# High-Speed, High-Performance DQPSK Optical Links with Reduced Complexity VDEE Equalizers
## 4 Optical Layer Simulation  
As shown in previous work [2; 12; 20; 25] the amount of dispersion that an equalizer can compensate is directly related to both the memory of the \(\mathrm{FF}\Big{(}M_{f}\Big{)}\) and \(\mathrm{FB}(M_{b})\) filters. As the values of \(M_{f}\) and \(M_{b}\) increase, the performance of the equalizer in compensating chromatic dispersion improves. In Figure 6 the performance of VDFE and SVDFE equalizers for different sets of \([M_{f}M_{b}]\) are presented accompanied with the total number of coefficients used for each case. It has become evident that, for both VDFE and SVDFE, large numbers of \(M_{f}\) and \(M_{b}\) (e.g., [13; 7] and [11; 6]) result in a dramatic increase of the number of coefficients but does not result in a notable increase in performance compared to the equalizers with smaller values of \([M_{f}M_{b}]\) (e.g., [9; 5]). When electronic equalization is used in conjunction with optical compensation, as in the cases suggested here, the memory of the FF and the FB part of VDFE type equalizers does not need to be high, and VDFE\([M_{f}M_{b}]\) with \([M_{f}M_{b}]\) = [5,3] and [9; 5] are sufficient [2]. As a result, the performance of the optical communications system can be significantly improved, in the sense of reaching an extended transmission distance, or by improving the bit error rate (BER) of the received signal. In order to provide the whole picture about the suggested electronic equalization solution, their efficiency is evaluated by means of two different numerical modeling sets of an optical link that operates at 40 Gb/s using a DQPSK modulation format (Figure 7). The first modeling setup (Figure 7a), referred hereafter as noise loading scenario, utilizes the OSNR metric to evaluate the performance of the optical transmission system, which can be defined as:  
\[OSNR|_{dB}=10\log_{10}\left(\frac{P_{signal}}{P_{noise}}\right) \tag{9}\]  
Any variation of the OSNR subsequently leads to variation in the quality and, hence, the BER value of the detected signal. Thus, the OSNR requirement to achieve a specific BER (referred as rOSNR) can provide a figure of merit for the performance of a system. The performance of each receiver/equalizer combination in an optical transmission system is evaluated through modelling of an uncompensated link, which consists of a single mode fiber, without utilizing any optical dispersion compensating module. While SMF is considered lossless, the total accumulated dispersion varies from 100 ps/nm to 1500 ps/nm. The OSNR value varies by adding Gaussian-distributed optical white noise  
Figure 6: Performance of (**a**) VDFE; (**b**) SVDFE, and the number of coefficients for each case. before the optical receiver emulating various levels of amplified spontaneous emission (ASE) at the receiver end, while a bandwidth of B\({}_{0}\) = 12.5 GHz is used to calculate the OSNR value. On the receiver side a bandpass optical filter with 40 GHz bandwidth is used to reduce the ASE noise that enters the MZDI and subsequently the PIN. For the second setup (Figure 7b), a multi-span transmission link is numerically simulated, which consists of eight identical spans (8 \(\times\) 100 km) where a partial compensation of the accumulated dispersion is performed by the means of DCF, while the residual dispersion is handled by the electronic equalizer. A metric that defines the amount of the optical dispersion compensation is introduced, called the optical compensation ratio, hereafter denoted as OCR, and varies from 80% to 99% of the total accumulated dispersion. For the simulations, each span consists of an SMF with D = 17 ps/nm/km, attenuation parameter of a = 0.2 dB/km, and a DCF with a dispersion parameter D = \(-\)85 ps/nm/km and a = 0.5 dB/km. The fiber model uses the split step Fourier method in order to solve the nonlinear Schroedinger (NLS) equation, taking into account fiber nonlinearities and the nonlinear coefficient n\({}_{2}\) has a value of 2.6 \(\times\) 10\({}^{-20}\) m\({}^{2}\)/W while PMD is not considered.