Basic Doppler effect t) Propagation time is a function of time due to mobile car. c is the light velocity and v m is the car speed
Doppler spread in Multipath freq |X(f)| f c f c + f d1 f c + f d2 f c + f d |Y(f)| freq Due to multipaths, a single sinusoid by base station is perceived as summation of 3 sinusioids f c +f d1 , f c +f d2 and f c +f d , where f d is maximum doppler frequency = f c *(v m /d). Due to different arrivals of angle due to multipaths, perceived velocity is different for multipaths. After passing through multipath channel v m v m cos ( θ 1 ) v m cos ( θ 2 ) θ 1 θ 2
Doppler Spectrum This is called classical Doppler spectrum & shows how a single sinusoid ends up having a broad spectrum due to multipath & relative motion between Tx and Rx. A popular model assumes that distribution of angle of arrival is distributed uniformly between 0 & 2 π which leads to following spectrum Imagine now multiple paths with different angles of arrival causing amagamalation of various frequencies between f c +f d & f c -f d .
Frequency Dual Fourier Transform T 0 Function denotes space time correlation for the channel response to a sinusoid . So this indicates the amount of correlation between two sinusoids sent at different times t 1 & t 2 .
Think wireless channel as a FIR filter with a practically finite impulse response. The response of the filter keeps on changing due to time varying coefficients. The taps of the filter are corresponding to multipaths’s amplitude.
Coherence bandwidth f0 is a statistical measure of the range of frequencies over which all the signal spectral components are affected in a similar way by the channel i.e. exhibiting fading or no fading. Coherence bandwidth is inversely proportional to excess delay spread. Same channel can show flat fading behaviour depending upon
This just illustrates how delay spread puts a limit on maximum achievable data rate without needing an eqaulizer. Of course, various communication standards use various techniques to overcome this limits.
Doppler shift will be positive or negative depending upon whether mobile is moving to or going away from base station.
Here the effect of time dispersion & time variant behaviour of the model can be seen easily. When Doppler spread is larger, time between two consecutive fades is shortened accordingly.