# A Pulse Shaping Based Optical Transmission System of 128 QAM for DWDM with N \(\times\) 904 Gbps
## 4 Simulations and Performance Analysis  
The transmission system is simulated by OPTISYSTEM and MATLAB. The transmission rate is configured as 900 Gbps; the transmitted sequence-length is configured as 262,144 bit; the number of samples per bit is configured as 4; the Guard-bits is configured as 10; the OSNR is configured above 30 dB; the transmitted optical signal power is configured as 0 dBm. The interference problems of the adjacent channels can be tested through eight channels in the DWDM system. The interfered degree of adjacent channels in the DWDM system with eight channels is almost the same as that in the DWDM system with more than eight channels. This is because the interference problems of the channels are caused by the bandwidth of the adjacent channels. In our proposed system, the wavelength spacing of adjacent channels is 0.7 nm; the wavelength spacing of non-adjacent channels is more than two times of 0.7 nm, that is to say, the wavelength spacing of non-adjacent channels is more than 1.4 nm. There will be almost no correlation between one channel and the other channels when the signal of each channel is filtered via the GOF, that is, the non-adjacent channels don't interfere with each other. From the configuration of parameters, we see that the optical spectral utilization efficiency of the transmission channels is up to 10.29 bps/Hz, and it can be calculated by:  
\[\frac{900 Gbps}{87.5 GHz}=10.2857 bps/Hz\approx 10.29 bps/Hz \tag{13}\]  
The DWDM transmission system with eight channels is simulated and analyzed. The spectrogram output from DWDM-Mux, the spectrogram output from EDFA 1, the spectrogram output from GOF\({}_{0}\) and the constellation diagram output from UDSP are shown in Figure 6a-d, respectively. In Figure 2, the ultra-high-speed photonic-carriers with the adjacent channel spacing of 0.7 nm are multiplexed via DWDM-Mux; the multiplexed signals are amplified via EDFA 1; the amplified signals are transmitted via SSMF; and the signals are amplified by EDFA 2, de-multiplexed by DWDM-Demux, and filtered by GOF\({}_{0}\) successively. Figure 6: _Cont._  
The spectrograms output from the other GOFs are similar to Figure 6c, and the locations of the center frequencies are different. The constellation diagram of the coherent receiver unit is shown in Figure 6d. From Figure 6d, it can be seen that the constellations are arranged orderly and clearly. The order of the GOF is 3; the bandwidth of the GOF is 70 GHz; and the insertion loss of the GOF is 1 mw. The mathematical model of the GOF can then be further described by:  
\[H(f)=\exp\left[-\ln\Bigl{(}\sqrt{2}\Bigr{)}\left(\frac{f-f_{c}}{35 GHz} \right)^{6}\right] \tag{14}\]  
when the bit rate of the transmission system is configured as 900 Gbps, the constellation diagrams and the diagram of the curve between the bandwidth of the GOF and bit error rate (BER) are shown in Figure 7. The constellation diagrams and the diagram of curve between the bandwidth of the GOF and error vector magnitude (EVM) are shown in Figure 8.  
Figure 6: Spectrograms and constellation diagram. (**a**) Spectrogram for DWDM, (**b**) Amplified Spectrogram for DWDM; (**c**) Spectrogram for one channel signal; (**d**) Constellation. Figure 7: Constellation-diagrams and diagram of curve between the bandwidth of GOF and bit error rate (BER). From Figure 7, it can be obtained that the BER of the transmission is greatly influenced by the bandwidth of the GOF. The BER of transmission channel will be worse when the bandwidth of the GOF that is on a wavelength-link diverges from 70 GHz. The BER of transmission channel will be seriously deteriorated when the bandwidth of the GOF that is on a wavelength-link is less than 67 GHz. The constellations output from the UDSP will be arranged orderly and clearly when the bandwidth of the GOF is configured as 70 GHz. However, the constellations output from the UDSP will become blurred when the bandwidth of the GOF diverges from 70 GHz.