# 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  
The target channel echo signal contains information about the target distance (i.e., fiber length), laser DPN, and other system errors. Using the compensation method described in Section 2, we compensated for the phase noise of the signal through various strategies. We then performed one-dimensional matched filtering on the compensated signal, and Figure 7 presents the results. Table 2 details the fitting parameters. \(FL_{1}\), \(FL_{2}\) and \(FL_{tar}\) are estimated values of the fiber lengths for reference channel 1, reference channel 2, and the target channel, respectively. \(N_{1}\) and \(N_{2}\) are the cascaded orders of differential phases with long and short delays, respectively. The PLE ratio refers to the mismatch delay ratio (\(\Delta\tau_{0}/\tau_{1}\)), as shown in Equation (10). Figure 7a illustrates the matched filtering result with uncompensated DPN. The system transmits the linear frequency-modulated signal through a 650 m optical fiber, creating an optical path approximately 34 times the laser coherence length. Ideally, a spike-shaped delta function (\(\delta\)) should be observed at the center; however, the laser phase noise leads to envelope broadening. Referring to the delayed self-heterodyne theory for linewidth measurement, which, in this case, far exceeds the laser coherence length, the extent of envelope broadening is roughly twice the laser linewidth. This matched filtering result complicates the extraction of peaks and the determination of the round-trip distance (delay time), thereby hindering subsequent ISAL imaging processing. To better demonstrate the inadequacy of relying solely on a single short-delay channel for DPN compensation, we present the results after compensation in Figure 7b. Due to the short-delay compensation, several orders accumulate during the CGP process (short-delay DP cascading order \(N_{2}=133\)), increasing the phase estimation error. This results in spurious peaks erroneously appearing near the central position, which do not correspond to any actual target. When the amplitude of these spurious peaks approaches or exceeds that of the central peak, it can lead to misjudgments in target distance determination, adversely affecting practical applications. Additionally, the estimated reference distance (\(FL_{2}=5.116\)) significantly deviates from the chosen fiber length (4 m). Figure 7c1 presents the matched filtering results of the single-channel long-delay compensation method when the cascade order estimation is accurate (long-delay DP cascading order \(N_{1}=31\)). The \(\delta\) function remains distinctly recognizable, indicating that this method effectively compensates for most of the DPN. Building on this coarse compensation, the data from the short-delay channel (reference channel 2) are utilized for \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Index** & \(FL_{1}\) **(m)** & \(N_{1}\) & \(FL_{2}\) **(m)** & \(N_{2}\) & **PLE Ratio** & \(FL_{tar}\) **(m)** \\ \hline Figure 7b & - & - & 5.116 & 133 & - & 680.428 \\ Figure 7c1 & 21.692 & 31 & - & - & - & 672.452 \\ Figure 7c2 & 21.692 & 31 & 4.340 & 1 & - & 676.792 \\ Figure 7c3 & 21.692 & 31 & - & - & 0.194 & 676.660 \\ Figure 7d1 & 21.687 & 30 & - & - & - & 650.610 \\ Figure 7d2 & 21.687 & 30 & 4.386 & 6 & - & 676.926 \\ Figure 7d3 & 21.687 & 30 & - & - & 1.186 & 676.331 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fitting parameters for different compensation strategies. fine compensation. As illustrated in Figure 7c2, the noise floor induced by phase noise continues to be suppressed, increasing the SNR of the signal. Simultaneously, the system maintains a high spurious peak suppression ratio (SPSR) (greater than 20 dB), which does not interfere with the subsequent two-dimensional compression. To compare the results of the DRC method illustrated in Figure 7c2, we also employed the phase linear estimation (PLE) method for fine compensation with the results presented in Figure 7c3.