# A Flexible FPGA-Based Channel Emulator for Non-Stationary MIMO Fading Channels
## 4 Resource Consumption and Measurements
### Measured Results and Analysis  
In order to verify the output channel of proposed emulator, we consider that both of the base station (BS) and MS are equipped with normalized omnidirectional antennas, the carrier frequency is \(f_{c}=2.4\) GHz, and the scatterers are randomly distributed around the BS and MS. The number of paths and sub-paths are six and sixty-four, respectively, i.e., \(N=6,M=64\). Moreover, all these six paths are assumed to be valid over the simulation period. The initial distance between the BS and MS is 318 m. The absolute speed, azimuth angle, and elevation angle of the moving MS are 40 km/h, 10\({}^{\circ}\)-8\({}^{\circ}\cdot t\), and 10\({}^{\circ}\)-0.1\({}^{\circ}\cdot t\), respectively. Other emulation parameters are as follows, \(T_{u}=25\) ms, \(L=10\). Based on the parameter calculation method of GBSM in [27], we can obtain the theoretical time-variant PDP under the above scenario as shown in Figure 8a. As we can see, as the MS has an initial distance of 318 m from the BS, the initial time delay of line-of-sight (LOS) path equals to \(318/(3\times 10^{8})=1.06\times 10^{-6}\) s. The time delay of non-line-of-sight (NLOS) paths can also be calculated and shown in Figure 8a with the dotted line. By using the ILA software, we store and export the data from the hardware emulator, and then analyze the data with Matlab. Finally, the measured time-variant PDP of emulator is given in Figure 8b, which clearly shows that it is consistent well with the theoretical one. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **The Method in [22]** & **The Proposed Method** \\ \hline System sample rate & 100 M & 256 M \\ Slice LUTs & 152,337 & 25,800 \\ Block RAMs & 191 & 116 \\ DSPs & 768 & 160 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hardware resource usage of a \(2\times 2\) MIMO channel emulator. Figure 7: The implementation scheme of interpolation module. Under the same condition, the time-variant DPSD is also tested and verified. With the help of (22) in [27], the theoretical time-variant DPSD is firstly calculated and shown in Figure 9a. For comparison purposes, we also give the simulated time-variant DPSD based on the model in [17] in Figure 9b. It is clearly showed that the part around circles is different from the theoretical one. The main reason is the output Doppler phase of that model is discontinuous which results in the output Doppler frequency or DPSD not accurate. In order to observe the output DPSD directly, a 2.4 GHz cosine signal generated by a Agilent E4438C is adopted as the input signal. Then, the measured DPSD of proposed emulator can be obtained by a spectrum analyzer of ROHDE&SCHWARZ FSV. The measured result is shown in Figure 9c. Due to the randomness and distortion caused by the fixed point process, the measured result can only be qualitatively compared with the theoretical one. Figure 9a,c show that the shape and trend of two DPSDs have a good approximation, which also validates the effectiveness of proposed emulator. Figure 8: **(a)** The theoretical results of time-variant power delay profile (PDP) and (**b**) the measured time-variant PDP of proposed emulator. Figure 9: **(a)** The theoretical results of time-variant Doppler power spectrum density (DPSD), **(b)** the simulated time-variant DPSD of the model in [17], and (c) the measured time-variant DPSD of proposed emulator. Without loss of generality, only the fading envelope PDF of first NLOS path for the first sub-channel is tested and validated. First, the theoretical time-variant PDF of channel fading is derived and shown in Figure 10a. It is apparently showed that the PDF changes over time due to the time-variant channel conditions. Similarly, with the help of Xilinx software development tool, we export the data of output fading envelope from the hardware, and then analyze the distribution by Matlab.