# Small Scale Fading - Wireless and Mobile Communication

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```					            Small-Scale Fading
Also known by other names such as
Rayleigh fading is a result of constructive and destructive interference
to attenuation of signal power or amplitude
– Usually over a fraction of the signal wavelength
– Attenuation between 20 to 30 dB
– multipath fading manifests as time spreading or time variation of the
signal (due to motion, foliage, reflections and scattering)
Rayleigh Distribution
If the impulse response h( , t) of the mobile
radio station is time invariant and has zero
mean, then the envelope of the impulse
response has a Rayleigh distribution given as:
r       r2 
pr   2 exp  
 2 2 

            
where      is the total power in the multipath
signal
If however the impulse response has a non zero mean then there is a
significant component of the direct path (line of sight, specular
component) signal and the magnitude of the impulse response has a
Ricean distribution
Ricean distribution is the combination of Rayleigh signal with the direct
line of sight signal. The distribution is:
r       r 2  s 2   rs 
pr   2 exp  
           I
2  0      
          2    2 
s2 is the power of the line of sight signal and I0 is a Bessel function of the
first kind
Characteristics of Small-Scale
Small-scale fading occurs as either of 4 types:
• frequency selective fading in which the bandwidth of the signal
is greater than the coherence bandwidth and the delay spread is
greater than the symbol rate; Signals at some frequency
components experience more fading than others - (caused by
• flat fading when the bandwidth of the signal is less than the
coherence bandwidth and the delay spread is less than the
symbol rate - (caused by multipath delay spread)
• fast fading when the Doppler spread is high and the coherence
time is less than the symbol period and
• slow fading with a low Doppler spread and coherence time is
greater than the symbol period - (caused as well by Doppler
• modulation techniques such as spread
spectrum

Type of fading               Frequency Effects               Time Effects
Frequency Selective fading   BW of signal > coherence BW     Delay spread > symbol period
Flat fading                  BW of signal < coherence BW     Delay spread < symbol period
Propagation of Cellular
Communication Signals
• Cellular communication is mostly land
based.
• There are a few applications on ships and airlines
using networks in a box and satellites

• Propagation considerations are therefore
based on
– urban, rural, suburban and
– in a few cases water and desert terrain
– sky or space propagation (satellites)
Free Space Propagation Model
• Free space propagation Model is used to
predict received signal stength when the
unobstructed line-of-sight path.
• The free space model predicts that received
power decays as function of TR separation
distance raised to some power.
Pr
Pt

Lp

Gt            Gr

d

7

```
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 views: 315 posted: 4/13/2011 language: English pages: 7