# Performance Analysis of Multi-User MIMO Schemes under Realistic 3GPP 3-D Channel Model for 5G mmWave Cellular Networks

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## Abstract

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## 1. Introduction

#### 1.1. State of the Art for Channel Modeling

#### 1.2. Paper Contribution

- Provide a step by step tutorial on the 3GPP Technical Report (TR) 38.901 channel model implementation along with MATLAB scripts to generate channel coefficients [39].
- Design an OFDM MIMO system with uniform planar arrays and dual polarized antenna elements with realistic radiation patterns.
- Implement SLNR precoding and MMSE combining to exploit Multi-User Multi-Layer MIMO and provide simulation results on the system behavior.

## 2. Scenario Description

#### 2.1. Network Layout

^{2}) is the average user density per unit area. A homogeneous process implies constant $\mu $, moreover $\mu $ does not depend on the location. Given K users of the Poisson process in $\mathcal{A}$, they are conditionally independent and uniformly distributed in the hexagon. Therefore, the positions of the randomly deployed K users can be determined by generating both the x and y coordinates. We denote with X, the abscissa of a generic user in the hexagon, where X is the marginal random variable of a uniform 2-D distribution in the cell site. In order to find it, let us first define the two random variables ${X}_{1}$ and ${X}_{2}$:

#### 2.2. Antenna Parameters

#### 2.2.1. BS Antenna and Array Model

#### 2.2.2. UT Antenna and Array Model

## 3. Link Level Parameters and Channel Coefficient Generation

#### 3.1. Propagation Conditions and Pathloss Calculation

#### 3.2. Large Scale Parameters

- The inter-UT correlation is calculated by generating a 2-D rectangular mesh based on the UT location for each of the M LSPs. For each mesh grid, M standard normally distributed random variables, which correspond to M LSPs, are assigned and filtered by their corresponding 2-D FIR filter separately. In the following formula, we can see the general expression of the impulse response ${h}^{m}\left(d\right)$ of the filter for the m-th LSP$${h}^{m}\left(d\right)=exp\left(\right)open="("\; close=")">-\frac{d}{{d}_{corr}^{m}}$$
- Intra-UT correlation is taken into account as follows: for each UT, the M correlated parameters can be obtained by the linear transformation$$\tilde{\mathbf{s}}=\sqrt{{C}_{xx}\left(0\right)}\phantom{\rule{0.166667em}{0ex}}\zeta $$$$\begin{array}{cc}{10}^{\mathcal{N}({\mu}_{x},\phantom{\rule{0.277778em}{0ex}}{\sigma}_{x}{\tilde{s}}_{m})}\hfill & \phantom{\rule{1.em}{0ex}}\mathrm{for}\mathrm{DS},\mathrm{ASA},\mathrm{ASD},\mathrm{ZSA},\mathrm{and}\mathrm{ZSD}\hfill \\ {10}^{\mathcal{N}\left(\right)open="("\; close=")">{\mu}_{x},\phantom{\rule{0.277778em}{0ex}}\frac{{\sigma}_{x}{\tilde{s}}_{m}}{10}}\hfill \\ \phantom{\rule{1.em}{0ex}}\mathrm{for}\mathrm{SF}\mathrm{and}\mathrm{K}\hfill \end{array}$$

#### 3.3. Small Scale Parameters

#### 3.3.1. Cluster Delays

#### 3.3.2. Cluster Powers

#### 3.3.3. Arrival and Departure Angles for Both Azimuth and Elevation

#### AOAs and AODs Generation

#### ZOAs and ZODs Generation

#### Coupling of Rays within a Cluster

- Couple randomly AOD angles ${\varphi}_{n,m,AOD}$ to AOA ${\varphi}_{n,m,AOA}$ within a cluster n;
- Couple randomly ZOD angles ${\theta}_{n,m,ZOD}$ to ZOA ${\theta}_{n,m,ZOA}$ angles within a cluster n;
- Couple randomly AOD angles ${\varphi}_{n,m,AOD}$ with ZOD angles ${\theta}_{n,m,ZOD}$ within a cluster n.

#### 3.3.4. Cross Polarization Power Ratio

#### 3.4. Coefficient Generation

## 4. Multi-User MIMO System Model

- resorts only to Space Division Multiple Access (SDMA) through precoding techniques;
- is able to process all $K\phantom{\rule{0.166667em}{0ex}}L$ users’ signals, therefore we impose no limitation on the number of RF chains, i.e., the BS is able to employ at least $K\phantom{\rule{0.166667em}{0ex}}L$ parallel precoders.

#### 4.1. Sector Assignment

#### 4.2. SLNR Precoding and MMSE Combining

## 5. Simulation Results

#### 5.1. Rates for Different UPA Configurations at the BS

#### 5.2. Rates for Different Transmitting Powers

#### 5.3. Rates for Different Indoor Percentage

#### 5.4. Rates for Different Layers and Antenna Polarizations

#### 5.5. Rates for Different Cell Radius Lengths

#### 5.6. Sum Rate and Spectral Efficiency for Different Traffic Conditions

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Mort, G.S.; Drennan, J. Mobile communications: A study of factors influencing consumer use of m-services. J. Advert. Res.
**2007**, 47, 302–312. [Google Scholar] [CrossRef][Green Version] - Linke, C. Mobile media and communication in everyday life: Milestones and challenges. Mob. Media Commun.
**2013**, 1, 32–37. [Google Scholar] [CrossRef] - Cisco. New Cisco Annual Internet Report Forecasts 5G to Support More than 10% of Global Mobile Connections by 2023. 2020. Available online: https://newsroom.cisco.com/press-release-content?type=webcontent&articleId=2055169 (accessed on 15 December 2021).
- Roh, W.; Seol, J.Y.; Park, J.; Lee, B.; Lee, J.; Kim, Y.; Cho, J.; Cheun, K.; Aryanfar, F. Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results. IEEE Commun. Mag.
**2014**, 52, 106–113. [Google Scholar] [CrossRef] - Han, S.; Chih-Lin, I.; Xu, Z.; Rowell, C. Large-scale antenna systems with hybrid analog and digital beamforming for millimeter wave 5G. IEEE Commun. Mag.
**2015**, 53, 186–194. [Google Scholar] [CrossRef] - Akdeniz, M.R.; Liu, Y.; Samimi, M.K.; Sun, S.; Rangan, S.; Rappaport, T.S.; Erkip, E. Millimeter Wave Channel Modeling and Cellular Capacity Evaluation. IEEE J. Sel. Areas Commun.
**2014**, 32, 1164–1179. [Google Scholar] [CrossRef] - Shafi, M.; Zhang, M.; Moustakas, A.; Smith, P.; Molisch, A.; Tufvesson, F.; Simon, S. Polarized MIMO channels in 3-D: Models, measurements and mutual information. IEEE J. Sel. Areas Commun.
**2006**, 24, 514–527. [Google Scholar] [CrossRef] - Ding, Z.; Lei, X.; Karagiannidis, G.K.; Schober, R.; Yuan, J.; Bhargava, V.K. A Survey on Non-Orthogonal Multiple Access for 5G Networks: Research Challenges and Future Trends. IEEE J. Sel. Areas Commun.
**2017**, 35, 2181–2195. [Google Scholar] [CrossRef][Green Version] - Mitola, J. Cognitive Radio Architecture Evolution. Proc. IEEE
**2009**, 97, 626–641. [Google Scholar] [CrossRef] - Sasipriya, S.; Vigneshram, R. An overview of cognitive radio in 5G wireless communications. In Proceedings of the 2016 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), Chennai, India, 15–17 December 2016; pp. 1–5. [Google Scholar] [CrossRef]
- Axell, E.; Leus, G.; Larsson, E.G.; Poor, H.V. Spectrum Sensing for Cognitive Radio: State-of-the-Art and Recent Advances. IEEE Signal Process. Mag.
**2012**, 29, 101–116. [Google Scholar] [CrossRef][Green Version] - Riviello, D.; Benco, S.; Crespi, F.L.; Ghittino, A.; Garello, R.; Perotti, A. Spectrum Sensing Algorithms for Cognitive TV White-Spaces Systems. In Cognitive Communication and Cooperative HetNet Coexistence: Selected Advances on Spectrum Sensing, Learning, and Security Approaches; Springer International Publishing: Cham, Switzerland, 2014; pp. 71–90. [Google Scholar] [CrossRef]
- Bagwari, A.; Tuteja, S.; Bagwari, J.; Samarah, A. Spectrum Sensing Techniques for Cognitive Radio: A Re-examination. In Proceedings of the 2020 IEEE 9th International Conference on Communication Systems and Network Technologies (CSNT), Gwalior, India, 10–12 April 2020; pp. 93–96. [Google Scholar] [CrossRef]
- Koyuncu, H.; Bagwari, A.; Tomar, G.S. Simulation of a Smart Sensor Detection Scheme for Wireless Communication Based on Modeling. Electronics
**2020**, 9, 1506. [Google Scholar] [CrossRef] - Spencer, Q.; Swindlehurst, A.; Haardt, M. Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels. IEEE Trans. Signal Process.
**2004**, 52, 461–471. [Google Scholar] [CrossRef] - Joham, M.; Utschick, W.; Nossek, J. Linear transmit processing in MIMO communications systems. IEEE Trans. Signal Process.
**2005**, 53, 2700–2712. [Google Scholar] [CrossRef] - Tarighat, A.; Sadek, M.; Sayed, A. A multi user beamforming scheme for downlink MIMO channels based on maximizing signal-to-leakage ratios. In Proceedings of the (ICASSP ’05)—IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, USA, 23–23 March 2005; Volume 3, pp. iii/1129–iii/1132. [Google Scholar] [CrossRef]
- Sadek, M.; Aïssa, S. Leakage Based Precoding for Multi-User MIMO-OFDM Systems. IEEE Trans. Wirel. Commun.
**2011**, 10, 2428–2433. [Google Scholar] [CrossRef] - Patcharamaneepakorn, P.; Armour, S.; Doufexi, A. On the Equivalence Between SLNR and MMSE Precoding Schemes with Single-Antenna Receivers. IEEE Commun. Lett.
**2012**, 16, 1034–1037. [Google Scholar] [CrossRef][Green Version] - Yang, C. An Enhanced Leakage-Based Precoding Scheme for Multi-User Multi-Layer MIMO Systems. arXiv
**2014**, arXiv:1407.3866. [Google Scholar] - 3GPP. Study on Channel Model for Frequencies from 0.5 to 100 GHz (Release 16) V16.1.0; Technical Report; Rep. TR 38.901; 3GPP: Sophia Antipolis, France, 2020. [Google Scholar]
- Osseiran, A.; Boccardi, F.; Braun, V.; Kusume, K.; Marsch, P.; Maternia, M.; Queseth, O.; Schellmann, M.; Schotten, H.; Taoka, H.; et al. Scenarios for 5G mobile and wireless communications: The vision of the METIS project. IEEE Commun. Mag.
**2014**, 52, 26–35. [Google Scholar] [CrossRef] - Kyösti, P.; Meinilä, J.; Hentilä, L.; Zhao, X.; Jämsä, T.; Schneider, C.; Narandžić, M.; Milojević, M.; Hong, A.; Ylitalo, J.; et al. WINNER II Channel Models, WINNER II D1. 1.2, v1. 2. WINNER, Rep. IST-4-027756. 2008. Available online: http://www.ero.dk/93F2FC5C-0C4B-4E44-8931-00A5B05A331B (accessed on 15 December 2021).
- 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] - Bian, J.; Sun, J.; Wang, C.X.; Feng, R.; Huang, J.; Yang, Y.; Zhang, M. A WINNER+ based 3-D non-stationary wideband MIMO channel model. IEEE Trans. Wirel. Commun.
**2017**, 17, 1755–1767. [Google Scholar] [CrossRef] - Xiao, H.; Burr, A.G.; Song, L. A time-variant wideband spatial channel model based on the 3GPP model. In Proceedings of the IEEE Vehicular Technology Conference, Melbourne, Australia, 25–28 September 2006; pp. 1–5. [Google Scholar]
- Baum, D.S.; Hansen, J.; Salo, J.; Del Galdo, G.; Milojevic, M.; Kyösti, P. An interim channel model for beyond-3G systems: Extending the 3GPP spatial channel model (SCM). In Proceedings of the 2005 IEEE 61st Vehicular Technology Conference, Stockholm, Sweden, 30 April–1 May 2005; Volume 5, pp. 3132–3136. [Google Scholar]
- QuaDRiGa. Quadriga: The Next Generation Radio Channel Model. 2014. Available online: https://quadriga-channel-model.de/ (accessed on 15 December 2021).
- Peter, M.; Haneda, K.; Nguyen, S.; Karttunen, A.; Järveläinen, J. Measurement results and final mmMAGIC channel models. Deliv. D2
**2017**, 2, 12. [Google Scholar] - Nurmela, V.; Karttunen, A.; Roivainen, A.; Raschkowski, L.; Hovinen, V.; Eb, J.Y.; Omaki, N.; Kusume, K.; Hekkala, A.; Weiler, R.; et al. METIS Channel Models. Deliverable D1.4. 2015. Available online: https://metis2020.com/wp-content/uploads/deliverables/METIS_D1.4_v1.0.pdf (accessed on 15 December 2021).
- Jämsä, T.; Kyösti, P. Device-to-device extension to geometry-based stochastic channel models. In Proceedings of the IEEE 2015 9th European Conference on Antennas and Propagation (EuCAP), Lisbon, Portugal, 13–17 April 2015; pp. 1–4. [Google Scholar]
- Wang, Z.; Tameh, E.; Nix, A. A sum-of-sinusoids based simulation model for the joint shadowing process in urban peer-to-peer radio channels. In Proceedings of the VTC-2005-Fall, 2005 IEEE 62nd Vehicular Technology Conference, Dallas, TX, USA, 28 September 2005; Volume 3, pp. 1732–1736. [Google Scholar] [CrossRef][Green Version]
- Wu, S.; Wang, C.X.; Alwakeel, M.M.; You, X. A general 3-D non-stationary 5G wireless channel model. IEEE Trans. Commun.
**2017**, 66, 3065–3078. [Google Scholar] [CrossRef] - Zhao, X.; Du, F.; Geng, S.; Sun, N.; Zhang, Y.; Fu, Z.; Wang, G. Neural network and GBSM based time-varying and stochastic channel modeling for 5G millimeter wave communications. China Commun.
**2019**, 16, 80–90. [Google Scholar] [CrossRef] - Samimi, M.K.; Rappaport, T.S. 3-D statistical channel model for millimeter-wave outdoor mobile broadband communications. In Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK, 8–12 June 2015; pp. 2430–2436. [Google Scholar]
- Samimi, M.K.; Rappaport, T.S. 3-D millimeter-wave statistical channel model for 5G wireless system design. IEEE Trans. Microw. Theory Tech.
**2016**, 64, 2207–2225. [Google Scholar] [CrossRef] - Samimi, M.K.; Rappaport, T.S. Statistical channel model with multi-frequency and arbitrary antenna beamwidth for millimeter-wave outdoor communications. In Proceedings of the 2015 IEEE Globecom Workshops (GC Wkshps), San Diego, CA, USA, 6–10 December 2015; pp. 1–7. [Google Scholar]
- Rappaport, T.S.; Sun, S.; Mayzus, R.; Zhao, H.; Azar, Y.; Wang, K.; Wong, G.N.; Schulz, J.K.; Samimi, M.; Gutierrez, F. Millimeter wave mobile communications for 5G cellular: It will work! IEEE Access
**2013**, 1, 335–349. [Google Scholar] [CrossRef] - Riviello, D.G. 3GPP Channel Model TR 38901 · GitLab. Available online: https://gitlab.com/daniel.riviello/3gpp-channel-model-tr-38901 (accessed on 15 December 2021).
- 3GPP. Study on 3D Channel Model for LTE (Release 12) V12.7.0; Technical Report; Rep. TR 36.873; 3GPP: Sophia Antipolis, France, 2017. [Google Scholar]
- Yang, Y.; Xu, J.; Shi, G.; Wang, C.X. 5G Wireless Systems; Springer: Berlin/Heidelberg, Germany, 2018. [Google Scholar]
- Kim, N.; Lee, Y.; Park, H. Performance Analysis of MIMO System with Linear MMSE Receiver. IEEE Trans. Wirel. Commun.
**2008**, 7, 4474–4478. [Google Scholar] [CrossRef] - Sadek, M.; Tarighat, A.; Sayed, A.H. Active Antenna Selection in Multiuser MIMO Communications. IEEE Trans. Signal Process.
**2007**, 55, 1498–1510. [Google Scholar] [CrossRef]

**Figure 4.**Representation of the main clusters angles for a UT–BS link w.r.t. their powers and directions, in case of LOS.

**Figure 6.**Cell site with 30 users after sector assignment. 3-D view on the left, 2-D top-view on the right.

**Figure 7.**Channel frequency response along 1024 subbands, with 16 transmit antennas at the BS. ${N}_{ty}=8$, ${N}_{tz}=2$, ${N}_{r}={N}_{ry}=2$. Single polarized.

**Figure 8.**UPA radiation pattern with SLNR precoder ${\mathbf{w}}_{k}$ targeted for UT k (${\theta}_{LOS,ZOD}=96.{46}^{\circ}$, ${\varphi}_{LOS,AOD}={30}^{\circ}$) with two interfering users, ${N}_{ty}=16$, ${N}_{tz}=8$, ${N}_{r}=1$ for all users.

**Figure 9.**CDF of UT rates for different UPA configurations at the TX, ${N}_{t}=72$, ${N}_{r}=1$, ${P}_{TX}=47$ dBm, traffic density = 2500 users/km${}^{2}$.

**Figure 10.**CDF of UT rates for different transmitting powers at the BS, ${N}_{t}=72$ with ${N}_{ty}=36$, ${N}_{tz}=2$, ${N}_{r}=1$, traffic density = 2500 users/km${}^{2}$.

**Figure 11.**CDF of UT rates for different user indoor percentages, ${N}_{t}=144$ with ${N}_{ty}=36$, ${N}_{tz}=4$, ${N}_{r}=2$, ${P}_{TX}=47$ dBm, traffic density = 2500 users/km${}^{2}$.

**Figure 12.**CDF of UT rates for different layers with single or dual polarized antenna elements, ${N}_{t}$ = $[{N}_{ty}\times $${N}_{tz}]$, ${N}_{r}$ = $[{N}_{ry}\times $${N}_{rz}]$, ${P}_{TX}$ = 47 dBm, traffic density = 2500 users/km${}^{2}$.

**Figure 13.**CDF of UT rates for different cell radius lengths, ${N}_{t}=72$ with ${N}_{ty}=36$, ${N}_{tz}=2$, ${N}_{r}=1$, ${P}_{TX}=47$ dBm, average number of UTs in the cell, $\mu \frac{3\sqrt{3}}{2}{R}^{2}\approx $ 65.

**Figure 14.**Sum rate and average spectral efficiency of the UTs for different traffic density, ${N}_{t}=72$ with ${N}_{ty}=36$, ${N}_{tz}=2$, ${N}_{r}=1$, single polarization, ${P}_{TX}=47$ dBm.

Parameter | Value |
---|---|

Scenario | UMi |

Radius of the cell R | 100 m |

Network loading or user density $\mu $ | 2500 users/km^{2} |

Carrier frequency ${f}_{c}$ | 28 GHz |

Sampling frequency ${f}_{s}$ | 61.44 MSamples/s |

OFDM Symbol time ${T}_{sym}$ | 16.67 $\mathsf{\mu}$s |

Cyclic Prefix ${T}_{CP}$ | $\frac{1}{16}\times {T}_{sym}$ |

Bandwidth B | 50 MHz |

Subcarrier spacing (SCS) $\Delta $ | 60 kHz |

Active Subcarriers | 792 |

${N}_{FFT}$ | 1024 |

Noise figure F | 7 dB |

Maximum TX power ${P}_{tot}$ | 47 dBm |

Total antennas per BS UPA ${N}_{t}$ | 72 |

Antennas along y for BS UPA ${N}_{ty}$ | 36, 24, 18 |

Antennas along z for BS UPA ${N}_{tz}$ | 2, 3, 4 |

Antennas along y for UT ${N}_{ry}$ | 1, 2 |

Antennas along z for UT ${N}_{rz}$ | 1 |

Polarizations | single, dual |

Indoor UTs | 80% |

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**MDPI and ACS Style**

Riviello, D.G.; Di Stasio, F.; Tuninato, R.
Performance Analysis of Multi-User MIMO Schemes under Realistic 3GPP 3-D Channel Model for 5G mmWave Cellular Networks. *Electronics* **2022**, *11*, 330.
https://doi.org/10.3390/electronics11030330

**AMA Style**

Riviello DG, Di Stasio F, Tuninato R.
Performance Analysis of Multi-User MIMO Schemes under Realistic 3GPP 3-D Channel Model for 5G mmWave Cellular Networks. *Electronics*. 2022; 11(3):330.
https://doi.org/10.3390/electronics11030330

**Chicago/Turabian Style**

Riviello, Daniel Gaetano, Francesco Di Stasio, and Riccardo Tuninato.
2022. "Performance Analysis of Multi-User MIMO Schemes under Realistic 3GPP 3-D Channel Model for 5G mmWave Cellular Networks" *Electronics* 11, no. 3: 330.
https://doi.org/10.3390/electronics11030330