www.WirelessCommunication.NL Chapter: Wireless Channels Section: Multipath Fading

Scatter Function

Figure: the basic idea behind the scatter functions is that it plots the expected power per Doppler shift and per excess delay

Each path can be described by its

• Angle of arrival and Doppler shift
• Excess delay

Thus we can plot the received energy in a two dimensional plane, with Doppler shift on one horizontal axis and delay on the other horizontal axis.

Example

• U-shaped Doppler spectrum, as it occurs with uniformly distributed angles of arrival of reflected waves. The maximum shift is f_m.
• an exponential delay spread with mean T_rms

            Plocal-mean      1               1          tau
p(f, tau) = ------- --------------------  ---- exp(- -----)
            4 pi fm            (f-fc)2     Trms        Trms
                     sqrt( 1 - -------)
                                fm2 

Figure: Scatter function. Received power per unit of frequency shift and per unit of excess time delay.
Frequency shift normalized to the maximum Doppler shift.
Delay time normalized to the delay spread.

Figure: Scatter function projected to frequency axis. This gives the Doppler spread. Received power per unit of frequency shift.
Frequency shift normalized to the maximum Doppler shift.

Figure: Scatter function project to delay time axis: This gives the delay profile. Received power per unit of excess time delay.
Delay time normalized to the delay spread.

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