## 5 Verification in Reverberation Chamber  
Based on the comparative analysis in Section 4.2, it is hypothesized that the RMS delay spread is independent of the frequency in the scenario where free space propagation and/or reflection are the main mechanisms. We used the RC to verify this hypothesis. The RC provides a reliable, controllable, and repeatable multipath environment where reflection is the main mechanism [30; 31; 32; 33].  
The RC is essentially an large, electric metal box, having dimensions of 5.09 m \(\times\) 6.43 m \(\times\) 5.57 m, as shown in Figure 8. In the RC, reflection is the main propagation mechanism [34]. Inside the chamber, the mechanical stirring was performed by two metal paddles that were moved stepwise. The measurement of RMS delay spread in the RC was repeated for 100 different fixed paddle positions spaced by \(360^{\circ}/100=3.6^{\circ}\). For the RMS delay spread estimation, the 100 measurement results were averaged to obtain the mean values. The RMS delay spread in the chamber can be changed by putting different numbers of RF-absorbing material inside the RC. We repeated the measurements for three and four absorbers, respectively. Each piece of the absorber is with 81 cones in a 9 \(\times\) 9 array, the cone width is 6.8 cm, and the cone height is 17.8 cm. The transmitting antenna was directed into a corner of the chamber, and the receiving antenna was placed in the middle of the RC.  
We measured the channel over the whole frequency range from 3.1 GHz to 15.1 GHz, using the same VNA-based measurement system, as shown in Figure 9. Because the sweep points of the VNA are limited to 60,001, sectional measurement was performed over the whole frequency range. We divided the whole range (3.1 GHz to 15.1 GHz) into 12 frequency bands. For each band, the \(S_{21}\) was measured in the 1 GHz bandwidth with 60,001 sweep points.  
Figure 8: NIM (National Institute of Metrology) RC (reverberation chamber). (**a**) appearance of the NIM RC; (**b**) absorbers in the NIM RC.  
Figure 10a shows the measurement results and the linear fitting lines. The slopes of these fitting lines are \(-0.0020\) ns/MHz and \(-0.0026\) ns/MHz for the 3 and 4 absorbers, respectively. It is confirmed that the difference is minimal in the RMS delay spread for the whole sweep frequency range. In order to analyze the behavior of the RMS delay spread for a given frequency band with higher frequency resolution, we use a 200 MHz bandpass filter in postprocessing. This filter is applied to the measured \(S_{21}\) frequency-domain data, and the RMS delay spread is calculated for different filter center frequencies. As shown in Figure 10b, the slopes of the fitting lines are \(-0.0023\) ns/MHz and \(-0.0032\) ns/MHz for the 3 and 4 absorbers, respectively.  
The coherence bandwidths in the RC are calculated via Equation (3) based on the measurement data. It is shown in Figure 11 that the coherence bandwidth is also similar in the frequency range. The slopes for the RMS delay spread and coherence bandwidth are summarized in Table 3. The measurement results imply that the RMS delay spread and coherence bandwidth are not sensitive to the frequency in the RC.  
Figure 10: (color online) RMS delay spread in the NIM RC calculated over (**a**) 1000 MHz bandwidth; and (**b**) 200 MHz bandwidth.  
Figure 9: RMS (root-mean-square) delay spread measurement setup in the NIM RC.