## 5 The CDS case study for the OFDM-Based Long-Haul Standard Single-Mode Fiber system  
To illustrate how CDS can control QoS (i.e., increase the data rate/improve the BER), we implemented the CDS with the simplified executive for the OFDM-based long-haul standard single mode fiber link. This is a proof-of-concept case study for the presented Algorithm 1, whose validity to other scenarios will be further studied. The fiber optic system simulation parameters are the same as in Section 3.1.1 (see Table 1), and the parameters of the CDS are as follows: precision factor, PF = 2 and 96% probability box is used. Figure 13 shows the conventional OFDM-based fiber optic system and Figure 14 shows the system with simplified CDS. The detailed describtion OFDM-based fiber optic system are presented in [29; 33]. At the transmitter, 256 subcarriers modulated by low data rate QAM-16 data are multiplexed using the inverse fast-Fourier transform (IFFT). Cyclic prefix (CP) is used in the guard interval between OFDM frames to preserve the orthogonality of the subcarriers and also to avoid inter-carrier interference (ICI) due to dispersive effects in the fiber [33]. After digital-to-analog conversion, the OFDM data modulates the laser output using an in-phase quadrature (IQ) modulator. The output of the IQ modulator passes through a fiber optic link consisting of 20 spans of standard single-mode fiber (SSMF) and each fiber span is followed by an inline erbium-doped fiber amplifier (EDFA). The signal propagation in the fiber optic link is governed by the NLSE which includes fiber dispersive effects, loss and third-order nonlinear susceptibility (also known as Kerr effect). The NLSE models the complex envelope of the signal and by solving it, we find the complex envelope of the signal at the output of the link given that the complex envelope of the signal at the transmitter is known. The output of the fiber optic link passes through a coherent receiver in which the OFDM signal is down-converted to the base band. After analog-to-digital conversion, the subcarriers are demultiplexed using the fast Fourier transform (FFT). The adaptive linear equalizer mitigates the linear distortions of the data in each subcarrier in parallel. The phase noise of the transmitter laser and that of local oscillator (LO) are compensated using the standard technique [41]. Now the QAM symbols modulating each subcarrier pass through the perceptor for statistical modeling and intelligent decision-making (see Figure 14). All the figures shown in this manuscript are obtained by simulating the fiber optic system (with or without CDS) using the parameters listed in Table 1.  
Figure 13: The conventional OFDM-based fiber optic system. (FEC: Forward error correction, P/S: Parallel to serial, DAC: Digital-to-analog converter, ADC: Analog-to-digital converter, S/P: Serial to parallel, IFFT: Inverse fast Fourier transform, FFT: Fast Fourier transform). The BER versus launch power of a conventional fiber optic communications system (i.e., without CDS) is shown in Figure 15. The BER is calculated based on the geometric boundaries between the symbols for the conventional system. At low launch powers, the BER decreases with the launch power since the SNR improves. However, at higher launch power (greater than \(-4\) dBm), the BER increases with launch power due to nonlinear impairments. If we consider \(1.03\times 10^{-2}\) (with 14.3% overhead) as the FEC threshold [40], we can see from Figure 15 that the maximum achievable data rate is 48 Gb/s. The adaptive linear equalizer (See Figures 13 and 14) mitigates the linear distortion, and hence, the nonlinear distortion is dominant for data rates greater than 48 Gb/s. The CDS now extracts the model for \(k=1\) (which corresponds to the data rate of 48 Gb/s) in the preceptor while operating in the BER improvement mode (see Figure 16) and saves the model for 48 Gb/s as \(P(\hat{Y}_{n}^{1}\,|\hat{X}_{n}^{1})\) in the model library.