Communication Networks 1 Infineonnts.uni-duisburg-essen.de/downloads/cn1/lecture-7.pdf · Dr.-Ing....

Dr.-Ing. Ch. KranzSMS IC CE DlfOctober, 2003

Communication Networks 1

Infi

neo

n

Principles of Mobile Communications

University Duisburg-EssenWS 2003/2004

N e v e r s t o p t h i n k i n g .


Wave PropagationOverview

• Large Scale Path Loss / Large Scale Fading

• Shadowing

• Path Loss Prediction

• Atmospherical Effects

• Channel Simulation

• Linear Time Variant Systems

• Linear Time Variant Channels - statistic description

• Special Channels

• Real mobile channels


Wave PropagationLarge Scale Path Loss

n Large scale path loss models

– predict the mean signal strength for an arbitrary TX-RX distance

– average attenuation as a function of distance: averaging over large distances so that the fast fading eliminate itself

– free space propagation (see first lectures):

– Lee‘s empirical approach of the propagation in real environments

2

RTT

Rp4

⋅⋅=

fdc

GGPP

000

0R kff

dd

PPn

⋅

⋅

⋅=

−−γ


– d0 and f0 are relative quantities to determine the parameters γ , n , and k0 experimentally

– the parameter γ , n , and k0 depend on the propagation environment

– LOS - line-of-sight: γ = 2

– typical values of the propagation exponent in urban areas: γ = 3 ... 4,5

– corresponds to 30 ... 45 dB attenuation per decade of distance

– numerous other empirical approaches, e.g. the COST-Hata-model for urban areas, that also includes the antenna height as a parameter

Wave PropagationLarge Scale Path Loss


Wave PropagationShadowing

n Shadowing

– shadowing effects lead to random fluctuations of the attenuation with respect to its mean, which is determined by the pass loss

– slow fading

– measurement result: attenuation is Gauß-distributed ⇒ log-normal-fading (normal in dB)

– received amplitude a(x) for radial movement away from the BS: (A(x) transmitted amplitude)

– alog-normal is Gauß-distributed with a standard deviation:

)(10)( 20

)(2

00

normal-log

xAdx

axa

xa

⋅⋅

⋅=

−γ

2normal-lognormal-log )(a=σ


Wave PropagationShadowing

– the log-normal distribution describes the random shadowing effect which occur over a large number of measurements at the same TX-RX distance

– standard deviation clearly depends on the propagation environment, values: σlog-normal = 4 ... 12 dB, typical value: σlog-normal = 8 dB

– shadowing effects are correlated over larger distances:

– in the literature very different numerical values are documented, e.g.:

n typical suburban area for 900 MHz: σlog-normal = 7,5 dB, Rlog-normal (∆x = 100 m) = 0,82

n microcellular area for 1700 MHz: σlog-normal = 4,3 dB, Rlog-normal (∆x = 10 m) = 0,3

2normal-log

normal-lognormal-lognormal-log

)(

)()()(

σ

xxaxaxR

∆+⋅=∆


Wave PropagationTypical Path Loss

– Typical behavior of the received signal power

Slow-Fading

Standard deviation of Slow-Fading

Average path loss

Rec

eive

d si

gnal

pow

er

in d

Bm

d/km


Wave PropagationPath Loss Prediction

Path Loss Prediction



n Predicting the propagation characteristics between two antennas belongs to the most important tasks for the planning of mobile communication systems

n Number of subscribers rises -> size of cells reducesfrom macro cells (> some km) to micro cells (few hundreds of meters) in urban areas

n With decreasing size the importance of path loss prediction increases

n Path Loss Prediction will provide only mean or median values

n Small scale fading is adequately represented by Rayleigh- or Rice-distributions



n path loss prediction

– empirical path loss models

– ray-tracing methods

n Tracing the rays for a prescribed number of reflections or some maximum attenuation

n precise collection of measurement data required (regarding geometry, material properties)

– diffraction theory

– combination of different approaches


Wave PropagationChannel Simulation

– geometry based models- most time consuming part is the determination of all relevant paths

from transmitter and receiver- the computations are performed with the help of the theory of

diffraction, reflection, scattering

BS



Example:

n Ray-Tracing Examples of the city center of Helsinki @2125MHz 5Mchips/s

n a) low antenna 5m below the rooftop of a 30-m building- the street canyon effect became more important

n b) high antenna 1.5m above the rooftop- the over rooftop propagation plays an important role

n surrounding buildings height is app. 20-25 meters

n BS directional antenna GT=11.5dB, downtilted by 7degree

n Path Losses are calculated by adding the mean absolute tap powers of the complex impulse response

n Delay Spread is calculated out of the impulse response

Free (limited) evaluation software: www.awe-communications.com

(What’s that for a communication system?)



Source: Verifying path loss and delay spread predictions of a 3D ray tracing propagation model in urban environment, Terhi Rautiainen1, Gerd Wölfle2, Reiner Hoppe3


Wave PropagationAtmospheric Effects

n atmospheric effects

– Attenuation due to resonance's of water and oxygen molecules for large frequencies (GHz-area)

– Additional attenuation due to rain, fog and snow

– Interpretation as layered wave guides

f/GHz

atm

osph

eric

alat

tenu

atio

n in

dB

/km H2O

O2



n Channel simulation: model of the propagation channel which includes all major effects

– Propagation channel without

time dispersion

τ (x)

Filter

αlog-normal

realGauß-

process

path loss

shadowing

complexGauß-

process

Rice fading

2010x

y =2

0

γ−

⋅

dx

k

Filter

(delay)

(large scale path loss only)

IR j)( AAtA +=



– Propagationchannel withtime dispersion

τN

path loss

power delay profile

2

0

γ−

⋅

dx

k

. . .

large scale fading

. . .

small scale fading

. . .

. . .

Dopplerprocess 1

Σ

Shadingprocess 1

Dopplerprocess 2

Shadingprocess 2

Dopplerprocess N

Shadingprocess N

τ2

τ1

h1

h2

hN



Linear Time Variant Systems


Wave PropagationLinear Timevariant Systems

n Linear timevariant systems

– mobile channel = linear timevariant systeme.g. time variation due to receiver motion in space

– input-output description in the complex baseband:

n h(t,τ) = timevariant impulse response = input delay-spread function

Linear Timevariant

System

}e)(Re{)( 0jHF

ttxtx ω= }e)(Re{)( 0jHF

ttyty ω=

∫∞

∞−−= τττ d),()()( thtxty



n Response to a single impulse

n causality: h(t,t − t0) = 0 if t < t0

substitution: t − t0 = τ ⇒ h(t,τ) = 0 for t < t − τ

⇒ h(t,τ) = 0 for τ < 0

h(t,τ))()( 0tttx −= δ ),()( 0ttthty −=

∫∞

∞−−=−−= ),(d),()()( 00 ttththttty τττδ



h(t,τ) = 0

τ

t

t0

t0 = 0

n timevariant impulse response - response to a single impulse

τ<0

t − t0 = τ

h(t0,τ)

h(t1,τ)

h(t2,τ)

h(t,τ) = 0 for t < t − τ



n „discrete time“ representation:

n FIR filter with timevariant coefficients

∑=

∆∆∆−=n

mmthmtxty

0),()()( τττ

x(t). . . .

. . . .y(t)

∆τ ∆τ ∆τ

h(t,0)⋅∆τ h(t,∆τ)⋅∆τ h(t,2∆τ)⋅∆τ h(t,n∆τ)⋅∆τ



– transfer to the frequency domain

n H(ν,ω) = output Doppler-spread function

∫∞

∞−−−= uuuHuXY d),()(

21

)( ωωπ

ω

x(t)

X(ω)

y(t)

Y(ω)

h(t,τ)

H(ν,ω)

∫ ∫∞

∞−

∞

∞−

−−= ττων ωτν ddee),(),( jj tthH t



– transfer to the frequency domain



n „discrete frequency“ representation

∑−=

∆∆−∆∆−=

n

nmmmHmXY

p2),()()(

ωωωωωωω

X(ω)

. . . .

. . . .

Y(ω)

−n∆ω

H(−n∆ω,ω)⋅∆f

−∆ω

H(−∆ω,ω)⋅∆f

0⋅∆ω

H(0,ω)⋅∆f

∆ω

H(∆ω,ω)⋅∆f

. . . .

. . . .

n∆ω

H(n∆ω,ω)⋅∆f



– time variant transfer function T(t,ω)

– delay Doppler spread function S(ν,τ) (e.g. time variance because of a moving receiver)

∫∞

∞−= ωωω ω de),()(

p21

)( j ttTXty

∫∞

∞−

−= ττω ωτ de),(),( jthtT

∫∞

∞−

−= tthS t de),(),( jνττν

∫ ∫∞

∞−

∞

∞−

−= τντντ ν dde),()(p2

1)( j tStxty

(Convolution integral with inverse transf. doppler spread function)



– Relation between the four presentation of a time variant linear system

– variables: t = observation time, τ = delay, ω = frequency, ν = Doppler frequency

– often true for real channels: slowly timevariant

h(t,τ)

S(ν,τ) T(t,ω)

H(ν,ω)

delay Doppler spread function

time variant transfer function

frequency Doppler-spread function

time variant impulse response



measurement no. 1:timevariant impulse response: f0 = 1,8 GHz, LOS - line-of sight, omnidirectional non-moving antennas, distance = 95 m, industrial area

Slowly time variant



measurement no. 1:timevariant transfer function: f0 = 1,8 GHz, LOS - line-of sight, omnidirectional non-moving antennas, distance = 95 m, industrial area



measurement no. 2:time variant impulse response: f0 = 1,8 GHz, NLOS - non-line-of sight, omnidirectional non-moving antennas, distance = 230 m, industrial area



measurement no. 2:time variant transfer response: f0 = 1,8 GHz, NLOS - non-line-of sight, omnidirectional non-moving antennas, distance = 230 m, industrial area



measurement no. 3:time variant impulse response: f0 = 1,8 GHz, LOS - line-of sight, omnidirectional antennas, driven distance = 1m,distance to base = 95 m, industrial area



measurement no. 3:time variant transfer response: f0 = 1,8 GHz, LOS - line-of sight, omnidirectional antennas, driven distance = 1m,distance to base = 95 m, industrial area



Linear Time Variant Channels

Statistic Description



– mobile channels are timevariant random systems ⇒ description with random methods

– restriction to (squared) means

n for computational costs

n Gauß-processes are completely described by (squared) means

n realistic approach: correlation

– auto correlation function of the received signal

[ ]{[ ]})j(

2*)j(

221

)j(1

*)j(12

12HF1HF

020020

010010

)()(

)()(E)}()({E

ϕωϕω

ϕωϕω

+−+

+−+

+

⋅+=⋅

tt

tt

etyety

etyetytyty



n averaging over the carrier phase ϕ0:

{

})2)(j(2

*1

*

)(j21

*

)(j2

*1

)2)(j(214

12HF1HF

0210

210

210

0210

e)()(

e)()(

e)()(

e)()(E)}()({E

ϕω

ω

ω

ϕω

++−

−−

−

++

+

+

+

=⋅

tt

tt

tt

tt

tyty

tyty

tyty

tytytyty

{ }{ }{ })(j

2121

)(j2

*12

12HF1HF

210

210

e),(Re

e)()(ERe)}()({E

ttyy

tt

ttR

tytytyty

−

−

=

=⋅

ω

ω



– auto correlation function of the complex amplitude of the received signal:

∫ ∫

∫ ∫

∞

∞−

∞

∞−

∞

∞−

∞

∞−

−−=

−−=

⋅=

2122*

1122*

11

2122*

22*

1111

2*

121

dd}),(),(}E{)()(E{

dd),()(),()(E

)}()({E),(

ττττττ

ττττττ

ththtxtx

thtxthtx

tytyttRyy



n auto correlation of the system functions

E{h(t1,τ1)⋅h*(t2,τ2)} = Rhh(t1,t2;τ1,τ2)

E{H(ν1,ω1)⋅H*(ν2,ω2)} = RHH(ν1,ν2;ω1,ω2)

E{T(t1,ω1)⋅T*(t2,ω2)} = RTT(t1,t2;ω1,ω2)

E{S(ν1,τ1)⋅S*(ν2,τ2)} = RSS(ν1,ν2;τ1,τ2) ACF of delay Doppler spread function

ACF of time variant transfer function

ACF of freq. Doppler-spread function

ACF of time variant impulse response



– relations between the auto correlation functions:

Rhh(t1,t2;τ1,τ2)

RSS(ν1,ν2;τ1,τ2) RTT(t1,t2;ω1,ω2)

RHH(ν1,ν2;ω1,ω2)



Special Channels



– special channels:

n WSS − wide-sense stationary channel: in between short time intervals the ACF Rhh(t1,t2;τ1,τ2) depends only on the time difference ∆t = t2 − t1.

Rhh(t1,t1+∆t;τ1,τ2) = Rhh(∆t;τ1,τ2)

RTT(t1,t1+∆t ;ω1,ω2) = RTT(∆t;ω1,ω2)

Ø consequences of the WSS-property:

)},(),({E),;,( 22*

112121 τντνττνν SSRSS ⋅=(ACF of delay Doppler spread function)



)(p2),;(

)(p2de)},;(

dde)},;(

dde)},(),({E

de),(de),(E),;,(

21212

21)j(

21

1)j(

21

21)j(

22*

11

*

2j

221j

112121

2

21211

2211

2211

ννδττν

ννδττ

ττ

ττ

ττττνν

ν

ννν

νν

νν

−⋅−=

−⋅∆∆=

∆∆=

=

⋅=

∫

∫ ∫

∫ ∫

∫∫

∞

∞−

∆

∞

∞−

∞

∞−

∆−−−

∞

∞−

∞

∞−

−−

∞

∞−

−∞

∞−

−

SS

thh

ttthh

tt

ttSS

P

ttR

tttR

ttthth

tthtthR



Ø consequence of the WSS-property:

scattering contributions with different Doppler frequencies are uncorrelated

n channel with uncorrelated scatterers (US − uncorrelated scattering channel): in the frequency domain the ACF RHH(ν1,ν2;ω1,ω2) depends only on the frequency difference ∆ω = ω2 − ω1, wide sense stationary in the frequency domain. (the mean and correlation do not depend on the choice offrequency)

RHH(ν1,ν2;ω1,ω1+∆ω) = RHH(ν1,ν2;∆ω)

RTT(t1,t2;ω1,ω1+∆ω) = RTT(t1,t2;∆ω)

Ø consequence of the wide sense stationary in the frequency property:

)},(),({E),;,( 22*

112121 ττττ ththttRhh ⋅=



)();,(

)(de)};,(

dde)};,(

dde)},(),({E

de),(de),(E),;,(

21221

21)j(

21p21

1)j(

21p)2(1

21)j(

22*

11p)2(1

*

2j

22p21

1j

11p21

2121

2

221112

22112

2211

ττδτ

ττδωω

ωωω

ωωωω

ωωωωττ

τω

τωτωτω

τωτω

τωτω

−⋅−=

−⋅∆∆=

∆∆=

=

⋅=

∫

∫ ∫

∫ ∫

∫∫

∞

∞−

∆−

∞

∞−

∞

∞−

∆−−

∞

∞−

∞

∞−

−

∞

∞−

∞

∞−

ttP

ttR

ttR

tTtT

tTtTttR

hh

TT

TT

hh

∆ω = ω2 − ω1



n consequence of the wide sense frequency stationarity:

– scattering of elementary scatters with different delays are uncorrelated -> US (uncorrelated scattering)

n WSSUS − wide-sense stationary uncorrelated scattering channel:

WSSUS is an important class of mobile channels with practical relevance:

– stationarity with respect to the observation time (small scale fading)e.g. GSM900, 150km/h -> 7.2ms/wavelength

– uncorrelated contributions due to scatterers with different time delay



n autocorrelation of the WSSUS-channel:

Rhh(t1,t1+∆t;τ1,τ2) = Phh(∆t;τ2) ⋅ δ(τ1−τ2)

RHH(ν1,ν2;ω1,ω1+∆ω) = PHH(ν2;∆ω) ⋅ 2π δ(ν1−ν2)

RTT(t1,t1+∆t ;ω1,ω1+∆ω) = PTT(∆t;∆ω)

RSS(ν1,ν2;τ1,τ2) = PSS(ν2;τ2) ⋅ 2π δ(ν1−ν2) ⋅ δ(τ1−τ2)

Phh(∆t,τ)

PSS(ν,τ) PTT(∆t,∆ω)

PHH(ν,∆ω)

ACF of delay Doppler spread function

ACF of time variant transfer function

ACF of freq. Doppler-spread function

ACF of time variant impulse response



– physical model of the WSSUS-channel:

n single scattering with a large number of scatterers

n each scatterer is assigned a time delay, a Doppler shift as well as a scattering coefficient

independent scatterers



n PSS(ν;τ) is proportional to the scattering function σ(ν,τ)

n σ(ν,τ) describes the

power distribution as

a function of the

Doppler frequency and

the time delay à

Doppler delay spectrum



Real Mobile Channels


Wave PropagationReal Mobile Channels

– real mobile channels

n are in general non-stationary – however, stationarity is often a reasonable assumption for short distances in areas of small size (mobile phone <-> DVB)

n assumption: stationarity in small areas, significant scattering regions do not vary inside these areas (small scale fading) àWSSUS-approach is valid

n for larger distances shadowing becomes remarkable, so that the significant scattering regions will vary (large scale fading)



– properties in the time domain (stationarity)

n no time delay for the observation time: ∆t = 0 ⇒ power delay profile = averaging of the delay Doppler spectrum over all Doppler frequencies:

n average time delay:

∫∞

∞−== ντνττ ν de);();0()( 0j

p21

SShhhh PPP

∫

∫∞

∞⋅

=

0

0

d)(

d)(

ττ

τττ

τ

hh

hh

P

P

(time invariant)



n standard deviation of the delay spread:

∫

∫∞

∞⋅−

=∆

0

0

2

)d(

)d()(

ττ

ττττ

τ

hh

hh

P

P



– properties in the frequency domain

n the correlation of the transfer function depends for different frequencies on the increasing frequency difference.

n coherence bandwidth = frequency shift for which there is still a significant correlation. (statistical measure over which the channel can be considered “flat”)

n frequency correlation without time delay of the observation time: ∆t = 0 ⇒ frequency-correlation spectrum = averaging of the frequency Doppler spectrum over all Doppler frequencies:

∫∞

∞−∆=∆=∆ νωνωω ν de);();0()( 0j

p21

HHTTTT PPP



n relation between the frequency correlation spectrum and the power delay profile:

Phh(0,τ) = Phh(τ) PTT(0,∆ω) = PTT(∆ω)

n example for the frequency-correlation: PTT(∆ω) / PTT(0)

∆ω / 2π MHz



Definition of coherence time Tc and coherence bandwidth Bc by using the autocorrelation function of the transfer function.



Coherence Bandwidth:

- It can be assumed that the transfer function is almost constant within the coherence bandwidth

Coherence Time:

- The transfer function changes only slightly during the coherence time

Both have considerable effect on the design of a transmission system which is adapted to the channel characteristics.

Symbol Duration

Channel varies during the transmission of a single symbol-> large distortions result -> high bit error probability -> strong time variant behavior.

Channel can be considered constant during symbol transmission. Time invariant behavior of received signal



Bandwidth B:

• The channel transfer function changes over the bandwidth B of a signal

• Multi-path spread is larger than symbol duration. IntersymbolInterference (ISI) occurs

• Frequency selective behavior of the radio channel

• Broadband Channel (frequency selective fading)

• Transfer function constant over the signal bandwidth B

• Only small ISI

• Narrowband channel (non frequency selective fading)

In practical mobile applications single Narrowband Channels are not applicable.

1. The velocity of the mobile is not small

2. Due to fading effects either very little or very strong attenuation occurs in a narrowband channel -> no technical possibility to improve the receive situation withsingle receivers

Communication Networks 1 Infineonnts.uni-duisburg-essen.de/downloads/cn1/lecture-7.pdf · Dr.-Ing....

Documents

Transcript of Communication Networks 1 Infineonnts.uni-duisburg-essen.de/downloads/cn1/lecture-7.pdf · Dr.-Ing....