## 1 Introduction  
Oscillators (or atomic clocks) are widely used in radar, communications, navigation, robot control and metrology electronic systems. Affected by the oscillator circuit itself and the external environment, their frequency or phase is constantly changing with the disappearing symmetry property, which affects the function and performance of the communication or measurement system. The phase noise of an oscillator is a key measure of oscillator performance. In the frequency domain, phase noise appears as a sideband spectrum distributed on both sides of the carrier signal, and in the time domain, it appears as phase jitter. Taking the communication system as an example, the phase noise of the received signal and the phase noise of the local oscillator signal are transmitted during the up-conversion process, so that the transmitted signal and the baseband signal to be processed contain a large amount of phase noise, which affects the anti-interference ability of the transceiver system and the reception. The signal-to-noise ratio of the signal will eventually result in bit errors. Therefore, it is very important to study and reasonably allocate phase noise indicators. In the field of satellite radio technology, there are more and more payload systems that couple communication and measurement functions, such as satellite navigation systems, formation satellite inter-satellite link systems and deep space exploration satellite-ground link systems. Previous studies on the performance of communication measurement systems focused on the analysis of thermal noise, focusing on the coupling relationship between the carrier-to-noise ratio and bit error rate. In recent years, scholars have gradually begun to study the influence of phase noise on the comprehensive performance of communication measurement. The authors of [1] analyzed the influence of phase noise on the performance of relay satellite TDRSS data transmission systems, and initially gave the relationship between phase noise and bit error rate. The authors of [2] analyzed the influence of the phase noise of the receiver's local oscillator on the communication performance and gave a BER prediction algorithm in the case of abrupt changes in the phase noise. The authors of [3; 4] focused on the effect of phase noise on the demodulation performance of the receiver under QPSK modulation. The authors of [5] present a method to suppress common-mode phase error and inter-carrier interference caused by phase noise in full-duplex OFDM systems. The simulation results show that compared with the traditional SI elimination scheme, the proposed method has significantly improved the SI elimination capability. Based on theoretical analysis and experimental research, the authors of [6] compared the influence of two local oscillator signals with different phase noise characteristics on the reception bit error rate (BER) performance of communication systems and found that the near phase noise of the local oscillator signal source has a significant effect on the bit error rate performance. In addition, the method of selecting the digital phase-locked loop bandwidth at the receiving end to suppress the phase noise of the local oscillator signal source is discussed. The authors of [7] discussed the phase noise problem in millimeter wave systems, and reviewed various emerging phase noise problems and corresponding solutions for future 5G wireless networks. A new pilot-assisted estimation and compensation (PEC) method is proposed to reduce phase noise, and the suppression ability of this method on phase noise in millimeter wave and microwave systems is comprehensively compared. The authors of [8] proposed a communication transceiver design method which can effectively reduce the phase noise contained in the multi-run interference components.