## 4 Simulation Model of DQPSK Modulated Data Transmission
Figure 8 illustrates an example of an eye diagram and power spectrum density (PSD) of the in-phase (real) part of an 80 Gb/s DQPSK-modulated signal after a 390-km transmission over the unrepeated ultra-long span system using three-segment hybrid fiber effective core area structure. The eye diagram monitored at the receiving side indicates the amplitude fluctuation of the signal power and also the timing jitter fluctuation of the sampling clock. In a phase-modulated format (in this case DQPSK) with an RZ pulse shape, the pulse trails are repeated at the same pulse amplitude at any given time, leading to a minor amplitude fluctuations. The eye diagram is widely open which indicates suitable filters are set at the receiver. Since the information data are coded in the signal phase, the transmission performance will be affected mainly by the accumulated phase shift and phase fluctuation along the transmission line. The absence of a zero-intensity rail in the eye diagram is characteristic of a phase-modulated format. The spectrum shows that the signal bandwidth of the RZ pulse up to the first null is twice the clock rate. Although twice the bandwidth is required compared to the NRZ format, the RZ format has much better nonlinear performance, which is mandatory for ultra-long span application. As an important transmission parameter, OSNR has two distinct meanings from an application point of view: delivered OSNR (OSNR\({}_{\text{Del}}\)) and required OSNR (OSNR\({}_{\text{Req}}\)) [41]. The delivered OSNR  
Figure 8: Eye diagram (**a**) and power spectrum density (PSD) (**b**) of the in-phase signal (real part) of an 80 Gb/s DQPSK signal using the three-segment hybrid fiber effective core area structure after transmission over 390 km. is a measurable parameter that shows the OSNR at the end of a transmission line and depends only on the transmission line parameters and launched signal powers but not on the modulation formats or transmission impairments. The required OSNR is a design parameter that specifies the minimum necessary OSNR that is required to achieve a certain target BER as an indication of the tolerance of a modulation format to ASE noise and any other transmission impairments. The OSNR of the Raman analysis in Sections 2 and 3 is a delivered OSNR, while the OSNR of the BER performance analysis in this section (Section 4) is a required OSNR. The simulated BER performance of 80 Gb/s RZ-DQPSK direct-detection system as a function of the required OSNR (OSNR\({}_{\text{Req}}\)) after propagation over the 390-km unrepeatered transmission span is illustrated in Figure 9. A comparison of the BER performance between the three-segment hybrid fiber effective core area structure and the conventional single-segment single fiber core structure shows that the span with the three-segment hybrid fiber core structure was superior. To achieve the target BER of \(10^{-9}\), the required OSNR (OSNR\({}_{\text{Req}}\)) of the three-segment hybrid fiber core structure is reduced by 2.71 dB, indicating improvement in the transmission performance. The required signal-to-noise ratio per bit (Eb/No) can be used as an alternative when measuring required optical signal-to-noise performance independent of the data bit rate and to free from the 0.1 nm noise bandwidth definition. Figure 10 shows BER performance for various data rates (40, 60, 80, and 100 Gb/s) when using the three-segment hybrid fiber effective core area structure. A high data rate has a narrow pulse width and is more sensitive to dispersions that trigger inter-symbol interference (ISI). The interaction between dispersion and the nonlinear Kerr effect (SPM in a single-channel system) enhance the pulse distortion, leading to a higher error rate. The stability and consistency of the system's performance across different data rates indicate the ability to meet various applications' demands.