Shaping Filter Method, Jakes Simulation Model and Its Multiple Improved Methods

In this paper, we first conduct a detailed analysis of the statistical characteristics of Rayleigh fading channels, examining their fading processes and underlying principles, and subsequently propose the Clarke model. To achieve more accurate simulation of wireless fading channels, we introduce a simulation approach based on the shaping filter method and Jakes simulation model, along with multiple improvements to the Jakes model. During the description of these simulation methods, we provide comprehensive details on their software implementation, including MATLAB-based computer simulations. The implementation involves generating complex Gaussian random processes through inverse Fourier transform techniques (for shaping filters) and sum-of-sinusoids approaches (for Jakes model). Key MATLAB functions like fft, ifft, and random number generators are utilized to create realistic fading waveforms. Through analysis of simulation results, we obtain simulated fading signals and perform detailed examination of the outcomes. Experimental results confirm that our proposed simulation models exhibit high correlation with theoretical curves, effectively simulating wireless fading channels and thereby providing robust support for the design and optimization of practical communication systems.