## 1 Introduction
### Long-Range Vehicular Communications State-of-the-Art
Again, although the results are quite impressive, the system is tested only in limited optical interferences conditions using standard fluorescent tubes driven at 50 Hz which provide a constant average illuminance of 150 lux. One of the most reliable automotive VLC systems is presented in [14]. The functionality of this system is demonstrated experimentally in vehicle-to-vehicle real-world driving scenarios. The experimental results confirmed that VLC is able to provide a reliable communication distance of up to 45 m in highway driving scenarios. One can see that neither of the upper-mentioned works presents a VLC system capable to work in direct sun exposure. High performances results in such conditions are only reported in [16]. Nevertheless, in [16], the communication distance is only of 0.19 m. Consequently, one can see that the approach proposed in this article can significantly improve the performances of vehicular VLC systems. Considerations Regarding the Usage of Logarithmic Transimpedance Circuits in Automotive Visible Light Communications Sensors  
Generally, a VLC sensor is based on a PIN photodiode working in the photoconductive mode and connected in a transimpedance configuration. The photodiode generates an electrical current proportional to the incident light. The transimpedance circuit transforms the produced photocurrent into a proportional voltage that is further processed in order to extract the data. Nevertheless, this article proposes a novel approach based on a transimpedance circuit having a logarithmic behavior (Figure 1). The development of the logarithmic transimpedance circuit basically follows the design of a linear transimpedance circuit except that the linear resistor (i.e., linear behavior) that establishes the gain of the circuit is replaced by a block/component/circuit that has a logarithmic behavior. It is well known that in VLC the background light represents the most important disturbing element. The light is fluctuating in time and in space, whereas its irradiance can range from few \(\mu\)W/cm\({}^{2}\) to more than 100.000 \(\mu\)W/cm\({}^{2}\). Thus, the difference between the minimum value and the maximum value can expand on five decades. Consequently, selecting the working range of the transimpedance circuit can be difficult. Insufficient sensibility can lead to circuit blockage and reduced communication ranges, whereas too much sensitivity can lead to photosensitive element saturation [2]. In this case, variations of the power of the incident light will have no effect on the output voltage, which means that the incoming data will be lost. On the other hand, the output voltage for a logarithmic transimpedance circuit is given by Equation (1). We must specify here that the logarithmic circuit can introduce significant signal distortion when this solution is used in analogical transmissions. In such a case, although the dynamic range is significantly improved, the shape of the signal is affected. Then again, in digital transmissions, this signal distortion is consists of an unequal amplitude distortion, which does not have an effect on the shape of the signal. \[U_{log}=k\cdot\log(I_{d}), \tag{1}\]  
Figure 1: Schematic design of the VLC sensor, emphasizing the logarithmic transimpedance behavior. where \(U_{log}\) is the output voltage, \(k\) is a constant of proportionality, and \(I_{d}\) is the current generated by the photodiode which is given by Equation (2); the \(k\) constant is introduced in the equation as the response of the circuit is not perfectly logarithmic but it has a logarithmic trend. \[I_{d}=s\cdot P_{incident\ light}, \tag{2}\]  
where \(s\) is spectral sensitivity of the photodiode in A/W and \(P_{incident\ light}\) is the total power of the incident light. Regarding its benefits, the logarithmic transimpedance circuit provides the VLC sensor with an expanded dynamic range and improved resilience to photoelectron saturation. Thus, the sensitivity of the circuit varies logarithmically in accordance with the incident light.