Antennas, Antenna Systems & Radio Propagation...

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(c) Patrick Eggers 201424/11/2014

Antennas, Antenna Systems & Radio Propagation 2014

PhD course 24-28 Nov 2014

Aalborg University

Room A6-111

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Schedule

http://kom.aau.dk/~pe/education/phd/AASRPC2014/AASRP_2014_phd.html

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ParticipantsNAME email institute

Nestor Hernandez

Emil Buskgaard

Ehsan Foroozanfard

Alex Oliveras Martinez

Jakob Lindbjerg Buthler

MATIULLAH KHAN

Karthikeya G. S Gulur

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Criteria

• Be present– Max 20% absence

– Sign participation sheet for every ½day session

• Solve and hand-in exercises– No later than 2 weeks after end of course

– Acceptable solutions/level

• Have returned any loaned material in good shape

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Resources and material for loan• You need

– online acces (AAU/I8 wireless access) to• see copy of slides and some of teh reading material• access to some of the measured data (some is BIG.. So wireless

download can be difficult)

– You need Matlab or similar hig level math/plotting package, to process expeirmental as part of exercises

• We could arrange for material you could loan during the course– Notebooks (Windows)– Memory sticks

• Can be used to hold/transfer measured data

• You have to sign for the loan (agree to deliver back in same state as received .. at end of course)

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(c) Patrick Eggers 2014

Signal -> link transition : channel impact SNR

• AWGN -> Fading

• Channel changes BER statistics drastically•http://www.raymaps.com/index.php/bit-error-rate-of-qpsk-in-rayleigh-fading/ber2/

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Channel impact : Doppler/Speed• Channel phase dynamics : Irreducible

BER floor

•http://ratnuu.wordpress.com/2011/03/03/the-theoretical-ber-under-fading/

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(c) Patrick Eggers 201424/11/2014 8

Propagation channel elements

Signal dynamics

Base

Mobile

Path loss

Transmission range

Localmeans

Global mean

Inverse power law

Shortterm

Link budget

IIII

II

I : Path loss

Power decay : global mean, d-n

II : Shadow fading

Blocking : local mean, log-normal

III : Short term fading

‘Vector interference’ : Rayleigh, Rice

Traditional distinctions for vehicular case. For handsets/nearfield terminals can

be near impossible to seperate these effects

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(c) Patrick Eggers 201424/11/2014 9

Wave types

Power dependence

vs range = ?

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(c) Patrick Eggers 201424/11/2014 10

Fresnel zones

=> ellipsoids•Fresnel zones : 180 phase difference•o

l d h d h d d d d h d d

l l d d

hd

hd

hd

hd

hd d

12 2

22 2

1 2 1 2 2 2 1 2

1 2 21 1

1 1 1 12

12

2

22

2

12

2

22

2

12

22

; ,

l nh

d dh r

nn

d d

2 2

1 12

12

22 1 1

12

22

as their property is a constant path lenght 'l'from focus to contour, and next focus point

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(c) Patrick Eggers 201424/11/2014 11

Smooth surface reflection

Reflection coefficient

Dielectric constant

Grazing incidence, small : v h 1 1; ;

v v

h

very small n

unconditionally

1 1 2 1

1

2, ; ,

,

c very large :

h v

c c

c c

,

sin cos

sin cos

2

2

c r r rj j

0

60

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(c) Patrick Eggers 201424/11/2014 12

Plane earth (2-path) model

dd

hhdd

hhhhddd

rtdddd

rtrt

;2

41111

;;

2

2

2

2

22

22

2222

Sum signal

240

22

0

2222

0

22

4

...sincos1...14

d

hhP

d

hh

dP

jed

PP

rtrt

jr

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(c) Patrick Eggers 201424/11/2014 13

Empirical path loss model

L [dB]

Log(range) [km]

2-path, n=4Regression, n=3.8

L=Clutter loss

clutter

Measurement

L

Measured power law d-n, typical n=3 to 5

Lreference=L2-path or Lregression or other power law

Signal(d-n)=1/Loss(dn)

n = path loss (power law) exponent

L=L + L ( ,R,h ,environment)2-path clutter b

Classification -> clutter constants

Experiments = big money

Urban, suburban, rural etc.

define how? -> operator experience

Frequency, Range, Hb and environment

Extra treatment for Terrain obstacles

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(c) Patrick Eggers 201424/11/2014 14

Link margin & budget• Link Budget

– Output power + Ant gain – cable losses– Path loss -> estimate/predict via models– Local mean variation -> provide ‘safety’

margin– Fast fading -> provide ‘safety’ margin– Receiver sensitivity for given spec BER or

QoS

Local mean -> distribution[dB] & spatial variation dependence [m]

40dBm

Lc=-6dB Ga=20dB Path loss Lp = -80dBShadow Ls=-6dB

Tx Power Rx Power

-52dBm

Fading = -20dB

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(c) Patrick Eggers 201424/11/2014 15

Multiplicative effects

1

2

34

Shadow lossL(x)

R

xL(R) = L(x)Global loss

L x L x L x L x L x L x L x

L L L L L L

N n

N

N n

N

1 2 3 41

1 2 31

.....

log log log log ... log log

Central limit theorem

Log(L) is asymptotically normal distributed. Approx. n=>8 sufficient

S s s

P S e

n n

n n n

nn

n

u

n n

n

n

; : ,

lim

,

2

21

2

2

2

Normal (Gaussian) probability density function (pdf)

Error function, cumulative distribution function (cdf)

f u N , 2

F u f x dx erf u Q uu

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Propagation channel elements

III. Short term fading

(vector interference)I. Path loss

(global decay d-n)

II: Shadow fading

(blocking, local mean)

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The two-source model (unidirectional)

2

sin2

22

00

000 2

k

exrekLkxja

j

eeaejaeaexE

xjkLj

kLkxjkLkxjkLjkLkxjkxj

x

L

’Frozen time’ – only look at space dependance

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What does it look like?

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.5

1

1.5

2

x in

|E|

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-100

-50

0

50

100

x in

Pha

se in

deg

rees

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The 2 source model: random directions

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The two source model: 2 directions

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Rayleigh fading

y

ii

x

iiii ajajaE sincosexp

Central limit theorem:•x, y are sums of a large number of random variables.

•x,y can be assumed to be

•Gaussian distributed,

•independent,

•zero mean

•of the same variance

•Joint probability density function (pdf)

2

22

2

2

2

2

22

2

2

2

2

22

1

2

1

2

1,

yxyx

eeeypxpyxp

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Rayleigh fading: from cartesian to polar

rrJ

rryxr

y

r

x

r

yxJ

ry

rx

x

y

ryx

erjyxE j

22

222

sincoscossin

sincos

,

,

sin

cos

arctan

2

2

2

22

22

2

22

2

2,,

2

1,

r

yx

er

yxpJrp

eyxp

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Rayleigh fading: from joint to the marginals

2

1,

,

2,,

0

22

2

0

22

2

2

2

2

2

drrpp

er

drprp

er

yxpJrp

r

r

Uniform distribution of the angle

Rayleigh distribution of the envelope

Phase and envelope

are related as?

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Pdf of the Rayleigh distribution

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Amplitude

PD

F

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Cdf of the Rayleigh distribution

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Amplitude

CD

F

-40 -30 -20 -10 0 10 2010

-4

10-3

10-2

10-1

100

Amplitude in dB

CD

F

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Doppler shift

Doppler shift -

R

d

far fieldR>>d

•Envelope r, envelope or power gradient

•Phase , phase gradient d/dd

•Max. Doppler shift : fd,max = 1/ [c/m]

•Actual Doppler shift : fd= fd,max cos() [c/m]

•Temporal : fd [Hz] = fd,[c/m] v[m/s]

2-source

2/,2/mod

2/cos2

2/sin

2/2sin22/sin2

½2/0

max,

Lxsignx

Lxkkadx

xdrxr

LxkLxksignx

LxfaLxkaxr

Lx

d

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Power azimuth distribution:

Antenna Gain:

How much power from each direction:

Multiple sources: Doppler spectrum

G

Gpx

y

What is the Doppler frequency:

α

p

ffff d cosmax,

Power spectrum due to a small range of angles da:

22

max,

2

max,max,max,

max, 1sincos

ff

GpGpbfS

df

ffdff

d

fd

d

df

dGpGpbdffS

d

ddd

d

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Example of Doppler spectrum

2

1p

4

1G

Omni directional source distribution

Omni directional antenna

22

max,22

max,

141

21

2ffff

fSdd

This is also known as the bathtub spectrum.

Put the limits

on the axes!

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Rayleigh fading distribution functions

x

yQuadrature components

Phase Envelope

UncorrelatedGaussian (Normal)

UniformRayleigh

=arctan(Y/X) r=sqrt(X +Y )2 2

r

0 d

Jacobi transform

J=d(x,y)/d(r, )

p(r, )=p(x,y)|J|

Random-FMStudent's t

d /dd

d

'

Power gradientLog-Student's t

d|r| /dd2

d

20log(r)'

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Reminder: definition of correlation

2222

**

,vEvEuEuE

vEuEvuEvu

For Gaussian random variables:

envelopecomplexpower 2

Often needed

Easier to treat analytically

Why??

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Spatial correlation• Correlation theorem:

Power density spectrum Auto-correlation

• How to find the Doppler spectrum from meas:

• For uniform angle of arrival

• When does the correlation =0?

2π∆d/λ=2.512 or equivalently ∆d=0.4λ

fSFddrdrEdR

smRHzscmcS

enveloper1

,/,/

dJdRr 20

2fHfS

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Wideband : A simple example

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The more general case

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How does it look at reception?

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Dispersion metrics

• Delay spread= Standard deviation of power delay profile (pdp)

• Defined similarly to Doppler spread.

• Delay spread is a fundamental limitation because of

–irreducible bit error rate (BER),

–receiver complexity

2 hpdph

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How to find it for a discrete channel

We can convert to expectation over space instead, why?

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How to calculate the ds

Where is the error in the expression??

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NB vs WB: it’s all relative

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Channel classificationEnvironment spread - system bandwidth product

Temporals [s] BW [Hz]

f

|h( )|

|H(f)|FFT

sBW<<1 sBW=1 sBW>>1Quasi narrowband :Selective fading butpaths not resolved

Wideband :Selective fading,paths resolved

Narrowband :Flat fading

=> Channel classification / wideband is RELATIVE!

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Wideband models

• Tapped delay lines often used

• Often Rayleigh distributed taps, but might include other distributions and/ or LOS component

• Mean tap power determined by the pdp

iN

iii tjtth

1

exp,

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Implications of tap delay line models

• Tap delay line model = transversal filter• Used for discrete model implementation • HW/SW emulators/ simulators

• If the inter-tap delay becomes comparable to the bit time, successive symbols interfere with each other= InterSymbol Interference (ISI)

a0 a1 a2 a3 a4

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COST 207/ GSM: PDPs

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Transfer function- typical urban

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Deterministic transfer functions: ’INSTANT’

• Four equivalent system functions (one specific ’sample’ of channel) :– h: Time/space variant impulse response– T: Time/space variant transfer function– S: Spreading function ->radar target scattering function– H: Doppler variant spreading function/transfer function

• Doppler Spatial fading, Delay Frequency fading

• 2 variables (space, time) (Doppler, frequency)

S(fd,)

h(x,)

T(x, f)

H(fd, f)

F

F

F

FF-1

F-1F-1

F-1

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Stochastic 2x2 wideband model: ’AVERAGE’

• Time invariant stochastic models are described by Correlation functions/ Power density spectra

• Stochastic correlation functions: General multipath ..’trend’

Rh(x1, x2, 1, 2)

RS(fd1, fd2, 1, 2) R(x1, x2, f1,f2)

RH(fd1, fd2, f1, f2)

FF

FF

FFFF

FF-1FF-1

FF-1

FF-1

R(x1,x2,y1,y2)=E[h(x1,y1)h*(x2,y2)]

2 param’s/ domain: 2x2 representation with 4 param’s each.

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WSSUS: Wide Sense Stationary Uncorrelated Scattering

• Stationarity: shift invariance

• Wide sense stationarity (WSS)

• Uncorrelated scattering (US)

tttttt nnxxpxxp ,,,,

11

xRxxR

21,

fixed

R

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WSS vs US duality behaviours

• Correlation domain behaviour:

• WSS: shift invariance in space, uncorrelated Doppler shifts

• US: singularity in t, shift invariance in f

(from time-frequency duality- Bello)

• ‘US’ in one domain ‘WSS’ in translated domain

xhFfHffff

xxxxx

ddddd

,,

,

1221

1221

hFfHfffff

,,

,

1221

1221

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Deterministic vs. WSSUS channels

Deterministic channel

WSSUS Equivalence WSSUS specials

Space variant impulse response function

h(x,) Rh(x,x+,1,2) = E[h(x,1) h*(x+,2)] = (2-1) Ph(x,1)

Ph(0, 1)= S is power delay profile (PDP)

Output Doppler scattering function

H(fd,f) RH(fd1,fd2,f,f+f) = E[H(fd1,f) H*(fd2,f+f)] = (fd2-fd1) PH(fd1,f)

PH is the Doppler-frequency cross-power spectral density

Doppler-delay scattering function

S(fd,) RS(fd1,fd2,1,2) = [S(fd1,1)S*( fd2,2)] =(fd2-fd1) (2-1) PS(fd1,1)

PS is the Doppler-echo cross-power spectral density (= radar target scattering function )

Space variant transfer function

T(x,f) RT(x,x+x,f,f+f) = E[T(x,f) T*(x+x,f+f)] = RT(x,f)

RT(0,f) is the frequency coherence function

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WSSUS 2x2 wideband model

Ph(x,)

PH(fd,f)

RT(x,f)PS(fd,)

F

F-1F

F-1

F

F-1F

F-1

WSSUS reduces correlation description with two paramters pr description,

i.e. 1 parameter pr domain

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Function: pdp

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(c) Patrick Eggers 201424/11/2014 51

DIVERSITY : WHAT IS GOOD FOR?• REMEMBER????????

– Estimation of wireless communication quality• Link budget, margins etc

– Examplify dependence of differenet paramter statistics• Exploit channel knowledge in one form to predict

impact in form usable for the modem/transceievr in question

– Present fundamental limits and methods to stablilise channel (improve com’s quality)• Diversity combing vs channel decorrelation

24/11/2014 51

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(c) Patrick Eggers 201424/11/2014 5224/11/2014 52

Link margin & budget : margin <-> %• Link Budget

– Output power + Ant gain – cable losses– Path loss -> estimate/predict via models– Local mean variation -> provide ‘safety’ margin– Fast fading -> provide ‘safety’ margin– Receiver sensitivity for given spec BER or QoS

Local mean -> distribution[dB] & spatial variation dependence [m].If no other system choosen..you can use this budget as example /

starting point

40dBm

Lc=-6dB Ga=20dB Path loss Lp = -80dB

Tx PowerRx Power

-52dBm

Fading = -20dB

Shadow Ls=-6dB

MM1 MM2-5

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(c) Patrick Eggers 201424/11/2014 53

Diversity definition

• Idea: Repair through redundancy

• Transmit/ receive several replicas of the same information signal over (uncorrelated)channel conditions

• Correlation coefficient used as figure of merit2

complexpwrenv

2222

**

complex

vEvEuEuE

vEuE]E[uvρ

Complex : u,v Power : |u|2, |v|2 Envelope : |u|,|v|

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(c) Patrick Eggers 201424/11/2014 54

Diversity combiners

• Selection: 1 branch active

• Summation: All branches active– Pre or post detection

• Criteria– Noise (RSSI)

– Interference (RSSI, ISI)

– Time dispersion (ISI)

?? How would you detect time dispersion problems in a radio modem?

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(c) Patrick Eggers 201424/11/2014 55

Selection (ONE branch active)

• IDEA: PICK THE BEST• Pure selection• Threshold selection

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(c) Patrick Eggers 201424/11/2014 56

Other selection criteria

? Is there a yet simpler form .. May not requiring two full receivers??

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(c) Patrick Eggers 201424/11/2014 57

Gain combining (ALL branches active)• Equal gain

combining• Maximal ratio combining

Cophasing & summing

r1

G

r2

G

rM

G

Cophasing & summing

r1

a1

r2

a2

rM

aM

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(c) Patrick Eggers 201424/11/2014 58

MRC: the math

M

iiout

i

iopti

M

iii

x

M

iii

M

iii

M

iii

x

M

iii

M

iii

M

iii

M

iii

iii

SNRSNR

N

ra

Na

Era

SNR

NanaEnoise

EraxraEsignal

naxray

nxry

1

*

1

2

2

1

1

22

1

2

1

2

1

11

,

If all Ni=N, i.e. noise floor equal

This reduces easily .. How?

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(c) Patrick Eggers 201424/11/2014 59

Mean gain (distribution shift)

M

kdiv k

snrsnr1

1

Selection vs. summing! (i.e. single branch active or all branches active ata time) Reference case : All SNR=equal, all env=0. RAYLEIGH FADING !!!!

Selection r = max(r1..rM) multi Rx (switch, scanning => single Rx):

Max. ratio p= ri2 ; multi Rx : weighted (with <SNR>) coherent addition

Equal gain r = ri /(MN) ; Multi Rx : coherent addition

(only 1.05dB difference to equal gain for M->)

41 11; MsnrsnrM

rr div

M

k k

r a r snr snr M SNRk kk

M

kk

M

1 1;

a r n r Nk k k k / /2

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(c) Patrick Eggers 201424/11/2014 60

Instant gain (distribution compression)

• Selection combining

• Maximum ratio combining (max output snr)

• Equal gain combining, M=2

M

ssksdivM

ssk

snr

snrksnrsnrsnrsnrP

snr

snrsnrsnr

snr

snr

snrsnrp

exp1,Pr

exp1Pr,exp1

M

k

k

s

ssdivM k

snr

snr

snr

snrsnrsnrP

1

1

!1exp1

sssssdiv snrerfsnrsnrsnrsnrsnrP exp2exp12 Reference case : All SNR=equal, all env=0. RAYLEIGH FADING !!!!

N

ra

aN

ra

N

rsnr k

kM

k k

M

k kk

total

R ;2

1

2

2

12

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(c) Patrick Eggers 201424/11/2014 61

Comparison of MRC and SC

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(c) Patrick Eggers 201424/11/2014 62

How does diversity affect the BER

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