## 3 Simulation Results and Discussion
Therefore, we statistically analyzed the effect of the sampling step on the TRP with the SA-AS-TRP algorithm. Figures 5 and 6 show the empirical cumulative distribution functions (CDFs) of the TRP error with different ranges of HPBWs for the spherical grid method. The TRP error is \(\Delta\)TRP in Equation (11). Here, \(\text{TRP}_{\text{measured}}\) was calculated by using the spherical grid method with different sampling steps, and \(\text{TRP}_{\text{target}}\) was calculated with the reference step in Equation (10). Specifically, the TRP error was made when not measuring a dense full sphere. In particular, the discretized grid adopted in this paper is \(\Delta\theta=\Delta\phi/2\). Although the \(\text{TRP}_{\text{target}}\) is considered to be the most accurate TRP, some HPBWs may yield a smaller TRP when sampled at more suitable angles, resulting in a negative error value. This negative error is not expected to be significant, as it is primarily caused by the discretized grid method and computational errors. Generally, TRP values obtained from other sampling steps are greater than those obtained under the reference step, as a larger sampling step corresponds to a larger value and the error is positive. The spherical grid method is a classical method of TRP testing for radio-frequency radiation, and its TRP error (caused by angular sampling) is always less than that of the two-cut method and the three-cut method. As shown in Figures 5 and 6, when the HPBWs of the spurious beam were in the range of \([10^{\circ},50^{\circ}]\), keeping the sampling step within \(10^{\circ}\) ensured that 95% of the TRP error was almost zero. However, when the  
Figure 4: \(\Delta\)TRP as a function of HPBWs and sampling steps with three method. HPBWs were in the range of \([2^{\circ},10^{\circ}]\), 95% of the TRP error was nearly above 2 dB if the sampling step was \(10^{\circ}\), and the step that was able to satisfy the 95% confidence interval was less than \(6^{\circ}\). Furthermore, according to the SA-AS-TRP algorithm, we used the STD to determine the measurement uncertainty is caused by angular sampling for the three methods. Figures 7 and 8 show the STDs of \(\Delta\)TRP for the three methods. When the HPBWs were in the range of \([10^{\circ},50^{\circ}]\), the curves calculated with the three methods all increased with the increase in the sampling step. The curves of the two-cut method and the three-cut method had a downward trend and an upward trend in the step range from \(5^{\circ}\) to \(15^{\circ}\). This was because some sampling steps symmetrically aligned beams with the orthogonal cuts of the coordinate system. Consistent with the conclusion obtained in Figure 5, when the sampling step was less than \(10^{\circ}\), the STDs of \(\Delta\)TRP were almost zero. This meant that the measurement uncertainty caused by a sampling step within \(10^{\circ}\) could be ignored for the spherical grid method. However, for the two-cut and three-cut methods, the STD of \(\Delta\)TRP reached 2.3 dB and 2.2 dB, even if the step was a reference step. Therefore, the acceptable sampling step was determined by the results of the spherical grid method. Consequently, when the HPBWs were in the range of \([10^{\circ},50^{\circ}]\), the maximum angular sampling should have been \(10^{\circ}\), but the measurement uncertainty of the two-cut method and three-cut method needed  
Figure 5: Empirical CDFs for HPBWs in the range of \([10^{\circ},50^{\circ}]\) and the spherical grid method based on 10,000 samples. Figure 6: Empirical CDFs for HPBWs in the range of \([2^{\circ},10^{\circ}]\) and the spherical grid method based on 10,000 samples. to be considered, and these were 2.19 dB and 2.08 dB, respectively. Similarly, when the HPBWs were in the range of \([2^{\circ},10^{\circ}]\), the curves also increased with the increase in the sampling step, and the curves of the two-cut and three-cut methods basically coincided.