# DLI-Based DP-QPSK Reception Scheme for Short-Range Optical Communication
## 5 Simulations
### FSR Optimization  
First, we compared the performances of the receivers with the DLI in different differential delays in a back-to-back configuration and the results are presented in Figure 7.  
The receiver's BER versus the DLI differential delay under the same optical signal-to-noise ratio (OSNR) is shown in Figure 7a and the given OSNR here is 15 dB. The Q pa  
Figure 6: Result of the frame synchronization code recognition: (**a**) no peak appeared if there was no frame synchronization code, and (**b**) a clear peak appeared if there was a frame synchronization code.  
Figure 7: DP-QPSK receiver performance with different delays in a back-to-back configuration: (**a**) Q factor versus DLI differential delay under a given optical signal-to-noise ratio (OSNR) of 15 dB, (**b**) the OSNR required for receivers with different DLI delays at the FEC (Forward Error Correction) threshold of BER = \(3.8\times 10^{-3}\).  
BER using the formula BER \(=\)\(\frac{1}{2}\)\(erfc(\frac{Q}{2})\). Figure 7b shows the OSNR required for receivers with different DLI delays at the FEC threshold of BER \(=3.8\times 10^{-3}\). The simulation results were consistent with the theoretical derivation above. Eye diagrams of a one-symbol-period delay and a 0.55-symbol-period delay are given in Figure 7a and a serious eye closure was created when the differential delay of DLI was a 0.55-symbol period. From Figure 7b, we can see that the OSNR penalty increased almost exponentially with the decrease of the differential delay.  
The chromatic dispersion tolerance of the receivers with different DLI delays were measured and the results are shown in Figure 8.  
In the simulations, the result of the back-to-back configuration with an exactly one-symbol-period delay was used as a zero point for the OSNR penalty. We recorded the OSNR penalty of different differential delays at BER \(=3.8\times 10^{-3}\) while gradually increasing the system's chromatic dispersion. The intersections of the curves and the \(y\)-axis in Figure 8 reflect the OSNR penalty of simply decreasing the differential delay without introducing dispersion. We can see that the OSNR penalty for receivers with a 0.9-symbol-period delay, a 0.8-symbol-period delay, and a 0.7-symbol-period delay were 0.3 dB, 0.9 dB, and 2.2 dB, respectively.  
In Figure 8a, the points marked on the curves indicate the dispersion tolerance due to the 2 dB OSNR penalty of the receivers. The 2 dB chromatic dispersion tolerances were 70.8 ps/nm, 74 ps/nm, 81.2 ps/nm, and 84.5 ps/nm for receivers with a 1-symbol-period delay, a 0.9-symbol-period delay, a 0.8-symbol-period delay, and a 0.7-symbol-period delay, respectively. It can be seen that the 2 dB dispersion tolerance was increased by nearly 20% when the DLI differential delay was a 0.7-symbol period. The OSNR penalty required for receivers with different delays to maintain a BER of \(3.8\times 10^{-3}\) under the same system dispersion are compared in Figure 8b. The results suggest that by considering the OSNR penalty introduced by only decreasing the differential delay, the optimal delay for a receiver with a system chromatic dispersion of 50 ps/nm was one symbol period, while the optimal delay was a 0.8-symbol period for a receiver with a dispersion of 95 ps/nm. It can be drawn from Figure 8b that the optimal delay of the DLI was inversely proportional to the chromatic dispersion, which is consistent with the previously reported results on BPSK demodulation [15].