## 3 Experimental Results, Verification, and Discussion  
To verify the correctness of the proposed correction method, we conducted measurements on a two-channel PADC system. As depicted in Figure 1, wavelengths of 1550.116 and 1540.577 nm are selected for these experiments, and the MZM modulator has a 3 dB  
Figure 4: Interpolation of channel 1 and shift process of channel 2.  
bandwidth of 28 G to ensure the loading of broadband RF signals. The bandwidth of the selected PD is 10 GHz, with a built-in, low-noise amplifier (LNA). The EADC has a 3 dB bandwidth of 8 GHz and a sampling rate of up to 5.2 GSa/s. The adjustable fiber delay line TDL with an adjustment accuracy of less than 10 fs is selected within a range of 330 ps. For a sampling rate of 5.2 GSa/s, the sampling period is \(t_{\mathrm{s}}=1/5.2\) G = 192.308 ps, which ensures that the EADC can find the peak of the optical pulse within one period. Two detection RF signals, i.e., \(f_{1}=100\) MHz and \(f_{2}=200\) MHz, were selected to measure the misalignment of the PADC system. Assuming that the refractive index n in the fiber core is \(n=1.5\), and the speed of light in vacuum is \(c=3\times 10^{8}\) m/s, for the \(f_{2}=200\) MHz optical pulse signal, the fiber length that light propagates in one period is \(L_{2}=c/(nf_{2})=1\) m, which ensures that the misalignment can be found within the 1 m fiber length range. For the \(f_{1}=100\) MHz optical pulse, the misalignment can be found within the \(L_{1}=2\) m range. In general, the fiber misalignment of our PADC system or the equivalent fiber length misalignment of the electrical phase misalignment from other optoelectronic or electronic devices (such as PD, EADC, RF lines, etc.) will not exceed 1 m. Therefore, these two detection RF signals can be used for determining the fiber length misalignment and correct it. According to the misalignment correction method proposed in Section 2.2, the EADC uses a 5.2 GSa/s sampling rate to process the collected 35 K of data. Assuming channel 2 shifts \(K_{\mathrm{f}}\) sampling periods forward or \(K_{\mathrm{b}}\) periods backward, respectively, two MRMSEs will be obtained. For the two selected detection RF signals, the measurement results are shown in Table 1. That is, for the \(f_{1}=100\) MHz RF signal, when channel 2 moves forward by 12 positions, an MRMSE_f = 44.4174 will be obtained, and the maximum root mean square error obtained in this direction is 1087.30. When channel 2 moves backward 40 positions, an MRMSE_b = 45.3537 will be obtained, and the maximum root mean square error in this direction is 1087.32. For the same PADC system detecting the \(f_{2}=200\) MHz RF signal, when channel 2 shifts forward by 12 positions or backward by 14 positions, an MRMSE_f = 28.9738 and MRMSE_b = 30.6193 will be obtained, and the maximum root mean square errors obtained in both directions are 1169.10 and 1169.17, respectively. So, for the two-channel PADC system with a 5.2 GSa/s sampling rate of each EADC, the misalignment between channels is 12 sampling periods, and channel 2 needs to lag by 12 sampling periods to synchronize with channel 1. Thus, the PADC system can be improved by lengthening the fiber length corresponding to channel 2 by approximately \(12\times(c/n)\times t_{\mathrm{s}}\), or shortening the fiber length of channel 1, which can synchronize the multi-channel PADC system. Alternatively, without changing the PADC system, here, the data should be phase shifted before directly synthesizing the original signal. The two channel signals of 100 MHz collected by the PADC system are shown in Figure 5. Figure 5(a1,b1) show the raw data collected by two channel EADCs, with the ENOBs of channel 1 and channel 2 being 4.9230 and 4.3192 bits and average peak-to-peak values of 1596 and 1484, respectively. It can be observed that the signal power of channel 2 is significantly lower than that of channel 1, and the maximum values of data collected by channel 2 have greater jitter, owing to the relatively higher PD noise in channel 2 and a corresponding lower ENOB.