# Measurement Grid Optimization for OTA Testing of 5G Smart Watches
## 4 Simulated and Measured Results
The allowance of additional 0.08 dB in the MU limit, specifically increasing from 0.0138 dB to 0.10 dB, could achieve a grid points reduction by approximately 75%. Similarly, an increase of 0.08 dB in the MU of the TRP grid could result in an increase in the final expanded uncertainty or the labs' assessed MU of much smaller than 0.08 dB;  
Figure 5: Sample histogram of the 10,000 normalized TRPs for the 15\({}^{\circ}\) constant step size measurement grid. Observation 6: based on the recommended criteria above, the TIS and TRP grids could be reduced to 45/45 (26 points) and 30/30 (62 points), respectively, with around a 60% and 75% reduction in grid points, respectively. Given that the overall test time is proportional to the total number of grid points used, a significant reduction in test time can be achieved. The TRP pattern data was collected for seven sample smart watches using standard settings and procedures from [14], covering over 50 bands supported by these devices. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Angular Step Size**} & \multicolumn{1}{c}{**\# of Unique**} & \multicolumn{1}{c}{**836**} & \multicolumn{1}{c}{**900**} & \multicolumn{1}{c}{**1575**} & \multicolumn{1}{c}{**1950**} & \multicolumn{1}{c}{**2350**} & \multicolumn{1}{c}{**2450**} & \multicolumn{1}{c}{**2590**} & \multicolumn{1}{c}{**Ave.**} \\ \hline \(\Delta\theta\) & \(\Delta\varphi\) & Grid Points & MHz & MHz & MHz & MHz & MHz & MHz & MHz & MHz & MHz & \\ \hline \multirow{3}{*}{\(\Delta\theta=15^{\circ}\)} & \(\Delta\varphi=15^{\circ}\) & 266 & 0.0125 & 0.0199 & 0.0052 & 0.0113 & 0.0234 & 0.0129 & 0.0117 & 0.0138 \\  & \(\Delta\varphi=30^{\circ}\) & 134 & 0.0744 & 0.0779 & 0.0368 & 0.0487 & 0.0482 & 0.0372 & 0.0380 & 0.0516 \\  & \(\Delta\varphi=45^{\circ}\) & 90 & 0.1668 & 0.1449 & 0.0590 & 0.0847 & 0.0924 & 0.0775 & 0.0700 & 0.0993 \\ \hline \multirow{3}{*}{\(\Delta\theta=30^{\circ}\)} & \(\Delta\varphi=30^{\circ}\) & 62 & 0.1191 & 0.1215 & 0.0669 & 0.0922 & 0.0820 & 0.0648 & 0.0570 & 0.0862 \\  & \(\Delta\varphi=45^{\circ}\) & 42 & 0.2004 & 0.1694 & 0.0866 & 0.1280 & 0.1166 & 0.0999 & 0.0889 & 0.1271 \\  & \(\Delta\varphi=60^{\circ}\) & 32 & 0.2373 & 0.2151 & 0.1315 & 0.2180 & 0.1859 & 0.1550 & 0.1417 & 0.1835 \\ \hline \multirow{3}{*}{\(\Delta\theta=45^{\circ}\)} & \(\Delta\varphi=45^{\circ}\) & 26 & 0.2748 & 0.2513 & 0.1233 & 0.1654 & 0.1703 & 0.1351 & 0.1179 & 0.1768 \\  & \(\Delta\varphi=60^{\circ}\) & 20 & 0.3450 & 0.2656 & 0.1571 & 0.2574 & 0.2395 & 0.1946 & 0.1778 & 0.2339 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analyses of 10,000 rotations for various constant step size grids [dB]. Figure 6: The comparison of calculated STDs: (**a**) at different bands; (**b**) highlighted illustration of the averaged STDs across all bands. During the TRP testing, only mid-channels were included in this analysis, as the patterns for the low and high channels were deemed similar to those of the mid-channel. The TRPs obtained with the 15/15 grid and Clenshaw-Curtis quadrature are used as the baseline, which is assumed to be accurate. Consequently, the uncertainty associated with various coarse grids, expressed as the delta in TRPs, can be calculated accordingly. The following Table 4 presents the comparison between measured and simulated STDs in the TRP for various coarse grid configurations. Good overall agreement could be observed, with the discrepancies falling within 0.06 dB. These discrepancies could be considered very small, given that during TRP testing, the UEs' output power (i.e., EIRP) could vary by up to 0.5 dB (or even more) throughout the measurement process. As this happens, the radiation pattern will inevitably be changed. However, this variation in output power is not a measurement error, but rather a DUT-related variation that could be unavoidable.