Channel Modelling ETI 085 Contents 1 - EIT, Electrical and ... › ... › 2012 › Lecture01_Intro.pdf · 2012-01-16 Fredrik Tufvesson - ETIN10 7 Lectures • Overview of the content

1

Fredrik Tufvesson

Department of Electrical and Information Technology

Lund University, Sweden

[email protected]

Channel Modelling – ETI 085

Lecture no:

2012-01-16 Fredrik Tufvesson - ETIN10 1

1

Introduction


Contents

• Course information

• Why channel modelling?

• Review of concepts


COURSE INFORMATION


Course web-site

• All course information is available at:

http://www.eit.lth.se/course/ETIN10

(or www.eit.lth.se, -Education, -Courses, -Channel mod.)

• Most important:

– Continuously updated schedule

– Lecture handouts (available before each lecture)

– Any additional material

2


Textbook

Andreas F. Molisch

Wireless Communications, 2nd ed

ISBN: 047084888X

Wiley/IEEE press

The second edition is available since

Dec 2010, which will be used 2012

• Available, e.g., through:

– Lexis, www.lexis.se

– Amazon U.K., www.amazon.co.uk

– Wiley, eu.wiley.com

• Authored by Andreas F. Molisch, former professor of Radio Systems at Lund University/LTH.


Schedule

• Three recurring components

– Lectures: Fredrik Tufvesson

Mondays (13-15, 2311) and Fridays(10-12, E:2311)

– Exercise classes: Meifang Zhu

Thursdays (8-10), E:2349

• Two special components

– Assignments:

Three assignments, where reports are handed in

– Oral exam:

– March 5-9, in groups of 6 students, time to be decided


Lectures

• Overview of the content in the textbook

• Additional material

• Application examples


Exercise classes

• Selection of suitable exercises on the course web-site in

advance

• During exercise classes, some of the exercises will be

analysed in detail

• By working through the exercises beforehand, you can give

valuable input on which exercises to focus on during

classes

3


Assignments

• There are three compulsory assingments.

• Performed in groups of two students.

• You will receive measured channel data in MATLAB-format,

– analysis

– parameter extraction

– conclusions

• Short reports are handed in within 7 days.

• THIS IS A COMPULSORY PART OF THE COURSE!


Oral exam

• How?

– appr 3 hours

– Both theoretical questions and calculations

– “A group discussion”, but with individual questions

– Prepare as for a written exam

– No assignments, no oral exam

• When?

March 5-9, depending on the group.

• Where?

Room E:2349 (?)


Why channel modelling?

• The performance of a radio system

is ultimately determined by the radio

channel

• The channel models basis for

– system design

– algorithm design

– antenna design etc.

• Trend towards more interaction

system-channel

– MIMO, multiple antenna systems

– UWB, ultra wideband

– Localization services

Without reliable

channel models, it

is hard to design

radio systems that

work well in real environments.


A rough breakdown into areas

Fundamental problems

in wireless communications

Propagation

and antennas

Deterministic Probabilistic

Channel models

Narrow-band

channels

Wide-band

channels

Antennas

Digital transmission

over wireless channels

Modulation

Speech and

channel coding

Equalization

Diversity

Mobile communications

systems

Multiple access

Cellular telephony

Wireless data networks

Speech coding

4


Noise

NNoise reference level

THE RADIO CHANNEL

... in the link budget

Transmitter Receiver

”POWER” [dB]

Transmit

power

TXP

Feeder

loss

TXfL ,

Antenna

gain

TXaG ,

Propagation

loss

pL

Antenna

gain

RXaG ,

Feeder

loss

RXfL ,

C

Received

power

Ga

in

Lo

ss

Required

C/N at

receiver

input

CRITERION

TO MEET:

This is a simple

version of the

link budget.


THE RADIO CHANNEL

It is more than just a loss

• Some examples:

– behavior in time/space?

– behavior in frequency?

– directional properties?

– bandwidth dependency?

– behavior in delay?


A narrowband system described in

complex notation (noise free)

exp 2 cj f expt j t exp 2 cj f

Transmitter Receiver Channel

Attenuation Phase

x t y t

expA t t j t t

expx t A t j tIn:

exp exp 2 exp exp 2c cy t A t j t j f t t j t j f t Out:

It is the behavior of the channel attenuation and phase we

are going to model.


THE RADIO CHANNEL

Some properties

• Path loss

– Roughly, received power decays exponentially with distance

• Large-scale fading

– Large objects, compared to a wavelength, in the signal path

obstruct the signal

• Small-scale fading

– Objects reflecting the signal causes multipath propagation

from transmitter to receiver

exponentn PropagatioDistance power dTransmitte power Received

5


THE RADIO CHANNEL

Path loss

Received power [log scale]

Distance, d [log scale]

TX RX

2/1 d

4/1 d


THE RADIO CHANNEL

Path loss

”POWER” [dB]

dBTXG |

dBTXP |

dBRXG |

10

| 2

10

420log , free space

20log , ground plane

dB

TX RX

d

L dd

h h

dBRXP |

|dBL

Two theoretical expressions for

the deterministic propagation loss as

functions of distance:

There are other models, which we

will discuss later.


Large-scale fading

Basic principle

d

Received power

Position

A B C C

A

B

C

D


Large-scale fading

Log-normal distribution

Measurements confirm that in many situations, the large-scale

fading of the received signal strength has a normal distribution

in the dB domain.

”POWER” [dB]

dBTXP |

dBRXP |

|dBL

2

| 0|

| 2

||

1exp

22

dB dB

dB

F dBF dB

L Lpdf L

Note dB

scale

dB Deterministic mean

value of path loss, L0|dB

|dBpdf L

Standard deviation | 4 10 dBF dB

6


Small-scale fading

Two waves

Wave 1 + Wave 2

Wave 2

Wave 1

At least in this case, we can see that the interference pattern

changes on the wavelength scale.


THE RADIO CHANNEL

Small-scale fading (cont.)

RX TX

With a large number of

reflection points the

interference pattern

becomes extremly

complicated.


Small-scale fading

Many incoming waves

1 1,r 2 2,r

3 3,r 4 4,r

,r

1 1 2 2 3 3 4 4exp exp exp exp expr j r j r j r j r j

1r1

2r 2

3r

3

4r4

r

Many incoming waves with

independent amplitudes

and phases

Add them up as phasors


THE RADIO CHANNEL

Small-scale fading (cont.)

Illustration of interference pattern from above

Transmitter

Reflector

Movement

Position

A B

A B

Received power [log scale]

7


Small-scale fading

Rayleigh fading

No dominant component

(no line-of-sight)

2D Gaussian

(zero mean)

Tap distribution

2

2 2exp

2

r rpdf r

Amplitude distribution

Rayleigh

0 1 2 3 0

0.2

0.4

0.6

0.8

r a

No line-of-sight

component

TX RX X

Im a Re a


Small-scale fading

Doppler shifts

c

rv

0f f

Frequency of received signal:

0 cosrvf

c

where the Doppler shift is

Receiving antenna moves with

speed vr at an angle θ relative

to the propagation direction

of the incoming wave, which

has frequency f0. The maximal Doppler shift is

max 0

vf

c


Small-scale fading

Doppler spectrum

Isotropic uncorrelated

scattering

RX

Uniform incoming

power distribution

(isotropic)

Uncorrelated

amplitudes

and phases

Time correlaion

*

0 max2t E a t a t t J t

0 0.5 1 1.5 2 -0.5

0

0.5

1

max t

RX movement


Small-scale fading

Rice fading

A dominant component

(line of sight)

2D Gaussian

(non-zero mean)

Tap distribution

A

Line-of-sight (LOS)

component with

amplitude A.

2 2

02 2 2

2

2

exp2

Power in LOS component

Power in random components 2

r r A rApdf r I

Ak

Amplitude distribution

Rice

r

0 1 2 3 0

0.5

1

1.5

2

2.5

k = 30

k = 10

k = 0

TX RX

Im a Re a

8


DELAY (TIME) DISPERSION


Delay (time) dispersion

A simple case

Transmitted impulse Received signal

(channel impulse response)

h

1 1 2 2 3 3h a a a

1

1a

2

2a

33a



One reflection/path, many paths

2 3 4 0

“Impulse

response”

Each bin consists

of incoming waves

that are too close in

time to resolve. What do we

mean by “too

close in time”? Delay in excess

of direct path

Since each bin consists of

contributions from several

waves, each bin will fade

if we introduce movement.



Bandwidth and time-resolution

Band-limiting

to B Hz

Radio systems are band-limited, which makes our infinitely short

impulses become waveforms with a certain width in time.

1

B

The time-width of the pulses is inversely

proportional to the bandwidth.

9


Narrow- versus wide-band

Channel impulse response

The same radio propagation environment is experienced

differently, depending on the system bandwidth.

“High” BW “Medium” BW “Low” BW

h h h


2B

A wide-band system

(bandwidth B2) will however

experience both frequency

selectivity and delay

dispersion.

1B

A narrow-band system

(bandwidth B1) will not

experience any significant

frequency selectivity or

delay dispersion.

Narrow- versus wide-band

Channel frequency response

|dB

H f

f

Note that narrow- or wide-band depends on the

relation between the channel and the system

bandwidth. It is not an absolute measure.


It’s much more complicated than

what we have discussed!


The WSSUS model

Assumptions

A very common wide-band channel model is the WSSUS-model.

Recalling that the channel is composed of a number of different

contributions (incoming waves), the following is assumed:

The channel is Wide-Sense Stationary (WSS), meaning

that the time correlation of the channel is invariant over time.

(Contributions with different Doppler frequency are

uncorrelated.)

The channel is built up by Uncorrelated Scatterers (US),

meaning that the frequency correlation of the channels is

invariant over frequency. (Contributions with different delays

are uncorrelated.)

10


The WSSUS model

The tapped delay-line

Recall that a narrow-band (complex) channel was modeled as

expt j t

where the fading characteristic depended on the time-varying

attenuation and phase.

The generalization we need to describe wide-band channels is

the delay characteristics (more than one “tap” in the channel):

1

, expN

i i i

i

h t t j t

Each of the N taps of the channel may have their own fading

characteristic (power, Doppler spectrum, etc.). They are

however required to be independent.


Condensed parameters

Power-delay profile

One interesting channel property is the power-delay profile (PDP),

which is the expected value of the received power at a certain delay:

2

E ,tP h t

Et denotes

expectation

over time.

2

1

2 2

1 1

E exp

E 2

N

t i i i

i

N N

t i i i i

i i

P t j t

t

For our tapped-delay line we get:

Average power of tap i.



Power-delay profile (cont.)

We can “reduce” the PDP into more compact descriptions of the channel:

mP P d

m

m

P dT

P

2

m

m

P dS T

P

2

1

2N

m i

i

P

2

1

2N

i i

im

m

TP

2 2

1

2N

i i

im

m

S TP

Total power (time integrated):

Average mean delay:

Average rms delay spread:

For our tapped-delay line

channel:

2 2



Frequency correlation

A property closely related to the power-delay profile (PDP) is the frequency

correlation of the channel. It is in fact the Fourier transform of the PDP:

exp 2f f P j f d

2

1

2

1

2 exp 2

2 exp 2

N

f i i

i

N

i i

i

f j f d

j f

For our tapped delay-line channel we get:

11



Coherence bandwidth

Given the frequency correlation of a channel, we can define the

coherence bandwidth BC:

f f

f

0f

0

2

f

CB

What does the coherence

bandwidth tell us?

It shows us over how large

bandwidth we can assume

that the channel is fairly

constant.

Radio systems using a

bandwidth much smaller

than BC will not notice

the frequency selectivity

of the channel.



The time correlation

A property closely related to the Doppler spectrun is the time correlation

of the channel. It is in fact the inverse Fourier transform of the Doppler

spectrum:

exp 2t Bt P j t d

2

2 21

,max

2

2 21

,max

2

0 ,max

1

2exp 2

2exp 2

2 2

Ni

t

ii

Ni

ii

N

i i

i

t j t d

j t d

J t

For our tapped-delay line channel we get

Sum of time

correlations for

each tap.



Coherence time

Given the time correlation of a channel, we can define the

coherence time TC:

t t

t

0t

0

2

t

CT

What does the coherence

time tell us?

It shows us over how long

time we can assume

that the channel is fairly

constant.

E.g. radio systems transmitting

data in frames much shorter

than TC will not experience any

fading within a single frame.

Documents

Channel Modelling ETI 085 Contents 1 - EIT, Electrical and ... › ... › 2012 › Lecture01_Intro.pdf · 2012-01-16 Fredrik Tufvesson - ETIN10 7 Lectures • Overview of the content