Doppler Shift Formula
When either the transmitter or the receiver is in motion, or when both are in motion, Doppler Shift is an essential parameter in wireless Communication. We notice variations in reception frequencies in vehicles, trains, or other similar environments. In plain language, the received signal frequency increases as the receiver moves toward the transmitter and drops as the receiver moves in the opposite direction of the transmitter. This phenomenon is called the Doppler shift or Doppler spread.
Doppler Shift Formula:
Or, Doppler spread, fD = |v/lambda * {cos(theta) - 1}|,
** '|' indicates mod
where, v = velocity of vehicle
lambda = wavelength = c/frequency
For example, when MS (in motion) reaches towards BS, cos = cos(0 degrees)=1, and when MS goes away from BS or base station, cos = cos(180 degrees)=-1.
As a result of the preceding equation, the receiving frequency increases if the receiver moves towards the receiver.
Similarly, when the receiver moves away from BS or the cell tower, the frequency decreases by v/lambda* cos ( 180 degrees) or v/lambda * (-1), as cos180 = -1. So, now the received frequency at the receiver side is,
fR = fT - fD
How Doppler Spread Affects Communication
The Doppler spread causes fading in wireless Communication. Fading occurs when the received power fluctuates or decreases at the receiver side for a short or large amount of time. Fast and slow fading in wireless channels is caused by Doppler spread. All of those topics have already been covered in another article. Please read the full article.
For practical communication systems, if the received symbol or signal is R[t,f], then
R[t, f] = S(Ï„)*h(Ï„, f)*exp(2*pi*(t - Ï„))
where S(Ï„) is the transmitted signal with some delay Ï„
h(Ï„, f) is the Doppler delay channel impulse (DD-CIR) response which characterizes how the signal's amplitude and phase change with respect to time delay Ï„ and frequency f
exp(2*pi*(t - Ï„)) represents the phase shift due to the Doppler effect
[1] Fading - Slow & Fast and Large & Small Scale Fading