Multipath fading and user mobility lead to a time and frequency dependent channel.
The Transfer function of a particular
does not necessarily provide enough details about the stochastic behavior of the radio channel. Such stochastic properties
are captured in the scatter function.
The scatter function combines information about
Figure: the basic idea behind the scatter function is that it
plots the expected power per Doppler shift and per excess delay bin.
Sometimes, angle of incidence (bearing) is plotted in stead of the Doppler shift.
Each path can be described by its
- Angle of arrival or 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.
Environment Delay Spread Angle spread Max. Doppler shift
at 1800 MHz
Macrocellular: Rural flat 0.5 ms 1 degree 200 Hz
Macrocellular: Urban 5 ms 20 degrees 120 Hz
Macrocellular: Hilly 20 ms 30 degrees 200 Hz
Microcellular: Factory, Mall 0.3 ms 120 degrees 10 Hz
Microcellular: Indoors, Office 0.1 ms 360 degrees 2..6 Hz
Table Source: A.J. Paulray and C.B. Papadias, "Space-Time Processing for Wireless Communications", Signal Processing Magazine, November 1997, pp. 49-83.
Audio commentary: Peter M. Grant, Distinguished IEEE Lecturer 1997,
discusses the table parameters (MPEG audio). See also: Full
talk, MPEG plug-in on
A Practical Example from Germany
Figure: measured scatter plot for DCS 1800 MHz system.
Doppler spread = 60.3 Hz; Coherence time = 5.9 msec.
Delay Spread = 1.2 msec; coherence BW = 1.3 MHz
Source: Research group of Prof. Paul Walter Baier, U. of Kaiserslautern, Germany.
Figure: Doppler spread corresponding to above scatter plot.
Note that the Doppler spread is the projection of the scatter plot on the Doppler frequency axis.
Figure: Distribution of angle of arrival corresponding to above scatter plot.
Figure: Delay spread profile corresponding to above scatter plot.
Note that the Doppler spread is the projection of the scatter plot on the
time delay axis.
An example from Edinburgh
Received power (according to color) versus time of arrival (horizontal axis)
and angle of incidence (vertical axis).
Source credit: Nortel.
Audio commentary: Peter M. Grant, Distinguished IEEE Lecturer 1997.
MPEG audio:
- MP2 ** Power versus delay and angle
- MP2 Measurement artifacts in delay-angle map
See also:
Full talk, MPEG plug-in
on
An indoor example from Zurich
A realization of the local Power Delay-Direction Profile
(PDDP). Carrier frequency 5.2 GHz, MT
velocity 1 m/s, delay spread
TRMS = 50 ns. Such a
situation is typical for a small room environment.
See the PDDP
evaluation by Peter E. Leuthold and Pascal Truffer.
Theoretical Example
Let's consider a
- U-shaped Doppler spectrum, as it occurs with
uniformly distributed angles of arrival of reflected waves.
The maximum shift is fm.
- an exponential delay spread with mean Trms
Moreover, we assume that the delay spread
and Doppler spread are separable. Then the amount
of (scatter power) per frequency and time bin
can be expressed as
Plocal-mean 1 1 t
p(f,t) = ------- -------------------- ---- exp(- -----)
4 p fm (f-fc)2 Trms Trms
sqrt( 1 - -------)
fm2
The integral over
p(f,t) gives to total received
local mean power
Plocal-mean.
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.
Channel simulations based on this theoretical model
have been contributed by Ralph Haas.