MATLAB Rayleigh Channel Phase and Envelope Probability Density Simulation

This simulation provides a complete analysis of phase and envelope probability density in MATLAB Rayleigh fading channels. The implementation captures both the phase variations and amplitude probability distributions characteristic of Rayleigh channels, which is essential for understanding wireless channel behavior and designing communication systems. Key implementation approaches include generating Rayleigh channel coefficients through methods like: - Using MATLAB's communication toolbox function rayleighchan to create a Rayleigh channel object with configurable parameters - Alternatively, creating complex Gaussian random variables with randn and calculating the envelope as the magnitude (abs function) and phase as the angle (angle function) - Analyzing probability distributions through histogram plotting functions with proper normalization to obtain PDF estimates The simulation allows adjustment of various parameters to observe channel performance characteristics, including signal-to-noise ratio (SNR), carrier frequency, Doppler shift, and sampling rate. This parametric analysis helps optimize signal transmission schemes and enhance communication system performance by providing insights into how different configurations affect the channel's statistical properties. The code typically involves statistical analysis functions to compute and visualize the probability density functions of both the envelope magnitude and phase components.