Error performance of an L-PPM modulated ADR-based MIMO-VLC system with and without channel estimation error

Vipul Dixit; Atul Kumar

doi:10.1364/AO.478994

Applied Optics
Vol. 62,
Issue 10,
pp. 2501-2509
(2023)
•https://doi.org/10.1364/AO.478994

Error performance of an L-PPM modulated ADR-based MIMO-VLC system with and without channel estimation error

Vipul Dixit and Atul Kumar

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Vipul Dixit and Atul Kumar, "Error performance of an L-PPM modulated ADR-based MIMO-VLC system with and without channel estimation error," Appl. Opt. 62, 2501-2509 (2023)

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Table of Contents Category
- Fiber Optics, Fiber Sensors, and Optical Communications
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: October 28, 2022
- Revised Manuscript: February 21, 2023
- Manuscript Accepted: February 28, 2023
- Published: March 22, 2023

Abstract

In recent years, visible light communication (VLC) has emerged as a potential technique for beyond 5G communication networks. In this study, an angular diversity receiver (ADR) is used to propose a multiple-input multiple-output (MIMO) VLC system employing $\textit{L}$-pulse position modulation ($L$-PPM). Repetition coding (RC) is used at the transmitter, while receiver diversity techniques such as maximum-ratio combining (MRC), selection best combining (SBC), and equal gain combining (EGC) are used at the receiver to improve performance. This study presents the exact probability of error expressions for the proposed system with and without channel estimation error (CEE). The analysis shows that the probability of error of the proposed system increases as the estimation error increases. Further, the study shows that the increase in signal-to-noise ratio is not enough to counter the impact of CEE, especially when the estimation error is large. The distribution of error probability of the proposed system using EGC, SBC, and MRC throughout the area of the room is presented. The simulation findings are compared to the analytical results.

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No data were generated or analyzed in the presented research.

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A	Active area of PD
$γ = - \ln 2 / \ln (\cos ϕ_{1 / 2})$	Mode number associated with half power angle of LED $(ϕ_{1 / 2})$
$l_{ij}$	$i$ th LED to $j$ th PD distance
$ϕ_{ij}$	$i$ th LED’s emission angle to $j$ th PD
$ψ_{ij}$	$i$ th LED’s incidence angle at $j$ th PD
$g (ψ_{ij}) = n^{2} / \sin^{2} ψ_{c}$	optical concentrator gain with refractive index $n$
$T (ψ_{ij})$	gain of optical filter
$P_{t}$	total power transmitted
$P_{s y m}$	average power transmitted by each LED
$v_{r}$	side PD’s normal vector
$v_{rt}$	vector between LED and side PD
$(.)$	dot product of vectors
$‖ . ‖$	vector norm
$R_{r}$	PD’s responsivity
$h_{j} = \sum_{i = 1}^{N_{t}} h_{ij}$	overall gain of channel at $j$ th PD
$x = L P_{s y m} s_{l}$	$L$ -PPM modulated signal
$L$	number of slots per symbol
$s_{l}$	slot data transmitted
$n_{j} (t)$	AWGN with $N (0, σ_{n}^{2})$ at $j^{th}$ PD
$H_{e} = \sum_{j = 1}^{N_{r}} h_{j}$	total gain of channel at EGC
$n_{e} = \sum_{j = 1}^{N_{r}} n_{j}$	equivalent noise at EGC output
$H_{m} = \sum_{j = 1}^{N_{r}} {(h_{j})}^{2}$	total channel gain at MRC
$n_{m} = \sum_{j = 1}^{N_{r}} h_{j} n_{j}$	weighted noise at $j$ th PD
$H_{J} = \sum_{i = 1}^{N_{t}} h_{iJ}$	total gain of channel at $J$ th PD in SBC
$Δ H$	error matrix of $N_{t} \times N_{r}$
$Δ H_{e} = \sum_{j = 1}^{N_{r}} \sum_{i = 1}^{N_{t}} Δ h_{ij}$	addition of CEE at EGC
$Δ h_{ij}$	error in estimation of channel

Parameters	Description	Values
Setup	Dimension of room	$5 m, 5 m, 3 m$
	Coordinates of LED
Source	LED-1	$1.25 m, 1.25 m, 3 m$
	LED-2	$1.25 m, 3.75 m, 3 m$
	LED-3	$3.75 m, 1.25 m, 3 m$
	LED-4	$3.75 m, 3.75 m, 3 m$
	half power angle of LED $(ϕ_{1 / 2})$	60º
Receiver	Number of PDs	7
	Angles of azimuth $(α_{ij})$	$(0^{\circ}, 0^{\circ}, 60^{\circ}, 120^{\circ}, 180^{\circ}, 240^{\circ}, 300^{\circ})$
	Angles of elevation $(β_{ij})$	$(0^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ})$
	User coordinates	$2.5 m, 2.5 m, 0.8 m$
	PD’s active area $(A_{r})$	$1 {c m}^{2}$
	ADR radius $(d)$	0.53 cm
	FOV $(ψ_{c})$	60º
	Refractive index $(n)$	1.5
	Responsivity $(R_{p})$	0.53 A/W
	Optical filter gain $(T_{s})$	1
	Noise bandwidth $(B)$	50 MHz

A	Active area of PD
$γ = - \ln 2 / \ln (\cos ϕ_{1 / 2})$	Mode number associated with half power angle of LED $(ϕ_{1 / 2})$
$l_{ij}$	$i$ th LED to $j$ th PD distance
$ϕ_{ij}$	$i$ th LED’s emission angle to $j$ th PD
$ψ_{ij}$	$i$ th LED’s incidence angle at $j$ th PD
$g (ψ_{ij}) = n^{2} / \sin^{2} ψ_{c}$	optical concentrator gain with refractive index $n$
$T (ψ_{ij})$	gain of optical filter
$P_{t}$	total power transmitted
$P_{s y m}$	average power transmitted by each LED
$v_{r}$	side PD’s normal vector
$v_{rt}$	vector between LED and side PD
$(.)$	dot product of vectors
$‖ . ‖$	vector norm
$R_{r}$	PD’s responsivity
$h_{j} = \sum_{i = 1}^{N_{t}} h_{ij}$	overall gain of channel at $j$ th PD
$x = L P_{s y m} s_{l}$	$L$ -PPM modulated signal
$L$	number of slots per symbol
$s_{l}$	slot data transmitted
$n_{j} (t)$	AWGN with $N (0, σ_{n}^{2})$ at $j^{th}$ PD
$H_{e} = \sum_{j = 1}^{N_{r}} h_{j}$	total gain of channel at EGC
$n_{e} = \sum_{j = 1}^{N_{r}} n_{j}$	equivalent noise at EGC output
$H_{m} = \sum_{j = 1}^{N_{r}} {(h_{j})}^{2}$	total channel gain at MRC
$n_{m} = \sum_{j = 1}^{N_{r}} h_{j} n_{j}$	weighted noise at $j$ th PD
$H_{J} = \sum_{i = 1}^{N_{t}} h_{iJ}$	total gain of channel at $J$ th PD in SBC
$Δ H$	error matrix of $N_{t} \times N_{r}$
$Δ H_{e} = \sum_{j = 1}^{N_{r}} \sum_{i = 1}^{N_{t}} Δ h_{ij}$	addition of CEE at EGC
$Δ h_{ij}$	error in estimation of channel

Parameters	Description	Values
Setup	Dimension of room	$5 m, 5 m, 3 m$
	Coordinates of LED
Source	LED-1	$1.25 m, 1.25 m, 3 m$
	LED-2	$1.25 m, 3.75 m, 3 m$
	LED-3	$3.75 m, 1.25 m, 3 m$
	LED-4	$3.75 m, 3.75 m, 3 m$
	half power angle of LED $(ϕ_{1 / 2})$	60º
Receiver	Number of PDs	7
	Angles of azimuth $(α_{ij})$	$(0^{\circ}, 0^{\circ}, 60^{\circ}, 120^{\circ}, 180^{\circ}, 240^{\circ}, 300^{\circ})$
	Angles of elevation $(β_{ij})$	$(0^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ}, 30^{\circ})$
	User coordinates	$2.5 m, 2.5 m, 0.8 m$
	PD’s active area $(A_{r})$	$1 {c m}^{2}$
	ADR radius $(d)$	0.53 cm
	FOV $(ψ_{c})$	60º
	Refractive index $(n)$	1.5
	Responsivity $(R_{p})$	0.53 A/W
	Optical filter gain $(T_{s})$	1
	Noise bandwidth $(B)$	50 MHz

Abstract

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Equations (42)

Applied Optics