Rayleigh Fading with Doppler Shift

In wireless communication systems, Rayleigh fading is a prevalent propagation channel model. When signals transmit through Rayleigh fading channels, the frequency characteristics change due to channel time-variation, resulting in what is known as Doppler shift. Therefore, in practical wireless communication environments, we need to consider Rayleigh fading models incorporating Doppler shift to more accurately characterize channel transmission properties. This is particularly crucial for wireless communication system design and performance analysis. Supplemental Materials: Rayleigh Fading: A fading phenomenon where Gaussian white noise with zero noise power level passes through a linear channel with bandwidth B and undergoes power equalization, resulting in amplitude whose square root follows Rayleigh distribution. In code implementations, this is typically modeled using complex Gaussian random variables where the magnitude follows Rayleigh distribution and phase follows uniform distribution. Common implementation approaches involve generating independent Gaussian random variables for in-phase and quadrature components. Doppler Shift: The phenomenon where signal frequency changes after transmission due to channel time-variation, primarily caused by relative motion between mobile stations and base stations. The greater the relative velocity between mobile stations and base stations, the larger the Doppler shift becomes. In simulation code, Doppler shift is often implemented using Jakes' model or similar spectral shaping techniques to generate time-correlated fading samples that replicate real-world mobility scenarios. Key parameters include maximum Doppler frequency calculated as f_d = (v*f_c)/c, where v is relative velocity, f_c is carrier frequency, and c is light speed.