Signal Propagation

Jie Gao

01/27/2010

Signal

• Signal are generated as physical representations of data

• A signal is a function of time and location

1ideal

digital signal

2

1

0

t

a special type of signal, sine waves, also called harmonics: s(t) = A sin(2π f t + ϕ)

with frequency f, period T=1/f, amplitude A, phase shift ϕ

0

digital signal

t

Fourier Transform: Every Signal Can be Decomposed

as a Collection of Harmonics

)2cos()2sin(2

1)(

11

nftbnftactgn

n

n

n ππ ∑∑∞

=

∞

=

++=

1 1

3

0 0

t t

ideal periodical

digital signaldecomposition

The more harmonics used, the smaller the approximation error.

4

Time Domain v.s. Frequency Domain

� Time domain � Frequency domain

1

0

1

0

5

0

f

t

1

0

t

1

0

f

Knowing one can recover the other.

Interference

� Signals add up1

0

t

1

0

t

6

� Apply Fourier transform

t t

1

0

ff 2f

1

0t

1

0t

Fundamental Question: Why Not Send Digital Signal in

Wireless Communications?

1

ideal

digital signal

7

0digital signal

t

Fundamental Question: Why Not Send Digital Signal in

Wireless Communications?

• May cause interference

– suppose digital frame length T, then signal

decomposes into frequencies at 1/T, 2/T, 3/T, …

– let T = 1 ms, generates radio waves at frequencies – let T = 1 ms, generates radio waves at frequencies

of 1 KHz, 2 KHz, 3 KHz, …

8

Bandwidth

9

Frequencies for Communications

1 Mm300 Hz

10 km30 kHz

100 m3 MHz

1 m300 MHz

10 mm30 GHz

100 µm3 THz

1 µm300 THz

visible lightVLF LF MF HF VHF UHF SHF EHF infrared UV

optical transmissioncoax cabletwisted pair

10

VLF = Very Low Frequency UHF = Ultra High Frequency

LF = Low Frequency SHF = Super High Frequency

MF = Medium Frequency EHF = Extra High Frequency

HF = High Frequency UV = Ultraviolet Light

VHF = Very High Frequency

Frequency and wave length:

λ = c/f

wave length λ, speed of light c ≅ 3x108m/s, frequency f

visible lightVLF LF MF HF VHF UHF SHF EHF infrared UV

Spectrum

11

Frequencies and Regulations

� ITU-R holds auctions for new frequencies, manages frequency bands

worldwide (WRC, World Radio Conferences)

Europe USA Japan

CellularPhones

GSM 450 - 457, 479 -486/460 - 467,489 -496, 890 - 915/935 -960,1710 - 1785/1805 -1880

AMPS , TDMA , CDMA824- 849, 869-894TDMA , CDMA , GSM1850 - 1910,1930 - 1990

PDC810- 826, 940-956,1429 - 1465, 1477 - 1513

12

1880UMTS (FDD) 1920 -1980, 2110 - 2190UMTS (TDD) 1900 -1920, 2020 - 2025

1930 - 1990

CordlessPhones

CT1+ 885 - 887, 930 -932CT2864-868DECT 1880 - 1900

PACS 1850 - 1910, 1930 -1990PACS -UB 1910 - 1930

PHS1895 - 1918JCT254-380

Wireless LANs

IEEE 802.112400 - 2483HIPERLAN 25150 - 5350, 5470 -5725

902-928I EEE 802.112400 - 24835150 - 5350, 5725 - 5825

IEEE 802.112471 - 24975150 - 5250

Others RF- Control27, 128, 418, 433,

868

RF- Control315, 915

RF- Control426, 868

Antennas and Signal Propagation

Antennas: Isotropic Radiator

� Isotropic radiator: a single point

� equal radiation in all directions (three dimensional)

� only a theoretical reference antenna

� Radiation pattern: measurement of radiation around an

antenna

14

antenna

zy

x

z

y x ideal

isotropic

radiator

Q: how does power level decrease as a function of d, the distance from the

transmitter to the receiver?

Real Antennas

• Real antennas are not isotropic radiators

• Some simple antennas: quarter wave λ/4 on car roofs or half

wave dipole λ/2

� size of antenna proportional to wavelength for better

transmission/receivingtransmission/receiving

15

λ/4λ/2

Q: Assume frequency 1 Ghz, λ = ?

Dipole: Radiation Pattern of a Dipole

16

http://www.tpub.com/content/neets/14182/index.htm

http://en.wikipedia.org/wiki/Dipole_antenna

Why Not Digital Signal (revisited)

• Not good for spectrum usage/sharing

• The wavelength can be extremely large to

build portable devices

– e.g., T = 1 us -> f=1/T = 1MHz -> wavelength = – e.g., T = 1 us -> f=1/T = 1MHz -> wavelength =

3x108/106 = 300m

17

Free-Space Isotropic Signal Propagation

• In free space, receiving power proportional to 1/d² (d = distance between transmitter and receiver)

2

4

=

dGG

P

Ptr

t

r

π

λ

� P : received power• The total radiation power

remains constant, but the surface area of a sphere with radius r increases like r2.

18

� Pr: received power

� Pt: transmitted power

� Gr, Gt: receiver and

transmitter antenna gain

� λ (=c/f): wave length

Sometime we write path loss in log scale:

Lp = 10 log(Pt) – 10log(Pr)

Signal Propagation

� Receiving power additionally influenced by

� shadowing (e.g. through a wall or a door)

� refraction depending on the density of a medium

� reflection at large obstacles

� scattering at small obstacles

19

� scattering at small obstacles

� diffraction at edges

reflection

scattering

diffraction

shadow fadingrefraction

Signal Propagation: Scenarios

Details of signal

propagation are very

complicated

We want to understand

20

We want to understand

the key characteristics

that are important to

our objective

Reason I: Shadowing

• Signal strength loss after passing through obstacles

• Some sample numbers

21

i.e. reduces to ¼ of signal

10 log(1/4) = -6.02

Distance power relationship in practice

� Received power decreases proportional to 1/dr where r varies

from 2 to 6.

� Long corridor, big indoor environment: r=2

� Metallic building: r=6.

� “Slow fading”

22

� “Slow fading”

Reason II: Multipath

� Signal can take many different paths between sender and

receiver due to reflection, scattering, diffraction

23

Multipath Can Reduce Signal Strength

� Example: reflection from the ground: received power decreases

proportional to 1/d4 instead of 1/d² due to the destructive

interference between the direct signal and the signal reflected

from the ground

24

ground

For detail, see page 9:

http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter2.pdf

Multipath Fading

25

� Due to constructive and destructive interference of

multiple transmitted waves, signal strength may vary

widely as a function of receiver position

� Listen to radio on a car.

Multipath Effect

(fixed receiver location)

� Channel characteristics change over location,

frequencyexample

26

d1d2

( )1

11 ][2cos

d

tfc

d−πα

( )ftπ2cos

πλ

πππππ +−

=+−

=+− 2121 22)(2 21dd

c

ddfff

c

d

c

d

( )2

22 ][2cos

d

tfc

d−

−πα

phase

difference:

Multipath

(fixed receiver location)

• Suppose at d1-d2 the two waves totally

destruct. (what does it mean?)

integer2121 =−

=−

λ

dd

c

ddf

• Q: can we find places where the two waves

construct?

27

λc

πλ

πππ +−

=+− 2121 22

dd

c

ddf

Option 1: Change Location

• If receiver moves to the right by λ/4:

d1’ = d1 + λ/4;

d2’ = d2 - λ/4;

-> πλ

π +− 21 ''

2dd->

28

ππλ

π

πλ

λλπ

λπ

πλ

π

++−

=

+−−

+−

=

+

21

21

2

)4/(4/22

2

dd

dd

By moving a quarter of wavelength, destructive

turns into constructive.

Option 2: Change Frequency

212

1'

dd

cff

−±=

� Change frequency:

29

� The change depends on delay spread

πλ

πππ +−

=+− 2121 22

dd

c

ddf

Multipath Fading: A Simple Two-path

Example

d2

30

d1 receiver

- Wavelength is about 0.3 m for 1 GHz cellular

Multipath Fading with Mobility: A

Simple Two-path Example

r0

31

r(t) = r0 + v t, assume transmitter sends out signal cos(2π fc t)

More detail see page 16 Eqn. (2.13):

http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter2.pdf

Multipath Effect

(moving receiver)

� Channel characteristics change over time (location)

example

d

32

d1d2

( )1

11 ][2cos

d

tfc

d−πα

( )ftπ2cos

( )2

22 ][2cos

d

tfc

d−

−πα

Suppose d1=r0+vt

d2=2d-r0-vtd1≈d2

d

Derivation

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0000

020020

00

)2(2

2

][2][2

2

][2][2

2

vtrdvtrvtrdvtr

tftftftf

c

vtrd

c

vtr

ftf

tftf

c

vtrd

c

vtr

c

vtrd

c

vtr

−−+−−−−++

−−−−+−

−−+

−−=

−=

−−−−−+−−+

ππππ

ππ

ππ

33

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

0

0

0

0000

2

2

)2(

2

2

cv

rd

c

vf

cd

c

dvtr

cd

c

dvtr

cd

c

vtrdvtr

c

vtrdvtr

ttf

ftf

ftf

ftf

−

−+

−+

−−+−−−−++

−−=

−=

−−−=

−−=

ππ

ππ

ππ

ππ

See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)

Received Waveform

10 ms])[sin(])[2sin(2 02

cv

rd

c

vf

cd ttf

−−− ππ

34

v = 65 miles/h, fc = 1 GHz: fc v/c = 109 * 30 / 3x108 = 100 Hz

Why is fast multipath fading bad?

deep fade

Small-Scale Fading

35

signal at sender

Multipath Can Spread Delay

36

signal at sender

signal at receiver

LOS pulsemultipathpulses

LOS: Line Of Sight

Time dispersion: signal is

dispersed over time

Delay Spread RMS: root-mean-square

37

signal at sender

Multipath Can Cause ISI

dispersed signal can cause interference

between “neighbor” symbols, Inter Symbol

Interference (ISI)

Assume 300 meters delay spread, the arrival

38

signal at receiver

LOS pulsemultipathpulses

LOS: Line Of Sight

Assume 300 meters delay spread, the arrival

time difference is 300/3x108 = 1 ms

�if symbol rate > 1 Ms/sec, we will have

serious ISI

In practice, fractional ISI can already

substantially increase loss rate

Summary: Wireless Channels

� Channel characteristics change over location, time, and

frequency

Large-scalefading

power

path loss

Received Signal Power (dB)

39

small-scale fadingtimelog (distance)

frequency