# RCLED Optimization and Nonlinearity Compensation in a Polymer Optical Fiber DMT System
## 2 RCLED Measurement and Modeling  
With the low cost consideration, most of the POF systems employ the intensity-modulation and direct-detection (IM/DD) structure rather than coherent modulation. In the IM/DD scheme, the power intensity of the RCLED is modulated by a real and non-negative DMT signal [15]. Therefore, owing to the bipolar DMT, the RCLED has to be biased before applying the modulating signal. The system diagrams of both the RCLED-based POF transmitter and the receiver are depicted in Figure 1. In the POF transmitter [14], the bias circuit is connected with the RCLED (FC300R-120(tm), Firecomms, Cork, Ireland), and the switches (\(S_{1}\), \(S_{2}\) and \(S_{3}\)) are used to switch between the measurement and communication status. The OptoLock(tm) (Firecomms, Cork, Ireland) is employed to connect the SI-POF (ESKAT(tm) Premier, Mitsubishi Rayon, Tokyo, Japan) between the RCLED emitter and Si-PIN photodetector (PD, FC1000D-120(tm), Firecomms, Cork, Ireland). In the POF receiver, the received optical signal is captured by the PD at \(P_{7}\), and the power intensity is converted into an electrical current, which is finally demodulated. In this paper, only the static case of the RCLED is measured and focused on. In the measurement status, \(S_{2}\) and \(S_{3}\) are toggled towards the nodes \(P_{2}\) and \(P_{4}\), respectively, and \(S_{1}\) is open. The output optical power of RCLED \(P_{\text{out}}(I_{\text{F}})\) is measured at \(P_{6}\) by an optical power meter (PM100 USB(tm), THORLABS, Newton, NJ, USA). Figure 2a shows the measured \(P_{\text{out}}(I_{\text{F}})\), where \(I_{\text{F}}\) denotes the RCLED forward current. To get photons emission from RCLED, it generally suffices to provide current to RCLED. When \(I_{\text{F}}\) is injected, an area forms in which there is a large concentration of holes and electrons in the p-n junction at the same time. However, the current-power characteristic only has linear with a small interval. The RCLED outputs only operate linearly in the range between 5 and 20 mA. Additionally, when \(I_{\text{F}}\) is above 40 mA, the RCLED is saturated and the nonlinear characteristic is more significant. The relationship between the measured internal signal voltage \(V_{\text{s}}\) at \(P_{8}\) and \(I_{F}\) is illustrated in Figure 2b. With the internal 50 \(\Omega\) source resistor and 47 \(\Omega\) series resistor, the relationship is nearly linear. As seen in the Figure 2b, the \(I_{\rm F}\) dramatically increases when \(V_{\rm s}>\)2 V, and the RCLED has a turn-ON voltage of around 1.8 V. Each diode has a minimum threshold voltage known as the turn-ON voltage, thus the RCLED is not conducting current when the \(V_{\rm s}\) is below the turn-ON voltage. So the transmitting signal below this value is considered as clipped. A polynomial model has been formulated to describe the nonlinear behaviors of white LED [12]. Similarly, the RCLED transfer function can be also numerically modeled by a Taylor series expansion  
\[P_{\rm out}\left(I_{\rm F}\right)=\sum_{n=0}^{\infty}b_{n}\left(I_{\rm F}-I_{ \rm DC}\right)^{n}, \tag{1}\]  
where \(I_{\rm DC}\) denotes the bias current, and \(b_{n}\) denotes the coefficient of the \(n^{\rm th}\) order polynomial. However, in this paper, to present the direct relationship between the input modulated signal voltage and the RCLED outputs, \(P_{\rm out}(V_{\rm s})\) is modeled by a function of \(V_{\rm s}\) rather than \(I_{\rm F}\). With the measured results in Figure 2, \(P_{\rm out}(V_{\rm s})\) can be approximated by a polynomial of \(V_{\rm s}\) based on the least-square fitting method, and the approximated results are shown in Figure 3, where the nonlinear behavior of the RCLED outputs are linear between 2.8 and 4 V. Additionally, the amplitudes of the input signal out of this range will be distorted. The accuracy of the polynomial approximation, in terms of root mean squared error (RMSE), depends on the fitting order. The RMSE is decreased as the fitting order increases.