multinode cooperative communications with generalized combining schemes

Republic of TunisiaMinistry of High Education, Scientific Research and Technology

University of Carthage

Tunisia Polytechnic School

Option:SIGNALS AND SYSTEMS (SISY)

Graduation Project Presentation

Multinode Cooperative Communicationswith Generalized Combining Schemes

Carried out by : Amir HADJTAIEB

Supervised by: Dr. Mohamed-Slim ALOUINIDr. Hatem BOUJEMAADr. Ferkan YILMAZ

Vis-a-vis: Dr. Issam MABROUKI

June 27, 2012

Multinode RelayingIncremental Relaying

Joint Adaptive modulation and incremental RelayingSummary

Introduction

Figure : Services evolution over time

Amir HADJTAIEB - Graduation Project Presentation 2 / 29



Outline

1 Multinode RelayingSystem model and protocol descriptionSymbol Error Rate: MRC caseSymbol Error Rate: GSC case

2 Incremental RelayingProtocol descriptionSymbol Error RateAverage number of time slots per burst

3 Joint Adaptive modulation and incremental RelayingProtocol descriptionSymbol Error Rate

4 Summary




System model and protocol descriptionSymbol Error Rate: MRC caseSymbol Error Rate: GSC case

Outline




4 Summary





System Model

hS,R hR,D

hS,D

Source Destination

Relay

Figure : System model

Slow and frequency-flat fading channel with additive white Gaussiannoise

No inter relay interference is considered

hS,D, hS,R and hR,D are channel fading coefficients.





Protocol description

· Reception

…...

· Forwarding

…...S

R1

Rk

RN

D

Rk-1 Rk+1

…...…...S

R1

Rk

RN

D

Rk-1 Rk+1

Figure : Protocol description in phase k

Arbitrary N-relay wireless network

Combining scheme: Maximum Ratio Combining(MRC) or GeneralizedSelection Combining(GSC)

Cooperation strategy: selective decode and forward





General expression of SER

Simplifying assumption

Relay

. . . .

Relay 1 Relay 2 Relay3 Relay N

Network

state SNBx,N= 1 1 0 1

Forwards : 1

Remains idle: 0

Probability that the network is in a given state

Pr(SN = Bi,N ) = Pr(SN [1] = Bi,N [1]

)× Pr

(SN [2] = Bi,N [2]

∣∣∣ SN [1] = Bi,N [1])

× . . .

× Pr(SN [N ] = Bi,N [N ]

∣∣∣ SN [N − 1] = Bi,N [N − 1], ..., SN [1] = Bi,N [1])






Probability that the kth relay is in a given state

Pk,i , Pr(SN [k] = Bi,N [k]∣∣ SN [k − 1] = Bi,N [k − 1], ..., SN [1] = Bi,N [1])

=

{Ψ(SNRRk ), if Bi,N [k]=0

1 − Ψ(SNRRk ), if Bi,N [k]=1

where ΨPSK(γ) ,1

π

∫ (M−1)π/M

0

exp

(− bPSKγ

sin2(θ)

)dθ

Instantaneous SER

Pe/CSI =

2N−1∑i=0

Pr(e∣∣ SN = Bi,N )Pr(SN = Bi,N )

Pr(e∣∣ SN = Bi,N ) = Ψ(SNRd)

Pr(SN = Bi,N ) =

N∏k=1

Pk,i






Probability that the kth relay is in a given state

Pk,i , Pr(SN [k] = Bi,N [k]∣∣ SN [k − 1] = Bi,N [k − 1], ..., SN [1] = Bi,N [1])

=

{Ψ(SNRRk ), if Bi,N [k]=0

1 − Ψ(SNRRk ), if Bi,N [k]=1

where ΨPSK(γ) ,1

π

∫ (M−1)π/M

0

exp

(− bPSKγ

sin2(θ)

)dθ

Instantaneous SER

Pe/CSI =

2N−1∑i=0

Pr(e∣∣ SN = Bi,N )Pr(SN = Bi,N )

Pr(e∣∣ SN = Bi,N ) = Ψ(SNRd)

Pr(SN = Bi,N ) =N∏k=1

Pk,i






Average SER

PSER =

2N−1∑i=0

ECSI[

Ψ(SNRd)] N∏k=1

ECSI[Pk,i

]where ECSI is expectation operator





Results for Rayleigh fading channel

0 5 10 15 20 2510

−10

10−8

10−6

10−4

10−2

100

P/N0

BE

R

N = 3

N = 2

N = 1

N = 0

Figure : BER versus SNR for different number of relays





SER expression

SER of one relay

Ps(E) =L∑

i1,i2,...,iL=1

i1 6=i2 6=,... 6=iL

1

π

∫ (M−1π/M)

0

L∏l=1

γil−1∑l

k=1 γik−1

×

(sin2 θ

gMPSKmin(l, Lc)(∑l

k=1 γik−1)−1

+ sin2 θ

)dθ

SER at destination

PGSC(E) =

2N−1∑i=0

PD(E∣∣ SN = Bi,N )

N∏k=1

Pk,i

where Pk,i =

{PRk (E), if Bi,N [k]=0

1 − PRk (E), if Bi,N [k]=1






0 5 10 15 20 2510

−12

10−10

10−8

10−6

10−4

10−2

100

Average SNR per Bit of first path[dB]

BE

R

Lc = 1

Lc = 2

Lc = 3

Figure : BER versus SNR of first path for different values of Lc, L = 3 and δ =0.2 γl = γ1 exp(−δ(l − 1)), l = 1,..., L, where δ is the power decay factor.




Protocol descriptionSymbol Error RateAverage number of time slots per burst

Outline




4 Summary






Phase 0

…...…...

S

R1

Rk

RN

D

Rk-1 Rk+1

Figure : Protocol description






After k phases

…...…...

S

R1

Rk

RN

D

Rk-1 Rk+1

Sent in phase 0

Sent in phase 1Sent in phase (k-1)







if γSD + ∑ k-1 γRiD < ζ

…...…...

S

R1

Rk

RN

D

Rk-1 Rk+1

Feedback







Phase k

…...…...

S

R1

Rk

RN

D

Rk-1 Rk+1







phase N

…...…...

S

R1

Rk

RN

D

Rk-1 Rk+1

Sent in phase 0

Sent in phase 1Sent in phase (k-1) Sent in phase (k+1)

Sent in phase N

Sent in phase k






Instantaneous SER

Instantaneous SER

Pe/CSI =

N∑l=0

2l−1∑i=0

Pr(e∣∣ Sl = Bi,l, phase = l) × Pr(Sl = Bi,l

∣∣ phase = l)

× Pr(phase = l)

Pr(e∣∣ Sl = Bi,l, phase = l) = Ψ(SNRd)

Pr(Sl = Bi,l∣∣ phase = l) =

N∏k=1

Pk,i

Pr(phase = l) =

Pr(γSD > ξ), if phase=0

Pr(γl > ξ , γl−1 < ξ), if phase=1,...,(N-1)

Pr(γN−1 < ξ), if phase=N





Average SER

PSER =Pr(γSD > ξ)E1(Ψ(SNRd))

+

N−1∑l=1

2l−1∑i=0

Pr(γl > ξ , γl−1 < ξ)k∏j=1

E∗(P lj,i)El(Ψ(SNRd))

+

2N−1∑i=0

Pr(γN−1 < ξ)

N∏j=1

E∗(PNj,i)EN (Ψ(SNRd))

where : E0(Ψ(γ)) =

∫ ∞0

Ψ(γ)fγSD (γ∣∣ γSD > ξ)dγ

El(Ψ(γ)) =

∫ ∞ξ

Ψ(γ)fγl(γ∣∣ γl−1 < ξ)dγ , 1 ≤ l ≤ N − 1

EN (Ψ(γ)) =

∫ ∞0

Ψ(γ)fγN (γ∣∣ γN−1 < ξ)dγ

E∗(P lk,j) =

∫ ∞0

P lk,jfγk−1(γ)dγ






2 4 6 8 10 12 14 1610

−5

10−4

10−3

10−2

10−1

100

SNR[dB]

BE

R

exact BERsimulated BER

ξ = 6 dB

ξ = ∞

ξ = 4.7 dB

ξ = 3dB

ξ = −∞

Figure : BER versus SNR in incremental relaying for different threshold values.The number of relays equals to 3 and the modulation scheme is BPSK





General expression

General expression

Np =

N+1∑l=1

2l−1−1∑i=0

l P r[Np = l∣∣ Sl−1 = Bi,l−1]

l−1∏k=1

E∗(P lk,i)

where : P lk,i = Pr(Sl−1 = Bi,l−1

∣∣ phase = l)

Pr[Np = 1] = Pr(γSD > ξ)

Pr[Np = l∣∣ Sl−1 = Bi,l−1] = Pr(γl−1 > ξ, γl−2 < ξ) , 2 ≤ l ≤ N

Pr[Np = N + 1∣∣ SN = Bi,N ] = Pr(γN−1 < ξ)






2 4 6 8 10 12 14 161

1.5

2

2.5

3

3.5

4

SNR[dB]

Ave

rage

num

ber

of ti

me

slot

s

exactsimulation

ξ = 3 dB

ξ = 6 dB

ξ = 10 dB

Figure : Average number of time slots per burst versus SNR for different thresholdvalues. The number of relays equals to 3 and the modulation scheme is BPSK






0 1 2 3 4 5 6 7 8 9 1010

−3

10−2

10−1

BE

R

0 1 2 3 4 5 6 7 8 9 101

1.5

2

2.5

3

3.5

ξ[dB]

Ave

rage

num

ber

of ti

me

slot

s

Figure : BER and average number of time slots per burst versus ξ for an SNRfixed to 10 dB. The number of relays equals to 3 and the modulation scheme isBPSK




Protocol descriptionSymbol Error Rate

Outline




4 Summary






Highest modulation (64-QAM)

ζ1Lower modulation

(16-QAM)

ζ2

Lowest modulation (4-QAM)

ζ3







0 5 10 15 20 2510

−4

10−3

10−2

10−1

100

SNR[dB]

BE

R

Figure : BER of incremental relaying(blue) for ξ = 25dB and joint adaptivemodulation and incremental relaying(red) for ξ = [25dB 4dB 1.6dB] versus SNR.




Outline




4 Summary




Summary

Summary

Study of different relaying techniques with different strategies

Performance analysis of multinode incremental relaying

Effect of adaptive modulation on performance of multinodeincremental relaying

Extensions

Use of other combining schemes in incremental relaying protocol

Performance analysis of amplify and forward incremental relayingprotocol.
