## 4 Simulation Results  
In the above sections, the proposed model and its analytical approach are presented in order to show that nonlinear effects can be mitigated using a simple DSP design of the receiver. In this section, based on the theoretical model, the simulations results are investigated in order to explore the performance of the proposed work. The results shown in Figure 2 are based on different values of nonlinear effective area against BER for four, eight, and 16 number of channels and \(5\times 10^{9}\) symbol/s symbol rate. Moreover, the results clearly depicts that the proposed work has optimum performance at 90 \(\upmu\)m\({}^{2}\) nonlinear effective area for all considered cases but the proposed receiver design effectively mitigates the nonlinear effects to a considerable extend. For instance, the same BER is achieved with 16 number of channels with the nonlinearities compensation, as with four channels without applying the compensation. Thus, the number of channels can be increased by four times with the proposed solution in cases where the system's performance is affected due to the nonlinearities. When considering the FEC limit of BER (\(3.8\times 10^{-3}\)), only 48 \(\upmu\)m\({}^{2}\) is required for all cases after the application of the nonlinearities compensation, which otherwise requires 53 \(\upmu\)m\({}^{2}\) for a four channel system and 63 \(\upmu\)m\({}^{2}\) for 16 channel system. The simulation results of the proposed model investigated in terms of input power against BER are mentioned in Figure 3 by putting several sequence length of bits. The transmission distance of 300 km has been considered here and it can be seen that the system performance improves with the increase in power up to a point where the nonlinearities are compensated by the DSP receiver. The optimum results are achieved at input power levels of 6 dBm, after which the BER increases even with the applied compensation, because the interaction of such high power level with the nonlinear optical fiber medium generates additional third order distortions. The transmit power of 6 dBm into the fiber is essential to achieve longer transmission distances. Figure 3 also shows that increasing the length of sequence results in broadening of the nonlinearities. The analysis for different sequence length shows that the sequence length dependent autocorrelation function amplitude do not affect the effectiveness of the proposed compensation technique and low BER can be achieve with any sequence length without the loss of generality. Figure 4 demonstrates an in-depth details of the results with a range of fiber lengths against BER at 2, 4, and 6 dBm input launch power levels. With the proposed compensation and 6 dBm launch power, the transmission distance up to 300 km satisfies the BER limit of \(3.8\times 10^{-3}\), which clarifies that the proposed system can be used for cumulative nonlinear effects due to long haul transmissions. Similarly, Figure 5 defines the performance of the proposed model with nonlinearities compensation as an untreated transmission with nonlinearities. In addition to the simulation results of the proposed model showing BER performance, Figure 5 describes the amount of power penalty due to nonlinearites at 12.5, 25, and 50 GHz channels spacing, which declares that the performance of the compensated system is better, but a penalty has to be paid for having low channel spacing, which is often required to accommodate large number of channels within a specific frequency span. Figure 6 shows the effect of reference wavelength, where the BER results are shown as a function of the reference wavelength for eight, 16, and 32 channels, where it can be seen that multiple nonlinearities depend on the reference wavelength and the proposed model has greater tolerance against nonlinearities with a general optical fiber transmission system. The symbol rate of 5 GSym/s has been used for eight and 16 channels which provides a data rate of 40 Gb/s and 80 Gb/s, respectively.