Stochastic Models

EidgenssischeTechnische Hochschule

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Stochastic Models 1

Lecture 4:

4. Stochastic Channel Models

Contents:

Radio channel simulation

Stochastic modelling

COST 207 model

CODIT model

Turin-Suzuki-Hashemi model

Saleh-Valenzuela model


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Stochastic Models 2

4. Stochastic Channel Models

Contents (contd):

WAND model

Spencer-Jeffs-Jensen-Swindlehurst model

IEEE 802.11 model

3GPP Stochastic Channel Model


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Stochastic Models 3

Main application fields of stochastic channel models:

Design and optimization of communication systems:- Design of the constituents of communication systems- Optimization of the behaviour and performance of these constituents- Analytical or simulation-based investigations of the performance of these

constituents

Monte Carlo simulations for system performance assessment- Link-level simulations (today)

- System-level simulations (today)

- Simulation of cooperative networks (coming soon)

in complex scenarios as close as possible to real operation conditions

Stochastic channel models (SCMs) are crucial and indispensable tools inthe design of communication systems.

The importance of stochastic channel modelling


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Stochastic Models 4

The different approaches for channel simulations:

Stored Channel Models (ATDMA)

Measured space-variant or time-variant delay spread func-tions (SFs) are selected according to some specified cri-teria to form classes of so-called reference channels.These delay SFs are stored and can be read on demandfor simulation purposes.

Example:Reference space-variant delay SF inan atypical microcellular urbanenvironments:



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Stochastic Models 5

The different approaches for channel simulations (contd):

Deterministic Channel Models

These models employ ray optical techniques (ray tracing, raylaunching combined with UTD method) to compute the delay SFor the direction-delay SF using some more or less extensive geo-graphical information (buildinglayout, electric properties ofwalls and floors, etc.) about thepropagation environment underconsideration.



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Stochastic Models 6

The different approaches for channel simulations (contd):

Stochastic Channel Models (COST 207, CODIT)

- A parametric model for the delay SFs is derived.

- Realizations of the delay SF are thengenerated according to specifiedprobability distributions of the modelparameters.

- These probability distributions aregathered by means of statisticalanalyses of measurement datacollected during extensive measure-ment campaigns.

0

5

10

15

20 05

1015

2025

0

0.2

0.4

0.6

0.8

1

real time [ms]delay [mys]Delay [ s] Time [ms]t

g t ;( )Example: COST 207 HT



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Stochastic Models 7

Comparison of the different approaches:

Channelsimulationapproaches

Computationalexpense

Intrinsicvariability of the

models

Retained channelfeatures

Challenge

Referencechannels

High(storage)

Low(=number of

stored channels)

All Choice of theappropriate

selection criteria

Deterministicchannel models

High(identification of

the dominantpropagation

paths)

Medium(=number ofenvironmentsconsidered)

Part of them(ray optical

methods are notexact)

Identification ofthe dominantprop. paths +

accurate methodfor computing

the path weights

Stochasticchannel models

Low High(probability

distributions)

Part of them(depending on the

model used)

Incorporate allrelevant channel

features



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Stochastic Models 8

Features to be incorporated into SCMs:

Stochasticchannel model

Environment:Type of environment

Frequency range

Transceiver characteristics:Trajectory, velocity

BandwidthAntenna (array) types

Short-term fluctuations:Fast fading

Long-term fluctuations:Path loss

ShadowingTransitionsDelay drift

Drift in directionsBirth & death of paths

Channel dispersionDelay

Direction of departureDirection of incidence

Doppler frequencyPolarization

Short range/term (fast)fading



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Stochastic Models 9

Requirements for SCMs:

Completeness

SCMs must reproduce all effects that impact on the performance of com-munication systems.

=> Guarantee simulation scenarios close to reality=> Full basis for system comparisons

Accuracy

SCMs must accurately describe these effects.=> Realistic results from analytical and/or simulation-based investigations

Simplicity/low complexity

Each effect must be described by a simple model.=> Enable theoretical study of some particular system aspects and performance=> Tractable computational effort to simulate the channel in Monte Carlo simulations



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Stochastic Models 10

Approach for SCM:

Specification of the area type additional system parame-

ters (array characteristics,mobile velocity, etc.)

Statistical processing of data obtained fromextensive measurement campaigns in the

identified areasEstimation of the probability density func-

tions of the parameters occurring in theparametric system function

Realizations of the system function,e.g. g t ;( )

Software package generating a specific para-metric system function of the channel, e.g.

g t ;( ) gi t( ) i t( )( )i 1=

N



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Model for :gi t( )

giST( )

t( ) gi c, t( ) gi d, t( )+=

Short-term fluctuations:

Specular part:

: Doppler frequency

gi c, t( ) hi c, j2it( )exp=i

Diffuse part:is a WSS zero-mean circular symmetric com-

plex Gaussian process specified by its ACF

or equivalently its (Doppler) spectrum :

gi d, t( )Ri t( )

Pi ( )

Ri t( ) Pi ( )t



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Model for (contd):

Long-term fluctuations (path loss & shadowing effect):

: time-dependent path loss computed from one of the modelspresented in Lecture 3.

: real zero-mean Gaussian process with ACF .

Usually,

gi t( )

gi t( ) 10L t( )10

----------

10

Li vt( )10

------------------

giST( )

t( )=

L t( )

Li d( ) RLi d( )

RLi d( ) 2 d2 2( )exp=

: standard deviation of

: decorrelation lengthSmall macrocells:

Li d( ) 6 8 dB=

5 8m=



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Models for :

Short-term fluctuations:

where is a specified random point process.

Long-term fluctuations:

where is the above random point process and

is a sequence of random processes describing the drift of the components inthe time-variant SF on the delay axis.

i t( )

i t( ) i=1 2 , i , , ,{ }

i t( ) i i t( )+=1 2 , i , , ,{ } i t( ){ }



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Main characteristics:

Cell type Macrocell

Area Typical non-hilly urban (TU), bad hilly urban (BU) Non-hilly rural area (RA), hilly terrain (HT)

Frequency range Around 1 GHz

Time-variant SF

Input Area type Vehicle velocity Number of components in Delay and Doppler resolution

g t ;( ) PN---- j 2it i+( ){ }exp i( )

i 1=

N

=

g t ;( )

COST 207 model


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Normalized delay-Doppler scattering function:

We can decompose as

The COST 207 models are specified by the two functions:

Pn ,( )1P---P ,( ) Pn ,( ) d d 1=( )

Pn ,( )

Pn ,( ) Pn ( ) Pn ( )=Normalized delayscattering function

Delay-dependent normalizedDoppler scattering function

Pn ( ) Pn ,( ) d( )

Pn ( )Pn ( )

COST 207 model


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Normalized delay scattering function:

Typical urban non-hilly area (TU):

MSvLocal

scattering

Pn ( )( )exp ; 0 s[ ] 7

0 ; elsewhere

0 1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

1.2Pn ( )

[s]

COST 207 model


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Normalized delay scattering function (contd):

Pn ( )( )exp ; 0 s[ ] 5

0.5 5 ( )exp ; 5 s[ ] 10 0 ; elsewhere

Typical bad urban hilly area (BU):

MSv Local

scattering

Distantscattering

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7Pn ( )

[s]

COST 207 model


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Typical rural non-hilly area (RA):

Pn ( )9.2( )exp ; 0 s[ ] 0.7

0 ; elsewhere

Pn ( )

[s]

MSv Localscattering

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

1

2

3

4

5

6

7

8

9

10

COST 207 model


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Pn ( )3.5( )exp ; 0 s[ ] 2

0.1 15 ( )exp ; 15 s[ ] 20 0 ; elsewhere

Typical hilly terrain (HT):

Pn ( )

[s]

MSv

Localscattering

Distantscattering

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

COST 207 model


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Normalized Doppler scattering function:

MSv

Many scattererswith nearly thesame featuresuniformly dis-tributed around

the MS

Pn ( )1

D---------- 1

1 v D( )2

---------------------------------- ; D The parameter settings in the COST 231 tables are not appropriate forinvestigating the performance of systems which exploit channelfrequency selectivity,e.g. GSM with frequency hopping.

Solution:Choose an irregularly spacing of the delays or randomly select them.

i mi= mi 0.2s=

COST 207 model


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The COST 207 tables (contd):Frequency hopping:

Real channel frequency transfer function:

Transfer function of the COST 207 channel:

B1 B2 B2'B1'

B1 B2 B2'B1'

Bc 0.2=

f

f

H f( )

H f( )

1------

COST 207 model


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Cell type Macro-, micro, picocell

Area Macrocell: urban, suburban, suburban hillyrural, rural hilly

Microcell: dense urban linear street, town square, industrial area Indoor: floor cell in buildings, corridor,

large and very large rooms

Frequency band 2 GHz range Up to 20 MHz signal bandwidth

Time-variant SF

Input Area type Vehicle velocity System bandwidth

g t ;( ) gi t( ) i t( )( )i 1=

N

CODIT model


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Short-term variations of :gi t( )

xxxxxxx

xxxxxxx

i c, i j,

xxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx

Specular part Diffuse part

giST( )

t( ) hi c, j2v--- i c,( )cos t exp hi j, j2

v--- i j,( )cos t exp

j 1=

J

+=

,

uniformly distributed over

: mean power of the th component

: coherent to diffuse power ratio of the th component

hi c, i c,=

hi c,{ }arg 0 2 ),[

hi j, N 01J---i d,

2,

E gi t( )2[ ] i c,

2i d,

2+ i

2= i

i c, i d,( )2

i

CODIT model


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Probability distribution of the azimuths and :i c, i j,

Scatterer i

v

i c,

i j,

MS0 2

pi j, ( )

i c,

i j, N i c, 0.15[radian]2

,( )mod2

CODIT model


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Long-term variations of :

Shadowing effects:

gi t( )

gi t( ) zi t( ) gi ST( ) t( )=Term describing the

long-term fluctuations

zi t( ) 1 zi2qi------ v---t i+ cos+ 1 2zi

zi t( )

tqiv ( )--------------: Random variable uniformly distributed overi 0 2 ),[

CODIT model


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Long-term variations of (contd):Emergence of the components:

Fading of the components:

is a random variable uniformly distributed over .

gi t( )

1zi t( )1

1vt z

5------------- 6

+

------------------------------- ; vt z

1 ; vt z>

zi t( )

tz v

1zi t( )1

1vt z

5------------- 6

+

------------------------------- ; vt z

1 ; vt z


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Short-term variations of :

Long-term variations of :

i t( )

i t( ) i=

i t( )

i t( ) i i 12pi------ v---t i+ cos++= i

2i

i t( )

tpiv ( )--------------: Random variable uniformly distributed overi 0 2 ),[

CODIT model


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Selection of the parameters of :

The number of components depends on the area type but is fixed for agiven area, .

The parameters describing the

behaviour of the components of are random variables specified by

probability distributions.

g t ;( )N

N max 20=

J 100=

i2

i c, i d,( )2 i c, zi qi i i pi, , , , , , ,gi t( )

CODIT model


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Setting Tables:

Example: Suburban hilly environment:

i2 zii i [s ] qi pi i [ns ]

E hi2[ ]2

Var hi2[ ]

--------------------------

Source: CODIT Report: Final Propagation Modeli

2

i

N

1=

CODIT model


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Setting Tables (contd):

Example: Power delay spectrum generated with the previous table:

S

o

u

r

c

e

:

C

O

D

I

T

R

e

p

o

r

t

:

F

i

n

a

l

P

r

o

p

a

g

a

t

i

o

n

M

o

d

e

l

CODIT model


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Example: Microcell LOS Area:

Contour plot of a realization of :g d ;( ) Evolution of the correspondingdelay scattering function

D

i

s

t

a

n

c

e

d

[

]

P

o

w

e

r

[

d

B

]

Delay [ns] Delay [ns]

Source: CODIT Report: Final Propagation Model

d 80=

d 0=

CODIT model


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Example: Indoor Picocell LOS Area:

Contour plot of a realization of :g d ;( ) Evolution of the correspondingdelay scattering function

P

o

w

e

r

[

d

B

]

Delay [ns] Delay [ns]

Source: CODIT Report: Final Propagation Model

D

i

s

t

a

n

c

e

d

[

]

CODIT model


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Cell type Macro-, micro- and picocell(by appropriately setting the probability densities of model parame-ters)

Area Urban

Frequency range 500MHz -1GHz

Time-invariant delay SF

Main features Time-invariant Clustering of the components in is reproduced by modelling

the sequence as a Poisson point process or a modificationthereof.

g t ;( ) h ( ) hi i( )i 1=

N

= =

h ( )i{ }



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Modelling as a Poisson point process:

is a Poisson point process with rate :

: Number of points in the time interval

i{ }i{ } ( )

( )

T

1 2 i N

T( )

i 1

T( ) ( ) dT

N T T

P N T n=[ ] T( )n

n!--------------- T( )( )exp= E N T[ ] Var N T[ ] T( )= =[ ]



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Modelling as a homogeneous Poisson point process:

In this case, the delay differences are independent randomvariables which are (identically) exponentially distributed with parameter :

Drawback of the Poisson model:It does not describe sufficiently accurately the clustering of the componentsas observed in measured delay SFs.

i{ } ( ) =i i 1

pi i 1 ( )

pi i 1 ( ) ( )exp=

Probability density of :i i 1

1



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Estimated rates in outdoor environments:

1ft 1ns

S

o

u

r

c

e

:

P

a

p

e

r

b

y

T

u

r

i

n

a

t

a

l

.



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Modelling as a modified Poisson point process:

The rate depends on the random sequence in the following way:

i{ } ( ) i{ }

The basic rate is multiplied by a factor

during a predetermined relaxation interval at

each :

: Clustering effect

: Poisson point process

: Isolated delay points

Values for and (macrocell):

(arbitrarily selected)

(estimated from measure-ments)

0 ( ) css

ics 1>

cs 1=

cs 1

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Stochastic Models