Jakes Simulation

8/10/2019 Jakes Simulation

1/36

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]


2/36

Outline

What is a Channel?

What is channel modeling?

Wireless channel modeling

Modeling Fading Rayleigh

Clarke's, Jakes' and modified Jakes' models


3/36

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


4/36

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


5/36

Wireless Channel Modeling

Three main mechanisms of electromagnetic wave progogation are

1) Reflection2) Diffraction3) Scattering


6/36

Reflection, Diffraction & Scattering


7/36

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


8/36

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.


9/36

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


10/36

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)


11/36

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


12/36

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


13/36

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.


14/36

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)


15/36

Clarke's Model...

(aseband)aussian

Random "ariable

(aseband)aussian

Random "ariable

cos(2Fct)

sin(2Fct)

Doppler

Filter*


16/36

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.


17/36

Simulating Clarke's Model


18/36

Simulating Clarke's Model...


19/36



20/36



21/36

Jakes' Channel Model

A sum of sinusoids model.

Assuming isotropic scattering i.e. receiver gets rays from all directihave a spacing of 2/N


22/36

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


23/36

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


24/36

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)


25/36

Simulating Jakes' Channel Model...


26/36



27/36



28/36

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


29/36


30/36

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


31/36

Simulating Modified Jakes' Channel Model...


32/36

Modified Jakes' Channel Model


33/36

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


34/36

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.


35/36

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


36/36

Thank You

Documents

Jakes Simulation