Part IV- Propagation Characteristics
Multi-path Propagation Fading
School of Computing, Engineering and
Information Sciences, University of Northumbria
U.K.
http://soe.unn.ac.uk/ocr
Z. Ghassemlooy

 Fading
 Doppler Shift
 Dispersion
 Summary
Z. Ghassemlooy

Fading
 Is due to multipath propagation.
With respect to a stationary base station, multipath propagation creates a stochastic standing wave pattern, through which the mobile station moves.
 Caused by shadowing: when the propagation environment is changing significantly, but this fading is typically much slower than the multipath fading.
 Modem design is affected mainly by the faster multipath fading, which can be normally assumed to be locally wide-sense stationary (WSS).
Z. Ghassemlooy

Multipath Propagation Fading a
Diffracted wave b
Reflected wave
No direct path a b
Antenna a & b are in phase
Z. Ghassemlooy y = a + b a b
Antenna y = 0 a & b are out of phase by

Complete fading when
2
 d /

= n

, d is the path difference

Multipath Propagation - contd.
• F or a stationary mobile unit with no direct path, the received signal can be expressed as a sum of delayed components or in terms of phasor notation:
Pulse train S r
 i
N 

1 a i
P
 t
 t i

A single pulse
S r
( t )
 i
N 

1 a i cos ( 2
 f c
  i
)
Where: a i is the amplitude of the scattered signal, p ( t ) is the transmitted signal (pulse) shape, t i is the time taken by the pulse to reach the receiver,
N is the number of different paths f c is the carrier frequency
Z. Ghassemlooy

Fading Types
•
Slow (Long) Term
•Fast (Short) Term (Also known as Rayleigh fading)
30
Fast fading
20
10
Slow fading
0
0 5 10 15 20 25 Distance (
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Exact representation of fading characteristics is not possible, because of infinite number of situation.

)

Fading Slow (Long) Term
 Slower variation in mean signal strength (distance 1-
2 km)
 Produced by movement over much longer distances
 Caused by:
- Terrain configuration (hill, flat area etc.):
Results in local mean (long term fading) attenuation and fluctuation.
- The built environment (rural and urban areas etc.), between base station and the mobile unit:
Results in local mean attenuation
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Fading Slow (Long) Term
Receiver t n,2 path n t k,2 t n,3
S r
( t ) t k,4 one subpath path k t k,3
Number of path
S r
 path attenuation factor i
N 

1 for the i th path a i
P
0
 t
 t i

C. D. Charalambous et al
Z. Ghassemlooy t n,1
Transmitter t k,1

FadingFast (Short) Term
 Describes the c onstant amplitude fluctuations in the received signal as the mobile moves.
 Caused by
- multipath reflection of transmitted signal by local scatters
(houses, building etc.)
- random fluctuations in the received power
 Observed over distances =

/2
 Signal variation up to 30 dB.
 Is a frequency selective phenomenon.
 Can be described using
- Rayleigh statistics, (no line of sight).
- Rician statistics, (line of sight).
Z. Ghassemlooy

FadingFast (Short) Term - contd.
A received signal amplitude is given as the sum of delayed components. In terms of phasor notation it is given as:
S r
( t )
 i
N 

1 a i cos ( 2
 f c
  i
)
Or
S r
( t )
 cos( 2
 f c t ) i
N 

1 a i cos (
 i
)
 sin( 2
 f c t ) i
N 

1 a i sin(
 i
)
In-phase Quadrature
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FadingFast (Short) Term - contd.
The phase
 i can be assumed to be uniformly distributed in the range (0, 2

), provided the locations of buildings etc. are completely random.
For a large N , the amplitude of the received signal is: where
S r
( t )

X cos( 2
 f c t )

Y sin( 2
 f c t )
X
 i
N 

1 a i cos (
 i
), Y
 i
N 

1 a i sin(
 i
)
X and Y are independent, identically distributed Gaussian random variables.
Z. Ghassemlooy

FadingFast (Short) Term - contd.
The envelope of the received signal is:
A

( X
2 
Y
2
)
0 .
5 Which will be Rayleigh distributed:
Assuming all components received have approximately the same power and that all are resulting from scattering.
Rayleigh
Probability density function
Exponential p
 
 s r
2 exp ж зз

2
Where 0< r <

, s 2 is r s
2
2 ц чч variance of A (the total received power in the multipath signal).
A or power P
Z. Ghassemlooy

Ricean Fading
If there is one direct component in addition to scattered components, the envelope received multipath is Ricean, where the impulse response has a non zero mean.
Ricean distribution = Rayleigh signal + direct line of sight signal. The distribution is: p
 
 s r
2 exp ж зз
 r
2
2
 s
2 s
2 ц чч I
0 s rs
2 s
2 is the power of the line of sight signal and I
0 the first kind is a Bessel function of
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 The probability that the realization of the random variable has a value smaller than x is defined by the cumulative distribution function: cdf ( r )
  pdf ( u ) du
 Applying it to the Rayleigh distribution cdf ( r )

1
 exp

( r 2 / 2 s 2 )
 For small r cdf ( r ) ~ r 2 / 2 s 2
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Fast Fading – Cases 1: Stationary Mobile
3
2
6 v
1 t
3 t
2 t
1 t
6 v
Stationary t
4 t
5
4
5
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Fast Fading – Cases 1
 The number of fading depends on:
– Traffic flow
– Distance between the mobile and moving cars
 The received signal at the MU is:
S r
 i
N 

1 a i
P
0
 t
 t i
 t i
 t   t i
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Fast Fading – Cases 1 where and
Thus
 t i is additional relative delay (positive or negative)
S r
  t

 x ( t
1
N
 i
N 

1 t
) t e i j 2
 f c
 
 j
 o envelope x
 a o i
N 

1 a i e
 j 2
 f c
 t i
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Fast Fading – Cases 2
T
T 1
2
= d
= d
1
2
/ c
/ c t
1
(t
1
) t
2
(t
2
)
S
       c j
 c t
 x
 i
N 

1 a c a i exp

 j
 c t i

18

Fast Fading – Cases 3: Non-stationary
Mobile
No scattered signals

V
Signal level
The received signal at the mobile is: s r
( t )
 a o e j ( 2
 f c
  o
  x cos

) x = Vt
Amplitude Wave number =2

/

Transmitting frequency
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Fast Fading – Cases 3: Doppler Frequency
A moving object causes the frequency of a received wave to change
Substituting for
 and x , the expression for the received signal is s r
( t )
 a o e j 2

( f c

V
 cos

) t
The Doppler frequency
The received signal frequency
Z. Ghassemlooy f
D

V
 cos
  f m cos
 f r
 f c
 f m cos


Fast Fading – Cases 3: Doppler Frequency
•
When

= 0 o (mobile moving away from the transmitter) f r
 f c
 f m
•
When

= 90 o (I.e. mobile circling around) f
 r f c
•
When

= 180 o (mobile moving towards the transmitter) f r
 f c
 f m
Z. Ghassemlooy

Fast Fading – Cases 4: Moving MU +
Stationary Scatterer
Standing Wave Pattern x ( t ) s o
( t )
MU t = 0
V s o t = round trip time
( t )
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Fast Fading – Cases 4
Received signal at the MU: s r
( t )
 a o e j

2
 f c t
  o
 
Vt cos

 and for q = 0 s r
( t )
 a o e j

2
 f c t
  o
 
Vt

 a o e j

2
 f c t
  o
 
Vt

2
 f c t

Incident signal Reflected signal s r
( t )
  j 2 a o sin

Vt

2
 f c t
2 ш e j

2
 f c t
  o
  f c t

Fading with zero amplitude occurs when

Vt
 n
   f c t
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Fast Fading – Cases 5: Moving MU and
Scatterers
The resultant received signal is the sum of all the scattered waves from different angles q i depending upon the momentary attitude of the various scatterers.
s r
( t )
 i
N 

1 a o a i e j

2
 f c t
  o
 
Vt cos
 i
  i

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Transmitting a short pulse over a
(i) frequency-selective (time-spread) fading channel:
Transmitted Received
T p t
T p t
+ d t
(ii) time-selective (Doppler-spread) fading channel:
Transmitted Received
T p t
T p t
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Effects of Doppler shifts
 Bandwidth of the signal could increase or decrease leading to poor and/or missed reception.
 The effect in time is coherence time variation and signal distortion
– Coherence time: Time duration over which channel impulse response is invariant, and in which two signals have strong potential for amplitude correlation
– Coherence time is expressed by:
T c
 9
16
 f
2
D-max
– where f
D-max is the maximum Doppler shift, which occurs when

= 0 degrees
 To avoid distortion due to motion in the channel, the symbol rate must be greater than the inverse of coherence time.
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Coherence Distance
 Coherence distance is the minimum distance between points in space for which the signals are mostly uncorrelated.
 This distance is usually grater than 0.5 wavelengths, depending on antenna beamwidth and angle of arrival distribution.
 At the BTS, it is common practice to use spacing of about 10 and 20 wavelengths for low-medium and high antenna heights, respectively (120 o sector antennas).
Z. Ghassemlooy

Coherence Bandwidth (Bc)
 Range of frequency over which channel is “flat”
 It is the bandwidth over which two frequencies have a strong potential for amplitude correlation
Power
Signal bandwidth B s
Describes frequency selective phenomenon of fast fading
Coherence
Bandwidth B c
Freq.
Effect of frequency selective fading on the received signal spectrum
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Estimation of Coherence Bandwidth
Coherence bandwidth is estimated using the value of delay spread of the channel, s t
For correlation > 0.9
For correlation > 0.5
Typical values of delay spreads for various types of terrain:
B c
 0 .
2 t t
Delay spread figures
B c at 900 MHz
Urban
Urban, worst-case
 0 .
02 t t
Delay in microseconds
1.3
10 - 25
Suburban, typical
Suburban, extreme
Indoor, maximum
0.2 - 0.31
1.96 - 2.11
0.27
Delay Spread at 1900 MHz
Buildings, average 0.07 - 0.094
Buildings, worst case
1.47
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Channel Classification
Based on Time-Spreading
Flat Fading
1.
B
S
< B
C
 T m
< T s
2.
Rayleigh, Ricean distrib.
3.
Spectral chara. of transmitted signal preserved
Channel
Frequency Selective
1.
B
S
> B
C
 T m
> T s
2.
Intersymbol Interference
3.
Spectral chara. of transmitted signal not preserved
4.
Multipath components resolved
Channel
Signal
B
C
B
S
Signal freq.
B
S
B
C freq.
C. D. Charalambous et al
Z. Ghassemlooy

Fading in Digital Mobile Communications
• If B s
>> B c
, then a notch appears in the spectrum. Thus resulting in inter-symbol interference (ISI) .
- To overcome this, an adaptive equaliser (AE) with inverse response may be used at the receiver.
Training sequences are transmitted to update AE .
• If B s
<< B c
, then flat fading occurs, resulting in a burst of error .
Error correction coding is used to overcome this problem.
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Multipath Delay Spread
 First-arrival delay ( τ
A
)
 Mean excess delay t e
 
( t  t
A
) P ( t
) d t
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Multipath Delay Spread
 The standard deviation of the distribution of multipath signal amplitudes is called delay spread. For directive antenna is characterized by the rms delay spread of the entire delay profile, which is defined as: t
2 rms
  j
P j t
2 j

( t avg
)
2 where t avg t j
= Σ j
P j t j
, is the delay of the j th delay component of the profile
P j
= (power in the j th delay component) / (total power in all components
• Delay spread varies with the terrain with typical values for rural, urban and suburban areas:

0 .
2 m s
 rural


3 .
0 m s
 urban


0 .
5 m s
 suburban

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Multipath Delay Spread Dispersion
 The delay spread limits the maximum data rate:
– No new impulses should arrive at the receiver before the last replica of the pervious impulse has perished.
– Otherwise symbol spreads (dispersion) into its adjacent slot, thus resulting in Inter Symbol Interference (ISI)
Transmitted symbols
Received symbols
 The signal arrived at the receiver directly and phase shifted
– Distorted signal depending on the phases of the different parts
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Mitigation Techniques for the Multipath
Fading Channel
 Space diversity –
– Signals at the same frequency using two or three antennas located several wavelengths a part.
– Antennas are connected to two or three radio receivers.
– The receiver will the strongest signal is elected
– Disadvantage: Uses two or more antennas, therefore the need for a large site.
 Frequency diversity –
– Signals at different frequencies received by the same antenna very rarely fade simultaneously. Thus the use of several carrier frequencies or the use of a wideband signal to combat fading.
– A single aerial connected to a number receiver, each tuned to a different frequency, whose outputs are connected in parallel.
The receiver with the strongest instantaneous signal will provide the output.
– Disadvantage: Uses two or more frequencies to transmit the same signal.
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Mitigation Techniques for the Multipath
Fading Channel
 Time diversity – Spread out the effects of errors through interleaving and coding
 Multipath diversity
– Consider the tapped delay line model of a channel shown previously
– If multipaths can be put together coherently at the receiver, diversity improvement results
– This is what the RAKE receiver does (see next viewgraph)
Z. Ghassemlooy

RAKE Multipath Signal Processing
R.E. Ziemer 2002
Z. Ghassemlooy

System Design and Performance
Prediction
 Base station placement dependent on
– Propagation environment
– Anticipated geographic distribution of users
– Economic considerations (minimize number of base stations)
– Political and public opinion considerations
– Traffic types (3G)
 Performance figure of merit
– Spectrum efficiency for voice: η v voice circuits/MHz/base station
– Spectrum efficiency for information: η i bps/MHz/base station
– Dropped call rate – fraction of calls ended prematurely
Z. Ghassemlooy

Summary
• The random fluctuations in the received power are due to fading.
• If there is a relative motion between transmitter and receiver
(mobile) the result is Doppler shift
• If maximum Doppler shift is less than the data rate, there is “slow” fading channel.
• If maximum Doppler shift is larger than the data rate, there is “fast” fading channel.
Z. Ghassemlooy

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