## 1 Introduction  
Chromatic dispersion (CD) is an important optical characteristic of optical fiber, which is caused by the different propagation speed of light with different frequencies in optical fiber. With the increase of the speed and distance of the optical transmission system, CD has become a huge obstacle to the development of optical transmission systems to ultra-high speed and ultra-long distance [1]. In analog transmission, CD causes harmonic distortion, which reduces the optical signal-to-noise ratio (OSNR) of the system; In digital transmission, CD causes the broadening of optical pulses, resulting in the superposition of front and rear pulses, aggravating inter-symbol crosstalk, increasing the system bit error rate, and limiting the transmission rate and communication capacity. Although optical amplification technology can effectively compensate the loss of optical power in optical fiber transmission, after long-distance transmission, the optical fiber communication system will accumulate a large amount of CD, which will lead to serious pulse broadening, signal distortion, and loss of information. Therefore, CD has become the main factor restricting the transmission distance of the high-speed optical fiber communication system. In Addition, CD and fiber nonlinearity are the main destructive phenomena in high-speed data rate fiber optic communication systems. In order to realize high-speed optical communication systems and networks, the pulse spread caused by group velocity dispersion (GVD) and optical Kerr effects must be compensated. With the further improvement of transmission baud rate, the system CD tolerance decreases rapidly, which greatly limits the growth of the transmission distance and the transmission rate of the system [2; 3; 4]. In a coherent optical communication system, CD compensation in a fixed optical fiber link can be realized by digital equalization in the receiver, but the premise is to know the final accurate cumulative dispersion value. Although this reduces the need for CD compensation in the optical domain, the CD range that needs to be monitored increases significantly in an uncompensated link. On the other hand, in dynamic reconfigurable optical networks, the CD exhibits dynamic time-varying characteristics with the dynamic switching of paths. Therefore, in order to compensate the CD by digital signal processing, it is necessary to obtain the accurate cumulative CD value in advance by CD estimation. With the improvement of the optical fiber communication rate, the increase of transmission capacity and the continuous growth of transmission distance, the accumulation of CD can easily exceed the CD tolerance of the system. Coupled with the random fluctuation of CD amount, CD compensation and real-time CD monitoring must be carried out for the system. In the signal processing flow of the coherent communication receiver, since the CD estimation is in the first step, at this time, other impairments in the link have not been compensated and equalized, so the CD estimation method needs to be able to resist the impact of all other link impairments, which puts forward higher requirements for the CD estimation method. Therefore, how to effectively monitor the CD of the system in real time has recently become a hot research topic of scholars at home and abroad [5]. The existing CD monitoring methods can be divided into two categories: one is for incoherent detection system and the other is based on a coherent detection system. Methods based on an incoherent detection system mainly include methods based on RF clock power detection [6; 7], methods based on relative group delay between vestigial sidebands (VSB) [8; 9], methods based on asynchronous delay tap sampling [8; 10], and methods of full spectrum analysis based on nonlinear optics [11]. The RF clock power detection scheme utilizes the principle that the optical link CD effect causes the phase difference between the upper and lower side-band phases of the optical signal spectrum.