# RCLED Optimization and Nonlinearity Compensation in a Polymer Optical Fiber DMT System
## 5 Results and Discussions
### Nonlinearity Compensation  
At the high operating point, to maintain the transmission performance at an acceptable BER below \(1\times 10^{-3}\), the proposed digital pre-distorter with the improved iteration algorithm is adopted for the RCLED nonlinearity mitigation. In addition, the high operating point \(I_{\text{DC}}\) = 22 mA is adopted. To obtain the optimal parameters of the LUT pre-distorter, the training procedure must be implemented first. The amplitude of \(\mathbf{X}_{\text{pilot}}\), designed as shown in Figure 6, is set from 2.2 to 5.236 V. In addition, the duration of the single sawtooth pulse is set as 1.024 \(\upmu\)s. For simplicity, \(P_{\text{Num}}=100\), \(\Psi=0.002\), \(\kappa=1\) and \(\lambda=1\) are adopted in Algorithm 1. The tradeoffs among the pilot symbol overheads, the convergence time and the RMSE must be evaluated by exploring the favorable \(N_{x}\), \(M_{\text{L}}\) and \(\mu_{\text{L}}\). Different from the traditional iteration in [14] (e.g., \(N_{x}=~{}1\)), the sub-portion pilot in our proposed algorithm is equally split into \(N_{x}\) slots. Figure 11a shows the RMSE performance comparisons with different split slots. In addition, \(M_{\text{L}}\) = 512 and \(\mu_{\text{L}}\) = 0.2 are adopted in this training procedure. As the Figure 11a shown, the pilot symbol overheads obviously decrease with the increasing \(N_{x}\), indicating that fewer pilot symbols used in the training can guarantee the algorithm convergence and improve the training work efficiency. In addition, the pilot overhead of the conventional pre-distorter is cost by 79, whereas that of the improved pre-distorter (eg.\(N_{x}=~{}4\)) is 21; the pilot's consumption is reduced to at least a third. Selecting the appropriate \(\mu_{\text{L}}\) and \(M_{\text{L}}\) can enhance the algorithm performance. Figure 11b,c demonstrate the RMSE and convergence time for different \(\mu_{\text{L}}\) and \(M_{\text{L}}\) on the condition of \(N_{x}=~{}4\), respectively. It can be seen that the RMSE is seriously degraded as \(\mu_{\text{L}}>0.28\), smaller step size is favorable for the algorithm reliability, but it conflicts with the convergence time, as illustrated in Figure 11c. Although the RMSE can be decreased by employing a larger LUT size, the computational  
Figure 10: (a) BER performance at different average DMT powers (b) the electrical signal power for different bias currents. complexity \(\mathcal{O}\left(N_{x}\cdot M_{\mathrm{L}}\right)\) increases, and costs more hardware resources. Therefore, based on the above analysis, the appropriate \(N_{x}=4\), \(M_{\mathrm{LUT}}=256\) and \(\mu_{\mathrm{L}}=0.22\) are selected in the iteration procedure to achieve the trade-off among the convergence time, the pilot symbol overheads and the system reliability. In this case, the training procedure will reach the stable convergence within 3 seconds approximately. The corresponding final training results in terms of the LUT gain values are illustrated in Figure 11d, in addition, the gains of the conventional LUT in [14] are also presented here. Clearly seen from Figure 11d, the gain values of the proposed LUT have the inverse characteristics of RCLED. Due to the fixed non-optimal parameters adopted in [14], the training outputs contain some noise components, which will affect the accuracy of the LUT prediction. Compared with the conventional LUT, the outputs of the improved LUT, based on an adaptive iterative algorithm, take on a steady and smooth curve. In addition, fewer pilot symbols are consumed in the training procedure, indicating the excellent performance achieved. It is worth noting that these final training results will be used in the following transmissions. Fixing the DMT modulation parameters, the signal power is set to be \(P_{\mathrm{Eave}}=8\) dBm. In addition, the Chow algorithm is also adopted. After 50 m SI-POF transmission, the received signals are then demodulated. Figure 12 plots one of the received constellations (32-QAM) without and with the nonlinearity compensation.