Massive MIMO technology is among the most promising solutions for achieving higher gain in 5G millimeter-wave (mmWave) channel models for high-speed train (HST) communication systems. Based on stochastic geometry methods, it is fundamental to accurately develop the associated MIMO channel model to access system performance. These MIMO channel models could be extended to massive MIMO with antenna arrays in more than one plane. In this paper, the proposed MIMO 3D geometry-based stochastic model (GBSM) is composed of the line of sight component (LOS), one sphere, and multiple confocal elliptic cylinders. By considering the proposed GBSM, the local channel statistical properties are derived and investigated. The impacts of the distance between the confocal points of the elliptic cylinder, mmWave frequencies of 28 GHz and 60 GHz, and non-stationarity on channel statistics are studied. Results show that the proposed 3D simulation model closely approximates the measured results in terms of stationary time. Consequently, findings show that the proposed 3D non-wide-sense stationary (WSS) model is better for describing mmWave HST channels in an open space environment.

Incorporating MIMO technology with 3D geometry-based stochastic models (GBSM) is a promising channel modeling technique for 5G and beyond. These models could be extended to high-speed train (HST) environments at mmWave bands. In this paper, the proposed 3D MIMO model is composed of the line of sight component (LOS), the non-line of sight component (NLOS) from one sphere, and multiple stochastic confocal elliptic cylinders. The model is applied in the viaduct and cutting environments with a time-varying Rician K-factor. The local channel statistical properties such as the auto correlation function, stationarity distance, and the level crossing rate (LCR) are derived and thoroughly investigated at the 41GHz frequency. These properties are compared with the corresponding measured results at the same wave frequency for an HST wireless channel. There is a strong correlation between the results from the derived model and the measured results. Therefore, this model can be extended to be used for viaduct and cutting channel modeling at the mmWave band.

During channel modeling for high-mobility channels, such as high-speed train (HST) channels, the velocity of the mobile radio station is assumed to be constant. However, this might not be realistic due to the dynamic movement of the train along the track. Therefore, in this paper, an enhanced Gauss–Markov mobility model with a 3D non-stationary geometry based stochastic model (GBSM) for HST in MIMO Wireless Channels is proposed. The non-isotropic scatterers within a cluster are assumed to be around the sphere in which the mobile relay station (MRS) is located. The multi-path components (MPCs) are modeled with varying velocities, whereas the mobility model is a function of time. The MPCs are represented in a death–birth cluster using the Markov process. Furthermore, the channel statistics, i.e., the space-time correlation function, the root-mean-square Doppler shift, and the quasi-stationary interval, are derived from the non-stationary model. The model shows how the quasi-stationary time increases from 0.21 to 0.451 s with a decreasing acceleration of 0.6 to 0.2 m/s2 of the HST. In addition, the impact of the distribution of the angles on the channel statistics is presented. Finally, the simulated results are compared with the measured results. Therefore, there is a close relationship between the proposed model and the measured results, and the model can be used to characterize the channel’s properties.