Performance analysis of atmospheric optical communication systems with spatial diversity affected by correlated turbulence

M. Álvarez-Roa; C. Álvarez-Roa; F. Fernández-Aragón; T. Raddo; T. Raddo; J. M. Garrido-Balsells; I. Tafur-Monroy; A. Jurado-Navas

doi:10.1364/JOCN.452044

Journal of Optical Communications and Networking
Vol. 14,
Issue 7,
pp. 524-539
(2022)
•https://doi.org/10.1364/JOCN.452044

Performance analysis of atmospheric optical communication systems with spatial diversity affected by correlated turbulence

M. Álvarez-Roa, C. Álvarez-Roa, F. Fernández-Aragón, T. Raddo, J. M. Garrido-Balsells, I. Tafur-Monroy, and A. Jurado-Navas

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M. Álvarez-Roa, C. Álvarez-Roa, F. Fernández-Aragón, T. Raddo, J. M. Garrido-Balsells, I. Tafur-Monroy, and A. Jurado-Navas, "Performance analysis of atmospheric optical communication systems with spatial diversity affected by correlated turbulence," J. Opt. Commun. Netw. 14, 524-539 (2022)

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Abstract

This paper presents a complete analytical framework for obtaining the performance associated with a free-space optical (FSO) communication system with a spatial diversity and equal gain-combining technique. The system is affected by gamma–gamma scintillations with different realistic degrees of channel correlation depending only on the physical parameters of the link. We derive new analytical closed-form expressions for the average bit error rate (ABER) considering different scenarios to provide very realistic behavior of the system including different numbers of FSO receivers in several geometric configurations, with different receiving areas, different path lengths, and a variety of turbulence conditions. Furthermore, a very accurate approximate closed-form expression is also derived for the ABER of any generic coding scheme with either a very complex or, directly, no closed-form expression for its associated conditional BER that is first obtained in the ideal case of absence of turbulence. Numerical results via Monte Carlo simulation are provided to corroborate the validity of all the derived analytical expressions.

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Code Rate	$a$	$b$	$c$
2/3	0.3870	2.7150	0.8890
6/12	0.6364	6.8958	0.8871
9/36	0.7246	42.4424	0.8600

Link Lengths	700 m	1500 m	1800 m
Link Lengths	$p \| ρ_{I}$	$p \| ρ_{I}$	$p \| ρ_{I}$
$C_{n}^{2} = 4 \times 10^{- 15}$	$0.052 \| 0.507$	$0.251 \| 0.610$	$0.316 \| 0.644$
$C_{n}^{2} = 10^{- 14}$	$0.052 \| 0.491$	$0.251 \| 0.598$	$0.316 \| 0.633$
$C_{n}^{2} = 10^{- 13}$	$\to 0 \| 0.375$	$\to 0 \| 0.375$	$\to 0 \| 0.375$

Link Length	700 m	1500 m	1800 m
Link Length	$p \| ρ_{I}$	$p \| ρ_{I}$	$p \| ρ_{I}$
$C_{n}^{2} = 4 \times 10^{- 15}$	$0.072 \| 0.517$	$0.292 \| 0.632$	$0.359 \| 0.666$
$C_{n}^{2} = 10^{- 14}$	$0.072 \| 0.502$	$0.292 \| 0.620$	$0.359 \| 0.656$
$C_{n}^{2} = 10^{- 13}$	$\to 0 \| 0.375$	$\to 0 \| 0.375$	$\to 0 \| 0.375$

$C_{n}^{2}$	$L$	$W_{e}$	Correlation Length ( $\sqrt{λ L}$ ) (Average Speckle Size)	First Fresnel Zone ( $\sqrt{L / k}$ )	Scattering Disk ( $L / (k ρ_{0})$ )	Spatial Coherence Radius ( $ρ_{0}$ )
$4 \times 10^{- 15} m^{- 2 / 3}$	700 m	2.5 cm	3.3 cm (3.3 cm)	1.31 cm	0.22 cm	8.01 cm
$4 \times 10^{- 15} m^{- 2 / 3}$	1500 m	2.53 cm	4.8 cm (4.8 cm)	1.92 cm	0.73 cm	5.07 cm
$4 \times 10^{- 15} m^{- 2 / 3}$	1800 m	2.59 cm	5.3 cm (5.3 cm)	2.11 cm	0.98 cm	4.55 cm
$10^{- 14} m^{- 2 / 3}$	700 m	2.51 cm	3.3 cm (3.3 cm)	1.31 cm	0.37 cm	4.62 cm
$10^{- 14} m^{- 2 / 3}$	1500 m	2.78 cm	4.8 cm (4.8 cm)	1.92 cm	1.26 cm	2.93 cm
$10^{- 14} m^{- 2 / 3}$	1800 m	3.20 cm	5.3 cm (5.3 cm)	2.11 cm	1.69 cm	2.62 cm
$10^{- 13} m^{- 2 / 3}$	700 m	3.51 cm	3.3 cm (1.16 cm)	1.31 cm	1.49 cm	1.16 cm
$10^{- 13} m^{- 2 / 3}$	1500 m	19.5 cm	4.8 cm (0.74 cm)	1.92 cm	5.03 cm	0.74 cm
$10^{- 13} m^{- 2 / 3}$	1800 m	31.7 cm	5.3 cm (0.66 cm)	2.11 cm	6.74 cm	0.66 cm

Code Rate	$a$	$b$	$c$
2/3	0.3870	2.7150	0.8890
6/12	0.6364	6.8958	0.8871
9/36	0.7246	42.4424	0.8600

J. M. Garrido-Balsells	https://orcid.org/0000-0003-3042-0076
I. Tafur-Monroy	https://orcid.org/0000-0002-2935-7682
A. Jurado-Navas	https://orcid.org/0000-0002-4381-5109

Abstract

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Equations (33)

Journal of Optical Communications and Networking