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Fredrik Tufvesson & Carl GustafsonDepartment of Electrical and Information Technology
Lund University, [email protected]
Channel Modelling – ETIN10Lecture no:
2012-01-16 Fredrik Tufvesson - ETIN10 1
1Introduction
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Contents
• Course information
• Why channel modeling?
• Review of concepts
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COURSE INFORMATION
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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
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Course web-site
• http://www.eit.lth.se/course/ETIN10
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Textbook
Andreas F. MolischWireless Communications, 2nd edISBN: 978-0-470-74186-3Wiley/IEEE pressThe second edition will be used!• Available, e.g., through:
– Lexis, www.lexis.se– Amazon U.K., www.amazon.co.uk– Wiley, eu.wiley.com– etc.
• Authored by Andreas F. Molisch, former professor of Radio Systems at Lund University/LTH.
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Schedule
• Three recurring components– Lectures: Carl Gustafson
Mondays (8-10, 2311) and Thursdays (10-12, E:2311)– Exercise classes: Xuhong Li
Wednesdays (8-10), 4116 (Starting next week)• Two special components
– Assignments:Two assignments, where reports are handed in
– Written exam:– March 13, 14-19.00
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Lectures
• Overview of the content in the textbook
• Additional material
• Application examples
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Exercise classes
• A selection of suitable exercises is listed on the course web-site
• During exercise classes, some of the exercises will be analysed in detail
• By working through the exercises beforehand, it becomes easier to ask questions about the parts You find difficult.
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Assignments
• There are two 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.• You are NOT allowed to share results or code between
groups!• THIS IS A COMPULSORY PART OF THE COURSE!• You need to submit the assignments in order to take the
written exam.
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Why channel modeling?
• The performance of a radio system is ultimately determined by the radio channel!
• The channel model is the basis for – system design– algorithm design– antenna design etc.
• Knowledge about system and channel interaction is vital:– MIMO: multiple antenna systems– UWB: ultra wideband– Localization services– Beamforming techniques
Without reliable channel models, it is difficult to design radio systems that work well in real environments.
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A rough breakdown into areas
Fundamental problemsin wireless communications
Propagationand antennas
Deterministic Probabilistic
Channel models
Narrow-bandchannels
Wide-bandchannels
Antennas
Digital transmissionover wireless channels
Modulation
Speech andchannel coding
Equalization
Diversity
Mobile communicationssystems
Multiple access
Cellular telephony
Wireless data networks
Speech coding
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Noise
NNoise reference level
THE RADIO CHANNELA simple link budget
Transmitter Receiver
”POWER” [dB]
Transmitpower
TXP
Feederloss
TXfL ,
Antennagain
TXaG ,
Propagationloss
pL
Antennagain
RXaG ,
Feederloss
RXfL ,
C
Receivedpower
Gai
nLo
ss RequiredC/N at
receiverinput
CRITERIONTO MEET:
This is a simple version of the link budget.
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THE RADIO CHANNELIt is more than just a loss• Some examples:
– behavior in time/space?– behavior in frequency?– directional properties?– bandwidth dependency?– behavior in delay?
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A narrowband system described in complex notation (noise free)
( )exp 2 cj fπ ( ) ( )( )expt j tα θ ( )exp 2 cj fπ−
Transmitter ReceiverChannel
Attenuation Phase
( )x t ( )y t
( ) ( ) ( ) ( )( )( )expA t t j t tα φ θ= +
( ) ( ) ( )( )expx t A t j tφ=In:
( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )exp exp 2 exp exp 2c cy t A t j t j f t t j t j f tφ π α θ π= −Out:
It is the behavior of the channel attenuation and phase weare going to model.
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THE RADIO CHANNELSome 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 -> constructive and destructive (self-)interference.
exponentn PropagatioDistance power dTransmitte power Received −×∝
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THE RADIO CHANNELPath loss
Received power [log scale]
Distance, d [log scale]
TX RX
2/1 d∝
4/1 d∝
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THE RADIO CHANNELPath loss
”POWER” [dB]
dBTXG |dBTXP |
dBRXG |
( )10
| 2
10
420log , free space
20log , ground planedB
TX RX
d
L dd
h h
πλ
⎧ ⎛ ⎞⎜ ⎟⎪⎝ ⎠⎪
= ⎨⎛ ⎞⎪⎜ ⎟⎪ ⎝ ⎠⎩
dBRXP |
|dBL
Two theoretical expressions forthe deterministic propagation loss asfunctions of distance:
There are other models, which wewill discuss later.
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Large-scale fadingBasic principle
d
Received power
PositionA B C C
A
B
C
D
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Large-scale fadingLog-normal distribution
Measurements confirm that in many situations, the large-scalefading of the received signal strength has a normal distributionin the dB domain.
”POWER” [dB]
dBTXP |
dBRXP |
|dBL
( ) ( )2| 0|| 2
||
1 exp22dB dB
dBF dBF dB
L Lpdf L
σπσ
⎛ ⎞−⎜ ⎟= −⎜ ⎟⎝ ⎠
Note dB scale
dBDeterministic meanvalue of path loss, L0|dB
( )|dBpdf L
Standard deviation: σF|dB is typically 3-10 dB.
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Small-scale fadingTwo waves
Wave 1 + Wave 2
Wave 2
Wave 1
λAt least in this case, we can see that the interference patternchanges on the wavelength scale.
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THE RADIO CHANNELSmall-scale fading (cont.)
RXTX
With a large number ofreflection points theinterference patternbecomes extremly
complicated.
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Small-scale fadingMany incoming waves
1 1,r φ2 2,r φ
3 3,r φ4 4,r φ
,r φ
( ) ( ) ( ) ( ) ( )1 1 2 2 3 3 4 4exp exp exp exp expr j r j r j r j r jφ φ φ φ φ= + + +
1r1φ
2r 2φ
3r
3φ
4r4φ
r
φ
Many incoming waves withindependent amplitudes
and phases
Add them up as phasors
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THE RADIO CHANNELSmall-scale fading (cont.)
Illustration of interference pattern from above
Transmitter
Reflector
Movement
Position
A B
A B
Received power [log scale]
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Small-scale fadingRayleigh fading
No dominant component(no line-of-sight)
2D Gaussian(zero mean)
Tap distribution
( )2
2 2exp2
r rpdf rσ σ
⎛ ⎞= −⎜ ⎟
⎝ ⎠
Amplitude distribution
Rayleigh
0 1 2 30
0.2
0.4
0.6
0.8
r a=
No line-of-sightcomponent
TX RXX
( )Im a ( )Re a
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Small-scale fadingDoppler shifts
c
rvθ
0f f ν= +
Frequency of received signal:
( )0 cosrvfc
ν θ= −
where the Doppler shift isReceiving antenna moves withspeed vr at an angle θ relativeto the propagation directionof the incoming wave, whichhas frequency f0.
The maximal Doppler shift is
max 0vfc
ν =
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Small-scale fadingDoppler spectrum
Isotropic uncorrelatedscattering
RX
Uniform incomingpower distribution
(isotropic)
Uncorrelatedamplitudesand phases
Time correlaion
( ) ( ) ( ){ } ( )*0 max2t E a t a t t J tρ πνΔ = +Δ ∝ Δ
0 0.5 1 1.5 2-0.5
0
0.5
1
max tν Δ
RX movement
J0 is the Bessel function of the first kind.
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Small-scale fadingRice 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 componentPower in random components 2
r r A rApdf r I
Ak
σ σ σ
σ
⎛ ⎞+ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠
= =
Amplitude distribution
Rice
r α=
0 1 2 30
0.5
1
1.5
2
2.5k = 30
k = 10
k = 0
TX RX
( )Im a ( )Re a