# A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands

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## Abstract

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## 1. Introduction

- A wideband non-stationary 3D GBSM for HAP-MIMO communication systems at mmWave bands is established, which consider the impact of large-scale parameters on the channel.
- The dynamic birth–death behavior of scatterers is modeled through Markov processes. Based on the proposed non-stationary 3D GBSM, some important statistical properties, i.e., temporal ACF, spatial CCF, and FCF, are derived and analyzed.
- The impacts of some parameters on ACF are compared, and the non-stationary characteristics in time, space, and frequency domains are investigated thoroughly by simulations.

## 2. Channel Model

#### 2.1. Descriptions of 3D GBSM for HAP-MIMO Channel

#### 2.2. Birth–Death Process

#### 2.3. Large-Scale Parameters

## 3. GBSM Non-Stationary Channel Statistical Properties

#### 3.1. Temporal ACF

#### 3.2. Spatial CCF

#### 3.3. FCF

## 4. Results and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Nguyen, D.C.; Ding, M.; Pathirana, P.N.; Seneviratne, A.; Li, J.; Niyato, D.; Dobre, O.; Poor, H.V. 6G Internet of Things: A Comprehensive Survey. IEEE Internet Things J.
**2022**, 9, 359–383. [Google Scholar] [CrossRef] - Wang, C.X.; You, X.; Gao, X.; Zhu, X.; Li, Z.; Zhang, C.; Wang, H.; Huang, Y.; Chen, Y.; Haas, H.; et al. On the Road to 6G: Visions, Requirements, Key Technologies, and Testbeds. IEEE Commun. Surv. Tutor.
**2023**, 25, 905–974. [Google Scholar] [CrossRef] - Cao, K.; Ding, H.; Li, W.; Lv, L.; Gao, M.; Gong, F.; Wang, B. On the Ergodic Secrecy Capacity of Intelligent Reflecting Surface Aided Wireless Powered Communication Systems. IEEE Wirel. Commun. Lett.
**2022**, 11, 2275–2279. [Google Scholar] [CrossRef] - Kırık, M.; Abusanad, N.A.; Arslan, H. Inter-HAP Based Geometrical 3D Channel Model Operating at 28 to 60 GHz for Future 6G Non-Terrestrial Networks. In Proceedings of the 2023 IEEE Wireless Communications and Networking Conference (WCNC), Glasgow, UK, 26–29 March 2023; Volume 16, p. 168. [Google Scholar]
- Zheng, W.; Gong, G.; Tian, J.; Lu, S.; Wang, R.; Yin, Z.; Li, X.; Yin, L. Design of a Modified Transformer Architecture Based on Relative Position Coding. Int. J. Comput. Intell. Syst.
**2023**, 16, 168. [Google Scholar] [CrossRef] - Chen, S.; Sun, S.; Kang, S. System integration of terrestrial mobile communication and satellite communication—The trends, challenges and key technologies in B5G and 6G. China Commun.
**2020**, 17, 156–171. [Google Scholar] [CrossRef] - Hassan, M.S.; Saha, C.; Lianghai, J.; Alvarino, A.R.; Ma, J.; Liu, L.; Wu, Q. NTN: From 5G NR to 6G; IEEE: Piscataway, NJ, USA, 2023; pp. 173–178. [Google Scholar]
- Omote, H.; Kimura, S.; Lin, H.Y.; Sato, A. HAPS propagation loss model for urban and suburban environments. In Proceedings of the 2020 International Symposium on Antennas and Propagation (ISAP), Osaka, Japan, 25–28 January 2021; pp. 681–682. [Google Scholar]
- Ma, K.; Li, Z.; Liu, P.; Yang, J.; Geng, Y.; Yang, B.; Guan, X. Reliability-Constrained Throughput Optimization of Industrial Wireless Sensor Networks With Energy Harvesting Relay. IEEE Internet Things J.
**2021**, 8, 13343–13354. [Google Scholar] [CrossRef] - Palanci, C.; Akleman, F.; Kurt, G.K. High Altitude Platform Station (HAPS) to Satellite Channel Models for 6G Networks. In Proceedings of the 2022 IEEE Aerospace Conference (AERO), Big Sky, MT, USA, 5–12 March 2022; pp. 1–10. [Google Scholar]
- Feasibility Study of High Altitude Platform Station (HAPS) Implementation for Urban Areas in Indonesia: A Case Study of East Kalimantan. In Proceedings of the 2023 IEEE International Opportunity Research Scholars Symposium (ORSS), Atlanta, GA, USA, 23 April–2 June 2023; pp. 92–95.
- Lian, Z.; Jiang, L.; He, C.; He, D. User Grouping and Beamforming for HAP Massive MIMO Systems Based on Statistical-Eigenmode. IEEE Wirel. Commun. Lett.
**2019**, 8, 961–964. [Google Scholar] [CrossRef] - Xu, J.; Cheng, X.; Bai, L. A 3D Space-Time-Frequency Non-Stationary Model for Low-Altitude UAV mmWave and Massive MIMO Aerial Fading Channels. IEEE Trans. Antennas Propag.
**2022**, 70, 10936–10950. [Google Scholar] [CrossRef] - Wang, Q.; Li, P.; Rocca, P.; Li, R.; Tan, G.; Hu, N.; Xu, W. Interval-Based Tolerance Analysis Method for Petal Reflector Antenna With Random Surface and Deployment Errors. IEEE Trans. Antennas Propag.
**2023**, 71, 8556–8569. [Google Scholar] [CrossRef] - Jiang, Y.; Li, X. Broadband cancellation method in an adaptive co-site interference cancellation system. Int. J. Electron.
**2022**, 109, 854–874. [Google Scholar] [CrossRef] - Yang, W.; Xie, D.; Jing, X.; Jiang, Q.; Zeng, J. High Altitude Platform Station Communication as an Enabler for Massive Internet of Things. In Proceedings of the 2020 IEEE 20th International Conference on Communication Technology (ICCT), Nanning, China, 28–31 October 2020; pp. 829–833. [Google Scholar]
- Ghazal, A.; Yuan, Y.; Wang, C.X.; Zhang, Y.; Yao, Q.; Zhou, H.; Duan, W. A Non-Stationary IMT-Advanced MIMO Channel Model for High-Mobility Wireless Communication Systems. IEEE Trans. Wirel. Commun.
**2017**, 16, 2057–2068. [Google Scholar] [CrossRef] - Lian, Z.; Jiang, L.; He, C.; Xi, Q. A Novel Channel Model for 3D HAP-MIMO Communication Systems. In Proceedings of the 2016 International Conference on Networking and Network Applications (NaNA), Hakodate, Japan, 23–25 July 2016; pp. 1–6. [Google Scholar]
- Hu, J.; Jiang, L.; He, C.; Lian, Z.; Liu, J. A 3D HAP-MIMO channel model based on dynamic properties of scatterers. In Proceedings of the 2017 9th International Conference on Wireless Communications and Signal Processing (WCSP), Nanjing, China, 11–13 October 2017; pp. 1–5. [Google Scholar]
- Lian, Z.; Jiang, L.; He, C. A 3D GBSM Based on Isotropic and Non-Isotropic Scattering for HAP-MIMO Channel. IEEE Commun. Lett.
**2018**, 22, 1090–1093. [Google Scholar] [CrossRef] - Michailidis, E.T.; Nomikos, N.; Trakadas, P.; Kanatas, A.G. Three-Dimensional Modeling of mmWave Doubly Massive MIMO Aerial Fading Channels. IEEE Trans. Veh. Technol.
**2020**, 69, 1190–1202. [Google Scholar] [CrossRef] - Zakia, I. Capacity of HAP-MIMO channels for high-speed train communications. In Proceedings of the 2017 3rd International Conference on Wireless and Telematics (ICWT), Palembang, Indonesia, 27–28 July 2017; pp. 26–30. [Google Scholar]
- Zou, S.; Jiang, L.; Ji, P.; He, C.; He, D.; Zhang, G. Beam Selection Algorithm for Beamspace HAP-MIMO Systems Based on Statistical CSI. In Proceedings of the 2021 International Conference on Networking and Network Applications (NaNA), Lijiang City, China, 29 October–1 November 2021; pp. 47–51. [Google Scholar]
- Yang, M.; Zhang, S.; Shao, X.; Guo, Q.; Tang, W. Statistical modeling of the high altitude platform dual-polarized MIMO propagation channel. China Commun.
**2017**, 14, 43–54. [Google Scholar] [CrossRef] - Lian, Z.; Su, Y.; Wang, Y.; Jiang, L. A Non-Stationary 3D Wideband Channel Model for Intelligent Reflecting Surface-Assisted HAP-MIMO Communication Systems. IEEE Trans. Veh. Technol.
**2022**, 71, 1109–1123. [Google Scholar] [CrossRef] - Toyoshima, M. Space Laser Communications for Beyond 5G/6G. In Proceedings of the 2023 Opto-Electronics and Communications Conference (OECC), Shanghai, China, 2–6 July 2023; pp. 1–2. [Google Scholar]
- Aliouane, M.A.; Conrat, J.M.; Cousin, J.C.; Begaud, X. Material Reflection Measurements in Centimeter and Millimeter Wave ranges for 6G Wireless Communications. In Proceedings of the 2022 Joint European Conference on Networks and Communications & 6G Summit (EuCNC/6G Summit), Grenoble, France, 7–10 June 2022; pp. 43–48. [Google Scholar]
- GSM Association. An Introduction to the WRC: A Beginners Guide to the World Radiocommunication Conference; GSM Association: Lodon, UK, 2017. [Google Scholar]
- Zhao, J.; Wang, Q.; Li, Y.; Zhou, J.; Zhou, W. Ka-band Based Channel Modeling and Analysis in High Altitude Platform (HAP) System. In Proceedings of the 2020 IEEE 91st Vehicular Technology Conference (VTC2020-Spring), Antwerp, Belgium, 25–28 May 2020; pp. 1–5. [Google Scholar]
- Lian, Z.; Jiang, L.; He, C. A 3D Wideband Model Based on Dynamic Evolution of Scatterers for HAP-MIMO Channel. IEEE Commun. Lett.
**2017**, 21, 684–687. [Google Scholar] [CrossRef] - Lian, Z.; Jiang, L.; He, C.; He, D. A Non-Stationary 3D Wideband GBSM for HAP-MIMO Communication Systems. IEEE Trans. Veh. Technol.
**2019**, 68, 1128–1139. [Google Scholar] [CrossRef] - Lian, Z.; Jiang, L.; He, C. A Non-stationary 3D Multi-cylinder Model for HAP-MIMO Communication Systems. In Space Information Networks, Proceedings of the First International Conference, SINC 2016, Kunming, China, 24–25 August 2016; Springer: Singapore, 2016; pp. 202–214. [Google Scholar]
- Bai, L.; Wang, C.X.; Wu, S.; Wang, H.; Yang, Y. A 3D wideband multi-confocal ellipsoid model for wireless MIMO communication channels. In Proceedings of the 2016 IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia, 22–27 May 2016; pp. 1–6. [Google Scholar]
- Bai, L.; Wang, C.X.; Goussetis, G.; Wu, S.; Zhu, Q.; Zhou, W.; Aggoune, E.H.M. Channel Modeling for Satellite Communication Channels at Q-Band in High Latitude. IEEE Access
**2019**, 7, 137691–137703. [Google Scholar] [CrossRef] - Lian, Z.; Su, Y.; Wang, Y.; Jiang, L.; Zhang, Z.; Xie, Z.; Li, S. A Nonstationary 3D Wideband Channel Model for Low-Altitude UAV-MIMO Communication Systems. IEEE Internet Things J.
**2022**, 9, 5290–5303. [Google Scholar] [CrossRef] - Lian, Z.; Jiang, L.; He, C.; Xi, Q. A novel multiuser HAP-MIMO channel model based on birth–death process. In Proceedings of the 2016 IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia, 22–27 May 2016; pp. 1–5. [Google Scholar]
- ITU-R P.676-11[R]; Attenuation by Atmospheric Gases. ITU: Geneva, Switzerland, 2019.
- ITU-R P.835-6[R]; Reference Standard Atmospheres. ITU: Geneva, Switzerland, 2017.
- ITU-R P.618-13[R]; Propagation Data and Prediction Methods Required for the Design of Earth-Space Telecommunication Systems. ITU: Geneva, Switzerland, 2017.
- Zhu, Q.; Yang, Y.; Chen, X.; Tan, Y.; Fu, Y.; Wang, C.X.; Li, W. A Novel 3D Non-Stationary Vehicle-to-Vehicle Channel Model and its Spatial-Temporal Correlation Properties. IEEE Access
**2018**, 6, 43633–43643. [Google Scholar] [CrossRef] - Bian, J.; Wang, C.X.; Gao, X.; You, X.; Zhang, M. A General 3D Non-Stationary Wireless Channel Model for 5G and Beyond. IEEE Trans. Wirel. Commun.
**2021**, 20, 3211–3224. [Google Scholar] [CrossRef]

**Figure 2.**An example of the MPCs evolution process in the time domain (${\lambda}_{G}$ = 0.13/m, ${\lambda}_{R}$ = 0.03/m).

Parameter | Meaning |
---|---|

${n}_{T}$, ${n}_{R}$ | The number of transmit antennas and receive antennas, respectively. |

${H}_{T}$, ${H}_{R}$ | The height of TMS and SBS, respectively. |

${\delta}_{T}$, ${\delta}_{R}$ | The spacing between two adjacent antenna elements at the TMS and the SBS, respectively. |

${v}_{a}$, ${v}_{b}$ | The velocity of TMS and SBS, respectively. |

${\beta}_{T}$ | The elevation angle of TMS relative to SBS. |

H | The height of the cylinder. |

R | The radius of the cylinder. |

${S}_{n}$ | The position of the nth scatterer. |

${\psi}_{R}$ | The elevation angle of the TMS antenna element in the x–y plane. |

${\theta}_{T}$, ${\theta}_{R}$ | The antenna orientations of TMS and SBS, respectively. |

Our Model | Model in [31] | Model in [32] |
---|---|---|

GBSM | GBSM | GBSM |

Consider birth–death process | Consider birth–death process | Not consider birth–death process |

Consider large-scale parameters | Not consider large-scale parameters | Not consider large-scale parameters |

Consider temporal ACF | Consider temporal ACF | Consider temporal ACF |

Consider spatial CCF | Consider spatial CCF | Not consider spatial CCF |

Consider FCF | Not consider FCF | Not consider FCF |

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## Share and Cite

**MDPI and ACS Style**

Zhang, W.; Gu, L.; Zhang, K.; Zhang, Y.; Wang, S.; Ji, Z.
A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands. *Electronics* **2024**, *13*, 678.
https://doi.org/10.3390/electronics13040678

**AMA Style**

Zhang W, Gu L, Zhang K, Zhang Y, Wang S, Ji Z.
A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands. *Electronics*. 2024; 13(4):678.
https://doi.org/10.3390/electronics13040678

**Chicago/Turabian Style**

Zhang, Wancheng, Linhao Gu, Kaien Zhang, Yan Zhang, Saier Wang, and Zijie Ji.
2024. "A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands" *Electronics* 13, no. 4: 678.
https://doi.org/10.3390/electronics13040678