Z. Ghassemlooy
Mobile Communications
Part IV- Propagation CharacteristicsMulti-path Propagation - Fading
Part IV- Propagation CharacteristicsMulti-path Propagation - Fading
Professor Z Ghassemlooy
School of Computing, Engineering and Information Sciences, University of Northumbria
U.K.http://soe.unn.ac.uk/ocr
Professor Z Ghassemlooy
School of Computing, Engineering and Information Sciences, University of Northumbria
U.K.http://soe.unn.ac.uk/ocr
Z. Ghassemlooy
Contents
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
AntennaAntennaab y = a + b
a & b are in phase a & b are out of phase by
Complete fading when 2d/ = n, d is the path difference
Diffractedwave Reflected
wave
No direct patha b
AntennaAntennab y = 0a
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Multipath Propagation - contd.
• For 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:
N
iicir fatS
1
)2(cos)(
N
iicir fatS
1
)2(cos)(A single pulse
Pulse train
Where: ai is the amplitude of the scattered signal, p(t) is the transmitted signal (pulse) shape, i is the time taken by the pulse to reach the receiver, N is the number of different paths fc is the carrier frequency
N
iiir tPatS
1
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Fading - Types
• Slow (Long) Term
0 5 10 15 20 25 Distance ()
Sig
nal s
tren
gth
rela
tive
to 1
uV (
db)
0
10
20
30
Slow fading
Fast fading
Exact representation of fading characteristics is not possible, because of infinite number of situation.
Exact representation of fading characteristics is not possible, because of infinite number of situation.
•Fast (Short) Term (Also known as Rayleigh fading)
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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
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
Z. Ghassemlooy
Fading - Slow (Long) Term
C. D. Charalambous et al
Transmitter
n,1
Receiver
k,1
ord
n,3n,2
k,2
k,3
k,4 one subpath
LOS
path k
path n
Sr(t)
N
iiir tPatS
10
path attenuation factorfor the ith path
Number of path
Z. Ghassemlooy
Fading- Fast (Short) Term
Describes the constant 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
Fading- Fast (Short) Term - contd.
N
iicir fatS
1
)2(cos)(
A received signal amplitude is given as the sum of delayed components. In terms of phasor notation it is given as:
Or
N
iiic
N
iiicr atfatftS
11
)sin()2sin()(cos)2cos()(
N
iiic
N
iiicr atfatftS
11
)sin()2sin()(cos)2cos()(
In-phase Quadrature
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Fading- Fast (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:
)2sin()2cos()( tfYtfXtS ccr
where
N
iii
N
iii aYaX
11
)sin(),(cos
X and Y are independent, identically distributed Gaussian random variables.
Z. Ghassemlooy
Fading- Fast (Short) Term - contd.
Rayleigh
Exponential
A or power P
Probabilitydensityfunction
The envelope of the received signal is:
5022 .)( YXA Which will be Rayleigh distributed:Assuming all components received have approximately the same power and that all are resulting from scattering.
2
2
2 2exp
rr
rp
Where 0< r < , is variance of A (the total received power in the multipath signal).
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:
2 is the power of the line of sight signal and I0 is a Bessel function of the first kind
202
22
2 2exp
rs
Isrr
rp
Fading- Fast (Short) Term - contd.
The probability that the realization of the random variable has a value smaller than x is defined by the cumulative distribution function:
Applying it to the Rayleigh distribution
For small r
Z. Ghassemlooy
duupdfr )()(cdf
)2/(exp1)(cdf 22 rr
22 2/~)(cdf rr
Z. Ghassemlooy
Fast Fading – Cases 1: Stationary Mobile
5
4
2
1
3
6
4
5
2
1
3
6
v
v
Stationary
tFie
ld s
tren
gth
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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:
N
iiir tPatS
10
ii
Z. Ghassemlooy
N
iiN 1
1 i is additional relative delay (positive or negative)where
and
oc jtfjr etxtS 2)(
N
i
fjio
iceaatx1
2envelope
Thus
Fast Fading – Cases 1
18
1(t1) 2(t2)
tjjtxtS cc expexp
N
iicic tjtaatx
1
exp
Fast Fading – Cases 2
2 = d2/c1 = d1/c
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Fast Fading – Cases 3: Non-stationary Mobile
The received signal at the mobile is:
)cos2()( xfjor
oceats
Amplitude
x = Vt
Wave number =2/
Transmitting frequency
VtF
ield
str
engt
h
Signal level No scattered signals
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Fast Fading – Cases 3: Doppler Frequency
tV
fj
or
c
eats)cos(2
)(
A moving object causes the frequency of a received wave to changeSubstituting for and x, the expression for the received signal is
The Doppler frequency
coscos mD fV
f
coscos mD fV
f
The received signal frequency
cosmcr fff cosmcr fff
Z. Ghassemlooy
Fast Fading – Cases 3: Doppler Frequency
• When = 0o (mobile moving away from the transmitter)
mcr fff mcr fff
• When = 90o (I.e. mobile circling around)
cr ff cr ff
• When = 180o (mobile moving towards the transmitter)
mcr fff mcr fff
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Fast Fading – Cases 4: Moving MU + Stationary Scatterer
x(t)
Vo
ltage Standing Wave Pattern
V
so(t)so(t)
t = 0 t = round trip time
MU
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cos2)( Vttfjor
oceats
cococ fVttfjo
Vttfjor eaeats 222)(
and for q = 0
Incident signal Reflected signal
coc ftfjcor e
fVtajts 2
2
2sin2)(
cfnVtFading with zero amplitude occurs when
Fast Fading – Cases 4
Received signal at the MU:
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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 qi depending upon the momentary attitude of the various scatterers.
N
i
Vttfjior
iioceaats1
cos2)(
Z. Ghassemlooy
Channel Fading Effects
Transmitting a short pulse over a
(i) frequency-selective (time-spread) fading channel:
(ii) time-selective (Doppler-spread) fading channel:
t tTp Tp + dt
Transmitted Received
t tTp Tp
Transmitted Received
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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:
– where fD-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.
216
9
D-max
cf
T
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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 (120o sector antennas).
Z. Ghassemlooy
Coherence Bandwidth (Bc)
Effect of frequency selective fading on the received signal spectrum
Signal bandwidth Bs
Freq.
Power
Describes frequency selective phenomenon of fast fading
CoherenceBandwidth Bc
Range of frequency over which channel is “flat”
It is the bandwidth over which two frequencies have a strong potential for amplitude correlation
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Estimation of Coherence Bandwidth
Coherence bandwidth is estimated using the value of delay
spread of the channel, st
For correlation > 0.9
For correlation > 0.5
Typical values of delay
spreads for various types
of terrain:
tcB
2.0
tcB
02.0
Delay spread figures
at 900 MHz
Delay in
microseconds
Urban 1.3
Urban, worst-case 10 - 25
Suburban, typical 0.2 - 0.31
Suburban, extreme 1.96 - 2.11
Indoor, maximum 0.27
Delay Spread at 1900 MHz
Buildings, average 0.07 - 0.094
Buildings, worst -
case
1.47
Z. Ghassemlooy
Channel Classification
Based on Time-Spreading
Flat Fading1. BS < BC Tm < Ts
2. Rayleigh, Ricean distrib.3. Spectral chara. of transmitted
signal preserved
Frequency Selective1. BS > BC Tm > Ts
2. Intersymbol Interference3. Spectral chara. of transmitted
signal not preserved4. Multipath components resolved
Signal
Channel
freq.BS
BC freq.BC
BS
Channel
Signal
C. D. Charalambous et al
Z. Ghassemlooy
Fading in Digital Mobile Communications
• If Bs>> Bc, 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 Bs>> Bc, 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 Bs<< Bc, then flat fading occurs, resulting in a burst of error.- Error correction coding is used to overcome this problem.
Z. Ghassemlooy
Multipath Delay Spread
First-arrival delay (τA)
Mean excess delay dPAe )()(
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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:
whereavg = Σj Pj j , j is the delay of the j th delay component of the profilePj = (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:
j
avgjjrms P 222 )(
rurals2.0 urbans0.3 suburbans5.0
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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)
The signal arrived at the receiver directly and phase shifted– Distorted signal depending on the phases of the different parts
Transmittedsymbols
Received symbols
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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.
Z. Ghassemlooy
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)
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RAKE Multipath Signal Processing
R.E. Ziemer 2002
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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: ηv voice circuits/MHz/base station
– Spectrum efficiency for information: ηi bps/MHz/base station
– Dropped call rate – fraction of calls ended prematurely
Z. Ghassemlooy
Summary
• 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.
• The random fluctuations in the received power are due to fading.
Z. Ghassemlooy
Questions and Answers
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