Multiple User Pair Scheduling in TWR Assisted FSO Systems

Parul Puri; Parul Garg; Mona Aggarwal

doi:10.1364/JOCN.8.000290

Journal of Optical Communications and Networking
Vol. 8,
Issue 5,
pp. 290-301
(2016)
•https://doi.org/10.1364/JOCN.8.000290

Multiple User Pair Scheduling in TWR Assisted FSO Systems

Parul Puri, Parul Garg, and Mona Aggarwal

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Parul Puri, Parul Garg, and Mona Aggarwal, "Multiple User Pair Scheduling in TWR Assisted FSO Systems," J. Opt. Commun. Netw. 8, 290-301 (2016)

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Abstract

In this paper, various multiuser scheduling schemes are applied to a two-way relay (TWR) assisted multiple user pair free-space optical (FSO) communication network, when the optical beam is subjected to path loss, misalignment errors, and atmospheric turbulence. The FSO network consists of a single, half-duplex, decode-and-forward, two-way optical relay that serves multiple user pairs by employing a scheduler. Three types of schedulers based on absolute signal-to-noise ratio (SNR), normalized SNR, and selective multiuser diversity are considered. Further, the atmospheric turbulence is modeled by a recently proposed statistical model, namely the Málaga $M$ –distribution. For the presented system and channel models, closed-form and asymptotic expressions for outage probability and bit error rate are derived. The mathematical analysis is accompanied by Monte Carlo simulations and several numerical examples to illustrate the effect of the key system parameters.

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Notation	Meaning
$H_{l}$	Path loss
$H_{a}$	Atmospheric turbulence
$H_{p}$	Pointing errors
$H$	Channel state information
$R$	Responsivity of photodetector
$η_{e}$	Quantum efficiency of photodetector
$L$	Link length
$C_{n}^{2}$	Refractive index structure constant
$σ$	Attenuation coefficient
$α$	Large-scale scintillation parameter
$β$	Small-scale scintillation parameter
$ρ$	Scattering power coupled to the LOS component
$γ^{'}$	Average power of independent scatter component
$2 b_{0}$	Average power of total scatter components
$Ω$	Average power of LOS component
$Ω^{'}$	Average power from coherent contributions
$A$	$M$ –distribution parameter
$σ_{R}^{2}$	Rytov variance
$r$	Aperture radius
$w_{e}$	Equivalent beam-width radius
$σ_{s}$	Standard deviation of pointing error displacement
$ξ$	Pointing error parameter
$σ_{n}^{2}$	Variance of noise power
$Γ_{S, u}$	Instantaneous SNR of intermediate link
$Ω_{u}$	Instantaneous SNR of $u$ th end–end link
${\bar{γ}}_{S, u}$	Average electrical SNR
$γ_{th}$	Threshold SNR
$f_{X} (\cdot)$	PDF of random variable $X$
$F_{X} (\cdot)$	CDF of random variable $X$
$Γ (\cdot)$	Gamma function
$Γ (\cdot, \cdot)$	Complementary incomplete gamma function
$K_{v} (\cdot)$	Modified Bessel function of second kind and order $v$
$G_{p, q}^{m, n} (\begin{matrix} {x \|}_{b_{1}, \dots, b_{q}}^{a_{1}, \dots, a_{p}} \end{matrix})$	Meijer’s G-function

Modulation Scheme	$b$	$a$
Coherent binary frequency shift keying	0.5	0.5
Coherent binary phase shift keying	0.5	1
Non-coherent binary frequency shift keying	1	0.5
Differential binary phase shift keying	1	1

Notation	Meaning
$H_{l}$	Path loss
$H_{a}$	Atmospheric turbulence
$H_{p}$	Pointing errors
$H$	Channel state information
$R$	Responsivity of photodetector
$η_{e}$	Quantum efficiency of photodetector
$L$	Link length
$C_{n}^{2}$	Refractive index structure constant
$σ$	Attenuation coefficient
$α$	Large-scale scintillation parameter
$β$	Small-scale scintillation parameter
$ρ$	Scattering power coupled to the LOS component
$γ^{'}$	Average power of independent scatter component
$2 b_{0}$	Average power of total scatter components
$Ω$	Average power of LOS component
$Ω^{'}$	Average power from coherent contributions
$A$	$M$ –distribution parameter
$σ_{R}^{2}$	Rytov variance
$r$	Aperture radius
$w_{e}$	Equivalent beam-width radius
$σ_{s}$	Standard deviation of pointing error displacement
$ξ$	Pointing error parameter
$σ_{n}^{2}$	Variance of noise power
$Γ_{S, u}$	Instantaneous SNR of intermediate link
$Ω_{u}$	Instantaneous SNR of $u$ th end–end link
${\bar{γ}}_{S, u}$	Average electrical SNR
$γ_{th}$	Threshold SNR
$f_{X} (\cdot)$	PDF of random variable $X$
$F_{X} (\cdot)$	CDF of random variable $X$
$Γ (\cdot)$	Gamma function
$Γ (\cdot, \cdot)$	Complementary incomplete gamma function
$K_{v} (\cdot)$	Modified Bessel function of second kind and order $v$
$G_{p, q}^{m, n} (\begin{matrix} {x \|}_{b_{1}, \dots, b_{q}}^{a_{1}, \dots, a_{p}} \end{matrix})$	Meijer’s G-function

Modulation Scheme	$b$	$a$
Coherent binary frequency shift keying	0.5	0.5
Coherent binary phase shift keying	0.5	1
Non-coherent binary frequency shift keying	1	0.5
Differential binary phase shift keying	1	1

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Journal of Optical Communications and Networking