## 5 ANN vs. IVSTF in Direct-Detected Optical Fast-OFDM  
The capability of ANN for nonlinearity compensation in optical Fast-OFDM with intensity-modulation and direct-detection is illustrated in Figure 4 in terms of BER vs. distance. In Figure 4, a 4-ASK modulation was considered for simplicity at a signal capacity of 9.69-Gb/s. The optimum transmitted power was found at \(-6\) dBm for ANN-NLE, as well for the benchmark IVSTF and without (W/O) using NLE (i.e., considering only linear equalization). It is revealed from Figure 4 that 160 km extension in transmission-reach is achieved by ANN compared to linear equalization for the adopted BER threshold. In the same manner, 80 km extension in transmission-reach is observed when using ANN compared to the Volterra-based NLE. The latter can be explained by the fact that while IVSTF compensates deterministic intra-channel nonlinearities, ANN can tackle both deterministic and stochastic nonlinearities, i.e., parametric noise amplification from concatenated EDFAs and the interplay between nonlinearity and polarization-mode-dispersion.  
On the other hand, the performance difference between ANN and linear equalization can be explained in Figure 5, where the BER distribution on the sub-carrier index is depicted. The figure essentially shows that a few Fast-OFDM sub-carriers under ANN equalization have decreased BER (corresponding to increased SNR) compared to linear equalization. This happens because ANN can reduce the effects of inter-carrier four-wave mixing.  
Figure 6 depicts the received optical power at the PIN versus the transition distance while adopting the 4-ASK modulation format; it is worth noting that the optical received power values are different at different fiber lengths, varying from \(-7\) dBm for 80 km to \(-18\) dBm for 560 km.  
Figure 7a shows the effect of the IVSTF and ANN equalizer on the optimum quantization bit. As it can be seen from this figure, utilizing the ANN equalizer relaxes the requirement of a high-resolution DAC/ADC, and reduces the requirement of high quantization bits by 2-bits for the same transmission distance (for the case of 580 km) when compared with case of without equalizer, and by 1 bit when compared with the case of utilizing the IVSTF equalizer. Similarly, this is also applied for the case of clipping ratio, as depicted in Figure 7b: using the established ANN equalizer, an increase in the transmission distance is observed when utilizing the optimum clipping ratio (7 dB); while for a fixed distance of 580 km, a 2-dB reduction in the required clipping ratio is observed when using ANN compared W/O ANN, moreover a reduction of 1 dB when compared with the IVSTF equalizer case.  
Figure 4: BER vs. transmission distance for 9.69-Gb/s optical Fast-OFDM at optimum launched optical power of \(-6\) dBm for Volterra-series transfer function (IVSTF)/ANN-NLEs and without (W/O) using NLE.  
Figure 5: BER vs. optical Fast-OFDM sub-carrier index, with IVSTF-NLE, ANN_NLE and without utilizing ANN at 320 km of fiber transmission.  
Figure 6: Received optical power vs. transmission distance for 9.69-Gb/s optical Fast-OFDM without (W/O) using NLE.  
Figure 7: Effect of DAC/ADC components on 4-ASK optical Fast-OFDM transmission performance with the use of IVSTF equalizer, with ANN equalizer and W/O ANN at a signal bit rate of 9.69-Gb/s for a transmitted power of \(-\)6 dBm: (**a**) Quantization bit vs. Distance. (**b**) Clipping ratio vs. Distance.