Doppler Shift Causes Aliasing in Wireless Channel Output Signals

(1) In certain wireless channels, Doppler shift can cause aliasing in the output signals. The primary causes include: signal propagation path obstacles, mobile device velocity, and transmission frequency. Implementation-wise, aliasing occurs when the Doppler spread exceeds half the sampling rate (Nyquist criterion), requiring proper sampling rate selection in channel simulation code. Key factors involve multipath propagation and relative motion between transmitter and receiver.

(2) The classic Doppler spectrum in wireless channels results from uniform scattering environments where multipath components arrive from all directions with equal probability. The spectral shape follows Jakes' model, mathematically represented by U-shaped distribution with maximum Doppler frequency (f_d = v*f_c/c, where v=velocity, f_c=carrier frequency, c=speed of light). Code implementation typically uses sum-of-sinusoids method or inverse Fourier transform of the spectrum.

(3) Using Simulink with S-Function, implement a single-path Rayleigh channel with classic Doppler spectrum for 120 km/h velocity. The S-Function should incorporate: Doppler frequency calculation (f_d = v*f_c/c), Rayleigh fading generator using multiple oscillators, and spectrum shaping filters. Validation methods include: comparing the power spectral density (PSD) with theoretical Jakes spectrum using MATLAB's pwelch function, analyzing autocorrelation properties, and verifying the 3-dB bandwidth matches theoretical f_d value. Additional verification can involve testing for proper Rayleigh distribution of envelope values and checking temporal correlation characteristics against Clarke's model.