Outage probability analysis of a vertical underwater wireless optical link subject to oceanic turbulence and pointing errors

Ikenna Chinazaekpere Ijeh; Mohammad Ali Khalighi; Mohammed Elamassie; Steve Hranilovic; Murat Uysal

doi:10.1364/JOCN.454191

Journal of Optical Communications and Networking
Vol. 14,
Issue 6,
pp. 439-453
(2022)
•https://doi.org/10.1364/JOCN.454191

Outage probability analysis of a vertical underwater wireless optical link subject to oceanic turbulence and pointing errors

Ikenna Chinazaekpere Ijeh, Mohammad Ali Khalighi, Mohammed Elamassie, Steve Hranilovic, and Murat Uysal

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Ikenna Chinazaekpere Ijeh, Mohammad Ali Khalighi, Mohammed Elamassie, Steve Hranilovic, and Murat Uysal, "Outage probability analysis of a vertical underwater wireless optical link subject to oceanic turbulence and pointing errors," J. Opt. Commun. Netw. 14, 439-453 (2022)

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Abstract

The reliability of an underwater wireless optical communication (UWOC) network is seriously impacted by beam misalignment between transmitters (Txs) and receivers (Rxs). Also, the performance of UWOC systems can be affected by oceanic turbulence-induced fading due to fluctuations in the water refractive index as a result of variations in the pressure, water temperature, and salinity. In this work, we investigate the performance analysis of a vertical UWOC link subject to oceanic turbulence and pointing errors and further investigate the appropriate selection of link parameters to optimize link performance. This study is based on an accurate mathematical framework for link modeling while taking into account realistic Tx/Rx and channel parameters under different turbulence and beam misalignment conditions. We provide an analytical expression for calculating the link outage probability, whose accuracy is validated through numerical simulations. Last, the necessity of optimal Tx/Rx parameter selection to minimize the link outage is demonstrated. A laser beam is considered at the Tx, as well as an ultra-sensitive photodetector (silicon photo-multiplier) at the Rx to enable working at relatively long link ranges. The presented results give valuable insight into the practical aspects of deployment of UWOC networks.

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(a) Tx Parameters
Parameter	Value
LD wavelength $λ$	450 nm
LD spectral width $Δ λ$	5 nm
LD peak transmit power $P_{T x, 1}$	4 W
OOK extinction ratio $ξ$	0.4
Bit rate $R_{b}$	1 Mbps
(b) Channel Parameters (used for turbulence modeling; see Appendix B)
Parameter	Value
Dissipation rate of mean-squared temperature $X_{T}$	$10^{- 5} K^{2} s^{- 1}$
Dissipation rate of turbulent kinetic energy, per unit mass of fluid	$10^{- 1} m^{2} s^{- 3}$
Thermal expansion coefficient $α_{k}$	Computed by TEOS^a
Saline contraction coefficient $β_{k}$	Computed by TEOS
Kinematic viscosity [28] $v_{k}$	Computed by FVCOM^b
Molecular thermal diffusivity $D_{T_{k}}$	Computed by FVCOM
Molecular salinity diffusivity $D_{S_{k}}$	$D_{S_{k}} \approx 0.01 D_{T_{k}}$
(c) Rx Default Parameters
Parameter	Value
Optical filter bandwidth $B_{o}$	2 nm
LPF bandwidth $B_{e}$	$\approx R_{b} / 2$
Lens aperture diameter $D_{r}$	75 mm
SiPM active area $A_{P D}$	$9 {m m}^{2}$
SiPM, number of SPADs	10,998
SiPM, fill factor	48%
SiPM gain $G$	$10^{6}$
SiPM photon detection efficiency $Y_{P D E}$	24%
SiPM dark count rate $f_{D C R}$	6.6 MHz
SiPM dead time $τ_{d}$	100 ns
SiPM probability of cross talk $P_{C T}$	0.03%
SiPM probability of after-pulsing $P_{A P}$	0.2%
SiPM excess noise factor $F$	1.1
TIA load resistance $R_{L}$	$1 k Ω$

(a)
	Simulation Based			Analytical Upper Bounds
$σ_{θ t}$ (deg.)	$w_{L, o p t}$ (m)	$θ_{F o V r, o p t}$ (deg.)	$P_{o u t}$	$w_{L, o p t}$ (m)	$θ_{F o V r, o p t}$ (deg.)	$P_{o u t}$
0.1	7.59	0.57	$9.3 \times 10^{- 4}$	7.09	0.52	$2.7 \times 10^{- 3}$
0.5	5.27	1.36	$9.69 \times 10^{- 2}$	4.67	1.29	$1.4 \times 10^{- 1}$
1	4.1	2.17	$4.06 \times 10^{- 1}$	3.75	2.05	$4.88 \times 10^{- 1}$
(b)
	Simulation Based			Analytical Upper Bounds
$L$ (m)	$w_{L, opt}$ (m)	$θ_{FoVr, opt}$ (deg.)	$P_{out}$	$w_{L, opt}$ (m)	$θ_{FoVr, opt}$ (deg.)	$P_{out}$
80	7.59	0.57	$9.3 \times 10^{- 4}$	7.09	0.52	$2.7 \times 10^{- 3}$
90	4.49	0.45	$7.8 \times 10^{- 2}$	4.47	0.38	$1.05 \times 10^{- 1}$
100	2.55	0.35	$4.43 \times 10^{- 1}$	2.53	0.33	$4.9 \times 10^{- 1}$

(a) Tx Parameters
Parameter	Value
LD wavelength $λ$	450 nm
LD spectral width $Δ λ$	5 nm
LD peak transmit power $P_{T x, 1}$	4 W
OOK extinction ratio $ξ$	0.4
Bit rate $R_{b}$	1 Mbps
(b) Channel Parameters (used for turbulence modeling; see Appendix B)
Parameter	Value
Dissipation rate of mean-squared temperature $X_{T}$	$10^{- 5} K^{2} s^{- 1}$
Dissipation rate of turbulent kinetic energy, per unit mass of fluid	$10^{- 1} m^{2} s^{- 3}$
Thermal expansion coefficient $α_{k}$	Computed by TEOS^a
Saline contraction coefficient $β_{k}$	Computed by TEOS
Kinematic viscosity [28] $v_{k}$	Computed by FVCOM^b
Molecular thermal diffusivity $D_{T_{k}}$	Computed by FVCOM
Molecular salinity diffusivity $D_{S_{k}}$	$D_{S_{k}} \approx 0.01 D_{T_{k}}$
(c) Rx Default Parameters
Parameter	Value
Optical filter bandwidth $B_{o}$	2 nm
LPF bandwidth $B_{e}$	$\approx R_{b} / 2$
Lens aperture diameter $D_{r}$	75 mm
SiPM active area $A_{P D}$	$9 {m m}^{2}$
SiPM, number of SPADs	10,998
SiPM, fill factor	48%
SiPM gain $G$	$10^{6}$
SiPM photon detection efficiency $Y_{P D E}$	24%
SiPM dark count rate $f_{D C R}$	6.6 MHz
SiPM dead time $τ_{d}$	100 ns
SiPM probability of cross talk $P_{C T}$	0.03%
SiPM probability of after-pulsing $P_{A P}$	0.2%
SiPM excess noise factor $F$	1.1
TIA load resistance $R_{L}$	$1 k Ω$

(a)
	Simulation Based			Analytical Upper Bounds
$σ_{θ t}$ (deg.)	$w_{L, o p t}$ (m)	$θ_{F o V r, o p t}$ (deg.)	$P_{o u t}$	$w_{L, o p t}$ (m)	$θ_{F o V r, o p t}$ (deg.)	$P_{o u t}$
0.1	7.59	0.57	$9.3 \times 10^{- 4}$	7.09	0.52	$2.7 \times 10^{- 3}$
0.5	5.27	1.36	$9.69 \times 10^{- 2}$	4.67	1.29	$1.4 \times 10^{- 1}$
1	4.1	2.17	$4.06 \times 10^{- 1}$	3.75	2.05	$4.88 \times 10^{- 1}$
(b)
	Simulation Based			Analytical Upper Bounds
$L$ (m)	$w_{L, opt}$ (m)	$θ_{FoVr, opt}$ (deg.)	$P_{out}$	$w_{L, opt}$ (m)	$θ_{FoVr, opt}$ (deg.)	$P_{out}$
80	7.59	0.57	$9.3 \times 10^{- 4}$	7.09	0.52	$2.7 \times 10^{- 3}$
90	4.49	0.45	$7.8 \times 10^{- 2}$	4.47	0.38	$1.05 \times 10^{- 1}$
100	2.55	0.35	$4.43 \times 10^{- 1}$	2.53	0.33	$4.9 \times 10^{- 1}$

Ikenna Chinazaekpere Ijeh	https://orcid.org/0000-0002-5158-6270
Mohammad Ali Khalighi	https://orcid.org/0000-0002-0522-6688
Mohammed Elamassie	https://orcid.org/0000-0001-9416-3860
Steve Hranilovic	https://orcid.org/0000-0003-0308-2489

Abstract

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Figures (11)

Tables (2)

Equations (52)

Journal of Optical Communications and Networking