Bell Curve Analysis of Coherent WDM Systems

Tool Used: OptSim

The objectives of this application note are (i) to demonstrate simulation of bell curves for coherent Nyquist WDM systems and (ii) to discuss various trade-offs from an accuracy and simulation speed perspective to help users choose a suitable approach for modeling such problems. A list of references is also provided to help further exploration.

The plots in the current analysis are called “bell curves” because of a bell-like shape (for the Q-factor, or inverted bell-shape for the BER) with respect to the per channel transmitted power. These plots are helpful in finding an optimum value of per channel power and estimating power penalty.

Consider a 5-channel PM-QPSK WDM system with 128 GBps (32 GBaud) data rate per channel. The channel plan involves grid spacing of 37.5 GHz. The 4500 km transmission distance comprises of 30 spans of 150 km fiber per span followed by an amplifier in each span that compensates for the fiber loss at the expense of adding its own noise in the process. The schematic is shown in Figure 1. The dispersion is allowed to accumulate and is fully compensated in electronic domain after the detection.

Schematic of the simulation setup

Figure 1. Schematic of the simulation setup

The dynamically tracking receiver uses a training sequence and has digital signal processing options for estimation of phase and counting of errors (excluding training bits). A benefit of plotting Q2 is that Q2 (dB) penalty is equivalent to OSNR nonlinear interference (NLI) penalty, measuring which is otherwise computationally expensive since it would require adjusting OSNR until you match the initial BER.

An alternate approach to the above, to save on simulation time, is to employ what’s widely known in literature as “noise-loading.” In this approach, we use a noiseless amplifier in the span, and add an equivalent noise after all the spans. Figure 2 shows conceptual schematic of the noise loading mechanism.

Using noise loading and VOA (bottom) to model an equivalent span on the top

Figure 2. Using noise loading and VOA (bottom) to model an equivalent span on the top

By introducing additional span loss and a reduction in OSNR by equivalent additional loss of the span, we mimic simulation of longer transmission without actually simulating a longer fiber thereby saving on simulation time. As will be seen later the penalty from noise-loading is minimal at optimal channel power for our case where fiber core size is larger compared to the standard single-mode fiber. For more treatment of this subject, please refer to References 1 to 3.

A further reduction in simulation time is possible using the Gaussian noise (GN) emulator instead of the fiber-amplifier spans of Fig. 1. It is shown experimentally [4], via OptSim-based modeling [5], and analytically [Ref. 6 and Chapter 7 of Ref. 3] that for uncompensated, long-haul coherent systems such as in this application note, nonlinear transmission impairments in fiber manifest as nonlinear interference (NLI) with Gaussian noise power spectral density. Using the GN model approach, the simulation time reduces by one-third compared to simulating actual fiber-amplifier spans. As will be seen later, the penalty from the GN emulator model is negligible at optimal channel power values.

Finisar Waveshaper type filters are used in practice to implement Nyquist filtering, and are modeled as super-Gaussian filters of orders 2 to 4 [8] as is also done in this application note.

Figure 3 shows BER vs. per channel transmitted power (top) comparing all three cases. 

log(BER) vs. per channel transmitted power (dBm) plots

Figure 3. log(BER) vs. per channel transmitted power (dBm) plots

For all three cases, the inverted bell curves show that the optimal per channel power is around 2dBm for the current design.

Figure 4 shows bell curves for the Q2(dB) for all three cases.

Q2(dB) vs. per channel transmitted power (dBm) plots

Figure 4. Q2(dB) vs. per channel transmitted power (dBm) plots

As we can see from the blue and red curves of Fig. 4, the GN-model approach, while cutting the simulation time by almost one-third, does not introduce any significant penalties compared to the time-consuming simulation of the layout with fiber-amplifier spans. Even the noise-loading approach (green curves), at the optimal per channel power, has negligible penalty of approximately 0.25 dB in our case.


1.       Curri, V., et al., “Dispersion compensation and mitigation of nonlinear effects in 1111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photonic Technology Letters, vol. 20, no. 17, 2008, pp. 1473-1475.

2.       Vacondio, F., et al., “On nonlinear distortions of highly dispersive optical coherent systems,” Optical Express, vol. 20, no. 2, 2012.

3.       Enabling Technologies for High Spectral-efficiency Coherent Optical Communication Networks, Ed. Xiang Zhou and Chongjin Xie, Wiley, 2016.

4.       Torrengo, E., et al., “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” Optics Express, vol. 19, no. 26, 2011.

5.       Carena, A., et al., “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” Journal of Lightwave Technology, vol. 30, no. 10, 2012, pp. 1524-1539.

6.       Poggiolini, P., et al., “The GN-model of fiber non-linear propagation and its applications,” Invited Paper, Journal of Lightwave Technology, vol. 32, no. 4, 2014, pp. 694-721

7.       Bosco, G., et al., “Performance limits of Nyquist-WDM and CO_OFDM in high-speed PM-QPSK systems,” IEEE Photonic Technology Letters, vol. 22, no. 15, 2010, pp. 1129-1131.