# Bi-LSTM-Augmented Deep Neural Network for Multi-Gbps VCSEL-Based Visible Light Communication Link
## 4 Proof of Concept Demonstration
### Communication Test Result  
To investigate the VLC performance with various driving conditions in the case of OOK modulation, the BER performance and the received eye-diagrams at a data rate of 3 Gbps, with different peak-to-peak (AC) signals and biases (DC), are investigated. In Figure 5(a),b, it can be observed from the eye-diagrams that, for the same DC bias, when the AC value is increased, the lower part is clipped due to it being driven below the threshold voltage of the VCSEL, although the received signal strength (peak-to-peak) increases. The eye-diagram in Figure 5(c) shows that, by applying a 1.5 V\({}_{\text{DC}}\) bias with a 688 mV peak-to-peak, the received signal strength becomes similar to that in the case of 1.4 V\({}_{\text{DC}}\) with 516 mVpp, but it shows marginally improved eye-opening. Figure 7 illustrates the BER performances. It is confirmed that the performance tends to improve by increased DC bias, regardless of the AC swing. The worst BER case is when the AC is 860 mV with 1.3 V\({}_{\text{DC}}\), as shown in Figure 5(b). The best case is when the AC is 860 mV with 1.3 V\({}_{\text{DC}}\) (as shown in Figure 5(b)) and the corresponding data rate is \(\sim\)3 Gbps, satisfying the forward error correction (FEC) with a BER threshold of 3.8 \(\times\) 10\({}^{-3}\). Figure 5: Experimental setup. Figure 6: Eye-diagram of the received 2-PAM signal of 3 Gbps applying (a) 516 mV AC with 1.3 V DC, (b) 860 mV AC with 1.3V DC, (c) 688 mV AC with 1.5 DC. Machine learning techniques can be applied to achieve a higher data rate, and the investigated structure is shown in Figure 8. The model consists of a Sequence Input Layer, two Fully Connected Layers, multiple Unidirectional LSTM or Bi-LSTM Layers, and a Classification Layer. The number of LSTM or Bi-LSTM Layers can be optimized empirically, considering the LSTM structure depicted in Figure 4. The model is trained with data generated by the arbitrary waveform generator and the data received from the photoreceiver. The data set is divided into a train set and a test set to train and evaluate the network. The 'Training data' shown in Figure 8 indicates the generated data labeled 0 or 1. The symbol \(y\) denotes the received aliased data to be recovered, and the symbol \(\hat{x}\) denotes the recovered data. The training model is formed through the operation of several layers in the network and a series of computations. Then, the data corrupted by noise and interference are compensated by the network, and it is shown in Figure 8 as 'Decoded data'. Finally, the decoded data are evaluated by the test set. The training options and the values used for the hyperparameters implemented to train the model are summarized in Table 1.  
To explore the relationship between the waveform shape and the LSTM network, we try to train the machine learning model, which includes a single LSTM layer with 300 LSTM units, and classify the received signal by changing the AC and DC values. In Figure 9, compared to the OOK case in Figure 7, the LSTM shows a noticeable BER performance improvement in all cases. It is especially notable that, for the case of an AC of 860 mV and a DC of 1.4 V (Figure 9b), the achieved data rate is improved to 8 Gbps from the previous OOK result of 3 Gbps. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline Optimizer & Adam \\ Learning Rate & 0.001 \\ Number of Epochs & 200 \\ Gradient Threshold & 1 \\ Shuffle & Once \\ Execution Environment & GPU \\ Sequence Length & Longest \\ Loss Function & Cross-entropy \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The training options and the hyperparameters’ values. Figure 7: BER performance according to different AC and DC values. It is also found that there are optimum machine learning configurations for the tested VCSEL-based VLC link. In particular, the type and depth of the layer and the number of units affect the machine learning performance. Such configurations are optimized to further increase the data rate.