## 4 Direct-Detected Optical Fast-OFDM System Model Equipped with NLEs and Performance over SMF  
The proposed direct-detected optical Fast-OFDM system equipped with either ANN or IVSTF was implemented in a hybrid MATLAB with VPI(r) simulation platform. Similar equalizers have been previously employed in [11; 14], which validates the model used in this work. Moreover, the Fast-OFDM system was modulated using 4-, 8- and 16-ASK signal formats at a signal capacity of 9.69, 14.53 and 19.3 Gb/s, respectively, for both equalizers using 64 sub-carriers and 1000 Fast-OFDM symbols. The transmission-reach of the developed system was set at 640 km (8 spans with a fiber-link  
Figure 2: (**a**) Optical Fast-OFDM received diagram showing the equalizer that is based on IVSTF [11]. (**b**) 16-ASK optical Fast-OFDM received diagram illustrating the ANN sub-neural network equalizer. LPF: low-pass filter; ADC: analogue-to-digital converter; CP: cyclic prefix; DCT: Discrete-Cosine Transform; NLE: nonlinear equalizer; ANN: artificial neural network; n: neuron; MMSE: minimum mean square error; HCD: nonlinear system chromatic dispersion.  
length of 80 km). The length of CP was set at 25% to ensure effective elimination of inter-symbol interference [28; 29]. At the receiver-end of the simulation set-up a single low pass filter (LPF) unit was employed having 3 dB bandwidth of approximately 3 GHz. For optical amplification per span, Erbium-doped fiber amplifiers (EDFAs) were used having a realistic noise figure of 6 dB.  
The sampling rate of the DAC at the transmitter and the ADC at the receiver was chosen at 6.25 GS/s, while the ratio of clipping and quantization bits were optimally set to 7 dB and 10, respectively, which has been reported as the optimum values for high level modulation formats in O-OFDM [6]. The optimum launched optical power for our system under test was found at \(-6\) dBm. A single unit positive-intrinsic-negative (PIN) photo-detector with 0.9 A/W of responsivity was adopted at the receiver-side for direct-detection, while the SMF-transmission-link had the following parameters: 16.9 ps/nm/km fiber dispersion, 0.21 dB/km fiber loss, 0.07 ps/km/nm\({}^{2}\) dispersion slope, 0.11 ps/km 0.5 polarization-mode-dispersion coefficient, 2.69 \(\times\) 10-20 m\({}^{2}\)/W Kerr-induced nonlinearity coefficient, and 80 \(\upmu\)m\({}^{2}\) effective core area. The key simulation parameters for the developed ANN-based Fast-OFDM transmission model are depicted in Table 1.  
The transmission performance of the direct-detected optical Fast-OFDM system over SMF links for different modulation formats is shown in Figure 3. It is evident from this figure that for a fixed BER at \(10^{-3}\) (the selected forward-error-correction limit at \(10^{-9}\)) the maximum transmission-reach is at about 380 km, 240 km, and 200 km for 4-, 8- and 16-ASK modulation, respectively. This can be explained by the fact that a higher level of modulation that carry higher data rate increases the SNR on Fast-OFDM sub-carriers, due to the increased amplitude distortions induced by the combined effects of fiber chromatic dispersion and nonlinearity at higher transmission distances.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Description \& Unit** \\ \hline Signal modulation format & 4-, 8-, 16-ASK \\ Signal data bit-rate & 9.69, 14.53, 19.37 Gb/s \\ Operating wavelength & 1550 nm \\ Number of sub-carriers & 64 \\ Cyclic prefix (CP) length & 25\% \\ Forward-error-correction & 7\% \\ ANN training vector length & 5\% \\ Photo-detector type & PIN \\ PIN sensitivity & \(-19\) dBm \\ DAC/ADC sampling rate & 6.25 GS/s \\ DAC/ADC count. bits & 7 \\ DAC/ADC clipping ratio & 13 dB \\ LPF roll-off function & Bessel-Thomson \\ LPF 3 dB bandwidth (order) & 3 GHz (2 nd order) \\ EDFA gain (noise figure) & 16 dB (6 dB) \\ SSMF span (length) & 8 (80 km) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Key optical Fast-OFDM transceiver parameters.  
Figure 3: Optical Fast-OFDM transmission-reach in terms of BER.