# Compensation of Limited Bandwidth and Nonlinearity for Coherent Transponder
## 4 Discussion  
During the measurement of limited bandwidth and nonlinearity, we adjust the bias voltage so that the MZM is biased at its null point. The optimal bias voltage can be obtained by turning off the  
Figure 6: Experimental setup. A power meter is used to perform initial calibration with sinusoidal stimulus. Coherent receiver and real-time oscilloscope are used to recover the constellation diagram. The processing steps of DSP are also shown.  
Figure 7: Constellation diagram without Volterra filter (**left**) and that with Volterra filter (**right**). Both results are obtained with bandwidth compensation and arcsin compensation.  
modulation signal and scanning the bias voltage. The bias voltage resulting in the minimum output power is the optimal voltage. The coherent IQ transmitter in our experiment is fabricated in Indium Phosphide (InP) material and its bias point is stable during the measurement. As seen from Table 1, the measured bias point factor is close to 1, indicating that the bias point is stably held at the optimal null point. During the measurement, the automatic bias control (ABC) circuit, which is based on the dithering of bias voltage, is turned off to avoid any potential interference. During the normal operation, the ABC circuit is enabled so that any long-term drift can be compensated.  
In addition to the limited bandwidth (\(\alpha\)) and the nonlinearity (\(\gamma\)), our method can also measure the power imbalance (\(P_{stdy}\)) among tributaries and the bias setting point (\(\beta\)). To achieve optimal performance, the power imbalance among the tributaries needs to be minimized. Our method offers a novel way to measure the power imbalance. Once measured, the power imbalance can be compensated by adjusting the variable optical attenuator or the semiconductor optical amplifier which can be integrated into the coherent transmitter [24]. The bias setting can be also optimized by adjusting the bias voltage applied to the MZM.  
The frequency and the amplitude of the sinusoidal stimulus are controlled in the digital domain. Thus, the sinusoidal stimulus is generated with high accuracy. \(N_{\text{sig}}\) and \(\omega\) can be scanned with a fine step, and the corresponding \(P_{avg}\) can be measured. It is well known that by measuring multiple data points and applying the curve fitting, the measurement accuracy can be greatly improved. Assuming \(K\) as the total measurement points, the improvement in the accuracy is proportional to the square root of \(K\). In this way, we can significantly improve the measurement accuracy of the limited bandwidth, the nonlinearity, the power imbalance and the bias point among the four tributaries.  
A Volterra filter which has multiple taps (memory) in the high-order kernels can mitigate the frequency-dependent nonlinear effect. In [7], the memory depth of the second-order kernel is 7 and the memory depth of the third order kernel is 7. Note that the frequency-dependent nonlinear response is also captured during our measurement. Thus, the coefficients of the Volterra filter with the memory can be determined accordingly. However, the Volterra filter with the memory has higher complexity, larger power consumption, and greater latency. The trade-off between performance and complexity should be carefully considered. In this work, we utilize the memoryless Volterra filter to mitigate the average nonlinearity for its simplicity. Thus, the frequency-dependent component of the nonlinearity is neglected. Still, a noticeable improvement was observed after the nonlinearity compensation was realized, particularly for MZM working in the nonlinear regime.