# Rainy Environment Identification Based on Channel State Information for Autonomous Vehicles
## 3 Wireless Communication Vehicle Network
Under no-rain conditions, the gain \(G_{0}\) can be estimated based on the free-space propagation model. This model assumes that the signal propagates in a straight line between two points without any obstructions. The gain calculation formula is as follows:  
\[G_{0}=\left(\frac{\lambda}{4\pi d}\right)^{2} \tag{6}\]  
where \(\lambda\) is the wavelength of the signal, and \(d\) is the propagation distance. The specific attenuation caused by rain can be quantified using the ITU model, which provides an empirical relationship based on extensive measurements and studies. The model calculates the specific attenuation \(k_{r}\) as a function of the rain rate \(R\) (in mm/h) and the frequency of the signal (GHz) [28]. The formula for specific attenuation is generally expressed as follows:  
\[k_{r}=k\cdot R^{\alpha} \tag{7}\]  
where \(k\) reflects the attenuation efficiency per unit rain rate. It increases with frequency, indicating that higher frequencies are more susceptible to rain attenuation. \(\alpha\) describes the non-linear effect of rain rate on attenuation. It also varies with frequency and generally decreases as frequency increases, suggesting that the effect of increasing rain rate on higher frequencies is less pronounced than on lower frequencies. \(R\) is the rate at which rain falls, typically measured in mm/h. It is a direct measure of the intensity of the precipitation and is a critical factor in determining the extent of signal attenuation. Delay is usually related to the length of the multipath propagation path. Rainy conditions may cause changes in the propagation path, thereby affecting the delay. If the additional scattering path caused by raindrops is considered, the delay can be expressed as follows:  
\[\tau=\tau_{0}+\Delta\tau \tag{8}\]  
where \(\tau_{0}\) is the delay under no-rain conditions, and \(\Delta\tau\) is the additional delay caused by raindrop scattering. The delay \(\tau_{0}\) under no-rain conditions is related to the straight-line distance of signal propagation. It can be calculated using the following formula:  
\[\tau_{0}=\frac{d}{c} \tag{9}\]  
where \(c\) is the speed of light, and \(d\) is the propagation distance. The additional delay \(\Delta\tau\) can be estimated by measuring the difference in signal propagation time between rainy and clear conditions. The formula is as follows:  
\[\Delta\tau=\frac{d}{c}(n_{r}-1) \tag{10}\]  
where \(d\) is the propagation distance, \(c\) is the speed of light, and \(n_{r}\) is the refractive index of raindrops. The calculation of the Doppler frequency shift can use the standard Doppler effect formula, taking into account the speed changes that may be caused by rainy conditions:  
\[f_{D_{rain}}=\frac{\upsilon_{rain}}{\lambda}\cos(\theta) \tag{11}\]  
where \(f_{D_{rain}}\) is the Doppler frequency shift under rainy conditions, \(\upsilon_{rain}\) is the vehicle speed in the rain, \(\lambda\) is the wavelength of the signal, and \(\theta\) is the angle of arrival of the signal. The Signal-to-Noise Ratio (SNR) is defined as the ratio of the effective signal power to the noise power, and it is a key metric for evaluating the performance of communication systems. The formula for calculating SNR is as follows:  
\[\text{SNR}=10\log_{10}\left(\frac{P_{\text{signal}}}{P_{\text{noise}}}\right) \tag{12}\]  
where \(P_{\text{signal}}\) represents the average power of the received signal and \(P_{\text{noise}}\) represents the total noise power. By accurately identifying these sources of noise and precisely calculating the total noise power, the reliability and accuracy of the SNR calculation can be ensured under various rainy conditions. This not only aids in assessing the performance of the communication systems but also ensures stable operation in complex environments. In order to reduce the impact of raindrop scattering on V2V channel performance, a new multipath component is proposed.