive MIMO with a Practical Number of Antennas. In Proceedings of the 2018 IEEE 87th Vehicular Technology Conference (VTC Spring), Porto, Portugal, 3–6 June 2018; pp. 1–5. [Google Scholar]
- Athley, F.; Durisi, G.; Gustavsson, U. Analysis of Massive MIMO with hardware impairments and different channel models. In Proceedings of the 2015 9th European Conference on Antennas and Propagation (EuCAP), Lisbon, Portugal, 13–17 April 2015; pp. 1–5. [Google Scholar]
- Yang, S.; Hanzo, L. Fifty years of MIMO detection: The road to large-scale MIMOs. IEEE Commun. Surveys Tuts.
**2015**, 17, 1941–1988. [Google Scholar] [CrossRef] [Green Version] - Albreem, M.A.; Juntti, M.; Shahabuddin, S. Massive MIMO Detection Techniques: A Survey. IEEE Commun. Surv. Tutorials
**2019**, 21, 3109–3132. [Google Scholar] [CrossRef] [Green Version] - Vordonis, D.; Paliouras, V. Sphere Decoder for Massive MIMO Systems. In Proceedings of the 2019 IEEE Nordic Circuits and Systems Conference (NORCAS): NORCHIP and International Symposium of System-on-Chip (SoC), Helsinki, Finland, 29–30 October 2019; pp. 1–6. [Google Scholar]
- Jeon, Y.; Lee, N.; Hong, S.; Heath, R.W. One-Bit Sphere Decoding for Uplink Massive MIMO Systems With One-Bit ADCs. IEEE Trans. Wirel. Commun.
**2018**, 17, 4509–4521. [Google Scholar] [CrossRef] [Green Version] - Albreem, M.A.M.; Salleh, M.F.M. Regularized Lattice Sphere Decoding for Block Data Transmission Systems. Wireless Pers. Commun., Kluwer
**2015**, 82, 1833–1850. [Google Scholar] [CrossRef] - Albreem, M.A. An efficient lattice sphere decoding technique for multi-carrier systems. Wirel. Pers. Commun.
**2015**, 82, 1825–1831. [Google Scholar] [CrossRef] - Burg, A.; Borgmann, M.; Wenk, M.; Zellweger, M.; Fichtner, W.; Bolcskei, H. VLSI implementation of MIMO detection using the sphere decoding algorithm. IEEE J. Solid State Circuits
**2005**, 40, 1566–1577. [Google Scholar] [CrossRef] - Romano, G.; Ciuonzo, D.; Rossi, P.S.; Palmieri, F. Low-complexity dominance-based sphere decoder for MIMO systems. Signal Process.
**2013**, 93, 2500–2509. [Google Scholar] [CrossRef] [Green Version] - Papa, G.; Ciuonzo, D.; Romano, G.; Salvo Rossi, P. A Dominance-Based Soft-Input Soft-Output MIMO Detector With Near-Optimal Performance. IEEE Trans. Commun.
**2014**, 62, 4320–4335. [Google Scholar] [CrossRef] - Studer, C.; Bölcskei, H. Soft–Input Soft–Output Single Tree-Search Sphere Decoding. IEEE Trans. Inf. Theory
**2010**, 56, 4827–4842. [Google Scholar] [CrossRef] - Tan, X.; Ueng, Y.; Zhang, Z.; You, X.; Zhang, C. A Low-Complexity Massive MIMO Detection Based on Approximate Expectation Propagation. IEEE Trans. Veh. Technol.
**2019**, 68, 7260–7272. [Google Scholar] [CrossRef] - Chihaoui, I.; Ammari, M.L.; Fortier, P. Improved LAS detector for MIMO systems with imperfect channel state information. IET Commun.
**2019**, 13, 1297–1303. [Google Scholar] [CrossRef] - Wang, F.; Zhang, C.; Liang, X.; Wu, Z.; Xu, S.; You, X. Efficient iterative soft detection based on polynomial approximation for massive MIMO. In Proceedings of the 2015 International Conference on Wireless Communications Signal Processing (WCSP), Nanjing, China, 15–17 October 2015; pp. 1–5. [Google Scholar]
- Mandloi, M.; Bhatia, V. Low-Complexity Near-Optimal Iterative Sequential Detection for Uplink Massive MIMO Systems. IEEE Commun. Lett.
**2017**, 21, 568–571. [Google Scholar] [CrossRef] - Jin, F.; Liu, Q.; Liu, H.; Wu, P. A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems. IEEE Commun. Lett.
**2019**, 23, 748–751. [Google Scholar] [CrossRef] - Albreem, M. Efficient Initialization of Iterative LinearMassive MIMO Detectors Using a Stair Matrix. Electron. Lett.
**2020**, 56, 50–52. [Google Scholar] [CrossRef] - Albreem, M.A.; Alsharif, M.H.; Kim, S. Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks. Symmetry
**2020**, 12, 71. [Google Scholar] [CrossRef] [Green Version] - Ivanov, A.; Yarotsky, D.; Stoliarenko, M.; Frolov, A. Smart Sorting in Massive MIMO Detection. In Proceedings of the 2018 14th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), Limassol, Cyprus, 15–17 October 2018; pp. 1–6. [Google Scholar]
- Ivanov, A.; Savinov, A.; Yarotsky, D. Iterative Nonlinear Detection and Decoding in Multi-User Massive MIMO. In Proceedings of the 2019 15th International Wireless Communications Mobile Computing Conference (IWCMC), Tangier, Morocco, 24–28 June 2019; pp. 573–578. [Google Scholar]
- Jaeckel, S.; Raschkowski, L.; Börner, K.; Thiele, L. QuaDRiGa: A 3-D Multi-Cell Channel Model With Time Evolution for Enabling Virtual Field Trials. IEEE Trans. Antennas Propag.
**2014**, 62, 3242–3256. [Google Scholar] [CrossRef] - Albreem, M.A.M.; Ismail, N.A.H.B. A review: detection techniques for LTE system. J. Telecommun. Syst. Springer
**2016**, 63, 153–168. [Google Scholar] [CrossRef] - Wai Wong, K.; ying Tsui, C.; Cheng, R.S.K.; ho Mow, W. A VLSI architecture of a K-best lattice decoding algorithm for MIMO channels. In Proceedings of the 2002 IEEE International Symposium on Circuits and Systems, Phoenix-Scottsdale, AZ, USA, 26–29 May 2002. [Google Scholar]
- Garrett, D.C.; Davis, L.M.; Woodward, G.K. 19.2 Mbit/s 4 times; 4 BLAST/MIMO detector with soft ML outputs. IEE Electron. Lett.
**2003**, 39, 233–235. [Google Scholar] [CrossRef] - Garrett, D.; Davis, L.; ten Brink, S.; Hochwald, B.; Knagge, G. Silicon complexity for maximum likelihood MIMO detection using spherical decoding. IEEE J. Solid-State Circuits
**2004**, 39, 1544–1552. [Google Scholar] [CrossRef] - Burg, A.; Haene, S.; Perels, D.; Luethi, P.; Felber, N.; Fichtner, W. Algorithm and VLSI architecture for linear MMSE detection in MIMO-OFDM systems. In Proceedings of the 2006 IEEE International Symposium on Circuits and Systems, sland of Kos, Greece, 21–24 May 2006. [Google Scholar]
- Burg, A.; Seethaler, D.; Matz, G. VLSI Implementation of a Lattice-Reduction Algorithm for Multi-Antenna Broadcast Precoding. In Proceedings of the 2007 IEEE International Symposium on Circuits and Systems, New Orleans, LA, USA, 27–30 May 2007; pp. 673–676. [Google Scholar]
- Ketonen, J.; Juntti, M.; Cavallaro, J. Performance-Complexity Comparison of Receivers for a LTE MIMO-OFDM System. IEEE Trans. Signal Process.
**2010**, 58, 3360–3372. [Google Scholar] [CrossRef] - Myllyla, M.; Cavallaro, J.; Juntti, M. Architecture Design and Implementation of the Metric First List Sphere Detector Algorithm. IEEE Trans. VLSI Syst.
**2011**, 19, 895–899. [Google Scholar] [CrossRef] [Green Version] - Larsson, E.G.; Edfors, O.; Tufvesson, F.; Marzetta, T.L. Massive MIMO for next generation wireless systems. IEEE Commun. Mag.
**2014**, 52, 186–195. [Google Scholar] [CrossRef] [Green Version] - Pappa, M.; Ramesh, C.; Kumar, M.N. Performance comparison of massive MIMO and conventional MIMO using channel parameters. In Proceedings of the 2017 International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), Chennai, India, 22–24 March 2017; pp. 1808–1812. [Google Scholar]
- Senel, K.; Larsson, E.G. Grant-Free Massive MTC-Enabled Massive MIMO: A Compressive Sensing Approach. IEEE Trans. Commun.
**2018**. [Google Scholar] [CrossRef] [Green Version] - Dawy, Z.; Saad, W.; Ghosh, A.; Andrews, J.G.; Yaacoub, E. Toward Massive Machine Type Cellular Communications. IEEE Trans. Wireless Commun.
**2017**, 24, 120–128. [Google Scholar] [CrossRef] - Yao, H.; Wornell, G.W. Lattice-reduction-aided detectors for MIMO communication systems. In Proceedings of the Global Telecommunications Conference, 2002. GLOBECOM ’02. IEEE, Taipei, Taiwan, 17–21 November 2002; pp. 424–428. [Google Scholar]
- Lim, Y.G.; Chae, C.B.; Caire, G. Performance Analysis of Massive MIMO for Cell-Boundary Users. IEEE Trans. Wireless Commun.
**2015**, 14, 6827–6842. [Google Scholar] [CrossRef] [Green Version] - Costello, D.J. Fundamentals of Wireless Communication. IEEE Trans. Inf. Theory
**2009**, 55, 919–920. [Google Scholar] [CrossRef] - Alwakeel, A.S.; Mehana, A.H. Multi-cell MMSE data detection for massive MIMO: new simplified bounds. IET Commun.
**2019**, 13, 2386–2394. [Google Scholar] [CrossRef] - Wu, M.; Yin, B.; Vosoughi, A.; Studer, C.; Cavallaro, J.R.; Dick, C. Approximate matrix inversion for high-throughput data detection in the large-scale MIMO uplink. In Proceedings of the2013 IEEE International Symposium on Circuits and Systems (ISCAS), Beijing, China, 19–23 May 2013; pp. 2155–2158. [Google Scholar]
- Lu, A.A.; Gao, X.; Zheng, Y.R.; Xiao, C. Low Complexity Polynomial Expansion Detector With Deterministic Equivalents of the Moments of Channel Gram Matrix for Massive MIMO Uplink. IEEE Trans. Commun.
**2016**, 64, 586–600. [Google Scholar] [CrossRef] - Wu, M.; Yin, B.; Wang, G.; Dick, C.; Cavallaro, J.R.; Studer, C. Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations. IEEE J. Sel. Topics Signal Process.
**2014**, 8, 916–929. [Google Scholar] [CrossRef] [Green Version] - Wang, F.; Zhang, C.; Yang, J.; Liang, X.; You, X.; Xu, S. Efficient matrix inversion architecture for linear detection in massive MIMO systems. In Proceedings of the 2015 IEEE International Conference on Digital Signal Processing (DSP), Singapore, 21–24 July 2015; pp. 248–252. [Google Scholar]
- Liu, X.; Zhang, Z.; Wang, X.; Lian, J.; Dai, X. A Low Complexity High Performance Weighted Neumann Series-based Massive MIMO Detection. In Proceedings of the 2019 28th Wireless and Optical Communications Conference (WOCC), Beijing, China, 9–10 May 2019; pp. 1–5. [Google Scholar]
- Zhang, C.; Liang, X.; Wu, Z.; Wang, F.; Zhang, S.; Zhang, Z.; You, X. On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems. IEEE Trans. Veh. Technol.
**2019**, 68, 6272–6285. [Google Scholar] [CrossRef] [Green Version] - Ciuonzo, D.; Rossi, P.S.; Dey, S. Massive MIMO Channel-Aware Decision Fusion. IEEE Trans. Signal Process.
**2015**, 63, 604–619. [Google Scholar] [CrossRef] - Lee, Y.; Sou, S. On Improving Gauss-Seidel Iteration for Signal Detection in Uplink Multiuser Massive MIMO Systems. In Proceedings of the 2018 3rd International Conference on Computer and Communication Systems (ICCCS), Nagoya, Japan, 27–30 April 2018; pp. 268–272. [Google Scholar]
- Zhang, C.; Wu, Z.; Studer, C.; Zhang, Z.; You, X. Efficient Soft-Output Gauss-Seidel Data Detector for Massive MIMO Systems. IEEE Trans. Circuits Syst. Regul. Pap.
**2018**, 1–12. [Google Scholar] [CrossRef] [Green Version] - Zeng, J.; Lin, J.; Wang, Z. An Improved Gauss-Seidel Algorithm and Its Efficient Architecture for Massive MIMO Systems. IEEE Trans. Circuits Syst. Ii: Express Briefs
**2018**, 65, 1194–1198. [Google Scholar] [CrossRef] - Nhat Cuong, C.; Thi Hong, T.; Duc Khai, L. Hardware Implementation of the Efficient SOR-Based Massive MIMO Detection for Uplink. In Proceedings of the 2019 IEEE-RIVF International Conference on Computing and Communication Technologies (RIVF), Danang, Vietnam, 20–22 March 2019; pp. 1–6. [Google Scholar]
- Jin, F.; Cui, F.; Liu, Q.; Liu, H. A Unified Model for Signal Detection in Massive MIMO System and Its Application. In Proceedings of the 2019 16th IEEE Annual Consumer Communications Networking Conference (CCNC), Las Vegas, NV, USA, 11–14 Jan 2019; pp. 1–2. [Google Scholar]
- Lee, Y. Decision-aided Jacobi iteration for signal detection in massive MIMO systems. Electron. Lett.
**2017**, 53, 1552–1554. [Google Scholar] [CrossRef] - Albataineh, Z. Iterative Signal Detection Based on MSD-CG Method for Uplink Massive MIMO Systems. In Proceedings of the 2019 16th International Multi-Conference on Systems, Signals Devices (SSD), Istanbul, Turkey, 21–24 March 2019; pp. 539–544. [Google Scholar]
- Yin, B.; Wu, M.; Cavallaro, J.R.; Studer, C. VLSI design of large-scale soft-output MIMO detection using conjugate gradients. In Proceedings of the 2015 IEEE International Symposium on Circuits and Systems (ISCAS), Lisbon, Portugal, 24–27 May 2015; pp. 1498–1501. [Google Scholar]
- Khoso, I.A.; Dai, X.; Irshad, M.N.; Khan, A.; Wang, X. A Low-Complexity Data Detection Algorithm for Massive MIMO Systems. IEEE Access
**2019**, 7, 39341–39351. [Google Scholar] [CrossRef] - Bjorck, A. Numerical Methods for Least Squares Problems; Society for Industrial and Applied Mathematics: Philadelphia, PA, USA, 1996. [Google Scholar]
- Shao, L.; Zu, Y. Joint Newton Iteration and Neumann Series Method of Convegence-Accelerating Matrix Inversion Approximation in Linear Precoding for Massive MIMO Systems. Math. Probl. Eng. Hindawi
**2016**, 2016. [Google Scholar] - Costa, H.; Roda, V. A Scalable Soft Richardson Method for Detection in a Massive MIMO System. Prz. Elektrotechniczny
**2016**, 92, 199–203. [Google Scholar] - Khoso, I.A.; Javed, T.B.; Tu, S.; Dong, Y.; Li, H.; Wang, X.; Dai, X. A Fast-Convergent Detector Based on Joint Jacobi and Richardson Method for Uplink Massive MIMO Systems. In Proceedings of the 2019 28th Wireless and Optical Communications Conference (WOCC), Beijing, China, 9–10 May 2019; pp. 1–5. [Google Scholar]
- Wu, M.; Dick, C.; Cavallaro, J.R.; Studer, C. FPGA design of a coordinate descent data detector for large-scale MU-MIMO. In Proceedings of the IEEE International Symposium on Circuits and Systems, Montreal, QC, Canada, 22–25 May 2016; pp. 1894–1897. [Google Scholar]
- Wu, M.; Dick, C.; Cavallaro, J.; Studer, C. High-Throughput Data Detection for Massive MU-MIMO-OFDM Using Coordinate Descent. IEEE Trans. Circuits Syst. I
**2016**, 63, 2357–2367. [Google Scholar] [CrossRef]

**Figure 1.**Performance of a detector based on several approximate matrix detection methods and the exact MMSE method for $16\times 128$ M-MIMO system and 64QAM.

**Figure 2.**Performance of a detector based on several approximate matrix detection methods and the exact MMSE method for $32\times 128$ M-MIMO system and 64QAM.

**Figure 3.**Performance of a detector based on several approximate matrix inversion methods and the exact MMSE method for $64\times 128$ M-MIMO system and 64QAM.

**Figure 4.**Number of multiplications among several approximate matrix inversion methods in $16\times 128$ MIMO.

Notation | Meaning |
---|---|

$\beta $ | ratio between user antennas and BS antennas |

5G | fifth generation |

K | number of user terminals |

N | number of BS antennas |

$\mathbf{x}$ | transmitted symbol vector |

$\mathbf{y}$ | received symbol vector |

$\mathcal{S}(.)$ | slicer |

n | additive white Gaussian noise (AWGN) |

H | channel matrix |

${\mathcal{O}}^{K}$ | decision variables |

A | equalization matrix |

${\mathbf{H}}^{+}$ | Moore-Penrose pseudo-inverse |

G | Gram matrix |

D | Diagonal matrix |

E | non-diagonal matrix |

L | lower triangular matrix |

U | upper triangular matrix |

$\omega $ | relaxation parameter |

$\mathit{n}$ | number of iterations |

Method | Number of Multiplications |
---|---|

NS | $4{K}^{3}(n-2)+(2K+1){K}^{2}+(4N-1)K$ |

RI | $(4N+4n){K}^{2}+2KN$ |

SOR | $(4N+4n-2){K}^{2}+2(N-n+1)K$ |

GS | $(4N+4n-2){K}^{2}+2(N-2n+1)K$ |

OCD | $(8NK+4K)n$ |

JA | $(4N+4n+1){K}^{2}$+2NK |

CG | $(N+2{K}^{2})n$ |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Albreem, M.A.; Alsharif, M.H.; Kim, S.
A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems. *Entropy* **2020**, *22*, 388.
https://doi.org/10.3390/e22040388

**AMA Style**

Albreem MA, Alsharif MH, Kim S.
A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems. *Entropy*. 2020; 22(4):388.
https://doi.org/10.3390/e22040388

**Chicago/Turabian Style**

Albreem, Mahmoud A., Mohammed H. Alsharif, and Sunghwan Kim.
2020. "A Low Complexity Near-Optimal Iterative Linear Detector for Massive MIMO in Realistic Radio Channels of 5G Communication Systems" *Entropy* 22, no. 4: 388.
https://doi.org/10.3390/e22040388