Fading Distributions

1. By-
Dr. Jesmin Akhter
Professor
Institute of Information Technology
Jahangirnagar University
Wireless and Mobile Communication
ICT-4203

2. Fading Distributions
• Describes how the received signal amplitude changes with time.
• Remember that the received signal is combination of multiple signals
arriving from different directions, phases and amplitudes.
• With the received signal we mean the baseband signal, namely the
envelope of the received signal (i.e. r(t)). (The envelope of
an oscillating signal is a smooth curve outlining its extremes)
• Fading Distribution is a statistical characterization of the multipath fading.
This fading characteristics of a mobile radio signal are described by the
following three statistical distributions -
• Rician Distribution
• Rayleigh Distribution
• Lognormal Distribution

3. Rayleigh Distributions
• Describes the received signal envelope distribution for channels,
where all the components are non-LOS:
• i.e. there is no line-of–sight (LOS) component.

4. Rayleigh Fading Distribution
• The Rayleigh distribution is commonly used to describe the statistical time
varying nature of the received envelope of a flat fading signal, or the
envelope of an individual multipath component.
• The Rayleigh distribution is given as:
•  is the rms value of the received voltage before envelope detection, 2 is
the time-average power/local average power of the received signal before
envelope detection and r2 is instantaneous power.
p r
r r
r
r
( )
exp( )

   






 
2
2
2
2
0
0 0

5. Ricean Distributions
• Describes the received signal envelope distribution for
channels where one of the multipath components is LOS
component.
• i.e. there is one LOS component.

6. Ricean Fading Distribution
• When there is a dominant stationary signal component present, the small-scale
fading envelope distribution is Ricean. The effect of a dominant signal arriving
with many weaker multipath signals gives rise to the Ricean distribution.
• The Ricean distribution degenerates to a Rayleigh distribution when the
dominant component fades away.
• The Ricean distribution is often described in terms of a parameter K which is
defined as the ratio between the deterministic signal power and the variance of
the multipath.
• K is known as the Ricean factor
• As A0, K  - dB, Ricean distribution degenerates to Rayleigh distribution.













0
0
0
,
0
)
(
]
2
)
(
exp[
)
( 2
0
2
2
2
2
r
A
r
Ar
I
A
r
r
r
p 


K
A

2
2
2

7. PDF
• Probability density function of Ricean distributions: K=-∞dB
(Rayleigh) and K=6dB. For K>>1, the Ricean pdf is approximately
Gaussian about the mean.

9. • Propagation path-loss models play an important role in the design
of cellular systems to specify key system parameters such as
transmission power, frequency, antenna heights, and so on.
• Several models have been proposed for cellular systems operating in
different environments (indoor, outdoor, urban, suburban, rural).
• Okumura Model
• Hata Model
• Cost 231 Model
Propagation Path-Loss Models

10. • The Okumura model is a Radio propagation model that was built
using the data collected in the city of Tokyo, Japan.
• The model is ideal for using in cities with many urban structures but
not many tall blocking structures.
• The model served as a base for the Hata Model.
• Okumura model was built into three modes.
• Urban, suburban and open areas.
• The model for urban areas was built first and used as the base for
others.
Okumura model

11. 50% of measured
values lie above
this threshold and
50% of measured
values lie below
this threshold value

18. Thank You