1 Mobile Radio Propagation - Small-Scale Fading and Multipath CS 515 Mobile and Wireless Networking Fall 2002 İbrahim Körpeoğlu Computer Engineering Department

1

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


Bandwidth of Baseband Signals

Highbandwidth(Wideband)Signal

Lowbandwidth(Narrowband)Signal

Continuous Wave (CW)Signal

t


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


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


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.


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:


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.


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.


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


Direct RF Pulse System

Pulse Generator

BPF DetectorDigital

Oscilloscope

RF Link

fc

Tx

Rx


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


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.


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


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.


RMS Delay Spread


PDP Outdoor


PDP Indoor


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.


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|


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.


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).


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.


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.


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


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.


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


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.


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



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.



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 <


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


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


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


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


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


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.


Rayleigh Fading


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)


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


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


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


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


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


Fading Model – Gilbert-Elliot Model

Fade Period

Time t

SignalAmplitude

Threshold

Good(Non-fade)

Bad(Fade)


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)

Documents

1 Mobile Radio Propagation - Small-Scale Fading and Multipath CS 515 Mobile and Wireless Networking Fall 2002 İbrahim Körpeoğlu Computer Engineering Department