Spectral Efficiency of Multihop Cellular I will answer ...Spectral Efficiency of Multihop Cellular...

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Spectral Efficiency of Multihop Cellular Systems and Cooperative Networks

Spectral Efficiency of Multihop Cellular Systems and Cooperative Networks

Asst. Prof. Koji Yamamoto, Ph. D.Graduate School of Informatics, Kyoto University

Asst. Prof. Koji Yamamoto, Ph. D.Graduate School of Informatics, Kyoto University

Multihop Networks Multihop Cellular

Cooperative Networks

2

Kyoto University Yoshida laboratory

I will answer these questions.

1. Multihop networks– Coverage can also be extended by using rate adaptation. Under

what conditions does multihop transmission really achieve higher spectral efficiency compared to lower rate transmission?

2. Multihop cellular systems– Does the correlation of shadowing degrade the performance of

multihop-type cellular systems?

3. Cooperative networks– Simultaneous transmissions in cooperative relaying increase

interference. Does introduction of cooperative relaying in interference-limited environments really enhance the performance?

1. Multihop Networks

4


Single-Isolated Multihop Transmission• Multihop transmissions

– Regenerative relaying– Path loss can be reduced

r α → (r/n) αn：Number of hopsα： path loss coefficient (2～4)

Transmit power can be reduced• Through use of rate adaptation,

coverage can also be enhanced

36Mbps

24Mbps

36Mbps

Rate adaptation

Multihop transmission

MAC (efficiency: 100%) → 18Mbps

Throughput of multihop transmission taking into account rate adaptation

Under what situation multihop transmissions are effective?

5


Rate Adaptation

• Adaptive modulation (M-ary QAM) (Quadrature Amplitude Modulation) [A]

• Symbol rate control [B]– K consecutive transmissions of QPSK

(Quadrature Phase Shift Keying) symbols– Required CINR→1/K

⎩⎨⎧

≤≤+<≤

=1112

111b1 /63/3)1(log

/34/33/2),(

βγβγββγβγβ

γ pf¼-rate QPSK～QPSK

QPSK～64QAM

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30

1/4-rate QPSK1/2-rate QPSK

full-rate QPSK

full-rate 16QAM

full-rate 64QAM

Shannon capacity

BER=10-3

BER=10-6

Ban

dwid

th e

ffici

ency

(bp

s/H

z)

Received CINR γ (dB)

Upper bound

(1)

[A] A.J. Goldsmith and S.G. Chua, IEEE Trans. Commun., vol.45, no.10, pp.1218–1230, Oct. 1997.

t1

1

End-to-end CNR:γ Required BER: pb

β1=−1.5/ln(5pb)

[B] T. Ue, et al., IEEE Trans. Veh. Technol., vol.47, no.4, pp.1134–1147, Nov. 1998. 6


n-hop transmission： Equally spaced (n-1) relaying nodes (best routing)Same transmit power, one channel, half-duplexOnly one node can transmit at a time (no spatial channel reuse)

BE of single-isolated n-hop route

Multihop Transmission

n1 n/

Error is additive(Regenerative relaying)

t

1 2 n

12

n

t

t

Single-hop transmission

t1

1

),( b1 pf γ

End-to-end CNR:γ Required BER: pb

α： path loss exponent (2～4)nαγ , pb/n

),(),( b1b pfpfn γγ = αn

7


BE of single-isolated n-hop route (cont’d)

• Both multihop relaying and symbol rate control can increase communication range at the loss of BE.

• Transmission with maximum power is effective in terms of BE.

• Under the condition that multihop relaying is effective, BE is not high.

)/,(1),( b1b npnfn

pfnαγγ ⋅=

End-to-end CNR:γ BER: pb

1 2 n

0.1

1

10

–30 –20 –10 0 10 20 30

Ban

dwid

th e

ffici

ency

(bp

s/H

z)

End-to-end CNR γ (dB)

single-hop

2-hop

4-hop

8-hop

16-hop

α=3.5pb=10-3

Evaluation assuming spatial channel reuse

Short end-to-end distanceLarge Tx power

Multihop

Lower rate

8


Area Spectral Efficiency (ASE)

full-rate QPSK vs. ¼-rate QPSK

64QAM vs. QPSK

QPSK single-hop vs. QPSK two-hop

0.1

1

10

–30 –20 –10 0 10 20 30

Ban

dwid

th e

ffici

ency

(bp

s/H

z)

End-to-end CNR γ (dB)

single-hop

2-hop

4-hop

8-hop

16-hop

High rateLow density

Low rateHigh density

Assumption• Interference limited

BE through multiple hops X density of simultaneous transmissions

9


Density of simultaneous transmissions

Density of Simultaneous Transmissions

QPSK,1ρ

QPSK1,

/2QPSK

QPSK1,2)(

ργ

γ

ργρα

⎟⎟⎠

⎞⎜⎜⎝

⎛=

= zn

Assumption: Same number of hops,Interference-limited

Required power: ConstantInterference power: x zα

γ=γQPSK/zα

QPSK Single-hopRequired CIR γQPSK

Required End-to-end CIR γ

Distance between Simultaneous transmissions

is reduced to 1/z

10


0.1

1

10

0.1 1 10

α=3.5, p=10-3

4-hop

8-hop

single-hop

2-hop

Are

a sp

ectr

al e

ffici

ency

ηn,

l (γ)

(×

η 1,1

,QP

SK)

Throughput fn,l (γ) (bps/Hz)

0.1

1

10

0.1 1 10

α=3.5, p=10-3

single-hop

Are

a sp

ectr

al e

ffici

ency

ηn,

l (γ)

(×

η 1,1

,QP

SK)

Throughput fn,l (γ) (bps/Hz)

ASE vs. throughput of each route

)(),(),( ,,, γργγη lll nnn pfp ⋅=BE through multiple hops X density of simultaneous transmissions

• Trade-off between ASE and throughput

• Multihop relaying and symbol rate control have the same effect of decreasing the BE.

• Only multihop relaying can increase ASE

The use of multihop relaying is more effective than symbol rate control to construct a large wireless networks.

Multihop

Lower rate

2. Multihop Cellular

12


Multihop Cellular Systems

Transmission at a higher rate

Cell radius must be decreased

Multihop relaying

Micro-cell

BS

MS

RS(Relaying Station)

MS

W-CDMA: 384kbpsCDMA 1X EV-DO: 2.4Mbps802.11a/g: 54Mbps802.11n: 500Mbps(?)

Required Rx power increases

Tx power can be reduced

BS

MS

MS

13


Why Spatially Correlated Shadowing?• Most of early studies

– Shadowing value of each link:Location independent log-normal random variable

• Real world– Adjacent shadowing values are spatially correlated– Gudmundson's correlation model [11]– Coverage enhancement may not be achieved as expected

BS

RSMS

RS

MS

[11] M. Gudmundson, "Correlation model for shadow fading in mobile radio systems,"Electron. Lett., vol. 27, no. 23, Nov. 1991. 14


Performance Formulation [9,10]

[8] S. Sampei, Applications of Digital Wireless Technologies …, 1997.[9] K. Yamamoto, et al., ICICS2005. (Single-cell)[10] A. Kusuda, et al., PIMRC 2005. (Multi-cell)

3. Lower rate transmission

2. Multihop transmission

1. Single-hop with QPSK

MSRS

MS

• Introduction of multihop may enhance the coverage at the loss of spectral efficiency.

• Lower rate transmission have the same effect.

Commonality between multihop and rate adaptaiton

Evaluation method for rate-adaptive cellular systems [8]

+

15


Outage Probability of TDMA Cellular

γγ d )()(-A

-A ∫=kD rk frp

BER of 1/2k-1-rate < required BER

})(,0;{ req-A-A βγβγγ >>= kkD

fr(γ ): PDF of received CNR γ at distance r

BER of minimal rate does not satisfy the required BER

∫=R

K rrprR

RP0 -A2A d )( 2)(

K: upper limit of k

nmmE rr

mmn

Ef

rrp

nmm

d),,(

),,,,(

,11,0,,

00

,11,0 +∫ += γγ

θθ

K

K

K

∫+=mV mmmNmN Vrrp

RRP d),,,,(

)(1)( 0012 θθ

πK

N: upper limit of n

BER of 1,…,n-hop < required BER

Integrate over the cell area (radius: R)

BER of any multihop routes does not satisfy required BER

Rate-adaptive systems [8] Multihop systems

= =

16


Wireless Channel

• Propagation loss with path loss exponent α

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

2

2 )(ln

21exp

21)(

rfr Γ

γσσγπ

γ

dB 10 610ln/10'

～== σσ

α

ΓΓ−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

00 )()(

rrrr

Mean CNR Γ(r) and Γ(r0)

• Joint PDF of γ1,..., γl (l different paths)

⎟⎠⎞

⎜⎝⎛−= −

=∏

ZMZM

f

kk

rr1T

1

1,, 21exp

det)2(

1),,(1 l

llK K

l

γπγγ

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

22,1,

,2221,2

,12,121

lll

l

l

M

σμμ

μσμμμσ

K

MOMM

K

K⎥⎦

⎤⎢⎣

⎡=

l

lLΓγ

Γγ

Γγ lnlnln

2

2

1

1TZ

jijiijji σσρμμ ,,, ==

Correlation coefficient

Covariance matrix M

• Log-normal shadowing– local mean CNR γ

17


Correlation Coefficient

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 2lnexp

cor, d

dji

Δρ

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−= 2lnexp

cor

RT, d

ddji

ΔΔρ

[12] Z. Wang, E. K. Tameh, A. R. Nix, O. Gasparini, Proc. 11th WWRF meeting, June 2004.

[11] M. Gudmundson, Electron. Lett., vol. 27, no. 23, pp. 2145-2146, Nov. 1991.

Correlation coefficientbetween lnγi and lnγj

m(indoor)5 ,m(Urban)20cor ≈d

( )( ) ( )( )[ ]ji

jjjiiiji

ddEσσ

ΓγΓγρ

lnlnlnln ,

−−=

Decorrelation distance

18


Coverage Enhancement

1

2

3

4

5

0 1 10 100

Cov

erag

e of

mul

tihop

sys

tem

/R0

Cell size of single-hop system R0/dcor

m=1

m=2

m=5

m=10

m=20

m=50

m=100

Highly correlated Coverage is almost the same as that under

independent shadowing

R0: Single-hop coverage with QPSKdcor: decorrelation distance~ 20m(urban), 5m(indoor)

R 0:

Sing

le-h

op c

over

age

with

QPS

K

R: T

wo-

hop

cove

rage

with

QPS

K

m: # candidates for RS

10-2Required end-to-end BER β req

8 dBVariance of log-normal distributed shadowing σ0

3.5Path loss exponent α

3. Cooperative Networks

20


Multihop Transmission

Bandwidth efficiency: End-to-end bit rate through multiple hops per unit bandwidth

Low SNR 2-hop > 1-hop

Path loss exponentα=3.5

Rayleigh fading

• Regenerative relaying• Path loss can be reduced

r α → (r/n) αn：Number of hopsα： path loss coefficient (2～4)

21


Cooperative Diversity

• In some cooperative relaying, multiple stations transmit signals simultaneously

• Destination combines these signalsDiversity gain

R

S D

22


Motivation: Shannon Capacity of Cooperative Relaying [5]

[5] R.U. Nabar, et al., IEEE J. Select. Areas. Commun., vol.22, no.6, pp.1099–1109, Aug. 2004.

Noise-limited

Cooperative relaying > 1-hop, 2-hop

Path loss exponentα=3.5

Rayleigh fading

• w/o co-channel interferenceCooperative relaying > 1-hop, 2-hop

– Combining of 1-hop and 2-hop– Total transmit power is increased

• Under co-channel interference– Simultaneous transmission

# interference is increased– Spectral efficiency under interference-

limited situation

Evaluation criterion

SR

D

23


Cooperation Protocols [1]

R

S D

R

S D

Slot 1

Slot 2R

S D

R

S D

R

S D

R

S D


DF (Decode-and-Forward)

(RD,SR) (RD,R) (R,SR)

24


Carrier-to-Noise Ratio

S

D

S

R D

S

R D

S

R D

2αγ

2αγ

γ γ

2αγ

S

R D

2αγAssumption:CNR = γ

1-hop 2-hop

α: path loss exponent

Assumption: R is on the center between S and D

(RD,SR)

25


Carrier-to-Interference Ratio (Interference-limited)

S

D

S

D

S

R D

SR

D

S

R D

SR

D

S

R D

SR

D

2αγ 2αγ γ

γ/2

2αγ/2

S

R D

SR

D

2αγAssumption:CIR = γ

1-hop 2-hop

Assumption: Interference power is almost same

(RD,SR)26


Capacity Formulation [1]

R

S D

SRSR hERDRD hE

R

S D

Slot 1 Slot 2SDSD hE SDSD hE

• Instantaneous (complex) amplitude

h~CN(0,1) Circularly symmetric complex Gaussian random variable

1|| 2 =h

E: Average signal energy


27


R

S D

SRSR hE

SDSD hE

RDRD hER

S DSDSD hE

Slot 1 Slot 2

maxrelay

1

2SRSR

21||1log R

IhER ≡⎟

⎠

⎞⎜⎝

⎛+≤

max1

2

2RDRD

1

2SDSD

21||||1log R

IhE

IhER ≡⎟

⎠

⎞⎜⎝

⎛++≤

max2

2

2SDSD

22||1log R

IhER ≡⎟

⎠

⎞⎜⎝

⎛+≤

Maximal ratio combining


Interference in Slot 1

Interference in Slot 2I1 x 2Rate of Slot 1 Rate of Slot 2

28



{ }max2

maxrelaytotal21 ,min RRRRR +<+

( ) totalH

2221 detlog RRR ≡+≤+ γAAI

2211

SD2RD2

SD1

/,/

0

IIIIhh

h

==

⎥⎦

⎤⎢⎣

⎡=

λλλνλ

λA

R

S D

SRSR hE

SDSD hE

RDRD hER

S DSDSD hE

Time slot 1 Time slot 2

29


Parameters

Interference-limitedArea environment1/106fDTs

Rayleigh fading channelChannel model3.5Path loss exponent αValuesParameters

Interference is treated as additive Gaussian noiseover the channel

30


Spectral Efficiency

Noise-limited Inteference-limited

Advantage of (RD,SR) is reduced

low CIR: 2-hop is better than (RD,SR)

Assumption: R is on the middle point between S and D

RS D

31


Summary

• Spectral efficiency of fundamental cooperative relaying under interference-limited situation

– Density of simultaneoustransmission: dense 2-hop

Cooperative relayingsparse 1-hop

• Future work– Other style of cooperative relaying– Power control in cooperative relaying

32


Summary

• Under what conditions multihop transmission will really achieve higher spectral efficiency compared to lower rate transmission?– In terms of bandwidth efficiency

• Large end-to-end distance / small Tx power– In terms of area spectral efficiency

• Does the correlation of shadowing degrade the performance of multihop-type cellular systems?– No effect if single-hop coverage > 10 x decorrelation distance dcor– dcor~ 20m(urban), 5m(indoor)

• Does introduction of cooperative relaying in interference-limited environments really enhance the performance?

[A] K. Yamamoto et al., IEICE Trans. Commun., vol.E88-B, no.9, pp.3532—40, Sept. 2005.[B] K. Yamamoto et al., "Impact of Shadowing Correlation on Coverage of Multihop Cellular

Systems," Proc. ICC, June 2006.[C] K. Yamamoto et al., IEICE Technical Report AN, Oct 2007.http://yoshida.kuee.kyoto-u.ac.jp/kyamamot/

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