## 3 Experimental Results  
### Number of Freezes and Freeze Intensities  
A frozen video frame occurs as a single frame of video content being repeatedly shown on the HMD. As such, a freeze is declared when at least two consecutive video frames are identical. The number of freezes counts the freeze events detected in an observed video stream irrespective of the frame length. Further, the freeze intensity as a relative measure of the number of frozen frames with respect to the total number of observed video frames can be defined as  
\[I_{\mathrm{f}}=\frac{N_{\mathrm{f}}}{N_{\mathrm{o}}} \tag{1}\]  
where \(N_{\mathrm{f}}\) denotes the number of frozen video frames and \(N_{\mathrm{o}}\) is the total number of observed video frames. Because the freeze intensity accumulates the contributions of the four quadrants, (1) can be expressed as  
\[I_{\mathrm{f}}=\frac{\sum\limits_{i=1}^{4}N_{\mathrm{f},i}}{\sum\limits_{i=1}^ {4}N_{\mathrm{o},i}} \tag{2}\]  
where \(N_{\mathrm{f},i}\) and \(N_{\mathrm{o},i}\), respectively, denote the number of frozen video frames and total number of observed video frames in the \(i\)-th quadrant. In the following, the number of freezes and the freeze intensities measured in this experimental study are reported. Table 1 shows the number of freezes and freeze intensity that were obtained from the data traces when accumulated over the four quadrants. It can be seen from the table that both measures increase with the increase of the distance from \(d=2.5\,\mathrm{m}\) to \(12.5\,\mathrm{m}\). A further increase of the distance to \(d=15\,\mathrm{m}\) results in a decrease of the number of freezes  
Figure 6: Definition of full-swivel chair rotational movement pattern in terms of initial azimuthal angle and covered quadrants: (**a**) \(\phi_{0}=0^{\circ}\) covering Q1 and Q4, (**b**) \(\phi_{0}=90^{\circ}\) covering Q2 and Q1, (**c**) \(\phi_{0}=180^{\circ}\) covering Q3 and Q2, (**d**) \(\phi_{0}=270^{\circ}\) covering Q4 and Q3. and freeze intensity. In this case, the transmitter is moved in the narrower extension of the multi-purpose lecture hall (see Figure 2) which may assist in directing energy residing in the antenna sidelobes toward the room similar as a waveguide. Figure 7 shows the number of freezes that were detected in the four quadrants for the selected six distances \(d\) between transmitter and receiver. No freezes were observed at the distances \(d=2.5\,\mathrm{m}\) and \(d=5\,\mathrm{m}\) while only two freezes were detected in Q3 at the distance \(d=7.5\,\mathrm{m}\). A further increase of the distance also increases the number of freezes in the quadrants with the highest impact observed in Q3. A reason for the dominance of freezes in Q3 may be attributed to the materials at the different walls of the multi-purpose lecture hall and the more ragged room topology in Q4 compared to Q1 that may influence secondary reflections (see Figure 2). It is also observed that the total number of freezes and the number of freezes associated with Q3 and Q4 reduces with the increase of distance from \(d=12.5\,\mathrm{m}\) to \(d=15\,\mathrm{m}\). This behaviors may also be attributed to the room topology as the transmitter moves into the more narrow extension of the multi-purpose lecture hall at the right-hand side of the floor plan (see Figure 2). It may be conjectured that the narrow extension acts as a waveguide that assists focusing the energy of the mainlobe and sidelobes of the beamforming antenna. Figure 8 shows the freeze intensities for the different scenarios, i.e., four quadrants and six distances:  
\[I_{t,i}=\frac{N_{t,i}}{N_{\mathrm{o},i}},\ \ \ i=1,2,3,4 \tag{3}\]  
where \(I_{t,i}\) denotes the freeze intensity in the \(i\)-th quadrant. The highest freeze intensities were observed in Q3 and Q4 for \(7.5\,\mathrm{m}\), \(10\,\mathrm{m}\), and \(15\,\mathrm{m}\) and tightly followed by Q3 for \(12.5\,\mathrm{m}\). Similar as for the number of freezes, reasons for the observed freeze intensities may