A Complete Study of Space-Time-Frequency Statistical Properties of the 6G Pervasive Channel Model

The sixth generation (6G) pervasive channel model (6GPCM) can characterize channels for all spectra from the sub-6 GHz band to the visible light communication (VLC) band and all scenarios, such as maritime, (ultra-)massive multiple-input multiple-output (MIMO), and industrial Internet of things (IIoT) communication scenarios in 6G wireless systems. The unified channel model can enable us to analyze channel statistical properties in systems using different scales of antenna arrays, different frequency bands, and different scenarios with different movement speeds. In this paper, we conduct a complete study on space-time-frequency (STF) statistical properties of the 6GPCM. Mathematical derivations and simulations are provided, including STF correlation function (STFCF), spatial/temporal/frequency correlation functions, angular/Doppler/delay power spectral densities (PSDs), root mean square (RMS) angular/Doppler/delay spreads, coherence distance/time/bandwidth, stationary distance/time/bandwidth, and level-crossing rates (LCRs)/average fade durations (AFDs) in STF domains. In addition, we classify these statistical properties according to their definitions and then reveal the complex relationships between them and channel model parameters. This work will lay a solid foundation and offer useful guidelines for research on 6G wireless communication systems.