Simulation of Multipath Fading Channels Using Sum-of-Sinusoids Method

In this document, we implement the sum-of-sinusoids method to simulate multipath fading channels and calculate the channel frequency response. This technique models multiple propagation paths by superimposing sinusoids with different amplitudes, phases, and Doppler shifts, effectively replicating real-world wireless channel behavior. The implementation typically involves generating multiple sine waves with randomized parameters to simulate various path components, then combining them to create the composite channel impulse response. Through this simulation approach, we can analyze signal propagation characteristics in multipath environments and study how channel effects impact signal quality. The frequency response calculation involves applying Fourier transform to the time-domain channel response, enabling frequency-selective fading analysis. This methodology allows communication engineers to optimize system design by evaluating channel performance metrics such as coherence bandwidth and delay spread, ultimately improving transmission reliability and overall system performance.