# FPGA-Based Pulse Compressor for Ultra Low Latency Visible Light Communications
## 6 Measurements and Results  
### Communication Distance and Packet Error Rate  
The set-up described in the previous section was used for measuring the Packet Error Rate (PER) at increasing distances. In particular, the 3 chirps of Table 1 were tested over the communication distances from 1.5 m to 4.0 m. For each experiment, at least 1 M packets were sent, corresponding to 1 M \(\times\) 24 = 24 M bits. Since the communication rate was \(1/T_{B}\) = 1.5625 Mb/s, each experiment lasted about 15 s. The PER was automatically calculated  
Figure 10: (**a**) Experimental setup composed by the VLC system, the host PC where the MATLAB interface runs, a power unit, an oscilloscope, the XHP50 LED, and the PDAPC2 detector held by a tripod. (**b**) Detail of the VLC system: the VLC custom board and the FPGA board are visible on the top and bottom, respectively.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \multicolumn{2}{c}{**Transmitter**} \\ \hline LED model & XHP50 (5000 K, Cree Inc.) \\ \hline LED mean current & 1 A \\ \hline Modulation current & \(\pm\)0.25 A \\ \hline LED bandwidth & 1.7 MHz (\(-\)3 dB), 2 MHz (\(-\)3.4 dB) \\ \hline DAC & 14-bit, 12.5 Msps \\ \hline \multicolumn{2}{c}{**Receiver**} \\ \hline Photodetector & PDAPC2 (Thorlab Inc.) \\ \hline Bandwidth & 11 MHz (0 dB), 1.4 MHz (10 dB) \\ \hline LNA gain & 30 dB \\ \hline ADC & 12-bit, 12.5 Msps \\ \hline \end{tabular}
\end{table}
Table 3: Parameters of the experimental set-up.  
in the FPGA by counting the transmitted packets and the packets received with no errors. Figure 11 reports the measurements.  
For distances below 180 cm, no errors were measured for any of the 3 chirps in the 1 M packets sent, corresponding to a PER \(<\) 10\({}^{-6}\) (or a BER \(<\) 4\(\cdot\)10\({}^{-8}\)). At a distance between 180 and 215 cm, the errors measured for the chirp with T = 4.48 \(\upmu\)s started to increase, whereas the other 2 chirps produced no errors. At a distance between 215 and 280 cm, the errors measured for the chirp with T = 8.96 \(\upmu\)s started to increase as well, whereas the longest chirp continued to produce no errors. Finally, at distances higher than 280 cm, the longest chirp also produced increasing errors, although the PER was still below 10\({}^{-1}\) up to 340 cm.  
In order to quantitatively compare the performance of the 3 chirps, we set a threshold, for example, at PER = 0.05 (see the red line in Figure 11). At this PER, we measured a communication distance of 212, 253, 320 cm for the 3 chirps, respectively. From these data, we can now calculate the gain in communication distance that we obtain by increasing the chirp temporal duration and compare this to its theoretical trend given by (5). It is useful to nominate the 3 chirps T\({}_{17.92}\), T\({}_{8.96}\), T\({}_{4.48}\), where the subscript reports the respective chirp temporal duration. If N is the ratio between chirp durations, see (5), we can compare T\({}_{17.92}\) against T\({}_{8.96}\) (N = 2); T\({}_{17.92}\) against T\({}_{4.48}\) (N = 4), and T\({}_{8.96}\) against T\({}_{4.48}\) (N = 2), for a total of 3 comparisons. For example, the length ratio between chirps T\({}_{17.92}\) and T\({}_{8.96}\) is N = 17.92/8.86 = 2, and we measured a distance gain of 320/253 \(\approx\) 1.26. The experimental data are represented by the red diamond, yellow cross, violet circle markers in Figure 12, which reports N along the x-axis and the distance gain along the y-axis. These data are compared to the theoretical gain in distance achievable by stretching the chirp duration, i.e., the blue curve given by (5). For example, in the case of T\({}_{17.92}\) against T\({}_{8.96}\) we measured a 320/253 \(\approx\) 1.26 gain (yellow cross) to be compared to the theoretical 1.2 (blue line at N = 2).  
Figure 11: PER measured at different communication distances with the 3 chirps of T = 4.48 (violet), T = 8.96 (green), T = 17.92 (light blue). Blue marks represent the measurement points.