## 3 Results and Discussion
### A 10-Gbaud Optical-Fiber Communication System  
In this subsection, we study the performance of the proposed ANN equalizer to compensate for the distortions of an IMDD short-haul fiber communication system operating at baud rate of 10 GBaud with optical-fiber transmission distance \(L\) ranging from tens of kilometers up to a few hundred kilometers. Such a communication system emulates typical communication scenarios in the area of metro and media access networks. Consider a communication scenario with optical-fiber transmission distance, i.e., optical-fiber length, \(L=140\) km. Due to pulse broadening caused by the chromatic dispersion and the square-law effect of the DD, the BER at the receiver without equalization and in the absence of noise is obtained as \(4\times 10^{-2}\). Using convergence analyses, the numbers of equalizer taps (i.e., the ISI span) and hidden-layer nodes required for this case are estimated as \(N=7\) and \(m=6\), respectively. For better readability, we refer to the artificial neural network equalizer (ANNE) consisting of \(N\) input nodes and \(m\) hidden layer's nodes, and trained using the advanced training (AT) scheme as ANNE-AT[\(N\),\(m\)]. Figure 5a shows the BER performance obtained with the ANNE-AT[7,6] compared to the case with no equalization and the back-to-back (B2B) transmission case, versus a sweep of the received optical power at the transmission distance of 140 km. The ANNE-AT[7,6] effectively compensates for the nonlinear distortions of the system, extending transmission distance feasibility. It achieves the BER \(=10^{-3}\) at a received optical power of \(-0.7\) dBm with \(\sim\)0.9 dB power penalty relative to the B2B transmission case. To achieve the BER \(=10^{-9}\), the required received optical power is 3.3 dBm, with a minor power penalty of \(\sim\)0.3 dB, compared to the B2B transmission case. To evaluate the efficiency of the proposed advanced training scheme, we compare the performance of the ANNE-AT to another identical ANN-based equalizer but trained using the extensive training scheme introduced in [21]. For a fair comparison, all optimization parameters as well as the ANN configuration are kept the same during the training process. Such an ANN equalizer configuration that is trained using the  
Figure 5: BER performance of the 10 Gbaud optical-fiber communication system versus received optical power with a noise-free EDFA. The optical-fiber transmission distance is (**a**) 140 km and (**b**) 200 km. The performance without equalizer, with ANNE-ET[7, 6], and with ANNE-AT[7, 6] are compared to the B2B transmission case. scheme and comprises \(N\) input nodes and \(m\) hidden-layer nodes is denoted as ANNE-ET\(\{N\),\(m\}\). As can be seen from Figure 5a, using ANNE-ET[7,6], the BER \(=10^{-3}\) is achieved at the received optical power of 1.3 dBm with a power penalty as high as \(\sim\)2.9 dB relative to the B2B transmission case. At BER \(=10^{-9}\), the ANNE-ET[7,6] requires a received optical power of 4.4 dBm, with a \(\sim\)1.4 dB power penalty compared to the B2B transmission case. Thanks to the proposed advanced training scheme, the ANNE-AT provides 2 dB and 1.1 dB power benefits over the ANNE-ET for achieving a BER of \(10^{-3}\) and \(10^{-9}\), respectively. In Figure 5b, we explore the performance of the proposed ANNE at a longer fiber transmission distance of \(L=200\) km. The same equalizer parameters \(N=7\) and \(m=6\) are utilized. The BER performance achieved using the ANNE-AT[7,6] versus received optical power are compared to that obtained with the no-equalization case, B2B transmission case, and the equalization using the ANNE-ET[7,6]. It is obvious that both ANNE-AT and ANNE-ET can extend the transmission distance up to 200 km. However, to obtain a BER \(=10^{-3}\), the ANNE-ET has a power penalty of 3.9 dB compared to the B2B case, while the ANNE-AT has only a 1.5 dB penalty. On the other hand, compared to the B2B case, to achieve a BER \(=10^{-9}\), power penalties using the ANNE-ET and ANNE-AT are 2.2 dB and 1.2 dB, respectively.