## 3 Experimental Results  
A thorough post-analysis of data is carried out to retrieve the errors' distribution observed in the packet delivery process considering the bidirectional communication. In particular, we analyzed the occurrences and sizes of clusters of errors for different PER values in order to estimate the statistical value of the latency occurring in the complete round-trip communication. By observing the positions of the packets over time containing at least one error, we can measure the latencies to receive each packet correctly. The latencies obtained in such way can be used to derive the probability to reach a target average latency. In other words, we aimed to derive the probability that a specific latency occurs, i.e., that  
Figure 2: The three different time scales in each picture represent: the TX1, sending a continuous data stream of \(10^{4}\) packets separated by an inter-packet delay (IPD) slightly greater then the packet time (PT) along the x direction; the TX2, after performing an active decoding and, if the packet is correct, back replies (\(-\)x direction) then, the final stage counts the correct received packets after a round trip. (a) If in all the round trip no packet is lost, the minimum latency is L\({}_{0}\). The loss of the packet could happen both in the first path (b), and in the second path (c), in each case, the latency of the bidirectional link grows as \(L_{N}=L_{0}+N_{Lost}(IPD+PT)\), where N\({}_{Lost}\) is the number of consecutive lost packets in the final stage. the message is correctly received by that time. The procedure is similar to the one reported in [30] for an I2V implementation. The communication performance of our bidirectional VLC system is evaluated through PER measurements in a _Flat_ configuration with a data rate of 57 kBaud. Since the number of transmitted packets is \(10^{4}\), our PER limit corresponds to \(10^{-4}\). Figure 3a shows the experimentally measured PER as a function of the distance between the motorbikes. The dots represent the statistical average over five repeated measurements, and both horizontal and vertical error bars, taken as standard deviations, are smaller than the symbols mark. The solid curve is a guide to the eye. As is well known, the PER depends monotonically from the Signal to Noise Ratio (SNR): as the distance increases the SNR decreases and, consequently, the PER increases, reaching a value of \(\approx\)0.1 at 15 m, while up to 9 m the PER is constantly below the \(10^{-4}\) limit. Figure 3: (**a**) PER of the VLC system with a baud rate of 57 kBaud. An error-free communication can be established for distances up to 9 m. To each symbol is associated an error bar, representing the standard deviation of the error. Horizontal and vertical error bars are smaller than the symbol mark. (**b**) Occurrences of the number of consecutively lost packets (errors cluster size) for different PER values. (**c**) SAL (ms) as a function of the success probability for different PER values. As discussed in Section 2, the statistical average latency (SAL) value is connected to the observed PER. The distribution of the number of consecutively lost packets during the experimental measurements is estimated and reported in Figure 3b for different PER values. The occurrences of the clusters of lost packets increases as the PER increases. The maximum observed cluster size is four (consecutive) packets with a PER of \(1.4\times 10^{-1}\), that corresponds to a latency of 15.1 ms. Following a procedure which has been recently employed in infrastructure-to-vehicle (I2V) applications [30], the number of consecutively lost packets has been sorted to obtain the SAL as a function of success probability, as depicted in Figure 3c. Table 1 shows the probability to reach a target SAL under a specific PER condition. As it can be observed, given a PER of \(10^{-2}\), the SAL exceeds its minimum value (2.5 ms) with a probability of 1%, and with a probability of 0.1% for a PER of \(10^{-3}\).