# An ANN-Based Adaptive Predistorter for LED Nonlinearity in Indoor Visible Light Communications
## 4 Simulations and Measured Results  
The relationship between the dissipated power and the luminous flux is used in the paper to describe the nonlinear behavior of an LED. A phosphor-based white LED (Crescent D01-A1-A33) was measured by using an integrating sphere (ISUZU SLM-12), and its dissipated power versus the output luminous flux is shown in Table 1. To implement a unified performance simulator, a normalized LED transfer function, as plotted in Figure 4, was used in the following performance evaluation of different considered predistortion algorithms. A Rapp-like model was adopted to fitting the normalized LED transfer function as follows [19]:  
\[\Phi_{norm}(p_{d,norm})=\frac{h(p_{d,norm})}{\left(1+\left(\frac{h(p_{d,norm} )}{p_{d,max}}\right)^{2k}\right)^{1/2k}}, \tag{8}\]  
where \(p_{d,max}\) is the maximum normalized dissipated power through the LED, \(h(p_{d,norm})\) is the function describing the measured characteristics between the normalized dissipated power \(p_{d,norm}\) and the normalized luminous flux \(\Phi_{norm}\), and \(k\) is the knee factor which controls the smoothness of the transition from the linear region to the saturation region. As shown in Figure 4, the Rapp-like model with knee factor \(k=3.0\) had a better fitting to the measured data of the considered LED and was adopted in the performance simulations of the LED nonlinearity predistorter detailed below. In the conducted computer simulations, \(10^{5}\) independent DCO-OFDM symbols were randomly generated with the parameters summarized in Table 2. To find the proper settings of the number of ANN training symbols \(N_{train}\) and the number of neurons in the hidden layer of the ANN predistorter \(J\), the BER versus the combination of the number of ANN training symbols and the number of hidden nodes are shown in Figure 5. Generally, as can be seen in Figure 5, the BER of the DCO-OFDM with the proposed ANN predistorter was decreased as the number of ANN training symbols was increased. The received scaling DCO-OFDM symbol \(\alpha\mathbf{y}^{\text{(DCO)}}\) was used to train the proposed ANN predistorter. When the setting of \(N_{train}=1\), it showed a limitation in effectively training the parameters in \(\boldsymbol{\varphi}\) because the distribution of the time-domain samples in one DCO-OFDM symbol might have been quite non-uniform in the domain of the desired predistorter function. When the value of \(N_{train}\) was increased, more time-domain samples in the \(N_{train}\) DCO-OFDM symbols were available, and these samples might have had a wider and uniform distribution within the domain of the desired predistorter function. As can be seen in Figure 5, the adaptation of \(N_{train}=5\) seems to have been enough to effectively train the parameters in \(\boldsymbol{\varphi}\) of the predistorter function. Moreover, the simulation results presented in Figure 5 indicated that the proposed ANN predistorter composed of a single hidden layer with 4 neurons was able to achieve a stable BER performance. Meanwhile, increasing the number of neurons in the hidden layer to more than 4 only seemed to increase the complexity of the network; thus, the number of neurons in the hidden layer \(J\) was set at 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Dissipated Power \(P_{d}\) (mW)** & **Luminous Flux \(\boldsymbol{\Phi}\) (lm)** \\ \hline
0.83 & 0 \\
19.77 & 0 \\
127.6 & 7474 \\
291.5 & 17,314 \\
497.4 & 19,434 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The measurements of the LED (Crescent D01-A1-A33). Figure 4: The characteristic function of the adopted LED. The convergence of the proposed ANN predistorter with different numbers of neurons in the hidden layer is shown in Figure 6. Consistent with the findings of Figure 5, the ANN with a 4-neuron hidden layer achieved the minimum mean-square error. The impacts of increasing the number of hidden layers are shown in Figures 7 and 8. Intuitively, the adoption of more layers in an ANN seemed to result in better achievable BER.