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

Source Destination

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

Rk-1 Rk+1

…...…...S

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 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])

Simplifying assumption

. . . .

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

∫ (M−1)π/M

(− bPSKγ

sin2(θ)

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

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

∫ (M−1)π/M

(− bPSKγ

sin2(θ)

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

Average SER

PSER =

2N−1∑i=0

Ψ(SNRd)] N∏k=1

ECSI[Pk,i

]where ECSI is expectation operator

Results for Rayleigh fading channel

0 5 10 15 20 2510

10−8

10−6

10−4

10−2

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

∫ (M−1π/M)

L∏l=1

γil−1∑l

k=1 γik−1

(sin2 θ

gMPSKmin(l, Lc)(∑l

k=1 γik−1)−1

+ sin2 θ

SER at destination

PGSC(E) =

2N−1∑i=0

PD(E∣∣ SN = Bi,N )

N∏k=1

where Pk,i =

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

1 − PRk (E), if Bi,N [k]=1

SER expression

SER of one relay

Ps(E) =L∑

i1,i2,...,iL=1

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

∫ (M−1π/M)

L∏l=1

γil−1∑l

k=1 γik−1

(sin2 θ

gMPSKmin(l, Lc)(∑l

k=1 γik−1)−1

+ sin2 θ

SER at destination

PGSC(E) =

2N−1∑i=0

PD(E∣∣ SN = Bi,N )

N∏k=1

where Pk,i =

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

1 − PRk (E), if Bi,N [k]=1

0 5 10 15 20 2510

10−10

10−8

10−6

10−4

10−2

Average SNR per Bit of first path[dB]

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

…...…...

Rk-1 Rk+1

Figure : Protocol description

After k phases

…...…...

Rk-1 Rk+1

Sent in phase 0

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

if γSD + ∑ k-1 γRiD < ζ

…...…...

Rk-1 Rk+1

Feedback

Phase k

…...…...

Rk-1 Rk+1

phase N

…...…...

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

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

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

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

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

10−4

10−3

10−2

10−1

SNR[dB]

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

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

SNR[dB]

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

10−2

10−1

0 1 2 3 4 5 6 7 8 9 101

ξ[dB]

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)

Lowest modulation (4-QAM)

0 5 10 15 20 2510

10−3

10−2

10−1

SNR[dB]

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

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.

Multinode Cooperative Communications with Generalized Combining Schemes

Education

Ultraviolet Spectroscopy of Protein Backbone Transitions in … · 2011-12-13 · A generalized approach combining quantum mechanics (QM) and molecular mechanics (MM) calculations

A fast and accurate computational approach to protein ionization: combining the Generalized Born model with an iterative mobile cluster method

Towards a Semantic Web Unifying Logic...Matthias Knorr - CENTRIA, UNL Towards a Semantic Web Unifying Logic 11/81 Combining non-monotonic rules and DLs Top-down querying Generalized

Generalized Optimal Matching Methods for Causal Inference · mal matching (KOM), which, as supported by new theoretical and empirical results, is notable for combining many of the

Soft Generalized Separation Axioms in Soft Generalized ... · Soft Generalized Separation Axioms in Soft Generalized Topological Spaces. Jyothis Thomas and Sunil ... Soft Generalized

Generalized Hopfield Networks and Nonlinear …papers.nips.cc/paper/280-generalized-hopfield-networks...Generalized Hopfield Networks and Nonlinear Optimization 355 Generalized Hopfield

Combining & No Combining

Application of Generalized Linear Models and Generalized ... · of Generalized Linear Models and Generalized Estimation Equations to model at-haulback mortality of blue sharks captured

Generalized Hough Transform. The Generalized Hough Transform

µ-Î²-generalized Î±-closed sets in generalized topological spaces

Computing Generalized Method of Moments and Generalized ... · Computing Generalized Method of Moments and Generalized Empirical Likelihood with R Pierre Chauss e Universit e du Qu

New Strategies for Combining Mindfulness with Integrative ......Introduction Generalized anxiety disorder (GAD) was regarded for several decades as a residual diagnosis to classify

MultiNode All-Electric Intelligent Well Systemthe MultiNode all-electric intelligent well system can help you achieve remote, selective flow control in an extended number of zones

Modeling Effects of Multinode Wells on Solute Transport Effects of Multinode Wells on Solute Transport by Leonard F. Konikow1 and George Z. Hornberger Abstract Long-screen wells or

Generalized Performance Characteristics of Instruments … · Generalized Performance Generalized Performance Characteristics of ... of Measuring Instrumentsof Measuring Instruments

SYmmETRY muLTiNODE m2150 iNTELLigENT CONTROLLER · 2014. 4. 24. · Symmetry AcceSS control DAtASHeet ACCESS CONTROL | muLTiNODE m2150 networK interFAce moDuleS Plug-in module that

Generalized Convexity, Generalized Monotonicity and Applications: Proceedings of the 7 th International Symposium on Generalized Convexity and Generalized Monotonicity

New Combining M odel for Ranking Generalized Fuzzy numbersijiepm.iust.ac.ir/article-1-866-fa.pdf · ³7HFKQLFDO1RWH´ New Combining M odel for Ranking Generalized A Fuzzy numbers

SYMMETRY MULTINODE M2150 INTELLIGENT CONTROLLER … · MULTINODE M2150 INTELLIGENT CONTROLLER. ... Each M2150 elevator controller supports 20,000 ... the maximum number of readers

General Linear Model General Linear Model Generalized Linear Model Generalized Linear Model Generalized Linear Mixed Model