## 3 Channel Statistics
### Characterization of SOFS for Outdoor and Indoor Radio Propagation Channels
Impact of changing the separation distance between the Tx and Rx on these SOFS is studied. It is observed that auto-covariance is decreasing from 1 to 0 when \(\frac{r}{\lambda}\) is increased from 0 to 0.5 at 3 m and then it remains constant at 0 for further increase in \(\frac{r}{\lambda}\). In addition, the change of separation distance has significant impact on auto-covariance, as it is observed auto-covariance is decreasing from 1 to 0 when \(\frac{r}{\lambda}\) is increased from 0 to 0.4 at 6 m. For the CD in indoor case at 28 GHz, it has converse behavior with respect to auto-covariance. CD increases linearly with increase in \(\lambda\). Moreover, change in separation distance of Tx and Rx has clear impact on CD which is observed as increasing while distance is changed from 3 m to 5 m and CD has interesting fact that while changing the separation distance from 5 m to 6 m, it is again decreasing. This shows that at 5 m, the channel can be used effectively for providing rich diversity for a multiple antenna system. Figure 6: LCR and AFD plotted against different values of maximum Doppler shift in (**a**,**b**), respectively; for different scenarios of indoor mmWave (Case 2 (a); 28 GHz) radio propagation environments. (\(m=1\), \(\rho=2\)). For Case 2 (b), when the measurement setup is indoor corridor environment and measurements are taken at 38 GHz, the normalized LCR and AFD are plotted in Figure 8a,b, respectively for different values of maximum Doppler frequency. Impact of changing the separation distance between the Tx and Rx on SOFS is studied. It is observed that LCR is increasing while we increase the Doppler frequency as well as the change of separation distance has significant impact on LCR. When the distance between Tx and Rx inside corridor is changed from 3 m to 5 m, LCR is observed to increase and with further increase in distance up to 6 m, LCR is decreasing. For the indoor case at 38 GHz, AFD has converse behavior with respect to LCR. AFD is decreasing with increase in maximum Doppler frequency. Moreover, change in separation distance of Tx and Rx has clear impact on AFD which is observed as decreasing while distance between Tx and Rx inside corridor is changed from 3 m to 5 m and with further increase in distance up to 6 m, AFD is increasing. This clearly shows that in an indoor corridor environment at higher frequency such as 38 GHz, the channel can be used effectively at 5 m separation for providing rich diversity for a multiple antenna system. Similarly, for the same Case 2 (b), when the measurement setup is indoor corridor environment and measurements are taken at 38 GHz, the spatial auto-covariance and CD are plotted in Figure 9a,b, respectively for different values of wavelength and distance. Impact of changing the separation distance between the Tx and Rx on these SOFS is studied. It is observed that auto-covariance is decreasing from 1 to 0 when \(\frac{r}{\lambda}\) is increased, then it remains constant at 0 for further increase in \(\frac{r}{\lambda}\). In addition, the change of separation distance has significant impact on auto-covariance, as it is observed auto-covariance is decreasing from with increase in separation distance up to 5 m and then it increases with further increase in distance up to 6 m. For the CD in indoor case at 38 GHz, it has converse behavior with respect to auto-covariance. CD increases linearly with increase in \(\lambda\). Moreover, change in separation distance of Tx and Rx has clear impact on CD which is observed as decreasing while distance is changed from 3 m to 5 m and CD has interesting fact that while changing the separation distance from 5 m to 6 m, it is again increasing. Figure 7: Spatial auto-covariance and CD for different scenarios of indoor mmWave (Case 2 (a); 28 GHz) radio propagation environments in (**a**,**b**), respectively. (\(m=1\), \(f_{d}=10\) Hz).