# Mitigation of Nonlinear Distortions for a 100 Gb/s Radio-Over-Fiber-Based WDM Network
## 3 Analytical Modeling  
The proposed WDM-RoF framework is discussed in Section 2 in detail, while this section elaborates the mathematical model of the proposed solution, to present the performance against PAPR and AWGN noises in the electrical domain, and NLIs and LDs in the optical domain. Furthermore, the mathematical modeling of the proposed model is studied in three portions: the mechanism of process in terms of transmitting information, the issues like NLIs, LDs and PAPR and, finally, \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Reference wavelength & 1550 nm \\ Fiber attenuation & 0.2 dB/ km \\ Input power & \(-20\) dBm to 0 dBm \\ Received power range & \(-40\) dBm to \(-20\) dBm \\ Channel spacing & 12 / 25/ 50 GHz \\ Length of the fiber & 0–10 km \\ Nonlinear effective area & 80 \(\upmu\)m\({}^{2}\) \\ Number of Channels & 16 \\ Nonlinear dispersion & \(-3\) ps\({}^{3}\)/km \\ Bits per symbol & 4 / 6 bits \\ RF Frequency & 5 GHz \\ RF Bandwidth per channel & 1.25 GHz \\ Data Bandwidth/ Preamble overhead & 1.05 GHz/ 200 MHz \\ Gain of EA & 10 dB \\ Extinction ratio & 15 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters with their values and units. Figure 1: (**a**) Wavelength division multiplexing (WDM)-based Radio over Fiber (RoF) proposed model using 16 and 64 quadrature amplitude modulation (QAM)-orthogonal frequency division multiplexing (OFDM) modulation schemes, (**b**) Internal schematic diagram of FDE block. evaluation and solution of the problems. Each portion of the analytical model contains an individual mathematical procedure which is analyzed as follows. The RF signals from BSs are achieved by the transmitter, 'Tx', of OFTL [27; 28] and can be computed as  
\[\epsilon=log(k)/log(2) \tag{1}\]  
where \(\epsilon\) represents the number of RF received pulses and \(k\) explains the length of sequence of the attained pulses. The received \(\epsilon\) pulses are then modulated to QAM format, which splits the waves into two cascaded sequences. Each sequence can be transmitted with varying their amplitude \(\sigma\)[29; 30] and is calculated as  
\[\sigma=(2_{n}-1-M),n=1,2,3,...,M. \tag{2}\]  
In Equation (2), the \(M\) denotes number of possible sequences of pulses and is defined as  
\[M=2^{i} \tag{3}\]  
where \(i\) denotes the number of bits per symbol and M represents the QAM level. The sequence of pulses at QAM output ports are subdivided into two cascaded sequences. The multilevel pulses are generated using M-ary pulse generator in terms of input signals, which are measured as [31; 32; 33; 34]  
\[N_{out}(t)= \begin{cases}a,0\leq t<t_{1}\\ bN_{in}(t)+a,t_{1}\leq t<t_{1}+t_{c}\\ a,t_{1}+t_{c}\leq t<T\end{cases}  \tag{4}\]  
where \(N_{in}\) shows input signals of M-ary pulse generator, \(b\) denotes linear gain, bias parameter s defined by \(a\), \(T\) presents bit period, \(t_{c}\) use for duty cycle and \(t_{1}\) is the pulse position. The waves explained in Equation (4) are interfered by QM in which output [35] is given as  
\[N_{out}(t)=D[I(t)cos(2\pi f_{c}t+\omega_{c})-Q(t)sin(2\pi f_{c}t+\omega_{c})]+a \tag{5}\]  
where \(I\) and \(Q\) are the input of electrical signals, gain of parameter is presented by \(D\), carrier frequency and phase are denoted by \(f_{c}\) and \(\omega_{c}\). The QAM symbols are passed through a FFT module with size of 512 to obtain the OFDM signal. As OFDM signals suffer from high PAPR values, the following analysis is performed. In order to calculate the PAPR in electrical form of signals, consider QAM transmission with \(n\) sub-carriers with frequencies (\(f_{i},i=1,2,...,n\)). The continuous time signal \(S(t)\) based on modulation interval \(T\) and \(nT\) duration of QAM symbols is defined as  
\[S(t)=\frac{0\leq t<nT^{max}|\zeta(t)|^{2}}{E|\zeta(t)|^{2}} \tag{6}\]  
The parameter \(E[\zeta(t)]\) explains the expectation function.