# Bi-LSTM-Augmented Deep Neural Network for Multi-Gbps VCSEL-Based Visible Light Communication Link
## 2 Characteristics of VCSEL
### Experimental Analysis of VCSELs' Characteristics  
This sub-section presents the characteristics of the off-the-shelf VCSEL (Thorlabs, L670 VH1) used for the characterization and VLC performance test. The VCSEL has a typical center wavelength of 670 nm. The threshold current, operating current and corresponding optical output are 0.6 mA, 2.5 mA and 1 mW, respectively. The beam divergence angle (full-width-half-maximum) is 10 degrees.  
Figure 2 shows the measured frequency response. A high-speed PIN photo-receiver (New-Focus, 1591), arbitrary waveform generator (Tektronics, 70002B), and oscilloscope (Tektronics, DPO70404C) are used for the experiment. The overall measurable bandwidth of the testbed is \(\sim\)4 GHz. A total of 21 frequency points are measured, which are extracted in the frequency range of 2 MHz to 1 GHz for the frequency measurement. It is confirmed from the measurement that the \(-3\) dB bandwidth of the VCSEL device is 500 MHz. The value is certainly more than an order of magnitude higher than that of typical LEDs, showing the potential of VCSELs for high-speed modulation.  
Figure 1: The basic structure of AlGaAs/GaAs VCSEL (**left**). The active region (**right**).  
The dynamic response to check the linearity of the VCSEL device and to find the suitable driving condition is shown in Figure 3. The testbed is the same as the frequency response measurement, except that three different levels of sinusoidal amplitudes (516 mV, 688 mV, 860 mV) are applied, while the DC bias is varied from 1.3 V to 1.5 V. The applied frequency is 10 MHz, at which value the dynamic characteristics of the VCSEL device are well observed. The output amplitude from the high-speed photo-receiver is captured by the oscilloscope, and the received signal shape is observed. The other parameters (such as the received optical power) are adjusted to monitor the response from the VCSEL device purely.  
Overall, for the higher DC bias, the peak-to-peak levels of the observed output signal are slightly reduced. This is due to the VCSEL's nonlinear DC characteristics. This tendency can be better seen with the smallest AC signal (516 mV). On the other hand, in the case of a DC bias of 1.3 V (Figure 3a) and an AC signal of more than 688 mV, a clear lower clipping is observed. This is due to the VCSEL's threshold voltage level being at \(\sim\)1 V. By increasing the DC bias level to 1.4 V (Figure 3b), it can be seen that the AC signal of 688 mV no longer causes the lower clipping, since the lowest level applied to the VCSEL is higher than the threshold voltage. For the same reason, Figure 3c shows no clipping even with the 860 mV applied to the VCSEL. A higher received signal strength could result in better communication performance; however, it could induce more nonlinear distortion. Additionally, the inclusion of a certain amount of nonlinear distortion while utilizing the high signal level could be beneficial, since it could lead to a higher signal-to-noise ratio (SNR) if the level of nonlinearity is well-compensated, given the other deterioration parameters in the system. The optimum amount of nonlinearity inclusion could depend  
Figure 3: Dynamic response and linearity of the VCSEL; sine wave outputs for (**a**) 1.3 V DC bias, (b) 1.4 V DC bias and (c) 1.5 V DC bias.  
Figure 2: VCSEL (L670 VH1) frequency response.  
on the applied communication schemes as well. These postulations are tested in the LSTM-augmented deep neural network in the following sections.