Multipath fading and reflections

The signal takes many paths to the destination. The propagation delay along each path is different.How many meters difference gives you 0.00001 seconds of delay difference?

Effects of Multipath Fading/Reflection

• “Ghost” on TV.

• GPS – incorrect position calculation.

• Frequency Selective Fading.

• Intersymbol interference.

Intersymbol Interference

Suppose that there are two paths.The shorter path has length d1, the longer path has length d2.What is the difference in propagation delay between the two paths?

301

2Symbols received over

the shorter path

Symbols received over

the longer path

Received signal – a

combination of the two

signals

How big does have to be to so that the 3 of the longer path arrives exactly when the 0 arrives on the shorter path?How big must the difference in paths be for this to happen?

301

2

Intersymbol Interference

P t( ) 0 t Tif

3

2

t T( ) t 2 T( )if

3

2

t 2 T( ) t 3 T( )if

3

2

2

t 3 Tif

Suppose we use differential phase shift keying to transmit 3 2 1 0

tPtfts c 2sin

3 2 1

0 1 2 3 4 51

0

11

1

f t( )

50 t

0?

Intersymbol Interference

0 0.5 1 1.5 2 2.5 31

0

11

1

f t( )

f tT

5

30 t

0 0.5 1 1.5 2 2.5 31

0

10.951

0.951

f t( ) f tT

5

2

30 t

Phasor addition of sine waves with the same frequency

ab

x a = (a cos() , a sin())

wtatx sin x = a magnitude phase

wtbwtatx sinsin x = b +a

b = (b cos() , b sin())

x = (b cos()+acos() , b sin()+asin())

coscos

sinsinarctan

ab

abA

= M

22 coscossinsin babaM

A

P t( ) 0 t Tif

3

2

t T( ) t 2 T( )if

3

2

t 2 T( ) t 3 T( )if

3

2

2

t 3 Tif

tPtfts c 2sin

0 0.5 1 1.5 2 2.5 31

0

1

21.571

0.785

A t( )

30 t

A t( ) atan

sin P t( )( ) sin P tT

5

cos P t( )( ) cos P tT

5

)5

()(T

tststx

R

Ttststx )(

R 10

0 1 2 31

0

1

f t( ) f tT

R

2

t

0 1 2 35

0

5

A t( )

Q t( )

t

R 3

0 1 2 31

0

1

f t( ) f tT

R

2

t

0 1 2 35

0

5

A t( )

Q t( )

t

R 2

0 1 2 31

0

1

f t( ) f tT

R

2

t

0 1 2 35

0

5

A t( )

Q t( )

tR 1

0 1 2 31

0

1

f t( ) f tT

R

2

t

0 1 2 35

0

5

A t( )

Q t( )

t

zero amplitude!

Intersymbol Interference

ISI can be avoided by making the baud rate small.

If the baud rate is 11MHz (802.11b), how much delay will cause complete ISI interference?

How much path length difference will cause complete ISI interference?

•In suburban areas, multiple signals arrive with timing differences up to 25microsec.

•Indoors, timing differences up to 300ns.

•What is the max baud rate so that complete ISI occurs

Frequency Selective Fading

The received signal is made up of many different, slightly delayed, versions of the same signal.

What is going on at these frequencies?

Frequency Selective Fading

tPDtftPtf

Dtststx

cc

2sin2sin

)(

160

1

80

R

T

fc

0 1 2 31

0

1

f t( ) f tT

R

2

t

0 1 2 35

0

5

A t( )

Q t( )

t

Phase is ok, but zero amplitude!

For what values of T/R does this happen?

c

c

fD

Df

2

1

2

Frequency Selective Fading

Indoor impulse responds

Frequency Selective Fading

delay = 1/(2*fc)

Suppose fc = 2.4GHz.Delay = 0.2 nsDistance = 0.2ns * 0.3m/ns = 0.06m (6cm)!!!!

So very small differences in path length cause very big changes in signal.

Frequency selective fading is be mitigated by• Using spread spectrum. Thus multiple frequencies are simultaneously

used. If a few frequencies suffer attenuation the others might not. (Used in 802.11b)

• Channel estimation and adaptation (used in GSM cell phones)• Use many narrow band frequencies. Then the good ones should work (like

spread spectrum). Used in 802.11a

Frequency Selective FadingNow suppose that there are many paths, each with a different delay.

Then the received signal is:

Q

I

received signal

The I component is modeled as a normally distributed random variable.The Q component is modeled as a normally distributed random variable.Both have zero mean and the same variance.

Then, the amplitude is a Raleigh random variable and the phase is uniform between 0 and 2.

This is called a Raleigh channel.Hence, the result is that the amplitude and phase are random. If they vary slowly, then the channel is called a slowly fading channel (indoors).If the channel varies quickly, it is a fast fading channel (driving with cell phone).If the channel changes too fast, then changes in phase and amplitude cannot be detected.

Effect of Movement

If the receiver or transmitter are moving, then the channel will vary.Hence, the I and Q components will vary with time.

Here is a plot of the magnitude of fading as a function of time and frequency. In this case, the channel does not change much over time. It is a slowly fading channel.

Effect of Movement

If the receiver or transmitter are moving, then the channel will vary.Hence, the I and Q components will vary with time.

Here is a plot of the magnitude of fading as a function of time and frequency.

In this case, the channel does not vary with frequency, it only varies over time.

Effect of Movement

If the receiver or transmitter are moving, then the channel will vary.Hence, the I and Q components will vary with time.

Here is a plot of the magnitude of fading as a function of time and frequency.

In this case, the channel varies both in time and frequency.

Doppler Effect

• When the receiver or transmitter are moving, the frequency is shifted by f = v/ cos(), v is velocity and is wave length

cm fc

vf isshift maximum The c is the speed of light.

If the the signal is sent at fc and passed through a fading channel, the spectrum of the received signal is:

Thus, not only one frequency is received, but many.

Doppler Effect

• To mitigate the Doppler effect:– Use low frequencies– Transmit in bursts so the channel is constant

during the burst.– Include training sequences on each frame so the

channel can be re-estimated for each transmission.

– Do move – indoor use only

Rician Channel Model

• A Raleigh channel assumes that all the paths arrive with random amplitude.

• A Rician channel assumes that there is a line of sight component that has much larger amplitude.