## 3 Results and Discussion  
Figure 4 shows the system setup used for evaluating the performance of the proposed ANN equalization method. At the transmitter side, independent and identically distributed input symbols \(a_{i}\) are randomly generated. The data are mapped into an on-off keying (OOK) modulation format with a non-return-to-zero (NRZ)-raised cosine pulse shaping whose roll-off factor is 0.6. An electrically modulated laser (EML) is used to convert  
Figure 3: Flow diagram of the introduced advanced training scheme algorithm used to train the proposed ANN-based equalizer. ANN: artificial neural network; AT: advanced training; MSE: mean square error; Adam: adaptive moment estimation. electrical signal into optical domain, obtaining the output transmitted optical signal \(x(t)\). Two data rates are considered during the simulations, namely, a 10-Gbaud- and 28-Gbaud-rate system. The optical transmission channel is a standard linear single-mode fiber (SMF) whose nominal parameters are given as dispersion coefficient \(\beta_{2}=-21\) ps\({}^{2}\)/ km, loss coefficient \(\alpha=0.2\) dB/km, and length \(L\) in km. The SMF is followed by an inline erbium doped-fiber amplifier (EDFA) that fully compensates for the fiber loss. Unless otherwise stated, the noise of the EDFA is neglected. The output of the EDFA passes through an optical Gaussian band-pass filter (BPF) of bandwidth 50 GHz or 100 GHz at the 10-Gbaud- or 28-Gbaud-system, respectively. At the receiver, a direct-detection (DD) receiver is first employed for optical-to-electrical conversion whose output is proportional to the square of the magnitude of the distorted optical received signal \(r(t)\). The linear distortions of the chromatic dispersion in the optical domain are converted into nonlinear distortions in the electrical domain because of the square-law detection of the DD. In other words, the phase information of the received optical signal is lost in the electrical domain. A Gaussian low-pass filter is placed after the DD to reduce the noise. Its 3 dB bandwidth is 7 GHz or 21 GHz for the 10-Gbaud- or 28-Gbaud-system, respectively. Note that the additive white Gaussian noise \(n(t)\) added by the DD consists of shot and thermal noise [1; 2]. At the DSP unit, an analog-to-digital converter (ADC) is used to reduce the sampling rate from 16 samples per symbol to 2 samples per symbol, which is sufficient for accurate reconstruction of time-continuous signals according to the Nyquist condition. The proposed ANN equalizer is then employed to compensate for the nonlinear electrical signal distortions. Finally, a decision circuit is placed at the end of the DSP unit to classify the equalized data \(\hat{X}_{i}\) to its nearest symbol \(\hat{a}_{i}=\{0,1\}\). For all results presented in this section, the performance, efficiency, and effectiveness of the proposed ANN equalizer are investigated using three figures of merit, namely, the bit error rate (BER) performance of the overall communication system in the presence of noise, the computational cost per symbol required by the equalizer, and the memory usage requirements of the equalizer. Firstly, the BER performance is calculated through Monte-Carlo simulations of the communication system described in Figure 4. Using a pseudo-random binary sequence (PRBS) \(2^{18}-1\), a stream of \(2^{17}\) unknown random data are generated and transmitted through the communication system. Then, to achieve better BER accuracy with a smaller  
Figure 4: Block diagram of the intensity modulation and direct detection short-reach optical-fiber communication system setup considered in the simulation. Tx: transmitter; EML: electrically modulated laser; SMF: single-mode fiber; EDFA: erbium-doped fiber amplifier; BPF: band-pass filter; Rx: receiver; DD: direct detector; AWGN: additive white Gaussian noise; LPF: low-pass filter; ADC: analog-to-digital converter; ANN: artificial neural network. number of required symbols, we estimate the BER from its corresponding quality factor \(Q\).