Amplify-and-forward multihop non-line-of-sight ultraviolet communication in the gamma–gamma fading channel

Sudhanshu Arya; Yeon Ho Chung

doi:10.1364/JOCN.11.000422

Journal of Optical Communications and Networking
Vol. 11,
Issue 8,
pp. 422-436
(2019)
•https://doi.org/10.1364/JOCN.11.000422

Amplify-and-forward multihop non-line-of-sight ultraviolet communication in the gamma–gamma fading channel

Sudhanshu Arya and Yeon Ho Chung

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Sudhanshu Arya and Yeon Ho Chung, "Amplify-and-forward multihop non-line-of-sight ultraviolet communication in the gamma–gamma fading channel," J. Opt. Commun. Netw. 11, 422-436 (2019)

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Abstract

In this paper, we propose amplify-and-forward-based multihop non-line-of-sight (NLOS) ultraviolet (UV) communication with subcarrier intensity modulation to mitigate turbulence-induced fading. Atmospheric turbulence is one of the main impairments in the performance of UV links, as it causes random fluctuation of the received signal. An aggregated UV channel model of both path loss and turbulence-induced gamma–gamma fading is considered. We derive the probability density function (PDF) of the end-to-end received signal-to-noise ratio (SNR). With this PDF and the random coding error exponent, an exact solution to the optimal number of hops in the proposed multihop UV system is presented. Over the turbulence-induced gamma–gamma fading channel, a closed-form expression for the moment-generating function (MGF) of the inverse of the instantaneous received SNR is also derived. Based on the derived MGF, two closed-form analytical expressions of average bit error rate and outage probability are further derived, together with an upper bound of the ergodic capacity of the proposed system. From the analytical expressions derived, the proposed multihop NLOS UV system is analyzed. Simulation results show that the proposed UV system can effectively mitigate the turbulence-induced fading, thus resulting in an increased coverage distance of the UV system without sacrificing important performance criteria such as the outage probability and the average bit error rate. It is also found that the optimal number of hops decreases with an increasing data rate.

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Parameter	Description
$λ$	UV wavelength
$N$	Number of relay nodes
$d_{T V n - 1}$	Propagation length from the ( $n - 1$ )th node to the common volume
$d_{R V n}$	Propagation length from the common volume to the $n$ th node
$α_{a}$	UV absorption coefficient
$α_{s r}$	UV Rayleigh scattering coefficient
$α_{s m}$	UV Mie scattering coefficient
$N_{0}$	Power spectral density of AWGN
$χ_{n}$	Instantaneous SNR at the $n$ th node
$ξ_{n}$	Average received SNR at the $n$ th node
$χ_{e q}$	Instantaneous end-to-end SNR
$C_{n}^{2}$	Refractive index structure parameter
$p$	Effective number of large-scale eddies for the gamma–gamma distributed turbulence channel
$q$	Effective number of small-scale eddies for the gamma–gamma distributed turbulence channel
$p_{_{V n - 1}}$	Effective number of large-scale eddies for the gamma–gamma distributed turbulence channel from the ( $n - 1$ )th node to the common volume
$q_{_{V n - 1}}$	Effective number of small-scale eddies for the gamma–gamma distributed turbulence channel from the ( $n - 1$ )th node to the common volume
$p_{_{R n}}$	Effective number of large-scale eddies for the gamma–gamma distributed turbulence channel from the common volume to the $n$ th receiver
$q_{_{R n}}$	Effective number of small-scale eddies for the gamma–gamma distributed turbulence channel from the common volume to the $n$ th receiver
$M_{χ_{n}^{- 1}} (s)$	MGF of the inverse of the instantaneous received SNR at the $n$ th node
$M_{χ_{e q}^{- 1}} (s)$	MGF of the inverse of the end-to-end received SNR

Parameter	Description
$λ$	UV wavelength
$N$	Number of relay nodes
$d_{T V n - 1}$	Propagation length from the ( $n - 1$ )th node to the common volume
$d_{R V n}$	Propagation length from the common volume to the $n$ th node
$α_{a}$	UV absorption coefficient
$α_{s r}$	UV Rayleigh scattering coefficient
$α_{s m}$	UV Mie scattering coefficient
$N_{0}$	Power spectral density of AWGN
$χ_{n}$	Instantaneous SNR at the $n$ th node
$ξ_{n}$	Average received SNR at the $n$ th node
$χ_{e q}$	Instantaneous end-to-end SNR
$C_{n}^{2}$	Refractive index structure parameter
$p$	Effective number of large-scale eddies for the gamma–gamma distributed turbulence channel
$q$	Effective number of small-scale eddies for the gamma–gamma distributed turbulence channel
$p_{_{V n - 1}}$	Effective number of large-scale eddies for the gamma–gamma distributed turbulence channel from the ( $n - 1$ )th node to the common volume
$q_{_{V n - 1}}$	Effective number of small-scale eddies for the gamma–gamma distributed turbulence channel from the ( $n - 1$ )th node to the common volume
$p_{_{R n}}$	Effective number of large-scale eddies for the gamma–gamma distributed turbulence channel from the common volume to the $n$ th receiver
$q_{_{R n}}$	Effective number of small-scale eddies for the gamma–gamma distributed turbulence channel from the common volume to the $n$ th receiver
$M_{χ_{n}^{- 1}} (s)$	MGF of the inverse of the instantaneous received SNR at the $n$ th node
$M_{χ_{e q}^{- 1}} (s)$	MGF of the inverse of the end-to-end received SNR

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Equations (57)

Journal of Optical Communications and Networking