## 3 Method to Control the BS Correlation  
Figure 2 illustrates two-dimensional channel models of the downlink and uplink channels at the MIMO terminal [30]. In Figure 2, \(K\) secondary wave sources arranged on a circle act as the radiating antennas (scatterers) and receiving antennas (probes) for the downlink and uplink channels, respectively. Figure 1: Propagation model for the uplink channel. Figure 2: Two-dimensional channel model: (**a**) downlink; (**b**) uplink. For the downlink channel, illustrated in Figure 2a, radio waves emitted from BS antennas are received by the antennas in the device under test (DUT) via the scatterers surrounding the DUT. In this paper, non-line-of-sight (NLOS) scenarios are examined; thus, [PERSON]'s model is used, which uniformly inputs radio waves from the full azimuth. In the fading emulator or Monte Carlo simulation, radio waves radiated from the scatterers that surround the DUT antennas, which are controlled phases of the signal used to emulate the Rayleigh fading channel, are summed around the DUT antennas, and the desired radio environment is generated. Furthermore, when the amplitudes of the signals radiated from the scatterers are controlled according to the power spectrum of the incident wave, a cluster propagation environment can be represented. The phase-shift of the carrier wave from the \(i\)-th scatterer according to the \(m\)-th BS antenna, \(P_{mi}(t)\), is calculated as follows:  
\[P_{mi}(t)=2\pi f_{D}t\cos(\phi_{i}-\phi_{v})+\phi_{mi}, \tag{1}\]  
where \(\phi_{i}\) is the azimuth angle of the \(i\)-th scatterer, and \(\phi_{v}\) is the direction of movement of the DUT antenna. \(f_{D}\) is the maximum Doppler frequency in Hertz, which is given by \(f_{D}=v/\lambda\), where \(v\) is the speed of the DUT antennas and \(\lambda\) is the wavelength of the carrier wave. \(\phi_{mi}\), which is set by a random number, is the initial phase of the \(i\)-th scatterer with respect to the \(m\)-th BS antenna, and this can control the correlation coefficient between the channels [7]. The correlation coefficient between the signals received via the downlink by the DUT antennas is determined by the radiation pattern around the antennas. In the case of the Jakes' model, the spatial correlation between the antennas can be expressed as  
\[\rho=J_{0}\left(\frac{2\pi d}{\lambda}\right), \tag{2}\]  
where \(J_{0}()\) is a zeroth-order Bessel function of the first kind, and \(d\) is the distance between the isotropic antennas. As indicated in Equation (2), the correlation coefficient between the signals received at the DUT antennas depends on the geometrical phase between the antennas regardless of the initial phase of the scatterers which can be represented by another channel from the BS antenna. Similarly, in the fading emulator, the correlation coefficient between the received signals, considering the phase difference generated by the geometrical relationship between the DUT antennas and each scatterer, is equivalent to the spatial correlation calculated by Equation (2). Hence, the geometrical relationships between the DUT antennas and the scatterers change with the position of the DUT antennas at the fading emulator, and this is very important for controlling the correlation coefficient. In the uplink illustrated in Figure 2b, channel reciprocity theory is used to describe that radio waves emitted from the DUT antennas received by the BS antennas via the probes surrounding the DUT. As mentioned in Section 2, in this paper, the initial phase of the probes represents the BS correlation characteristics for the whole uplink channel including the path and the BS antenna properties. The incoming signal at the BS is calculated by combining the signals from all the probes that are superimposed on the received signal and the phase-shift values of the probes.