## 1 Introduction
The link CD value is accurately calculated by analyzing the relationship between the RF power spectrum and the residual CD. The principle of the relative group delay scheme between VSB is to use the clock component technology for detection, by extracting the two side-bands of the base-band signal, recovering the clock signal from the two received VSB components, and then analyzing the phase difference between the upper and lower side-band components to realize the monitoring of CD. The principle based on asynchronous delay tap sampling is to extract the characteristic value corresponding to CD from the statistical chart according to the statistical characteristics of the amplitude histogram obtained by asynchronous delay sampling, so as to realize the monitoring of CD. The principle of full spectrum analysis based on nonlinear optics is to map the influence of CD on the signal peak power to the output signal spectrum through nonlinear effects such as cross-phase modulation (XPM), self-phase modulation (SPM), and four-wave mixing (FWM). The corresponding CD information of the system can be obtained only by monitoring the change of the output signal spectrum. These methods often have the disadvantages of a small monitoring range, low accuracy, the need to change the transmitter structure, or the vulnerability to interference by other effects, such as polarization mode dispersion, which cause the cost of the monitoring system to increase, so they are not suitable for high-speed coherent optical communication systems and dynamically reconfigurable optical networks. With the emergence of a modern coherent receiving technology, the complex electric field of optical signals can be accurately measured at a sufficiently high sampling rate, so that numerical algorithms can be developed to monitor and mitigate the impairments caused by transmission. The most common method of performance monitoring using a coherent receiver is the digital signal processing technology developed by a wireless communication system. [12] explained how to use adaptive linear equalizers to mitigate the time-varying damage caused by CD and polarization effects. In order to avoid the additional overhead caused by transmitting known training signals, blind estimation methods such as the constant modulus algorithm (CMA) are adopted. [13; 14; 15; 16] avoided gradient-based optimization on a large number of filter taps by scanning the dispersion value in increments of 200 ps/nm in the range of 15,000 ps/nm and detecting the minimum depth in the CMA cost function. [17] proposed a fast CD estimation method usingthe auto-correlation of the signal power waveform (ACSPW) algorithm. The method obtains the dispersion monitoring curve by performing an autocorrelation on the received signal waveform sampling sequence. A spike will be generated, and the position of the spike represents the magnitude of the dispersion. A CD monitoring method based on CD scanning was proposed by [18]. The peak power-to-average power ratio (PAPR) of the received signal sampling sequence is related to the size of the CD, and the PAPR will reach a minimum value when the CD is zero. By scanning the CD value in a specific range, and then performing CD compensation and calculating the size of PAPR, the size of excellent dispersion can be estimated by finding the minimum value of PAPR [19; 20]. A CD monitoring method based on signal spectrum superposition was proposed. By superimposing the spectrum of the upper and lower side-bands of the signal and performing autocorrelation, the obtained autocorrelation curve will generate two symmetrical peaks, and the position of the peaks indicates the size of the CD. Traditional CD monitoring methods mostly rely on temporary CD compensation or temporary cost function calculation by scanning the CD within a specific range. Estimating the accumulated CD usually takes quite a long time, and the tentative CD compensation scheme needs to consume a lot of processing power in the DSP equalization unit.