## 2 Definition and Methods of Analysis
### SA-AS-TRP Algorithm  
As previously stated, spurious emissions include harmonic emissions, parasitic emissions, intermodulation products, and frequency conversion products. The FCC first designated the TRP as an indicator for spurious testing and proposed two testing methods that are not commonly used in traditional RF testing: the two-cut method and three-cut method. Regardless of which TRP testing method is used, angular sampling is a key parameter. Proper angular sampling can improve testing efficiency while ensuring measurement accuracy. Angular sampling is also the issue of greatest concern for various testing organizations. Currently, the determination of angular sampling is still based on traditional TRP testing for radio-frequency radiation. However, the DUT in spurious emission testing cannot be treated as an antenna array as in traditional TRP testing for RF radiation, and the two-cut and three-cut methods are also not applicable to traditional statistical methods. The specific reasons are as follows. Firstly, there are many types of millimeter-wave terminal antennas [5], and only the main radiation frequency depends on the antenna type. Spurious emissions are not directly related to the antenna type unless there are defects in the antenna design. Spurious emissions are unwanted emissions that accidentally occur. Secondly, in practical testing, the location information of spurious emissions is unknown, and the DUT behaves like a \"black box\". In principle, spurious emissions may be emitted from anywhere within the \"black box\". Finally and most importantly, in the three-step spurious testing specified by the FCC, it is explicitly required to record the frequency and location information of the maximum EIRP during the initial exploratory scan (including the position of the turntable, the height of the antenna tower, and the orientation of the DUT). Then, in TRP testing, the DUT needs to be repositioned based on the information recorded during the initial exploratory scan to ensure that the beam of spurious emissions can be aligned with the orthogonal cuts of the coordinate system to include the beam peak. Figure 3: Geometry of orthogonal cuts. The red and blue indicate two mandatory cut grids (two-cut method), while the yellow indicates an optional cut grid (three-cut method). In this section, we propose the SA-AS-TRP algorithm. The algorithm assumes the DUT is a \"black box\" with the entire mechanical dimensions. Namely, its antenna structure is ignored, and the focus is only on the HPBW of the DUT radiation beam. As in practical tests, the beam radiation from the DUT always orients toward the center of the coordinate system, as shown in Figure 1. Thus, the beam can be aligned with the orthogonal cuts of the coordinate system to include the beam peak based on exploratory scans. The statistical variable in the algorithm is the HPBW of the emission beam. The beams are random and cannot be predicted in advance. In order to cover all possible situations, two ranges of the HPBW model are considered in this study, i.e., \([10^{\circ},50^{\circ}]\) and \([2^{\circ},10^{\circ}]\). Furthermore, the \(\Delta\theta_{\text{ref}}\) and \(\Delta\phi_{\text{ref}}\) are determined by the physical size of the DUT. One of the main features of the discrete summation method is the tradeoff between the measurement time and the accuracy of TRP estimation. The reference angular step, which is the angular step required for accurate TRP assessment when using the full spherical grid without errors, is defined as follows:  
\[\Delta\theta_{\text{ref}}=\min\left(15^{\circ},\frac{180^{\circ}}{\frac{ \pi D}{\lambda}}\right) \tag{8}\] \[\Delta\phi_{\text{ref}}=\min\left(15^{\circ},\frac{180^{\circ}}{ \frac{\pi D_{\text{ref}}}{\lambda}}\right)\]  
where \(\lambda\) is the wavelength. \(D\) and \(D_{\text{cyl}}\) are the spherical diameter and cylindrical diameter, respectively. In principle, any part of the equipment can act as an active or passive radiator.