# An ANN-Based Adaptive Predistorter for LED Nonlinearity in Indoor Visible Light Communications
## 4 Simulations and Measured Results
However, the proposed ANN predistorter did not benefit from an increase in the number of hidden layers. This was mainly because the feedback replica of the original electrical source through PD, used as training set for the ANN, was noisy. The ANN became increasingly complicated with each increase in the number of hidden layers, and thus it could not be well trained using this noisy training set. In addition, the inverse function to the characteristic function of the adopted LED is expected to be simple and monotonic. As such, using more hidden layers might cause the ANN to be particularly sensitive to the noise, rather than the desired signal, resulting in overfitting. The BERs of several LED predistortion algorithms, including the NLMS [12], the Chebyshev polynomial [13], and the proposed ANN predistortion, plotted against the electrical energy per bit to single-sided noise power spectral density \(E_{b}/N_{0}\) for the cases of 16 QAM (\(M=16\)) and 64 QAM (\(M=64\)) are shown in Figures 9 and 10, respectively. In the cases of both 16 QAM and 64 QAM, it was evident that the BERs reached by the proposed ANN predistortion were lower than those reached by using the NLMS and the Chebyshev polynomial. The NLMS had the worst performance since the NLMS only used a one-dimensional LUT to approximate the predistorter function. In contrast, the Chebyshev polynomial method achieved a better performance than the NLMS method because the Chebyshev polynomial method adds polynomial expansion compensation terms onto the predistortion factors stored in the LUT. Meanwhile, the proposed ANN method, using a cascade of nonlinear functions to approximate the nonlinear predistorter \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Subcarriers number, \(N\) & 128 \\ QAM Modulation order, \(M\) & \{16, 64\} \\ DC bias in DCO-OFDM, \(x_{DC}\) (dB) & 13 \\ Number of ANN training symbols, \(N_{train}\) & \{1, 2, 3, 4, 5, 6\} \\ Number of neurons in the hidden layer, \(J\) & \{3, 4, 5, 6\} \\ Number of hidden layers, \(N_{h}\) & \{1, 2, 3\} \\ Knee factor in Rapp model, \(k\) & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of simulation parameters. Figure 5: Illustration of the proposed ANN predistorter: (**a**) 16 QAM DCO-OFDM with \(E_{b}/N_{0}=25\) dB; (**b**) 64 QAM DCO-OFDM with \(E_{b}/N_{0}=30\) dB. function, was capable of revealing the LED nonlinearity and could adaptively learn it through the training set, i.e., through the scaling feedback signal \(\mathsf{ay}^{\text{(DCO)}}\). Figure 8: BER in AWGN versus \(E_{b}/N_{0}\) of the proposed ANN predistorter for different numbers of hidden layers with 64 QAM. Figure 6: Convergence of the proposed ANN predistorter with different nodes in the hidden layer. Figure 7: BER in AWGN versus \(E_{b}/N_{0}\) of the proposed ANN predistorter for different numbers of hidden layers with 16 QAM. Notably, there were noise components contained in \(\alpha\)y\({}^{\text{(DCO)}}\), and this resulted in almost no performance difference among the NLMS, the Chebyshev polynomial, and the proposed ANN predistortion when the system was under a low \(E_{b}/N_{0}\) scenario. In contrast, in the scenario of moderate \(E_{b}/N_{0}\), the quality of \(\alpha\)y\({}^{\text{(DCO)}}\) was better, and thus the proposed ANN predistortion was apparently able to manifest its superiority over the NLMS and Chebyshev polynomial methods in that scenario. The effectiveness of the ANN predistorter in a DCO-OFDM VLC system was also validated in this study through experimental verification. The system setup of the self-built DCO-OFDM VLC testbed is shown in Figure 11. A pseudo-random binary sequence was programmed, modulated, and predistorted using the considered predistortion algorithms in the computer. To conduct the D/A conversion, the computer was connected to an arbitrary waveform generator (AWG) (Tektronix AFG3151C) under the constraint of modulation bandwidth of the LED.