Figure: Phasor diagram of a set of scattered waves (in blue), resulting in a Rayleighfading envelope (in black) 
If the mobile antenna moves a small distance e, the nth incident wave, arriving from the angle a_{n} with respect to the instantaneous direction of motion, experiences a phase shift of
2p e  cos(a_{n}) l
Thus all waves experience their own phase rotation. The resulting vector may significantly change in amplitude if individual components undergo different phase shifts.
Java animation  Figure: Phasor diagram of a set of scattered waves after antenna displacement (in blue) and before motion (in light blue), resulting in a Rayleighfading envelope (in black) 
In mobile radio channels with high terminal speeds, such changes occur rapidly. Rayleigh fading then causes the signal amplitude and phase to fluctuate rapidly.
If e is in the order of half a wave length (l/2) or more, the phases of all incident waves become mutually uncorrelated, thus also the amplitude of the total received signal becomes uncorrelated with the amplitude at the point of departure.
The normalised covariance L(e) of the electric field strength for an antenna displacement e is of the form
2 2p e L(e) = J () 0 l
with J_{0}(.) the zeroorder Bessel function of the first kind.
The signal remains almost entirely correlated for a small displacement, say e<
l/8, but becomes rapidly independent for larger displacements, say for e >
l
/2.
Figure: Autocovariance L(e) of the electric field strength in a Rayleighfading channel versus the normalised antenna displacement e/ l (or T f_{m}) in horizontal direction. 
The antenna displacement can also be expressed in the terminal velocity v and the time difference T between the two samples (e = v T). So with f_{m} the maximum Doppler shift (f_{m} = v f_{c} / c).
System  Countermeasure  
Analog 
 
GSM 
 
DECT 
 
IS95 Cellular CDMA 
 
Mobile data networks, Wireless LANs 
