Lecture 6_fading channel

7/29/2019 Lecture 6_fading channel

1/78

1

Lecture 6 Fading

Chapter 5Mobile Radio Propagation:

Small-Scale Fading and Multipath


2/78

2

Last lecture

Large scale propagation properties of wireless

systems - slowly varying properties that dependprimarily on the distance between Tx and Rx.

Free space path loss

Power decay with respect to a reference point

The two-ray model General characterization of systems using the path

loss exponent.

Diffraction

Scattering

This lecture: Rapidly changing signalcharacteristics primarily caused by movementand multipath.


3/78

3

I. Fading

Fading: rapid fluctuations of received signal strength

over short time intervals and/or travel distances Caused by interference from multiple copies of Tx

signal arriving @ Rx at slightly different times

Three most important effects:

1. Rapid changes in signal strengths over small travel

distances or short time periods.

2. Changes in the frequency of signals.

3. Multiple signals arriving a different times. When added

together at the antenna, signals are spread out in time.

This can cause a smearing of the signal and interference

between bits that are received.


4/78

4

Fadingsignals occur due to reflections from

ground & surrounding buildings (clutter) aswell as scattered signals from trees, people,

towers, etc.

often an LOS path is not available so the first

multipath signal arrival is probably the desired

signal (the one which traveled the shortest distance)

allows service even when Rx is severely obstructed

by surrounding clutter


5/78

5

Even stationaryTx/Rx wireless links can

experience fading due to the motion of objects(cars, people, trees, etc.) in surrounding

environment off of which come the reflections

Multipath signals have randomly distributed

amplitudes, phases, & direction of arrival

vector summation of (A ) @ Rx of multipath

leads to constructive/destructive interference as

mobile Rx moves in space with respect to time


6/78

6

received signal strength can vary by Small-scale fading

over distances ofa few meter(about 7 cm at 1 GHz)!

This is a variation between, say, 1 mW and 10-6 mW.

If a user stops at a deeply faded point, the signal quality

can be quite bad.

However, even if a user stops, others around may still

be moving and can change the fading characteristics.

And if we have another antenna, say only 7 to 10 cm

separated from the other antenna, that signal could be

good.

This is called making use of________which we

will study in Chapter 7.


7/787

fading occurs around received signal strength predicted

from large-scale path loss models


8/788

II. Physical Factors Influencing Fading in Mobile Radio Channel (MRC)

1) Multipath Propagation

# and strength of multipath signals

time delay of signal arrival

large path length differences large differences indelay between signals

urban area w/ many buildings distributed over largespatial scale

large # of strong multipath signals with only a fewhaving a large time delay

suburb with nearby office park or shopping mall

moderate # of strong multipath signals with small tomoderate delay times

rural few multipath signals (LOS + groundreflection)


9/789

2) Speed of Mobile

relative motion between base station & mobilecauses random frequency modulation due to

Doppler shift (fd)

Different multipath components may have different

frequency shifts.3) Speed of Surrounding Objects

also influence Doppler shifts on multipath signals

dominates small-scale fading if speed of objects >

mobile speed

otherwise ignored


10/7810

4) Tx signal bandwidth (Bs)

The mobile radio channel (MRC) is modeled asfilter w/ specific bandwidth (BW)

The relationship between the signal BW & the

MRC BW will affect fading rates and distortion,

and so will determine:

a) if small-scale fading is significant

b) if time distortion of signal leads to inter-symbol

interference (ISI)

An MRC can cause distortion/ISI or small-scale

fading, or both.

But typically one or the other.


11/7811

Doppler Shift

motion causes frequency modulation due to Doppler

shift (fd)

v : velocity (m/s)

: wavelength (m)

: angle betweenmobile direction

and arrival direction of RF energy

+ shift mobile moving toward S

shift mobile moving away from S


12/78

12

Two Doppler shifts to consider above

1. The Doppler shift of the signal when it is received atthe car.

2. The Doppler shift of the signal when it bounces off

the car and is received somewhere else.

Multipath signals will have different fds forconstant vbecause of random arrival directions!!


13/78

13

Example 5.1, page 180

Carrier frequency = 1850 MHz

Vehicle moving 60 mph

Compute frequency deviation in the following

situations.

(a) Moving directly toward the transmitter

(b) Moving perpendicular to the transmitter


14/78

14

Note: What matters with Doppler shift is not

the absolute frequency, but the shift infrequency relative to the bandwidth of a

channel.

For example: A shift of 166 Hz may be significant

for a channel with a 1 kHz bandwidth.

In general, low bit rate (low bandwidth) channels

are affected by Doppler shift.


15/78

15

III. MRC Impulse Response Model

Model the MRC as a linear filter with a timevaryingcharacteristics

Vector summation of random amplitudes &

phases of multipath signals results in a "filter"

That is to say, the MRC takes an original signal and

in the process of sending the signal produces a

modified signal at the receiver.


16/78

16

Time variation due to mobile motion time

delay of multipath signals varies with locationof Rx

Can be thought as a "location varying" filter.

As mobile moves with time, the location changes

with time; hence, time-varying characteristics.

The MRC has a fundamental bandwidth

limitation model as a band pass filter


17/78

17

Linear filter theoryy(t) = x(t)h(t)or

Y(f) = X(f)H(f) How is an unknown h(t) determined?

letx(t) = (t) use a delta or impulse input

y(t) = h(t) impulse response function

Impulse response for standard filter theory is the sameregardless of when it is measured time invariant!


18/78

18


19/78

19

How is the impulse response of an MRC

determined? channel sounding like radar

transmit short time duration pulse (not exactly an

impulse, but with wide BW) and record multipath

echoes @ Rx


20/78

20

short duration Tx pulse unit impulse

define excess delay bin as

amplitude and delay time of multipath returns change as mobilemoves

Fig. 5.4, pg. 184 MRC is time variant

1i i


21/78

21

model multipath returns as a sum of unit

impulses

aii= amplitude & phase of each multipath

signal

N= # of multipath components

aiis relatively constant over an local area

But iwill change significantly because of different

path lengths (direct distance plus reflected distance) at

different locations.


22/78

22

The useful frequency span of the model :

The received power delay profile in a local area:

Assume the channel impulse response is time invariant, or

WSS

2( ) ( ; )bP k h t

2/

R l i hi b B d id h d R i d P


23/78

23

Relationship between Bandwidth and Received Power

A pulsed, transmitted RF signal of the form


24/78

24

For wideband signal


25/78

25

The average small-scale received power

The average small scale received power is simplythe sum of the average powers received in each

multipath component

The Rx power of a wideband signal such asp(t)

does not fluctuate significantly when a receiver ismoved about a local area.


26/78

26

CW signal (narrowband signal ) is transmitted in

to the same channel


27/78

27

Average power for a CW signal is equivalent to the

average received power for a wideband signal in a

small-scale region.

The received local ensemble average power of

wideband and narrowband signals are equivalent.

Tx signal BW > Channel BW Rx power variesvery small

Tx signal BW < Channel BW large signal

fluctuations (fading) occur

The duration of baseband signal > excess delay of channel

due to the phase shifts of the many unsolved multipath

components


28/78

28


29/78

29

The Fourier Transform ofhb( t,)gives the spectral

characteristics of the channel frequency response

MRC filter passband Channel BW or Coherence

BW =Bc range of frequencies over which signals will be transmitted

without significant changes in signal strength channel acts as a filter depending on frequency

signals with narrow frequency bands are not distorted by the

channel


30/78

30


31/78

31


32/78

32


33/78

33


34/78

34


35/78

35

IV Multipath Channel Parameters


36/78

36

IV. Multipath Channel Parameters

Derived from multipath power delay profiles

(Eq. 5-18) P(k): relativepower amplitudes of multipath

signals (absolute measurements are not needed)

Relative to the first detectable signal arriving at

the Rx at 0

use ensemble average of many profiles in a

small localized area typically 2 6 m spacing

of measurements to obtain average small-scale response


37/78

37


38/78

38

Time Dispersion Parameters

excess delay : all values computed relative to the

time of first signal arrival o

mean excess delay

RMS delay spread

where Avg( 2) is the same computation as above as

used for except that

A simple way to explain this is the range of time

within which most of the delayed signals arrive


39/78

39

outdoor channel ~ on the order of microseconds

indoor channel ~ on the order of nanoseconds


40/78

40

maximum excess delay ( X): the largest time where the

multipath power levels are still withinXdB of the

maximum power level worst case delay value

depends very much on the choice of the noise threshold


41/78

41

and provide a measure of propagation delay

of interfering signals

Then give an indication of how time smearing

might occur for the signal.

A small is desired.

The noise threshold is used to differentiate between

received multipath components and thermal noise


42/78

42


43/78

43


44/78

44

Coherence BW (Bc) and Delay Spread ( )

The Fourier Transform of multipath delay showsfrequency (spectral) characteristics of the MRC

Bc: statistical measure of frequency range where MRC

response is flat

MRC response is flat= passes all frequencies with equal gain & linear phase

amplitudes of different frequency components are

correlated

if two sinusoids have frequency separation greaterthanBc, they are affected quite differently by the

channel


45/78

45

amplitude correlation multipath signals have

close to the same amplitude if they are then

out-of-phase they have significant destructive

interference with each other (deep fades)

so a flat fading channel is both good and bad

Good: The MRC is like a bandpass filter andpasses signals without major attenuation

from the channel.

Bad: Deep fading can occur.


46/78

46

so the coherence bandwidth is the rangeof frequencies over which two frequency

components have a strong potential for

amplitude correlation. (quote fromtextbook)


47/78

47

estimates

0.9 correlation Bc 1 / 50 (signals are 90%

correlated with each other)

0.5 correlation Bc 1 / 5 Which has a larger

bandwidth and why?

specific channels require detailed analysis for a

particular transmitted signalthese are just rough

estimates


48/78

48

A channel that is not a flat fading channel is

calledfrequency selective fadingbecausedifferent frequencies within a signal are

attenuated differently by the MRC.

Note: The definition of flat or frequency selectivefading is defined with respect to the bandwidth of

the signal that is being transmitted.


49/78

49

Bcand are related quantities that

characterize time-varying nature of the MRC

for multipath interference from frequency &

time domain perspectives


50/78

50


51/78

51


52/78

52

these parameters do NOT characterize the time-varying

nature of the MRC due to the mobility of the mobile

and/or surrounding objects

that is to say,Bcand characterize thestatics, (how

multipath signals are formed from scattering/reflections and

travel different distances)

Bcand do not characterize the mobility of the Tx or Rx.


53/78

53

Doppler Spread (BD) & Coherence Time (Tc)

BD: measure of spectral broadening of the Tx

signal caused by motion i.e., Doppler shift

BD= max Doppler shift =fmax = vmax /

In what direction does movement occur to create this

worst case?

if Tx signal bandwidth (Bs) is large such thatBs>>BD

then effects of Doppler spread are NOT important so

Doppler spread is only important for low bps (data rate)

applications (e.g. paging)


54/78

54

Tc: statistical measure of the time interval over

which MRC impulse response remainsinvariant amplitude & phase of multipath

signals constant

Coherence Time (Tc)= passes all received signalswith virtually the same characteristics because the

channel has not changed

time duration over which two received signals have

a strong potential for amplitude correlation


55/78

55

Two signals arriving with a time separation

greater than Tcare affected differently by the

channel, since the channel has changed withinthe time interval

For digital communications coherence time and

Doppler spread are related by

2

9 0.423

16c

m m

Tf f

V. Types of Small-Scale Fading


56/78

56

yp g

Fading can be caused by two independent MRC

propagation mechanisms:

1) time dispersion multipath delay (Bc , )

2) frequency dispersion Doppler spread (BD , Tc)

Important digital Tx signal parameters symbol

period & signal BW


57/78

57

A pulse can be more than two levels, however,

so each period would be called a "symbolperiod".

We send 0 (say +1 Volt) or 1 (say -1 Volt) one

bit per symbol

Or we could send 10 (+3 Volts) or 00 (+1 Volt) or

01 (-1 Volt) or 11 (-3 Volts) two bits per

symbol

illustrates types of small-scale fading


58/78

58

yp g


59/78

59

1) Fading due to Multipath Delay

AFlat Fading Bs

signal fits easily within the bandwidth of the channel

channel BW >> signal BW

most commonly occurring type of fading

10s

T


60/78

60

spectral properties of Tx signal are preserved

signal is called a narrowbandchannel, since the

bandwidth of the signal is narrow with respect to thechannel bandwidth

signal is not distorted

What does Ts>> mean??

all multipath signals arrive at mobile Rx during 1 symbol

period

Little intersymbol interference occurs (no multipathcomponents arrive late to interfere with the next symbol)


61/78

61


62/78

62

flat fading is generally considered desirable

Even though fading in amplitude occurs, the signal

is not distorted

Forward link can increase mobile Rx gain

(automatic gain control) Reverse link can increase mobile Tx power

(power control)

Can use diversity techniques (described in a later

lecture)


63/78

63

B)Frequency Selective Fading Bs>BcorTsBc certain frequency components of the signal

are attenuated much more than others

10sT


64/78

64


65/78

65

Ts < delayed versions of Tx signal arrive

during different symbol periods e.g. receiving an LOS 1 & multipath 0 (from

prior symbol!)

This results in intersymbol interference (ISI)

Undesirable

it is very difficult to predict mobile Rx

performance with frequency selective channels


66/78

66

But for high bandwidth applications, channels withlikely be frequency selective

a new modulation approach has been developed tocombat this.

Called OFDM

One aspect of OFDM is that it separates awideband signal into many smaller narrowbandsignals

Then adaptively adjusts the power of each narrowband

signal to fit the characteristics of the channel at thatfrequency.

Results in much improvement over other widebandtransmission approaches (like CDMA).


67/78

67

OFDM is used in the new 802.11g 54 Mbps

standard for WLANs in the 2.4 GHz band.

Previously it was thought 54 Mbps could only be

obtained at 5.8 GHz using CDMA, but 5.8 GHz

signals attenuate much more quickly.

Signals are split using signal FFT, break into

pieces in the frequency domain, use inverse FFT to

create individual signals from each piece, then

transmit.


68/78

68

2) Fading due to Doppler Spread

Caused by motion of Tx and Rx and reflection

sources.

A)Fast FadingBs Tc

Bs Tc

MRC changes within 1 symbol period

rapid amplitude fluctuations

uncommon in most digital communication systems


69/78

69

B)Slow Fading Ts>BD

MRC constant over many symbol periods

slow amplitude fluctuations

forv = 60 mph @fc= 2 GHz BD= 178 Hz

Bs 2 kHz >>BD

Bsalmost always >>BDfor most applications

** NOTE: Typically use a factor of 10 to

designate >> **


70/78

70

VI. Fading Signal Distributions


71/78

71

Rayleigh probability distribution function

Used for flat fading signals.

Formed from the sum of two Gaussian noise signals.

: RMS value of Rx signal before detection (demodulation)

common model for Rx signal variation

urban areas heavy clutter no LOS path

probability that signal does not exceeds predefined threshold

levelR

2

2 2( ) exp 02

r rP r r


72/78

72


73/78

73

rmean: The mean value of Rayleigh distribution

r2 : The variance of Rayleigh distribution; ac power of signal

envelope

: RMS value of Rx signal before detection (demodulation)

0[ ] ( ) 1.25332meanr E r rp r dr

22 2 2 2

0

2 2

[ ] [ ] ( )2

2 0.42922

r E r E r r p r dr


74/78

74


75/78

75

Ricean Probability Distribution Function

one dominant signal component along with weaker

multipath signals

dominant signal LOS path

suburban or rural areas with light clutter

becomes a Rayleigh distribution as the dominantcomponent weakens


76/78

76


77/78

77

The remainder of Chapter 5 gives many models

for correlating measured data to a model of anMRC.

Nothing else in Chapter 5 will be covered here,

however. Next lecture: Modulation techniques

particularly suited for mobile radio.


78/78

HW-4

5.6, 5.7, 5.16, 5.28, 5.31

Documents

Lecture 6_fading channel