## 2 Principles  
The V2X communication system based on MIMO VLC and radar includes two phases: training and testing as shown in Figure 1. In the training phase, the radar determines the calibration points where the VLC system estimates the SNR. The discrete SNR points are then interpolated to form a continuous SNR table. Due to the propagation of light, the interpolation should divide into linear and nonlinear parts based on a certain boundary of distance \(D_{\text{th}}\). With the distance less then \(D_{\text{th}}\), the SNR provided by the light intensity is high enough to support the high data rate communication, which is the linear area. With the distance more than \(D_{\text{th}}\), the SNR is not enough to support the highest data rate. The SNR is limited by the light intensity, which is nonlinear. Then, the interpolated SNR table can thus guide the test phase, in which the PS bitloading VLC system takes the SNR from the SNR table directly according to the distance acquired by the radar. With radar and PS bitloading VLC integration, a dynamic high data rate V2X communication can be achieved. In this section, the details of the principles are described. In the training phase, the radar and the VLC work simultaneously to generate the signal-to-noise ratio (SNR) table. A quadrature phase shift keying (QPSK) signal is modulated with discrete multitone  
Figure 1: The process of the VLC-Radar fusion V2X communication. (DMT) modulation to estimate the SNR for each subcarrier [13]. The SNR is estimated by calculation the error vector magnitude (EVM) of the receiving signal as  
\[SNR\approx EVM_{RMS}^{2} \tag{1}\]  
Ref. [14], and the \(EVM_{RMS}\) is derived by  
\[EVM_{RMS}=\left(\frac{\frac{1}{\sum_{t=1}^{T}\left|I_{t}-I_{0,t}\right|^{2}+ \left|Q_{t}-Q_{0,t}\right|^{2}}}{\frac{1}{N}\sum_{n=1}^{N}\left(\left(I_{0,n} \right)^{2}+\left(Q_{0,n}\right)^{2}\right)}\right)^{\frac{1}{2}} \tag{2}\]  
Ref. [14], where \(T\) denotes the total number of the received symbols, \(N\) denotes the number of unique symbols, \(I_{t},Q_{t}\) denote the in-phase (I) and quadrature (Q) components of the \(t\)-th symbol and \(I_{0,t},Q_{0,t}\) denote I and Q components of the standard constellation of the \(t\)-th symbol [14]. The SNR is estimated at several discrete calibration points guided by the radar, covering the supporting communication distance range. To get a continuous SNR table which is available for every point within the range, an interpolation algorithm combining linear and nonlinear methods is proposed according to the light field distribution.The light field intensity of an LED is described with the illuminance, which is \(I(\theta)=I(0)\cos^{m}(\theta)\), where \(I(0)\) denotes the center intensity of the light, \(\theta\) denotes the angle, and \(m=-\log 2/\log(\cos(\Phi_{1/2}))\) denotes the Lamberitian order with \(\Phi_{1/2}\) denotes the half power angle of the LED. Thus, the illuminance at the point \((x,y,z)\) is  
\[E(x,y,z)=I(\theta)\cdot\cos(\psi)/L^{2}, \tag{3}\]  
where \(L\) denotes the distance between the point and the transmitting LED, and \(\psi\) denotes the incident angle. The equation shows that the illuminance of a Lamberitian LED is inversely proportional to the second square of the distance. Though the LED headlights include the lenses that concentrate the light, the illuminance of the headlights follows the similar trend as described for the fixed \(I(\theta)\) and \(\psi\). Furthermore, the SNR of VLC signals is proportional to the light intensity within the linear working range. Hence, the SNR is inversely proportional to the second square of the distance between the transmitting LED and the receiver. The light intensity satisfies the SNR requirement of the VLC in the near field, which means the quality of the communication is directly related to the conditions of the LED and the light path. Therefore, the SNR is linear correlated with the distance, and the SNR table can be derived with linear interpolation.