slides13 [compatibility mode]

8/6/2019 Slides13 [Compatibility Mode]

1/23


2/23

6/3/20

Recapitulation

TE 702 Dr. Imran Khan, 2011 3

Understanding the Multipath Channel Impulse response model of Multipath Channel

Discrete Time Impulse response


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


3/23

6/3/20


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


Example power delay profile


4/23

6/3/20


Example: Outdoor Power Delay Profile


Example: Indoor Power Delay Profile


5/23

6/3/20

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)




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


6/23

6/3/20



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.


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


7/23

6/3/20


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


RMS Delay Spread


8/23

6/3/20


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|


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|


9/23

6/3/20


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.


Coherence Bandwidth

50

1=CB

Frequency correlation between two sinusoids: 0


10/23

6/3/20


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).


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.


11/23

6/3/20


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.


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.


12/23

6/3/20


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.


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


13/23

6/3/20


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


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


14/23

6/3/20


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.


Flat Fadingh(t,)

s(t) r(t)

0 TS 0 0 TS+

BC: Coherence bandwidthBS: Signal bandwidth

TS: Symbol period: Delay Spread


15/23

6/3/20


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.


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 <


16/23

6/3/20


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


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


17/23

6/3/20


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


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


18/23

6/3/20


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


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.


19/23

6/3/20


Rayleigh Fading


Rayleigh

slides13 [compatibility mode]

Documents