MIMO-OFDM Wireless Communications with MATLABMIMO-OFDM Wireless Communications with MATLAB® Yong Soo Cho | Jaekwon Kim Won Young Yang | Chung G. Kang Chapter 1. The Wireless Channel

MIMO-OFDM

Wireless

Communications

with MATLAB®

Yong Soo Cho | Jaekwon Kim

Won Young Yang | Chung G. Kang

Chapter 1. The Wireless Channel :

Propagation and Fading

Page ▪ 2MIMO-OFDM Wireless Communications with MATLAB®

Yong Soo Cho, Jaekwon Kim, Won Young Yang, and Chung G. Kang

© 2010 John Wiley & Sons (Asia) Pte Ltd

Chapter 1. Kablosuz Kanal: Yayılım ve Sönümlenme

▪Reflection:

▪Diffraction

▪Scattering

▪Fading

▪Multipath fading

▪Shadowing




Chapter 1. Kablosuz Kanal: Yayılım ve Sönümlenme

▪ 1.1 LARGE-SCALE FADING

- 1.1.1 General Path Loss Model

- 1.1.2 Okumura/Hata Model

- 1.1.3 IEEE 802.16d Model

▪ 1.2 SMALL-SCALE FADING

- 1.2.1 Parameters for Small-Scale Fading

- 1.2.2 Time-Dispersive vs. Frequency-Dispersive Fading

- 1.2.3 Statistical Characterization and Generation of Fading Channel




Chapter 1. Kablosuz Kanal

Figure 1.1 Sönümlü Kanalların Sınıflandırması





Figure 1.2 Large-scale fading vs. small-scale fading





Figure 1.3 Link budget for the fading channel(1994 IEEE. Reproduced from Greenwood, D. and Hanzo, L.,

“Characterization of mobile radio channels,” in Mobile Radio Communications, R. Steele(ed.), pp. 91–185,1994,

with permission from Institute of Electrical and Electronics Engineers (IEEE).)




1.1 Büyük Çağlı Sönümlenme1.1.1 Genel Yol Kaybı Modeli

▪ ( )

2

2 2( )

4

t t r

r

PG GP d

d L

= (1.1)

( )

2

2 2( )[ ] 10log 10log

4

t t r

F

r

P G GPL d dB

P d

= = −

(1.2)

( )

2

2 2( )[ ] 10log 10log

4

t

F

r

PPL d dB

P d

= = −

(1.3)




1.1.1 Genel Yol Kaybı Modeli

0

0

( )[ ] ( ) 10 logLD F

dPL d dB PL d n

d

= +

(1.4)

Figure 1.4 Free-space path loss model





Environment Path Loss Exponent ( )

Free Space 2

Urban area cellular radio 2.7 to 3.5

Shadowed urban cellular radio 3 to 5

In building Line-Of-Sight 1.6 to 1.8

Obstructed in building 4 to 6

Obstructed in factories 2 to 3

n





0

0

( )[ ] ( ) ( ) 10 logF

dPL d dB PL d X PL d n X

d

= + = + +

(1.5)

Figure 1.5 Log-distance pathloss model





Figure 1.6 Log-normal shadowing path loss model




1.1.2 Okumura/Hata Modeli

( )[ ] ( , )Ok F MU Rx Tx AREAPL d dB PL A f d G G G= + − − + (1.6)

( ), ( )[ ] 69.55 26.16log 13.82log 44.9 6.55log logHata U c Tx Rx TxPL d dB f h C h d= + − − + − (1.7)

( )0.8 1.1log 0.7 1.56logRx c Rx cC f h f= + − −(1.8)





( )( )

( )( )

2

2

8.29 log 1.54 1.1 150 200

3.2 log 11.75 4.97 200 1500

Rx c

Rx

Rx c

h if MHz f MHzC

h if MHz f MHz

− = −

(1.9)

2

, ,( )[ ] ( ) 2 log 5.428

c

Hata SU Hata U

fPL d dB PL d

= − −

(1.10)

( )2

, ,( )[ ] ( ) 4.78 log 18.33log 40.97Hata O Hata U c cPL d dB PL d f f= − + − (1.11)





Figure 1.7 Hata path loss model




1.1.3 IEEE 802.16d

( )802.16 0 10 0

0

( )[ ] 10 log forF f Rx

dPL d dB PL d C C d d

d

= + + +

(1.12)

106log ( / 2000)f cC f= (1.13)

10

10

10.8log ( / 2) for TypeAand B

20log ( / 2) for TypeC

RxRx

Rx

hC

h

−=

−(1.14)

10

10

10log ( / 3) for 3

20log ( / 3) for 3

Rx RxRx

Rx Rx

h h mC

h h m

− =

− (1.15)




1.1.3 IEEE 802.16d

Parameter Type A Type B Type C

a 4.6 4 3.6

b 0.0075 0.0065 0.005

c 12.6 17.1 20




1.1.3 IEEE 802.16d

Parameter Type A Type B Type C

a 4.6 4 3.6

b 0.0075 0.0065 0.005

c 12.6 17.1 20




1.1.3 IEEE 802.16d

' ' '0 0 0

10 10 10

0

4 420log 20log 10 log f Rx

d d dC C

d

= + + +

(1.16)

10'0 010

f RxC C

d d

+ − = (1.17)

'10 0

802.16 ''0

10 10 0

0

420log for

( )[ ]4

20log 10 log for

M

f Rx

dd d

PL d dBd d

C C d dd

=

+ + +

(1.18)




1.1.3 IEEE 802.16d

Figure 1.8 IEEE 802.16d path loss model Figure 1.9 Modified IEEE 802.16d path loss model




1.2 Küçük Çaplı Sönümlenme1.2.1 Zaman ve Frekans Yayılımlı Sönümlenme

(a) Frequency-non-selective fading channel (b) Frequency-selective fading channel

▪ Power Delay Profile

▪ Tap

▪ Relative Delay

▪ Relative average power

▪ Mean excess delay

▪ RMS Delay Spread




1.2.1 Zaman ve Frekans Yayılımlı Sönümlenme

Tap Relative delay ( ) Average Power ( )

1 0 0.0

2 110 -9.7

3 190 -19.2

4 410 -22.8

ns dB





▪ Düz sönümlenme

▪ Frekans seçici sönümlenme

▪ Mean excess delay

▪ RMS Delay Spread

2

2

( )

( )

k k k k

k k

k k

k k

a P

a P

= =

(1.21)

2 2( ) = − (1.22)

2 2 2

2

2

( )

( )

k k k k

k k

k k

k k

a P

a P

= =

(1.23)

S C

S

B B

T

(1.19)

S C

S

B B

T

(1.20)




1.2.1 Time-Dispersive vs. Frequency-Dispersive Fading

▪ Tutarlılık Bandı

▪ 0.9 ilintili tutarlılık bandı

▪ 0.5 ilintili tutarlılık bandı

▪ Hızlı sönümlenme

▪ Yavaş sönümlenme

1

50CB

(1.25)

1

5CB

(1.26)

1CB

(1.24)

S C

S D

T T

B B

(1.27)

S C

S D

T T

B B

(1.28)




1.2 Küçük Çaplı Sönümlenme1.2.1 Zaman ve Frekans Yayılımlı Sönümlenme

(a) Frequency-non-selective fading channel (b) Frequency-selective fading channel

Figure 1.10 Characteristics of fading due to time dispersion over multi-path channel





▪ Tutarlılık zamanı



1C

m

Tf

2D mB f= (1.29)

9

16C

m

Tf

(1.30)

9 0.423

16C

m m

Tf f

= = (1.31)




1.2.3 Statistical Characterization and Generation of Fading Channel

Figure 1.11 Planewave arriving at receiver moves in the direction of x with a velocity of v




1.2.3 Sönümlü Kanalın İstatistiksel Karakterizasyonu ve Üretimi

▪ Alıcıdaki sinyal

▪ Kanal modeli

▪ Yol gecikmesi sembol zamanından kısaysa

( )

1

( ) ( )i

Ij t

i i

i

y t C e x t −

=

= − ( ) ( ) 2i c i i it f f f = + − (1.35)

( )

1

( , ) ( )i

Ij t

i i

i

h t C e t −

=

= − (1.36)

( )

1

ˆ ˆ( , ) ( ) ( ) ( )i

Ij t

i

i

h t C e t h t t −

=

= − = − (1.37)





▪ Rayleigh dağılımlı olarak modellenebilir

( ) ( )cos2 ( )sin 2I c Q cy t h t f t h t f t = − (1.38)

1

( ) cos ( )I

I i i

i

h t C t=

= (1.39)

1

( ) sin ( )I

Q i i

i

h t C t=

= (1.40)

( ) ( ) ( )

( ) ( ) cos2 ( ) ( ) sin 2

( )cos2 ( )sin 2I I I Q

yy

I I Q I

h h c h h c

E y t y t

E h t h t f E h t h t f

f f

= +

= + − +

= −

(1.41)





( )

,( ) ( ) ( ) cos 22

cos 2 cos2

I I i

p

h h I I i

p

m

E h t h t E f

E f

= + =

=

τ θ

(1.42)

( ),( ) ( ) ( ) sin 2 cos2I Q

p

h h I Q mE h t h t E f

= + = τ θ(1.43)

1 2

1 2

2 2 2

1

, , ,

, , ,

( ) ( )

I

I

I

p I Q i

i

E h t E h t C

=

=

=

= + =

τ

θ (1.44)





( ) ( ) ( )

( ) ( )0

( ) cos 2 cos2

1cos 2 cos 2

2 2 2

I I

p

h h m

p p

m m

f p G d

f d J f

−

−

=

= =

(1.45)

( )1

( ) sin 2 cos 02 2I Q

p

h h mf d

−

= = (1.46)

( )0

( ) ( )cos 2 sin 2

2 cos 22

I I I Qyy h h c h h c

p

m c

f f

J f f

= −

=

(1.47)





▪ Klasik Doppler skeptrumu

( )2

1

2( ) ( ) ( ) 1 /

0 otherwise

I I Q Q I I

p

m

mh h h h h h m

f ffS f S f F t f f

= = =

(1.48)

*1( ) ( ) ( )

2

( ) ( )I I I Q

hh

h h h h

E h t h t

j

= +

= +

(1.49)

( ) ( ) ( )I I I Qhh h h h hS f S f jS f= + (1.50)





2( ) Re ( ) cj f

yy hh e =

*

Re2

a aa

+=

*( ) ( )hh hh = −

( ) ( )2

1

41( ) 1

2

0 otherwise

p

c m

mc

yy hh c hh c

m

f f ff

f fS f S f f S f f

f

−

− = − + − + = −

(1.51)

(1.52)

(1.53)

(1.54)





( ) ( ) ( ) ( ) ( )4

p

yyS f df G p G p d

= + − − (1.55)

( )22sinm m cdf f d f f f d = − = − − (1.56)

( )( ) ( ) ( ) ( )

22

4( )

p

yy

m c

S f G p G p

f f f

= + − −

− −

(1.57)





▪ Rice sönümlenmesi

( ) ( ) ( )0

1

1 1

Kp p

K K = + −

+ +

2

22

cK

=

( ) ( )0

1( ) 2 cos 2 cos

1 2 1 2I I

p p

h h m m

KJ f f

K K

= +

+ +

(1.58)

(1.59)

(1.60)





( )( ) sin 2 cos1 2I Q

p

h h m

Kf

K

=

+(1.61)

( )( )0

2

1( ) ( ) ( )

1 1

1 1cos

1 2 1 21

0

c d

hh hh hh

p p

m m

mm

KS f S f S f

K K

Kf f f f

K f Kf f

otherwise

= ++ +

+ −

+ += −

(1.62)

Documents

MIMO-OFDM Wireless Communications with MATLABMIMO-OFDM Wireless Communications with MATLAB® Yong Soo Cho | Jaekwon Kim Won Young Yang | Chung G. Kang Chapter 1. The Wireless Channel