Opportunistic Cooperation for FSO Links Aided by Decode and Forward - - PowerPoint PPT Presentation

Opportunistic Cooperation for FSO Links Aided by Decode and Forward Relay

Michael (Qunfeng) He*, Zhengyuan Xu+

*Department of Electrical Engineering

University of California, Riverside

+Department of Electronic Engineering

Tsinghua University, China

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Outline

2



Motivations and Setup



Problem Formulation and Signal Model



Channel Model



Link Outage Analysis: DT, dDF and oDF



Numerical Results

Motivations and Setup

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 Motivations

 FSO link in IR wavelength is challenged by turbulence  Traditional approaches: time and spatial diversity  Recent advances: user cooperation in Poisson domain [Karimi 09], [Abou-Rjeily 11]

 Our work: Gaussian noise assumption, opportunistic relay [Safari 08]

 System setup

 DT phase: S-R & S-D  DF phase: S-D or R-D (conditional)  R-S: CSI feedback link

 Categories

 Non-cooperation (Direct transmission)  Deterministic cooperation  Opportunistic cooperation

A three-way FSO network for opportunistic cooperation.

Problem Formulation and Signal Model

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 Problem formulation: outage probability of a FSO link

 Characterize the outage over fading channel  Given SNR, the instantaneous rate  Probabilistic event s.t. R meets required R0

 SNR model

 Consider binary PPM,  Electrical SNR

(1) (2) (3)

𝑆 = 𝑚𝑝𝑕2(1 + 𝑇𝑂𝑆) 𝑄𝑝𝑣𝑢 𝑆0 = 𝑄

𝑠 𝑚𝑝𝑕2 1 + Γ < 𝑆0 = 𝑄 𝑠 Γ < Γ𝑢ℎ

𝑠

𝑂𝐷 =

𝑠𝑇𝑂𝐷 𝑠𝑜𝑂𝐷 = 𝑄𝑡𝑕𝑡𝑒 + 𝑆𝑈𝑡𝑄𝑐 + 𝑜𝑡𝑒 𝑆𝑈𝑡𝑄𝑐 + 𝑜𝑜𝑒

Γ =

𝜈𝑡−𝜈𝑜 2 𝜏2

𝑜

Γ𝑂𝐷 =

𝑄𝑡𝑕𝑡𝑒

2

𝜏2

𝑜

Channel Model

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 Channel coefficient, described by [Safari 08]

 Path loss:  Turbulence model, weak turbulence: log-normal distribution

 Outage probability of a DT FSO link

 Plugging SNR and fading models

(4) (5) (6) (7)

𝒉 = 𝜷𝟑𝑴(𝒆) 𝑀 𝑒 = 𝐵𝑠 Ω𝑒 2 exp (−𝜊𝑒) 𝑔(𝛽) = 1 2𝜌𝜏𝑦

2𝛽

exp (− 𝑚𝑜𝛽 − 𝜈𝑦 2𝜏𝑦

2

)

𝜏𝑦

2 𝑒 = 0.124𝑙

7 6𝐷𝑜

2 𝑒

11 6

𝑄𝑝𝑣𝑢, 𝐸𝑈 = 𝑄

𝑠 Γ < Γ𝑢ℎ = Pr 𝛽𝑡𝑒 2 <

Γ𝑢ℎ𝜏𝑜2 (𝑀𝑡𝑒𝑄𝑡)2

= Q

ln 𝐿𝑡𝑒,𝑢ℎ,𝐸𝑈 −2𝜏𝑦

2(𝑒𝑡𝑒)

2𝜏𝑦(𝑒𝑡𝑒)

𝑄𝑝𝑣𝑢, 𝑒𝐸𝐺 = Q ln 𝐿𝑡𝑒, 𝑢ℎ, 𝑒𝐸𝐺 − 2𝜏𝑦

2(𝑒𝑡𝑒)

2𝜏𝑦(𝑒𝑡𝑒) . 1 − 1 − Q ln 𝐿𝑡𝑠, 𝑢ℎ, 𝑒𝐸𝐺 − 2𝜏𝑦

2(𝑒𝑡𝑠)

2𝜏𝑦(𝑒𝑡𝑠) 1 − Q ln 𝐿𝑠𝑒, 𝑢ℎ, 𝑒𝐸𝐺 − 2𝜏𝑦

2(𝑒𝑠𝑒)

2𝜏𝑦(𝑒𝑠𝑒)

A Deterministic Cooperative FSO Link

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 Deterministic cooperation: dDF

 Parallel links in nature: S-D and S-R-D  Outage happens when both paths fail

 Outage of dDF:

 Assume the same signal expressions

(8) (9) (10)

𝑄𝑝𝑣𝑢, 𝑒𝐸𝐺 = 𝑄𝑝𝑣𝑢, 𝑡𝑒, 𝐸𝑈 𝑄𝑝𝑣𝑢, 𝑡𝑠𝑒, 𝐸𝐺

where, 𝑄𝑝𝑣𝑢, 𝑡𝑠𝑒, 𝐸𝐺 = 1 − (1 − 𝑄𝑝𝑣𝑢, 𝑡𝑠)(1 − 𝑄𝑝𝑣𝑢, 𝑠𝑒)

 Outage probability for opportunistic cooperation of FSO links  Each component can be retrieved from prev. analysis

 Obtaining the signal representation  Developing the SNR  Applying the outage probability expression

 Numerical study

 Direct computation on analytical outage probability equations  Monte-Carlo simulation on SNR and numerical outage probability  Compare above results to validate the analysis

𝑄𝑝𝑣𝑢, 𝑝𝐸𝐺 = 𝑄𝑝𝑣𝑢, 𝑡𝑠𝑄𝑝𝑣𝑢, 𝑝𝐸𝐺 − 𝐸𝑈 + 1 − 𝑄𝑝𝑣𝑢, 𝑡𝑠 𝑄𝑝𝑣𝑢, 𝑝𝐸𝐺 − 𝐸𝐺

An Opportunistic Cooperative FSO Link

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Numerical Results (1)

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 A special case where relay lies on the middle point of S-D

 To verify cooperation does improve the link  Contrast the analytical form against Monte-Carlo simulation

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10 PtotTb, dBJ NC, Analytical NC, Numerical dDF Coop, Analytical dDF Coop, Numerical

• DF Coop, Analytical
• DF Coop, Numerical

Outage performance of opportunistic FSO system aided by DF relay, dsr= drd= 500m,dsd= 1000m.

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 Increasing the S-R separation, equivalent to downgrading the S-R quality

 Opportunistic cooperation excels deterministic version in high power regime  Opportunistic cooperation has wider adaptability  There exists an range within which cooperation is applicable

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10 PtotTb, dBJ NC, Analytical NC, Numerical dDF Coop, Analytical dDF Coop, Numerical

• DF Coop, Analytical
• DF Coop, Numerical

Outage performance of opportunistic FSO system aided by DF relay, dsr= drd= dsd= 1000m.

Numerical Results (2)

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 Checking the outage performance on multiple separations of S-R

Outage performance of opportunistic cooperation vs. S-R link distance, drd= dsd= 1000m.

Numerical Results (3)

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rsr, meters dDF Coop, MC

• DF Coop, MC

Thank you!