# RCLED Optimization and Nonlinearity Compensation in a Polymer Optical Fiber DMT System
## 4 Nonlinearity Mitigation
### Nonlinear Compensation  
Owing to the mode attenuation of SI-POF, high optical power outputs are required at the transmitter in the case of the detection sensitivity demanding at the receiver. When the high optical power is obtained by operating the RCLED at the large working point, the nonlinear distortion will be introduced [17; 18; 19]. To mitigate the RCLED nonlinearity in the practical POF transmitter, an improved digital pre-distorter is proposed in the signal generator, considering both the computational complexity and the bandwidth efficiency. The basic idea of the digital pre-distorter is shown in Figure 4. The pre-distorter adjusts the modulating signal \(x_{k}\) to be a desired one \(x_{\text{new}}\), which drives the RCLED to produce the correct output \(P_{\text{new}}\), thus the cascade response of the pre-distorter and RCLED chain can be linear [14]. Note that if \(P_{\text{new}}\) is larger than the saturation level of RCLED, the corresponding \(x_{\text{new}}\) cannot fully compensate the nonlinearity. Therefore, the RCLED must be back off from SAV to the corresponding peak, to the average level of the signal. In the communication status, as shown in Figure 1, \(S_{2}\) and \(S_{3}\) are toggled towards the nodes \(P_{3}\) and \(P_{5}\), respectively, and \(S_{1}\) is connected to \(P_{1}\). The desired linear curve \(L\left(x\right)\), shown in Figure 4, can be expressed as  
\[L\left(x\right)=k_{l}V_{\text{S}}-b_{l} \tag{12}\]  
where \(k_{l}=0.5278\) and \(b_{l}=1.0017\). The pre-distorter based on an adaptive digital LUT is shown in Figure 5. The nonlinear signal \(x_{k}\) is adjusted to a linear one \(x_{\text{new}}=\eta_{\text{L}}x_{k}\), where \(\eta_{\text{L}}\) denotes the gain coefficient. \(\eta_{\text{L}}\) can be sought by a quantization function \(Q_{\text{ua}}\left(\cdot\right)\), which indicates the corresponding index of the gain vector \(\eta=\left[\eta_{1},\eta_{2},\cdots,\eta_{M_{\text{L}}}\right]^{T}\), where \(M_{\text{L}}\) denotes the LUT size. With the input \(x_{\text{new}}\), the linear output power can be captured by an optical power meter and detected as \(P_{\text{new}}=g\left(x_{\text{new}}\right)\). Figure 4: The principle of the pre-distorter. To obtain \(\eta\), a training procedure must be implemented first. However, the maximum amplitude of the linear input \(x_{k}\) depends on the turn-ON voltage and SAV of the RCLED. Thus, considering the commercially available RCLED used in this paper, the operating region of the pre-distorter must be set between 2.2 and 5.236 V, so that the values out of this range are clipped. Therefore, in the training procedure, a pilot signal \(\mathbf{X}_{\text{pilot}}\) with a sawtooth shape, as shown in the Figure 6, is sent through the pre-distorter firstly. We propose an adaptive iterative algorithm with three main sections. First, \(\mathbf{X}_{\text{pilot}}\) is quantized equally into \(M_{\text{L}}\) parts, and each sub-portion is split equally into \(N_{x}\) slots. Second, the differences between the ideal linear and the actual output of RCLED are obtained. Third, the gain value \(\eta\) is obtained based on the LMS criterion. Algorithmically, the details are given in Algorithm 1. Figure 5: Block diagram of the digital look-up-table (LUT) pre-distorter in the discrete multi-tone (DMT) transmitter. Figure 6: Sawtooth pilot signals. ```
Input: Initial gain vector \(\eta=\left[\eta_{1},\eta_{2},\cdots,\eta_{M_{L}}\right]^{T}\) and \(\mathbf{W}=\left[w_{1},w_{2},\cdots,w_{M_{L}}\right]^{T}\), quantized pilot signal \(\mathbf{X}_{\text{pilot}}=\left[\mathbf{X}_{1},\mathbf{X}_{2},\cdots,\mathbf{X }_{M_{L}}\right]^{T}\), slot number \(N_{x}\), step factor \(\mu_{L}\), stop criteria \(\Psi\), the maximum pilot number \(P_{\text{Num}}\), and the adaptive adjustment factor \(\kappa\) and \(\lambda\). Initialization:\(\eta=1\), \(\mathbf{W}=\mathbf{0}\), \(P_{\text{Cnt}}=1\). Step1.