## 1 Introduction  
The fifth-generation (5G) mobile communication network has opened up a new paradigm through the organic integration of ubiquitous communication, computing, and control capabilities. The sixth-generation (6G) mobile communication network will further connect the physical world and the digital world through the \"intellicise\" network architecture [1, 2]. This is envisioned with many new technologies for enhancing network performance [3, 4]. Among them, the millimeter-wave (mmWave) and terahertz technologies are considered the key technologies of the intellicise communication system. With the application of these technologies, the antenna systems of transmitters have changed greatly [5, 6]. The most important change is that antenna systems are permanently integrated into distributed transmitter terminals to reduce space and interconnection losses [7, 8]. This change has brought great challenges to the electromagnetic compatibility (EMC) testing of transmitters [9, 10]. At present, many organizations worldwide, such as the European Telecommunication Standard Institute (ETSI), the China Communications Standards Association (CCSA), and the Third-Generation Partnership Project (3 GPP), are actively specifying EMC standards for transmitter terminals. However, most of the standards are for the FR1 (410 MHz-7125 MHz) frequency band, while for the FR2 (24,250 MHz-52,600 MHz) band, the standards are still under discussion. For the United States, which is the main market for mmWave terminalsat present, the Federal Communications Commission (FCC) stipulates the certification requirements for such equipment, and only terminals that meet its requirements can be sold in America. The main technical parameters involved in the regulations are the radiated RF output power, occupied bandwidth, unwanted radiated emissions, and frequency tolerance [11]. The test for unwanted radiated emissions is much different from that in the FR1 band. The regulations specify that the limit for unwanted radiated emissions from mmWave terminals is the total radiated power (TRP) rather than the traditional equivalent isotropically radiated power (EIRP) limits. The main idea of TRP testing for unwanted radiated emissions is the same as that of traditional TRP testing with radio-frequency radiation. It is essentially calculated by using the integral of the power flux in the corresponding state on a spherical surface in the far field. In practical tests, the discrete sampling method is usually used to approximate the continuous integral to a discrete summation. For discrete methods, the sampling step in the azimuth and elevation directions is a critical parameter in TRP testing. The test accuracy increases with the decrease in the sampling step, but the testing time also increases. Therefore, it is necessary to explore a way to have the best of both worlds. On one hand, the sampling step must be small enough to ensure measurement accuracy. On the other hand, unnecessary oversampling should be avoided to improve measurement efficiency. The full spherical grid method with uniform sampling is usually used for the traditional TRP testing with radio-frequency radiation. The impact of angular sampling on the testing accuracy of this method can be analyzed using statistical analysis [12; 13]. First, antenna array patterns with different numbers of elements are randomly generated as the sources. Then, a random rotation matrix is used to rotate the source positions. Simultaneously, the TRP for the grid can be calculated using the angular step of interest. The above steps are repeated 10,000 times, and the TRP error for each angular step is counted. The Cellular Telecommunications Industry Association (CTIA) stipulates that TRP errors from angular sampling within 15\({}^{\circ}\) are negligible in TRP testing with radio-frequency radiation.