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TRANSCRIPT
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Recapitulation
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Understanding the Multipath Channel Impulse response model of Multipath Channel
Discrete Time Impulse response
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Parameters of Mobile MultipathChannels Derived from the Power Delay Profile
Power delay profile can be measured in Time domain
Frequency domain
Important Parameters are Time Dispersion Parameters
Coherence Bandwidth Coherence Time
Doppler Spread
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For small-scale fading, the power delay profile of the channel is found bytaking the spatial average of over a local area (small-scale area).
If p(t) has a time duration much smaller than the impulse response of themultipath channel, the received power delay profile in a local area is given by:
Power Delay Profile
2);( thb
2);()( thkP b
Gain k relates the transmitter power in the probing pulsep(t) to the totalreceived power in a multipath delay profile.
The bar represents the average over the local area of2
);( thb
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Example power delay profile
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Example: Outdoor Power Delay Profile
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Example: Indoor Power Delay Profile
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Time Dispersion Parameters
Grossly quantifies the multipath channel
Determined from Power Delay Profile
Parameters include Mean Access Delay
RMS Delay Spread
Maximum Excess Delay (X dB)
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Time Dispersion Parameters
Determined from a power delay profile.Mean Excess Delay: Is the first moment of the power delay profile.
Mean excess delay( ):
==k
k
k
kk
k
k
k
kk
P
P
a
a
)(
))((
2
2
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Time Dispersion Parameters
Rms delay spread (((():):):):
Each multipath signal travels different path length, sothe time of arrival for each path is different.
A single transmitted pulse will be spread in timewhen it reaches the receiver. This effect whichspreads out the signal is called Delay Spread.
Delay Spread leads to increase in the signalbandwidth.
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Rms delay spread (((())))
Characterizes time-dispersiveness of the
channel Obtained from power delay-profile
Indicates delay during which the power of the received signal isabove a certain value.
It is the square root of the second central moment of the powerdelay profile.
( )
==
=
k
k
k
kk
k
k
k
kk
P
P
a
a
)(
))(( 2
2
22
2
22
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Timer Dispersion Parameters
Maximum Excess Delay (X dB):
Defined as the time delay value after which the multipath energyfalls to X dB below the maximum multipath energy (not necesarilybelongingto the first arriving component).
It is also called excess delay spread.
M.E.D. (X dB)=
Where is the first arriving signal, and is the maximum delay at whicha multipath component is within X dB of the strongest arriving multipathsignal (which does not necessarily arrive at )
0 X
0 X
0
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RMS Delay Spread
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Coherence Bandwidth (BC) A statistical measure of the range of frequencies over
which the channel can be considered flat.
That is, the channel passes all spectral components withequal gain and linear phase.
Represents correlation between 2 fading signalenvelopes at frequencies f1 and f2.
Is a function ofRMS delay spread.
Receiver
f1
f2
Multipath Channel Frequency Separation: |f1-f2|
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Coherence Bandwidth (BC) Range of frequencies over which the channel can be
considered flat (i.e. channel passes all spectralcomponents with equal gain and linear phase).
It is a definition that depends on RMS Delay Spread.
Two sinusoids with frequency separation greater than Bcare affected quite differently by the channel.
Receiver
f1
f2
Multipath Channel Frequency Separation: |f1-f2|
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Coherence Bandwidth (BC)
Two frequencies that are larger thancoherence bandwidth fade independently.
Concept useful in diversity reception. Multiple copies of same message are sent
using different frequencies.
These frequencies are separated by more thanthe Coherence Bandwidth of the channel.
Coherence Bandwidth indicates frequencyselectivity during transmission.
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Coherence Bandwidth
50
1=CB
Frequency correlation between two sinusoids: 0
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Coherence Bandwidth
Example: For a multipath channel, is given as 1.37s (outdoor). 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 (channelbandwidth) should not exceed 146kHz, so that allfrequencies in this band experience the same channelcharacteristics.
Equalizers are needed in order to use transmissionfrequencies 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 aGSM channel (200kHz needed per channel).
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Coherence Time Delay spread and Coherence bandwidth
describe the time dispersive nature of thechannel in a local area.
They dont offer information about the time varyingnature of the channel caused by relative motion oftransmitter and receiver.
Doppler Spread and Coherence time areparameters which describe the time varyingnature of the channel in a small-scale region.
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Doppler Spread (BD)
Measure of spectral broadening caused bymotion
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 muchgreater than BD then effect of Doppler spread
is negligible at the receiver.
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Doppler Spread (BD) Characterizes frequency-dispersiveness of
the channel, or the spreading of transmittedfrequency due to different Doppler shifts.
Obtained from Doppler Spectrum.
Indicate range of frequencies over which thereceived Doppler spectrum is above a certain
value.
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Doppler Spread (BD)
If the baseband signal bandwidth is muchgreater than BD then effect of Doppler spreadis negligible at the receiver.
This a slow fading channel.
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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 signalbandwidth) 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
f1f2
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Coherence Time
Coherence time is also defined as (Thumb rule Definition):
mfC f
Tm
423.02
16
9 =
Coherence time definition implies that two signals arriving with a timeseparation greater than TC are affected differently by the channel.
A large coherence time => Channel changes slowly
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Types of Small-scale FadingSmall-scale Fading(Based on Multipath Tme Delay Spread)
Flat Fading
1. BW Signal < BW of Channel2. 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 receivedsignal changes with time
For example Rayleigh Distribution
Occurs when symbol period of thetransmitted signal is much larger than theDelay Spread of the channel
Bandwidth of the applied signal is narrow.
May cause deep fades. Increase the transmit power to combat this situation.
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Flat Fadingh(t,)
s(t) r(t)
0 TS 0 0 TS+
BC: Coherence bandwidthBS: Signal bandwidth
TS: Symbol period: Delay Spread
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Frequency Selective Fading
Occurs when channel multipath delay spreadis greater than the symbol period. Symbols face time dispersion
Channel induces Intersymbol Interference (ISI)
Bandwidth of the signal s(t) is wider than thechannel impulse response.
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Frequency Selective Fadingh(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 <
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Fast Fading
Due to Doppler Spread Rate of change of the channel characteristics
is largerthan 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 Spread
TS: Symbol PeriodTC: Coherence Bandwidth
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Slow Fading Due to Doppler Spread
Rate of change of the channel characteristicsis much smallerthan the
Rate of change of the transmitted signal
Occurs when:BS >> BD
and
TS
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Different Types of Fading
Transmitted Symbol Period
Symbol Period ofTransmitting Signal
TS
TS
TC
Flat SlowFading
Flat FastFading
Frequency SelectiveSlow Fading
Frequency SelectiveFast Fading
With Respect To SYMBOL PERIOD
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Different Types of Fading
Transmitted Baseband Signal Bandwidth
BSBD
Flat FastFading
Frequency SelectiveSlow Fading
Frequency SelectiveFast Fading
BS
TransmittedBaseband
Signal Bandwidth
Flat SlowFading
BC
With Respect To BASEBAND SIGNAL BANDWIDTH
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Fading Distributions
Describes how the received signal amplitudechanges with time.
Remember that the received signal is combination of multiplesignals arriving from different directions, phases andamplitudes.
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 multipathfading.
Two distributions Rayleigh Fading Ricean Fading
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Rayleigh and Ricean Distributions Describes the received signal envelope
distribution for channels, where all thecomponents are non-LOS:
i.e. there is no line-ofsight (LOS) component.
Describes the received signal envelopedistribution 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