www.WirelessCommunication.NL

Chapter: Wireless Channels
Section: Multipath fading, Rayleigh fading

Rayleigh Fading Simulator

Narrowband Rayleigh fading is modelled often as a random process that multiplies the radio signal by a complex-valued Gaussian random function. The spectrum of this random function is determined by the Doppler spread of the channel. Thus one can generate two appropriately filtered Gaussian noise signals and use these to modulate the signal and a 90 degree phase shifted version of the signal.


Figure: Block diagram of a narrowband Rayleigh fading simulator (in baseband)

Jakes' Simulator

It is common practice to generate the two filtered noise components by adding a set of six or more sinusoidal signals. Their frequencies are choosen as to approximate the typical U-shaped Doppler spectrum.


Figure: Crude approximation (orange) of the theoretical Doppler spectrum (Black) used in animation taking only 4 components. (N=3)

N Frequency components are taken at 

                     2 pi i
f_i  =   f_m  cos  --------   with i = 1, 2, .., N
                    2(2N+1)
with different amplitudes. One component at the maximum Doppler shift is also added, but at lesser amplitude.



www.WirelessCommunication.NL © Jean-Paul M.G. Linnartz, 1993, 1995.