# Rainy Environment Identification Based on Channel State Information for Autonomous Vehicles
## 3 Wireless Communication Vehicle Network  
Firstly, a wireless communication vehicular network is constructed. In this network, each vehicle is equipped with a half-duplex transmitter/receiver, enabling communication with other vehicles while limiting the ability to send and receive signals simultaneously. This half-duplex communication mechanism is crucial in dense vehicular environments as it helps reduce channel congestion and signal interference. In this network, vehicles process the received CAM characterized by Channel State Information (CSI) in a wireless channel. CSI provides a precise characterization of the wireless channel and contains detailed information about the signal propagation path, such as signal attenuation, phase changes, and time delay characteristics. The proposed V2X network operates based on the IEEE 802.11p standard. The main physical layer (PHY) of the IEEE 802.11p standard is based on Orthogonal Frequency-Division Multiplexing (OFDM) waveforms [25]. Figure 2 illustrates the frame structure of the Physical Protocol Data Unit (PPDU) specified by the IEEE 802.11p standard. Figure 2: IEEE 802.11p PHY layer frame structure. The vehicular wireless channel is constructed as a dual-selective fading propagation channel, where multipath effects cause the signal to experience varying degrees of fading at different times and frequencies. And the Doppler effect affects the signal's frequency due to changes in moving speed. In the high-speed moving vehicular communication environment, the time-varying nature of multipath effects poses a significant challenge to signal transmission quality. To adapt to this dynamic change, the baseband time-varying response of the multipath channel is represented as follows:  
\[h(t,\tau)=\sum_{i=1}^{L-1}A_{i}(t)e^{-f2\pi f_{d}\tau_{i}(t)}\delta(\tau-\tau_ {i}(t)) \tag{1}\]  
\(L\) represents the total number of non-zero paths, \(A_{i}(t)\) is the \(i\)-th time-varying complex amplitude, and \(\tau_{i}(t)\) denotes the \(i\)-th time-varying path delay. The expression \(e^{-f2\pi f_{d}\tau_{i}(t)}\) indicates the \(i\)-th phase shift due to the Doppler frequency shift, where \(f_{d}\) is the Doppler frequency shift caused by the relative velocity change between the signal transmitter and receiver. It is noteworthy that the phase of the complex amplitude \(A_{i}(t)\) is affected by changes due to the Doppler effect. As the signal propagates through the channel, Doppler frequency shifts may occur on each independent path. By incorporating the factor \(e^{-f2\pi f_{d}\tau_{i}(t)}\), it is possible to accurately describe and compensate for the phase changes caused by the Doppler effect during signal propagation, thereby enabling a more accurate recovery of the transmitted signal. Assuming that the channel characteristics are stationary within a constant time \(T_{c}\), which is inversely proportional to the maximum Doppler frequency shift \(f_{d}\)[26].The formula is as follows:  
\[T_{c}\approx\frac{0.423}{f_{d}} \tag{2}\]  
In vehicle communication, the Doppler frequency shift \(f_{d}\) can be represented by the velocity difference \(\Delta V\) between two communicating vehicles as follows:  
\[f_{d}=\frac{\Delta V}{c}f_{0} \tag{3}\]  
\[\Delta V=|V_{1}-V_{2}| \tag{4}\]  
where \(c\) represents the speed of light and \(f_{0}\) denotes the central frequency of the communication system. Based on the channel's coherence bandwidth \(1/T_{c}\), if this bandwidth is greater than the bandwidth of the signal itself, the channel exhibits flat fading characteristics. Conversely, if the channel's coherence bandwidth \(1/T_{c}\) is less than the signal bandwidth, the channel exhibits frequency-selective fading, which causes intersymbol interference in the time domain. In vehicular networks, V2X communication scenarios significantly impact the propagation of electromagnetic waves, and these factors are key determinants in channel model construction.