# Measurement Grid Optimization for OTA Testing of 5G Smart Watches
## 4 Simulated and Measured Results  
Based on the settings aforementioned, various constant step size grids with reduced angular resolution are analyzed. For the example of the \(15^{\circ}\) constant step size grid, the histogram for the normalized TRP is shown in Figure 5. The sample histogram of theoretical normal distribution is also provided for comparison. The histogram of the normalized TRP exhibits a normal distribution from the comparison. The calculated STDs at different bands are tabulated in Table 3 and also illustrated in Figure 6 for comparison. The following observations could be obtained from the comparison:  
Observation 1: with the same grid configuration, radiation patterns that exhibit larger variations over angles (i.e., the more lobed patterns) could have higher calculated STDs (i.e., higher MU for grid configuration);  
Observation 2: typically, as the grid resolution decreases, the total number of grid points decreases, whereas the calculated STD increases. Furthermore, it is worth noting that the more evenly distributed grid configurations (where \(\Delta\theta\) and \(\Delta\phi\) are closer in value), even with fewer grid points, may exhibit smaller calculated STDs. For instance, the 15/45 grid with 90 grid points exhibits larger calculated STDs than the 30/30 grid with 62 grid points, across almost all bands; \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **836 MHz** & **900 MHz** & **1575 MHz** & **1950 MHz** & **2350 MHz** & **2450 MHz** & **2590 MHz** \\ \hline Directivities [dBi] & 5.05 & 5.00 & 6.02 & 7.56 & 6.51 & 7.40 & 7.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The measured directivities at different bands. Figure 4: Illustration of reference patterns at different bands: (**a**) 836 MHz; (**b**) 900 MHz; (**c**) 1575 MHz; (**d**) 1950 MHz; (**e**) 2350 MHz; (**f**) 2450 MHz; (**g**) 2590 MHz. Observation 3: at 836 and 900 MHz, the measured patterns exhibit significantly greater variations over angles, which can be attributed to the low radiation efficiency of lower band antennas in a very limited space. Moreover, these two bands are not the major bands used for smart watches;  
Observation 4: for TIS testing, the 30/30 grid, which is the currently required TIS grid in both CTIA and 3 GPP specifications, especially for smartphones and notebooks, corresponds to an average STD of 0.0862 dB across all bands being analyzed. From the test-time reduction perspective, the required minimum number of grid points can be reduced to speed up TIS testing, albeit at the expense of a proper relaxation of the realized MU limits. Accordingly, it is proposed that a proper relaxation in MU can be allowed for grid point reduction, such that the calculated STDs remain below 0.20 dB. In other words, it is recommended to adopt 0.20 dB as the resulting MU limit for TIS grids of 5G smart watches, which is approximately one-tenth of the currently defined expanded uncertainty limits for TIS testing. Compared to the benefit of approximately 60% grid points reduction, the expense of additional 0.12 dB in MU could be deemed acceptable and is thus recommended. Given that the expanded uncertainties for TRP/TIS testing are calculated using the root-sum-of-squares method, rather than being directly summed in dB, the impact of using the coarse grid on the final expanded uncertainty or the labs' assessed MU could be significantly smaller than the increase in MU for the TIS grid itself, specifically, much smaller than 0.12 dB;  
Observation 5: for TRP testing, the 15/15 grid--which is the currently required TRP grid in both CTIA and 3 GPP specifications--corresponds to an average STD of 0.0138 dB across all bands being analyzed, implying that the impact of the currently defined grid on TRP testing accuracy can be considered negligible. Therefore, in pursuit of grid point reduction, it is recommended to adopt 0.10 dB as the maximum MU limit for 5G smart watch TRP grids.