1 mobile radio propagation - small-scale fading and multipath cs 515 mobile and wireless networking...
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Mobile Radio Propagation - Small-Scale Fading and Multipath
CS 515 Mobile and Wireless NetworkingFall 2002İbrahim KörpeoğluComputer Engineering DepartmentBilkent University
CS 515 © İbrahim Körpeoğlu 2
Relationship between Bandwidth and Receiver Power What happens when two different signals with
different bandwidths are sent through the channel? What is the receiver power characteristics for both signals?
We mean the bandwith of the baseband signal The bandwidth of the baseband is signal is inversely
related with its symbol rate.
One symbol
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Bandwidth of Baseband Signals
Highbandwidth(Wideband)Signal
Lowbandwidth(Narrowband)Signal
Continuous Wave (CW)Signal
t
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A pulsed probing signal (wideband)
TREP
Tbb
p(t)
Transmitter
x(t): transmitted signal
)2cos()(})(Re{)(
:2
maxmax
tftpetptx
T
ctfj
REP
c
)( delay excess measured maximum
Multipath Wireless Channel
x(t) y(t) Multipath Wireless Channel
p(t) r(t)
Bandpass signals Baseband signals
CS 515 © İbrahim Körpeoğlu 5
Received Power of Wideband Sİgnals
)(2
1)(
1
0i
N
i
ji tpeatr i
Multipath Wireless Channel
p(t) r(t)
The output r(t) will approximate the channel impulse response sincep(t) approximates unit impulses.
Assume the multipath components have random amplitudes and phases at time t.
][][1
0
21
0
2
,, WB
N
ii
N
i
jiaWBa PEaeaEPE i
CS 515 © İbrahim Körpeoğlu 6
Received Power of Wideband Sİgnals
This shows that if all the multipath components of a transmitted signal isresolved at the receiver then:
The average small scale received power is simply the sum of received powers in each multipath component.
In practice, the amplitudes of individual multipath components do not fluctuate widely in a local area (for distance in the order of wavelength orfraction of wavelength).
This means the average received power of a wideband signal do not fluctuate significantly when the receiver is moving in a local area.
CS 515 © İbrahim Körpeoğlu 7
Received Power of Narrowband Sİgnals
2)( tc
1
0
),()(N
i
tji
ieatr
c(t)
Transmitterx(t): transmitted signalA CW Signal
Assume now A CW signal transmitted into the same channel.
Let comlex envelope will be:
21
0
),(2)(
N
i
tji
ieatr The instantaneous power will be:
The instantaneous complex envelope of the received signal will be:
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Received Power of Narrowband Sİgnals
Over a local area (over small distance – wavelengths), the amplitude a multipath component may not change signicantly, but the phase may change a lot.
For example: - if receiver moves meters then phase change is 2. In this case the component may add up posively to the total sum .
- if receiver moves /4 meters then phase change is degrees) . In this case the component may add up negatively to the total sum , hence the instantaneous receiver power.
Therefore for a CW (continues wave, narrowband) signal, the small movements may cause large fluctuations on the instantenous receiver power, which typifies small scale fading for CW signals.
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Wideband versus Narrowband Baseband Signals
However, the average received power for a CW signal over a local area is equivalent to the average received power for a wideband signal on thelocal area.
This occurs because the phases of multipath components at different locations over the small-scale region are independently distributed(IID uniform) over [0,2].
In summary:1. Received power for CW signals undergoes rapid fades over small distances2. Received power for wideband signals changes very little of small distances. 3. However, the local area average of both signals are nearly identical.
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Small-Scale Multipath Measurements
Several Methods Direct RF Pulse System Spread Spectrum Sliding Correlator Channel
Sounding Frequency Domain Channel Sounding
These techniques are also called channel sounding techniques
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Direct RF Pulse System
Pulse Generator
BPF DetectorDigital
Oscilloscope
RF Link
fc
Tx
Rx
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Parameters of Mobile Multipath Channels Time Dispersion Parameters
Grossly quantifies the multipath channel Determined from Power Delay Profile Parameters include
Mean Access Delay RMS Delay Spread Excess Delay Spread (X dB)
Coherence Bandwidth Doppler Spread and Coherence Time
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Measuring PDPs
Power Delay Profiles Are measured by channel sounding techniques Plots of relative received power as a function of
excess delay They are found by averaging intantenous power
delay measurements over a local area Local area: no greater than 6m outdoor Local area: no greater than 2m indoor
Samples taken at /4 meters approximately For 450MHz – 6 GHz frequency range.
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Timer Dispersion Parameters
kk
kkk
kk
kkk
P
P
a
a
)(
))(( 2
2
22
2
22
Determined from a power delay profile.
Mean excess delay( ):
Rms delay spread
kk
kkk
kk
kkk
P
P
a
a
)(
))((
2
2
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Timer Dispersion Parameters
Maximum Excess Delay (X dB):
Defined as the time delay value after which the multipath energy falls to X dB below the maximum multipath energy (not necesarily belongingto the first arriving component).
It is also called excess delay spread.
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RMS Delay Spread
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PDP Outdoor
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PDP Indoor
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Noise Threshold
The values of time dispersion parameters also depend on the noise threshold (the level of power below which the signal is considered as noise).
If noise threshold is set too low, then the noise will be processed as multipath and thus causing the parameters to be higher.
CS 515 © İbrahim Körpeoğlu 20
Coherence Bandwidth (BC)
Range of frequencies over which the channel can be considered flat (i.e. channel passes all spectral components with equal gain and linear phase).
It is a definition that depends on RMS Delay Spread.
Two sinusoids with frequency separation greater than Bc are affected quite differently by the channel.
Receiver
f1
f2
Multipath Channel Frequency Separation: |f1-f2|
CS 515 © İbrahim Körpeoğlu 21
Coherence Bandwidth
50
1CB
Frequency correlation between two sinusoids: 0 <= Cr1, r2 <= 1.
If we define Coherence Bandwidth (BC) as the range of frequencies over which the frequency correlation is above 0.9, then
If we define Coherence Bandwidth as the range of frequencies over which the frequency correlation is above 0.5, then
51
CB
is rms delay spread.
This is called 50% coherence bandwidth.
CS 515 © İbrahim Körpeoğlu 22
Coherence Bandwidth
Example: For a multipath channel, is given as 1.37s. The 50% coherence bandwidth is given as: 1/5 =
146kHz. This means that, for a good transmission from a transmitter
to a receiver, the range of transmission frequency (channel bandwidth) should not exceed 146kHz, so that all frequencies in this band experience the same channel characteristics.
Equalizers are needed in order to use transmission frequencies that are separated larger than this value.
This coherence bandwidth is enough for an AMPS channel (30kHz band needed for a channel), but is not enough for a GSM channel (200kHz needed per channel).
CS 515 © İbrahim Körpeoğlu 23
Coherence Time
Delay spread and Coherence bandwidth describe the time dispersive nature of the channel in a local area.
They don’t offer information about the time varying nature of the channel caused by relative motion of transmitter and receiver.
Doppler Spread and Coherence time are parameters which describe the time varying nature of the channel in a small-scale region.
CS 515 © İbrahim Körpeoğlu 24
Doppler Spread
Measure of spectral broadening caused by motion
We know how to compute Doppler shift: fd
Doppler spread, BD, is defined as the maximum Doppler shift: fm = v/
If the baseband signal bandwidth is much greater than BD then effect of Doppler spread is negligible at the receiver.
CS 515 © İbrahim Körpeoğlu 25
Coherence time is the time duration over which the channel impulse responseis essentially invariant.
If the symbol period of the baseband signal (reciprocal of the baseband signal bandwidth) is greater the coherence time, than the signal will distort, sincechannel will change during the transmission of the signal .
Coherence Time
mfCT 1
Coherence time (TC) is defined as: TS
TC
t=t2 - t1t1 t2
f1
f2
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Coherence Time
Coherence time is also defined as:
mfC f
Tm
423.0216
9
Coherence time definition implies that two signals arriving with a time separation greater than TC are affected differently by the channel.
CS 515 © İbrahim Körpeoğlu 27
Types of Small-scale FadingSmall-scale Fading
(Based on Multipath Tİme Delay Spread)
Flat Fading
1. BW Signal < BW of Channel 2. Delay Spread < Symbol Period
Frequency Selective Fading
1. BW Signal > Bw of Channel2. Delay Spread > Symbol Period
Small-scale Fading(Based on Doppler Spread)
Fast Fading
1. High Doppler Spread2. Coherence Time < Symbol Period3. Channel variations faster than baseband
signal variations
Slow Fading
1. Low Doppler Spread2. Coherence Time > Symbol Period3. Channel variations smaller than baseband
signal variations
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Flat Fading
Occurs when the amplitude of the received signal changes with time
For example according to Rayleigh Distribution
Occurs when symbol period of the transmitted signal is much larger than the Delay Spread of the channel
Bandwidth of the applied signal is narrow.
May cause deep fades. Increase the transmit power to combat this situation.
CS 515 © İbrahim Körpeoğlu 29
Flat Fading
h(t, s(t) r(t)
0 TS 0 0 TS+
TS
Occurs when:BS << BC
andTS >>
BC: Coherence bandwidthBS: Signal bandwidthTS: Symbol period: Delay Spread
CS 515 © İbrahim Körpeoğlu 30
Frequency Selective Fading
Occurs when channel multipath delay spread is greater than the symbol period. Symbols face time dispersion Channel induces Intersymbol Interference (ISI)
Bandwidth of the signal s(t) is wider than the channel impulse response.
CS 515 © İbrahim Körpeoğlu 31
Frequency Selective Fading
h(t, s(t) r(t)
0 TS 0 0 TS+
TS
TS
Causes distortion of the received baseband signal
Causes Inter-Symbol Interference (ISI)
Occurs when:BS > BC
andTS <
As a rule of thumb: TS <
CS 515 © İbrahim Körpeoğlu 32
Fast Fading
Due to Doppler Spread Rate of change of the channel characteristics
is larger than theRate of change of the transmitted signal
The channel changes during a symbol period. The channel changes because of receiver motion. Coherence time of the channel is smaller than the symbol
period of the transmitter signal
Occurs when:BS < BD
andTS > TC
BS: Bandwidth of the signalBD: Doppler SpreadTS: Symbol PeriodTC: Coherence Bandwidth
CS 515 © İbrahim Körpeoğlu 33
Slow Fading
Due to Doppler Spread Rate of change of the channel characteristics
is much smaller than theRate of change of the transmitted signal
Occurs when:BS >> BD
andTS << TC
BS: Bandwidth of the signalBD: Doppler SpreadTS: Symbol PeriodTC: Coherence Bandwidth
CS 515 © İbrahim Körpeoğlu 34
Different Types of Fading
Transmitted Symbol Period
Symbol Period ofTransmitting Signal
TS
TS
TC
Flat SlowFading
Flat Fast Fading
Frequency SelectiveSlow Fading
Frequency Selective Fast Fading
With Respect To SYMBOL PERIOD
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Different Types of Fading
Transmitted Baseband Signal BandwidthBS
BD
Flat Fast Fading
Frequency SelectiveSlow Fading
Frequency Selective Fast Fading
BS
Transmitted Baseband
Signal Bandwidth
Flat Slow Fading
BC
With Respect To BASEBAND SIGNAL BANDWIDTH
CS 515 © İbrahim Körpeoğlu 36
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)).
Its is a statistical characterization of the multipath fading.
Two distributions Rayleigh Fading Ricean Fading
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Rayleigh and Ricean 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.
Describes the received signal envelope distribution for channels where one of the multipath components is LOS component.
i.e. there is one LOS component.
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Rayleigh Fading
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Rayleigh
)(
)(
00
0)(2
2
2
2
r
rer
rp
r
Rayleigh distribution has the probability density function (PDF) given by:
2 is the time average power of the received signal before envelope detection. is the rms value of the received voltage signal before envelope detection
Remember: 2rmsVP power) (average (see end of slides 5)
CS 515 © İbrahim Körpeoğlu 40
Rayleigh
R R
r edrrpRrPRP0
2 2
2
1)()()(
The probability that the envelope of the received signal does not exceed a specified value of R is given by the CDF:
2
)(2
1177.1
2533.12
)(][
0
0
rms
r
median
mean
r
drrpr
drrrprEr
median
solvingby found
CS 515 © İbrahim Körpeoğlu 41
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5
Rayleigh PDF
mean = 1.2533median = 1.177variance = 0.4292
CS 515 © İbrahim Körpeoğlu 42
When there is a stationary (non-fading) LOS signal present, then the envelope distribution is Ricean.
The Ricean distribution degenerates to Rayleigh when the dominant component fades away.
Ricean Distribution
CS 515 © İbrahim Körpeoğlu 43
Level Crossing Rate (LCR)
Threshold (R)
LCR is defined as the expected rate at which the Rayleigh fading envelope, normalized to the local rms signal level, crosses a specified threshold level R in a positive going directionpositive going direction. It is given by:
second per crossings
rms) to normalized value envelope (specfied
where
:
/
22
R
rms
mR
N
rR
efN
CS 515 © İbrahim Körpeoğlu 44
Average Fade Duration
Defined as the average period of time for which the received signal isbelow a specified level R.
For Rayleigh distributed fading signal, it is given by:
rmsm
RR
r
R
f
e
eN
RrN
,2
1
11
]Pr[1
2
2
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Fading Model – Gilbert-Elliot Model
Fade Period
Time t
SignalAmplitude
Threshold
Good(Non-fade)
Bad(Fade)
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Gilbert-Elliot Model
Good(Non-fade)
Bad(Fade)
1/ANFD
1/AFD
The channel is modeled as a Two-State Markov Chain. Each state duration is memory-less and exponentially distributed.
The rate going from Good to Bad state is: 1/AFD (AFD: Avg Fade Duration)The rate going from Bad to Good state is: 1/ANFD (ANFD: Avg Non-Fade Duration)