# A Scalable Spatial-Temporal Correlated Non-Stationary Channel Fading Generation Method
## 4 Measurement Results and Analysis  
### Statistical Properties of Generated Fading  
To validate the proposed method in this paper, a \(4\times 4\) MIMO channel fading emulation is implemented on a Xilinx XC7 VX690T FPGA chip using the method proposed in this paper. Channel parameters such as carrier frequency, number of transmitting antennae, number of receiving antennae, delay, power, fading type, maximum Doppler frequency, subchannel correlation coefficients, emulation time, status update interval, and others are input into the FPGA platform using the VIVADO2020.2 software to generate output fading with specific channel characteristics. Additionally, the ILA tool in the VIVADO platform is utilized to capture the output data into MATLAB for the analysis of statistical characteristics of the output fading. Furthermore, the output fading envelope is observed using the Rohde & Schwarz RTM1054 oscilloscope, and the DPSD of the output fading is observed using the Agilent N9340B spectrum analyzer. In order to verify the correctness of the method proposed in this paper in the generation of different output fading envelope distributions, the general scene parameters are set. Specifically, the number of transmitting antennae, the number of receiving antennae, the maximum Doppler frequency and data width are \(P=1\), \(Q=1\), \(f_{m}^{\rm max}=50\) Hz, and \(16\) bit, respectively. The fading type \(i\) as is set as Rice, lognormal, Nakagami, or Weibull, and the emulation time of each fading is \(t=15\) ms. The parameters are sent to the FPGA, and the data are captured by the ILA of the VIVADO platform and fed back to MATLAB for analysis. By using (3)-(6), Figure 6 shows the theoretical value, generated value, and hardware simulation value of the PDF of the time-varying correlation fading in the above scenario. It can be seen from the figure that the theoretical value is in good agreement with the generated value and the simulated value, and the average absolute deviation is about \(1.52\%\) and \(2.47\%\), respectively. Based on the above scenarios, we set A\({}_{0}=0\), m\({}_{\beta}=0,\sigma_{0}^{\rm Sha}=1\), m\({}_{k}=1\), and w\({}_{m}=2\), and use the RTM1054 oscilloscope from Rohde & Schwarz, to observe the waveforms of the relative fading envelopes in different scenarios, as shown in Figure 7. Taking Rice fading as an example, according to the actual simulation results, its fading shape meets the theoretical requirements. Figure 5: Complex multiplier based on data selector. In addition, to verify the reliability of the spatial-temporal correlation characteristics of channel fading, we set the carrier frequency, the number of transmitting antenna, the number of receiving antenna, the fading type, the emulation time, and the status update interval to \(f_{c}=2.4\) GHz, \(P=4\), \(Q=4\), \(i=\) Ric, \(t=25\) s, and \(t_{0}=20\) ms. In Figure 8a, the values of the theoretical time-varying TCF and the generated TCF, simulated TCF at \(t=0\) s and \(12\) s are compared in this simulation scenario. As shown in Figure 8a, the simulated TCF is in good agreement with the theoretical value, and the normalized TCF varies with the theoretical value. Figure 6: PDFs of (**a**) Rice, (**b**) Lognormal, (**c**) Nakagami, and (**d**) Weibull fading envelope. Figure 7: Fading envelopes of (**a**) Rice, (**b**) Lognormal, (**c**) Nakagami, and (**d**) Weibull. time and has time-varying properties. Through the Fourier transform of TCF, one can further compute DPSD, and the measured results are shown in Figure 8c. For the sake of comparison, the DPSDs at the time points of \(t=0\) s and \(t=12\) s were extracted from Figure 8c, whereas their corresponding simulated counterparts are displayed in Figure 8b. The temporal evolution of DPSDs can be observed, exhibiting time-varying characteristics. Based on the parameter setting of the above scene, the normalized omnidirectional antenna is used at the transceiver end, and the distance between the array elements is \(0.5\lambda\).