Rayleigh Fading Simulation: Single-Path and Multi-Path Implementations

This documentation provides two MATLAB programs: Rayleigh_Doppler_singlePath.m and Rayleigh_Doppler_multiPath.m. First, Rayleigh_Doppler_singlePath.m generates single-path Rayleigh fading using six distinct implementation methods with comprehensive comparison. The algorithm implements methods including inverse Fourier transform, filtering approaches, and sum-of-sinusoids techniques. Method 6 demonstrates superior performance in terms of statistical properties and computational efficiency, making it our strongly recommended approach. The program includes power spectrum density calculation code using periodogram or Welch's method, facilitating direct analysis of the Doppler spectrum characteristics. Second, Rayleigh_Doppler_multiPath.m generates frequency-selective fading channels based on specified path delays and intensity profiles. The implementation involves convolving individual path responses with appropriate delay taps and power weighting, effectively modeling multipath propagation effects. The code handles power delay profile input and generates composite channel responses with correct frequency selectivity properties. Similar to the single-path version, this program includes power spectrum output functionality employing FFT-based spectral estimation techniques for comprehensive channel analysis. We hope these implementations prove valuable for your wireless communication system simulations. The codes are structured with clear parameter configuration sections and include comments explaining key algorithmic steps. For any technical inquiries or enhancement suggestions regarding the fading channel modeling approaches, please feel free to contact us.