## 1 Introduction
In addition, some special angular sampling methods can be used to reduce the TRP error caused by sparse sampling--for instance, by modifying the equi-angle to eliminate the effect of the metric coefficient and by using generalized spiral scanning to uniformly pick up measured data [14]. Alternatively, the Clenshaw-Curtis quadrature method can be adopted in TRP tests [15]. This method can achieve higher accuracy without increasing the number of sampling points or the measurement time. However, it must be noted that the quadrature method must be judiciously selected by considering the practical OTA setting. These methods have been validated through simulations to demonstrate their effectiveness in traditional TRP testing. However, a TRP testing method for unwanted radiated emissions was already introduced by the 3 GPP [16; 17] and the American National Standards Institute (ANSI) [11] in recent years. Although the main idea of TRP testing for unwanted radiated emissions is the same as that of traditional TRP testing for radio-frequency radiation, the specific test methods and operations are different due to the large frequency band coverage and the unknownness of radiation. The testing procedure for unwanted radiated emissions regulated by the FCC is divided into three steps [18]. 1. An initial exploratory scan is conducted to optimize the test time by identifying a set of frequencies that need to be further measured by using the EIRP/TRP. It is acceptable to perform maximum EIRP measurements over the required frequency range and compare the measurements with the limit to verify compliance, which is herein referred to as an \"early exit\" condition. If the measured EIRP levels are below the TRP limit, the early exit condition is met, and the device is compliant. If the device does not meet the emission limit at one or some frequencies, then TRP measurements need to be performed only at those frequencies. 2. The decision process involves performing TRP measurements based on the results of the first step and determining which frequencies meet the early exit conditions (based on EIRP measurements) and which frequencies require TRP measurements. 3. The final scan involves the use of various methods of measuring the TRP according to the results of the second step, and the measurements are compared with the limit to verify compliance. Spurious emissions include harmonic emissions, parasitic emissions, intermodulation products, and frequency conversion products, but exclude out-of-band emissions [19]. For these kinds of emissions with narrow radiation beams, the FCC also proposes some simpler TRP testing methods for the third step to improve the measurement efficiency as much as possible. These are the two-cut method and the three-cut method. Similarly to traditional TRP testing for radio-frequency radiation, angular sampling is still the balancing factor for ensuring measurement accuracy and improving measurement efficiency, while it is also a concern for manufacturers and test labs. In the techniques used, the beam of spurious emissions should be aligned with the orthogonal cuts of a coordinate system to include the beam peak based on exploratory scans. Furthermore, any part of the device can act as an active or passive radiator, so it cannot be assumed to be a simple antenna array. Therefore, traditional statistical analysis is no longer applicable to the two-cut and the three-cut methods. To address this problem, we evaluated the correction factor for different TRP measurement methods. In order to verify the effects of angular sampling on TRP, a method of measurement uncertainty analysis based on statistical analysis is proposed. This method is carried out by measuring the TRP of radiation sources with different half-power beamwidths (HPBWs). In particular, the dimensions of the source refer to the entire mechanical dimensions of the device under test (DUT). In the end, simulation results are presented. The rest of this study is organized as follows.