Error analysis of L-PPM modulated MIMO based multi-user NOMA-VLC system
with perfect and imperfect SIC

Vipul Dixit; Atul Kumar

doi:10.1364/AO.440511

Applied Optics
Vol. 61,
Issue 4,
pp. 858-867
(2022)
•https://doi.org/10.1364/AO.440511

Error analysis of L-PPM modulated MIMO based multi-user NOMA-VLC system with perfect and imperfect SIC

Vipul Dixit and Atul Kumar

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Vipul Dixit and Atul Kumar, "Error analysis of L-PPM modulated MIMO based multi-user NOMA-VLC system with perfect and imperfect SIC," Appl. Opt. 61, 858-867 (2022)

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Related Topics
Table of Contents Category
- Fiber Optics, Fiber Sensors, and Optical Communications
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: August 16, 2021
- Revised Manuscript: December 15, 2021
- Manuscript Accepted: December 19, 2021
- Published: January 24, 2022

Abstract

By offering a wide license-free spectrum, visible light communication (VLC) has emerged as a game-changing technology for networks beyond 5G. In this study, the multiple-input multiple-output (MIMO) technology is combined with a non-orthogonal multiple access VLC (NOMA-VLC) system to provide a reliable error-free high data rate network for multi-user scenarios. A generalized $L$-PPM modulated MIMO based multi-user NOMA-VLC system with $M \times N$ line-of-sight connections for each user is presented. Considering a practical scenario of imperfect successive interference cancellation, a novel, to the best of our knowledge, closed form formulation of error probability for the proposed system is obtained. This study also includes a comprehensive analysis of two-user and three-user $L$-PPM modulated $2 \times 2$ MIMO-NOMA-VLC systems, and exact error probability expressions are derived. With the identical set of parameters, the $L$-PPM modulated MIMO-NOMA-VLC system totally outperforms the on–off keying modulated MIMO-NOMA-VLC system. As the number of photodetectors per user increases, the error probability of the considered system decreases. An $L$-PPM modulated $2 \times 2$ MIMO based three-user NOMA-VLC system offers the best performance at a power allocation co-efficient of $\,0.3$. The simulation results validate the derived error probability expressions.

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No data were generated or analyzed in the presented research.

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$h_{1}$	Height of receivers above the ground
$A_{m}$	Active area of $m$ th PD
$d_{mn}$	Distance between $n$ th LED and $m$ th PD
$ϕ_{mn}$	Angle of emission from $n$ th LED to $m$ th PD
$ψ_{mn}$	Angle of incidence at $m$ th PD from $n$ th LED
$T (ψ_{mn})$	Optical filter gain of the $m$ th PD from $n$ th LED
$g (ψ_{mn}) = n^{2} / \sin^{2} ψ_{c},$	Gain of optical concentrator
$n$	Refractive index
$ψ_{c}$	Field of view (FOV) of the PD
$ℓ = - \ln 2 / \ln (\cos ϕ_{1 / 2})$	Lambertian order
$ϕ_{1 / 2}$	Semi-angle at half-power of LED
$x_{n}$	Transmitted signal from $n$ th LED
$P_{t}$	Total transmit power
$P_{avg} = P_{t} / N$	Average transmit power per LED
$h_{m}^{k} = \sum_{n = 1}^{N} h_{mn}^{k}$	Equivalent channel gain at the $m$ th PD
$R_{p}$	Responsivity of PD
$n_{m}^{k}$	Additive white Gaussian noise (AWGN) with $N (0, σ_{n}^{2})$ at $m$ th PD of the $k$ th user
$w_{m}^{k} = h_{m}^{k}$	Assigned weight at $m$ th PD of $k$ th user
$n^{k}$	Weighted noise at $k$ th user
$α$	Power allocation co-efficient with $0 < α < 1$
$s_{l}$	Slot data transmitted
$P_{l}^{sym}$	Transmitted symbol power

Description	Value
Room dimension	$5 m \times 5 m \times 3 m$
No. of LED’s $(N)$	2
Source co-ordinates LED 1LED 2	$2.5 m \times 2.4 m \times 3 m$ $2.5 m \times 2.6 m \times 3 m$
Semi-half-angle of LED $(Φ_{1 / 2})$	$60^{\circ}$
Inter-LED distance ( $D_{Tx}$ )	$0.2 m$
No. of PD’s ( $M$ )	$2$
Near user co-ordinates $(U_{1})$	${P D}_{1} (3 m \times 2.95 m \times 0.8 m)$ ${P D}_{2} (3 m \times 3.05 m \times 0.8 m)$
Middle user co-ordinates $(U_{2})$	${P D}_{1} (3.5 m \times 1.45 m \times 0.8 m)$ ${P D}_{2} (3.5 m \times 1.55 m \times 0.8 m)$
Far user co-ordinates $(U_{3})$	${P D}_{1} (1 m \times 0.95 m \times 0.8 m)$ ${P D}_{2} (1 m \times 1.05 m \times 0.8 m)$
Inter-PD distance ( $D_{Rx}$ )	$0.1 m$
Active area of PD $(A_{r})$	$1 c m^{2}$
FOV ( $ψ_{c}$ )	$60^{\circ}$
Responsivity $(R_{p})$	$1$ A/W
Refractive index $(n)$	$1.5$
Gain of optical filter $(T_{s})$	$1$
Noise bandwidth $(W)$	$50 M H z$
Transmission rate $(R_{b}$ )	$50 M p s$

Users	$M = 3$	$M = 4$
$U_{1}$	${P D}_{1} (3 m, 2.9 m, 0.8 m)$ ${P D}_{2} (3 m, 3 m, 0.8 m)$ ${P D}_{3} (3 m, 3.1 m, 0.8 m)$	${P D}_{1} (3 m, 2.85 m, 0.8 m)$ ${P D}_{2} (3 m, 2.95 m, 0.8 m)$ ${P D}_{3} (3 m, 3.05 m, 0.8 m)$ ${P D}_{4} (3 m, 3.15 m, 0.8 m)$
$U_{2}$	${P D}_{1} (3.5 m, 1.4 m, 0.8 m)$ ${P D}_{2} (3.5 m, 1.5 m, 0.8 m)$ ${P D}_{3} (3.5 m, 1.6 m, 0.8 m)$	${P D}_{1} (3.5 m, 1.35 m, 0.8 m)$ ${P D}_{2} (3.5 m, 1.45 m, 0.8 m)$ ${P D}_{3} (3.5 m, 1.55 m, 0.8 m)$ ${P D}_{4} (3.5 m, 1.65 m, 0.8 m)$
$U_{3}$	${P D}_{1} (1 m, 0.9 m, 0.8 m)$ ${P D}_{2} (1 m, 1 m, 0.8 m)$ ${P D}_{3} (1 m, 1.1 m, 0.8 m)$	${P D}_{1} (1 m, 0.85 m, 0.8 m)$ ${P D}_{2} (1 m, 0.95 m, 0.8 m)$ ${P D}_{3} (1 m, 1.05 m, 0.8 m)$ ${P D}_{4} (1 m, 1.15 m, 0.8 m)$

$h_{1}$	Height of receivers above the ground
$A_{m}$	Active area of $m$ th PD
$d_{mn}$	Distance between $n$ th LED and $m$ th PD
$ϕ_{mn}$	Angle of emission from $n$ th LED to $m$ th PD
$ψ_{mn}$	Angle of incidence at $m$ th PD from $n$ th LED
$T (ψ_{mn})$	Optical filter gain of the $m$ th PD from $n$ th LED
$g (ψ_{mn}) = n^{2} / \sin^{2} ψ_{c},$	Gain of optical concentrator
$n$	Refractive index
$ψ_{c}$	Field of view (FOV) of the PD
$ℓ = - \ln 2 / \ln (\cos ϕ_{1 / 2})$	Lambertian order
$ϕ_{1 / 2}$	Semi-angle at half-power of LED
$x_{n}$	Transmitted signal from $n$ th LED
$P_{t}$	Total transmit power
$P_{avg} = P_{t} / N$	Average transmit power per LED
$h_{m}^{k} = \sum_{n = 1}^{N} h_{mn}^{k}$	Equivalent channel gain at the $m$ th PD
$R_{p}$	Responsivity of PD
$n_{m}^{k}$	Additive white Gaussian noise (AWGN) with $N (0, σ_{n}^{2})$ at $m$ th PD of the $k$ th user
$w_{m}^{k} = h_{m}^{k}$	Assigned weight at $m$ th PD of $k$ th user
$n^{k}$	Weighted noise at $k$ th user
$α$	Power allocation co-efficient with $0 < α < 1$
$s_{l}$	Slot data transmitted
$P_{l}^{sym}$	Transmitted symbol power

Description	Value
Room dimension	$5 m \times 5 m \times 3 m$
No. of LED’s $(N)$	2
Source co-ordinates LED 1LED 2	$2.5 m \times 2.4 m \times 3 m$ $2.5 m \times 2.6 m \times 3 m$
Semi-half-angle of LED $(Φ_{1 / 2})$	$60^{\circ}$
Inter-LED distance ( $D_{Tx}$ )	$0.2 m$
No. of PD’s ( $M$ )	$2$
Near user co-ordinates $(U_{1})$	${P D}_{1} (3 m \times 2.95 m \times 0.8 m)$ ${P D}_{2} (3 m \times 3.05 m \times 0.8 m)$
Middle user co-ordinates $(U_{2})$	${P D}_{1} (3.5 m \times 1.45 m \times 0.8 m)$ ${P D}_{2} (3.5 m \times 1.55 m \times 0.8 m)$
Far user co-ordinates $(U_{3})$	${P D}_{1} (1 m \times 0.95 m \times 0.8 m)$ ${P D}_{2} (1 m \times 1.05 m \times 0.8 m)$
Inter-PD distance ( $D_{Rx}$ )	$0.1 m$
Active area of PD $(A_{r})$	$1 c m^{2}$
FOV ( $ψ_{c}$ )	$60^{\circ}$
Responsivity $(R_{p})$	$1$ A/W
Refractive index $(n)$	$1.5$
Gain of optical filter $(T_{s})$	$1$
Noise bandwidth $(W)$	$50 M H z$
Transmission rate $(R_{b}$ )	$50 M p s$

Abstract

Data Availability

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Figures (6)

Tables (3)

Equations (43)

Applied Optics