# Laser Phase Noise Compensation Method Based on Dual Reference Channels in Inverse Synthetic Aldar
## 4 Results and Analysis
### Fiber-Based Signal Transmission Experiment
#### 4.1.1 One-Dimensional Matched Filtering
Although the envelope broadening resulting from the phase noise remains evident, it does not compromise the purity of the central \(\delta\) function. We also considered a potential issue: when the SNR is low or there are inadvertent errors during the optimization process, the estimation of the cascade order in coarse compensation may be biased. The results depicted in Figure 7d1 illustrate the scenario when only the longer delay channel is employed for compensation, but the cascade order is underestimated (\(N_{1}=30\)). Even one order of uncompensated error can result in envelope broadening. The noise component obscures the effective signal peak, preventing the achievement of satisfactorily matched filtering. Based on the inadequate compensation result illustrated in Figure 7d1, the phase extracted from the short delay channel (reference channel 2) is utilized to complete the fine compensation. Figure 7d2 demonstrates that at the delay time position corresponding to the target distance, a spike-shaped \(\delta\) function emerges, which is free from noise interference. In summary, the DRC compensation method can effectively \"remediate\" the residual error associated with the single-channel long-delay compensation method even when the cascade order is insufficiently estimated, achieving significant range compression. Similarly, we employed the PLE method for fine compensation with \(N_{1}=30\). Due to the longer mismatch delay, the deviation between the linear estimation result and the actual phase increases. Consequently, in Figure 7d3, the suppression of the noise floor is not as effective as shown in Figure 7d2, resulting in a slightly lower SNR. Figure 7: Pulse matching filtering results of the echo signal with different compensation strategies. (**a**) Without compensation; (**b**) only short delay coarse compensation; (**c1**) coarse compensation with \(N_{1}=31\); (**c2**) fine compensation with dual reference channel (DRC) using \(N_{1}=31\); (**c3**) fine compensation with phase linear estimation (PLE) using \(N_{1}=31\); (**d1**) coarse compensation with \(N_{1}=30\); (**d2**) fine compensation with DRC using \(N_{1}=30\); (**d3**) fine compensation with PLE using \(N_{1}=30\). We use peak power and SNR as evaluation indicators to quantify the effects of various compensation strategies. Higher values indicate better compensation effects. Figure 8 illustrates that the fine compensation method with DRC can improve the performance of the SRC coarse compensation method and achieve slightly better results than the PLE method in terms of SNR, whether the cascading order is accurate ((c1)-(c3)) or biased ((d1)-(d3)). In addition, it is important to note that when \(N_{1}=31\), precise compensation yields the best results, with parameter estimates closely aligning with nominal values, although some deviations are observed: \(FL_{tar}=676.792\) (nominal value: 650), \(FL_{1}=21.692\) (nominal value: 20), and \(FL_{1}=4.340\) (nominal value: 4). These deviations can be attributed to several factors:  
1. Measurement Errors: Inaccuracies in the fiber length and refractive index can lead to incorrect nominal values. 2. Optical Path Contributions: The \(FL_{tar}\) of the target channel includes the optical paths through various devices, such as the EOM, EDFA, and beam splitter. Notably, EDFA often employs optical fibers extending over tens of meters for laser amplification. Similarly, the estimated values of \(FL_{1}\) and \(FL_{2}\) incorporate optical paths associated with the AOM, EVOA, and beam splitter. 3. System-Related Errors: Random errors within the system and the precision of the algorithm's search capabilities can also influence the results. In the optical frequency domain reflectometry (OFDR) system, achieving high estimation accuracy of the target channel distance is essential with acceptable errors in the order of microns. In contrast, in ISAL imaging, the focus shifts to image quality, which diminishes the importance of optical path differences introduced by optical fiber devices, offering minimal benefits.