# Compensation of Limited Bandwidth and Nonlinearity for Coherent Transponder
## 3 Experimental Results  
### Measured Bandwidth and Nonlinearity  
The proposed technique is validated on a pluggable CFP2-ACO module (CFP2 form factor analog coherent optics) and a DSP ASIC [18]. The pluggable module is a class-2 CFP2-ACO with a linear RF amplifier, which can support 200 Gb/s (gigabit per second) traffic using 16-QAM or 300 Gb/s traffic using 64-QAM, at the baud rate of \(\sim\)30 GBd. The DSP ASIC has the built-in RAM, allowing the scanning of sinusoidal amplitude and frequency as discussed above. To minimize any interruption during the initial calibration, the gain of the RF amplifier and the bias point of MZM remain constant. Figure 2 shows the results over four tributaries with \(\omega\) = 3.77 GHz. Table 1 shows the fitting parameters and relative RMS error. The fitting curves and the measured curves almost overlap, which indicates that the proposed model in Equation (6) is very accurate. In addition, the power imbalance between tributaries and the bias point are determined accordingly. Figure 2: Measurement results versus theoretical analysis for four tributaries. \(\omega\) = 3.77 GHz. Next, we scan the frequency of the sinusoidal stimulus, repeat the measurement and extract the fitting parameters. The purpose is to determine those parameters' dependency on the frequency component. Ideally, we can also extract four fitting parameters from the measurement curve. However, the output power from MZM is quite low at the high frequency close to the baud rate due to the limited bandwidth. We experience a large fitting error if we use four fitting parameters. As the steady-state power remains relatively unchanged, and the bias point has a negligible drift over time, we can assume that \(P_{stdy}\) and \(\beta\) remain unchanged over the different frequencies. Thus, we only extract four fitting parameters from the measurement curve using a sinusoidal stimulus running at a low-frequency \(\omega\), for example at 3.77 GHz as shown in Figure 2. We then apply the same \(P_{stdy}\) and \(\beta\) values to all other measurement curves at different frequencies. We extracted the fitting parameters \(\alpha\) and \(\gamma\) for various frequencies. This improves the fitting error, particularly when \(\omega\) is close to the baud rate. Over the different frequency, the model is accurate as shown in Figure 3.  
Then, we determine the limited bandwidth by dividing the \(\alpha\) value at a higher frequency with the \(\alpha\) value at 3.77 GHz, which is low enough to be used as the reference point. The limited bandwidth \(\alpha\) is plotted in Figure 4 on the left axis. We also calculate the limited bandwidth determined through traditional power measurement. It is done through the following steps: one fixes \(N_{sig}\), then scans \(\omega\), and measures the average output power \(P_{avg}\). Then, the \(P_{avg}\) at the higher frequency is divided by the \(P_{avg}\) close to the DC frequency to determine the limited bandwidth. It is noticeable that both the small-signal result (for example, \(N_{sig}=32\)) and the large-signal result (for example, \(N_{sig}=127\)) show the deviation against the actual bandwidth (\(\alpha\) curve). The reason is that the nonlinear response causes the actual phase shift applied to MZM to be smaller than the intended value. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters 1** & **XI Trib** & **XQ Trib** & **YI Trib** & **YQ Trib** \\ \hline \(P_{stdy}(mW)\) & 0.2712 & 0.2423 & 0.2891 & 0.2613 \\ \(\alpha\) & 1.7396 & 1.7042 & 1.6991 & 1.7803 \\ \(\beta\) & 1.0000 & 1.0000 & 1.0000 & 1.0000 \\ \(\gamma\) & \(-0.4503\) & \(-0.4421\) & \(-0.4429\) & \(-0.4542\) \\ \(Err_{rms}\) & \(4.02\times 10^{-2}\) & \(4.18\times 10^{-2}\) & \(3.95\times 10^{-2}\) & \(3.98\times 10^{-2}\) \\ \hline \hline \end{tabular} \({}^{1}\)\(\omega=3.77\) GHz.  
\end{table} 
Table 1: Fittings parameters for four tributaries. Figure 3: Results over different frequencies. Measurement results agree well with the theoretical analysis.