## 5 Numerical Results  
Figures 6 and 7 represent the ONU and the OLT implementation, with the Optisystem simulator version 17, respectively.  
As shown in Figure 6, a pseudorandom binary sequence (PRBS) is used to generate a random bit user, then followed by an NRZ generator, followed by a 16-QAM generator and finally a Fast-OFDM subcarrier modulator is putted at the end of the first pipeline. A Mach-Zehnder modulator (MZM) is used to convert the electrical signal to an optical one based on a continuous wave (CW) laser source. The output signal of the MZM modulator will be multiplied by the signature generated by the 2D-OCDMA encoder. Finally, the output signal from the 2D-OCDMA encoder will be sent towards the optical channel.  
On the OLT side, a 2D-OCDMA decoder is used to eliminate the user signature as depicted in Figure 7. Then, an APD photodetector is employed to convert the optical signal into an electrical one. In addition, a Fast-OFDM subcarrier demodulator followed by a 16-QAM decoder is useful to recover the received symbol as a user bit. In our simulation setup, the system provides 10 GHz spacing between 9 channels, with a 40 Gb/s signal capacity (25 GS/s sampling rate) per-channel, using 16-QAM. The OFDM block is composed of 64 electronic subcarriers (only 5 Ghz spacing among subcarriers is used thanks to the Fast-OFDM technique), a cyclic prefix of 2% to eliminate inter-symbol interference, 10 pilot subcarriers for carrier recovery and digital-to-analog/analog-to-digital converter clipping ratio, and quantization bits set at 13 and 10 dB, respectively. For Fast-OFDM-CDMA on this setup, 9 electrical subcarriers are also considered, supporting 4 simultaneous users in the network. The 5 th middle channel is investigated, which suffers the most from nonlinear crosstalk effects, while the launched optical power per channel/optical subcarrier was fixed at the optimum 2 dBm for both cases of downstream link. The PRBS generated bits were 219-1, and hard-error decoding was performed at the receiver to calculate the BER. The CW laser, Fast-OFDM modulator, MZM modulator and related APD detector for IM/DD Fast-OFDM-CDMA were simulated at an aggregate bit rate of 40 Gb/s. The developed Fast-OFDM bloc, as well as the 2D-OCDMA block, was implemented in the Optisystem(r) simulator environment (electrical and optical components with SSMF). It should be noted that phase  
Figure 6: ONU implementation.  
Figure 7: OLT implementation.  
noise and frequency offset have been considered here using three OFDM pilot subcarriers. Our system setup considered 1000 symbols per subcarrier. The adopted SSMF parameters for signal transmission over an 80 km length are the following: fiber nonlinear Kerr parameter, CD, CD-slope, fiber loss and differential group delay (DGD) of 1.1 W\({}^{-1}\)km\({}^{-1}\), 16 ps/nm/km, 0.06 ps/km/nm\({}^{2}\), 0.2 dB/km and 0.2 ps/km, respectively. Likewise, in order to recover the phase after the photodetector, a low pass Bessel filter is used after the photodetector in the setup. In addition, a Bessel optical filter is employed before the photodetector at the third optical window to preserve the received signal phase shape.  
As shown in Figure 8, the eye diagrams for four users generated by the Optisystem(r) BER analyzer are open, indicating the feasibility of our hybrid IM/DD Fast-OFDM-CDMA system in the PON context operating at 40 Gb/s. However, the eye becomes more closed when the number of users is raised; this is due to the MAI, which is considered as the most dominant degradation factor of OCDMA system.