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PHENOMENOLOGY
Wireless Channel ModelingClarke's, Jakes' and modified Jakes' models
Koyalkar Raman Kishore [email protected]
Sathish Kumar B [email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected] -
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Outline
What is a Channel?
What is channel modeling?
Wireless channel modeling
Modeling Fading Rayleigh
Clarke's, Jakes' and modified Jakes' models
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What is a Channel?
A Communcation Channel is the medium used to transmit informone point to the other.
Though wired channels are fast, cost-effective and secure, they aranged, motion restricted.
Channel
Wired
- Single Path- Motion Restricted
Wireless
- Multipath- Mobile to Mobile
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Channel Modeling
Ideally, modeling a channel is calculating all the physical processa signal from the transmitter to the receiver.
Why do we need to model?
Channel Models
Digital ChannelModels
-The modeled signals
are discrete
Analog ChannelModels
-The modeled signals
are analog
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Wireless Channel Modeling
Three main mechanisms of electromagnetic wave progogation are
1) Reflection2) Diffraction3) Scattering
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Reflection, Diffraction & Scattering
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Wireless Channel Modeling...
Due to these EM wave propogation mechnisms, radio propagationroughly described by three nearly independent phenomenon :
Path loss Shadow Fading Multipath Fadin
-Long term attenuation-Deterministic
-Depends only on T-Rdistance
-Short term !luctuationin attenuation-Stochastic
-"arying terrain conditions
-Short term !luctua-Stochastic
-Superposition o! di!paths
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Wireless Channel Modeling...
a(t) = aP L
(t) aSH
(t) aF A
(t)
The total attenuation can be decomposed into path loss, shadowinmultipath fading as follows:
In this presentation, we shall focus more on the modeling and simu
multipath fading.
Multipath fading in wireless communication systems is commonly mRayleigh and Rician distributions.
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Rayleigh and Rician Distribution
A close approimation o! attenuation due to multipath !ading in wireless channels can be !ading #!or the case where no line o! sight component present$ and Rician !ading #!or the c
sight component present$%
Rayleigh Rician
&o line o! sightcomponent present
Line o! sightcomponent present
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Rayleigh Distribution
A Rayleigh Random Variable R has the probability distribution:
Rayleigh distribution can also be got by taking two independent andistributed zero mean gaussian random random variables as real aparts of a complex number and then taking its magnitude.
PR(r)=2rexp(
r2
)
where=E(R2)
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Rayleigh Fading Model
For a wireless channel, the envelope of the channel response is mhave a Rayleigh distribution.
Rayleigh Fading is a reasonable model when there are many objecenvironment that scatter the radio signal before it reaches the rece
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Delay spread & Doppler Spread
' N paths
' Different delays for each path Delay Spread
' Different attenuation for each path
' Constant channel vs effect of motion
' Change in the carrier frequency Doppler Spread
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Clarke's Model
Rayleigh fading model
Assumes isotropic scattering
Assuming linear relationship between input and output
Generating Rayleigh Channel model using two different Gaussian
Gans developed a spectrum analysis for Clarke's model to includeeffect.
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Clarke's Model...
Defining Tc(t) and Ts(t) be Gaussian random processes.
At any time, Tc and Ts are uncorrelated zero mean Gaussian rand
The channel response envelope, r(t), has a Rayleigh pdf.
As derived by Gans, Doppler shift can be included into this channepassing r(t) through the filter s(t) given by:
r(t)=Tc(t)2+Ts(t)2
S(f)=1.5/(Fd1(fFc /Fd)2)
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Clarke's Model...
(aseband)aussian
Random "ariable
(aseband)aussian
Random "ariable
cos(2Fct)
sin(2Fct)
Doppler
Filter*
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Clarke's model simulation algorithm (Rappap
Refer the section 'Clarke's Model for flat fading' in 'Wireless CommPrinciples and Practice' by Rappaport.
The steps are clearly given in the section 'Simulating Clarke's and model' with a block diagram showing the frequency domain implemRayleigh fading simulator at baseband.
Repeat the above process to generate 3 such waveforms r(t) and fcorrelation values among them. Tabulate it.
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Simulating Clarke's Model
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Simulating Clarke's Model...
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Simulating Clarke's Model...
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Simulating Clarke's Model...
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Jakes' Channel Model
A sum of sinusoids model.
Assuming isotropic scattering i.e. receiver gets rays from all directihave a spacing of 2/N
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Jakes' Channel Model...
So Jakes' gets rid of the possibilities that all the rays might be comsector.
Jakes' gives pdf of scaling as a function of angle of arrival for each
The equation for r(t) now becomes:
Cn2=f()d
f()=1/2 ;d=2/N
Cn=1/N
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Jakes' Channel Model...
rI=1
Nm=1
N
cos(2Fdcosm t+am) ; rQ=1
Nm=1
N
sin(2Fdcosm t+bm
r(t)=rI(t)+jrQ(t)
.
Where is the angle of arrival, and are random phases unifdistributed over (0, )2
m am bm
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Jakes' Model simulation algorithm
Generate uniform random values for lying between 0 a
Generate a large number of samples of
Using them, generate the vector
Find the autocorrelation of
Repeat the above process to generate 3 different waveforms across-correlation coefficient values among them. Tabulate it.
am,bm,m
rI(t) and rQ(t)
r(t)=rI(t)+jrQ(t)
r(t)
r(t)
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Simulating Jakes' Channel Model...
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Simulating Jakes' Channel Model...
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Simulating Jakes' Channel Model...
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Modified Jakes' Channel Model
Ideally, each waveform generated must be uncorrelated to the othewas a very high cross-correlation in Clarke's model.
In Jakes' model, though the cross-correlation was lower than Clarkcan be still be reduced
Modified Jakes' model :
Aim: To have negligible cross-correlation between different wavefo
This is achieved my multiplying each waveform with a Hadamard C
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Modified Jakes' model simulation algorithm
After generating three waveforms r(t) as given in Jakes' model:
Make sure that each r(t) generated has samples(for any intege
Generate first 3 rows of a x Hadamard matrix or you can use matlab function 'hadamard' to generate the whole matrix and then
rows.
Multiply the 3 waveforms r(t) with a unique row of Hadamard matri
Find the cross-correlation values among the 3 waveforms generatemultiplying with the rows of Hadamard matrix. Tabulate it.
2k
2k
2k
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Simulating Modified Jakes' Channel Model...
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Modified Jakes' Channel Model
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Conclusion
Two major attenuations in a wireless signal: Path loss and Fading.
Rayleigh fading channel models are fairly good approximations to multipath fading in real life.
Clarke's model, one of the first Rayleigh implementations, has a hu
correlation.
Sum of sinusoids (Jakes') Rayleigh implementations give a better much less cross correlation.
Hadamard codes can be used to reduce the cross correlation even
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Future Work
Better implementations of Rayleigh pdf than the sum of sinusoids m
Coming up with models more complex than Rayleigh which can mowireless channels even better.
Using in the DRM+ radio receiver implementation.
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References
JAKES, w. c., JUN. (Ed.): Microwave mobile communications (WYork, 1974)
R. H. Clarke, A statistical theory of mobile-radio reception, in BelTechnical Journal vol. 47, 1968, pp. 9571000
T. S. Rappaport (December 31, 2001). Wireless Communications:and Practice (2nd ed.). Prentice Hall PTR
P. Dent, G. E. Bottomley and T. Croft (24 June 1993). "Jakes FadiRevisited". Electronics Letters
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Thank You