Discrete Hartley transform-based dual-mode index modulation OFDM for visible light communications

Xian-Ying Xu; Qi Zhang; Dian-Wu Yue

doi:10.1364/AO.504221

Applied Optics
Vol. 62,
Issue 31,
pp. 8442-8450
(2023)
•https://doi.org/10.1364/AO.504221

Discrete Hartley transform-based dual-mode index modulation OFDM for visible light communications

Xian-Ying Xu, Qi Zhang, and Dian-Wu Yue

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Xian-Ying Xu, Qi Zhang, and Dian-Wu Yue, "Discrete Hartley transform-based dual-mode index modulation OFDM for visible light communications," Appl. Opt. 62, 8442-8450 (2023)

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- Fiber Optics, Fiber Sensors, and Optical Communications
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About this Article
History
- Original Manuscript: August 28, 2023
- Revised Manuscript: October 6, 2023
- Manuscript Accepted: October 10, 2023
- Published: October 26, 2023

Abstract

Using discrete Hartley transform (DHT) instead of discrete Fourier transform (DFT) in the optical index modulation (IM) aided orthogonal frequency division multiplexing (OFDM) systems for visible light communications (VLC) results in improvement in terms of the spectral efficiency, energy efficiency, peak-to-average power ratio, and bit error rate (BER) performance with a lower computational complexity, benefiting from the removal of the Hermitian symmetry. In this paper, by employing dual-mode (DM) index modulation in the DHT-based OFDM systems, more spectral efficient schemes for VLC are proposed. A reduced-complexity maximum likelihood (ML) detector and a simple log-likelihood ratio (LLR) detector for the DM-OFDM-IM systems are presented, achieving a better performance with a lower complexity over the traditional detectors. The spectral efficiency and the average BER are analyzed. The minimum distance between different transmitted subblock vectors is calculated for characterizing the performance. The simulation results demonstrate that the DHT-based DM-OFDM-IM systems achieve significant performance gains over the DHT-based OFDM-IM counterparts and perform better than the DFT-based counterparts in terms of the spectral efficiency and BER performance.

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The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Index Bits	$T_{A}$	$T_{B}$	Subblock Vectors
[0 0]	[1,2]	[3,4]	$[S_{A}^{1}, S_{A}^{2}, S_{B}^{1}, S_{B}^{2}]^{T}$
[0 1]	[2,3]	[1,4]	$[S_{B}^{1}, S_{A}^{1}, S_{A}^{2}, S_{B}^{2}]^{T}$
[0 1]	[3,4]	[1,2]	$[S_{B}^{1}, S_{B}^{2}, S_{A}^{1}, S_{A}^{2}]^{T}$
[1 1]	[1,4]	[2,3]	$[S_{A}^{1}, S_{B}^{1}, S_{B}^{2}, S_{A}^{2}]^{T}$

DM Schemes	$X_{m a i n}$	$X_{D M}$
DM-DCO	[] $^{T}$	[0, $, 0, X_{N_{F} / 2 - 1}^{} \dots, X_{1}^{}]^{T}$
DM-HDCO	[] $^{T}$	[0,0,] $^{T}$
DM-ACO	[] $^{T}$	$[0,$ $\dots, 0,$ $0, X_{N_{F} / 4}^{}, \dots, 0, X_{1}^{}]^{T}$
DM-HACO	[] $^{T}$	$[0,$ $\dots, 0,$ ] $^{T}$

	Optimal Spectral Efficiency			Optimal Energy Efficiency
Optical OFDM-IM Schemes	$K$	Spectral Efficiency Improvement	Energy Efficiency Improvement	$K$	Energy Efficiency Improvement
DM-HDCO/HACO	$K = 15$	90.63%	0	–	–
DM-DCO/ACO	$K = 15$	45.31%	0	–	–
HDCO/HACO-IM	$K = 19$	46.88%	40.62%	$K = 9$	71.88%

			Complexity of Detectors
Spectral Efficiency (bits/s/Hz)	DM-OFDM Schemes	Minimum Distance	ML	(S-)LLR /RC-ML
1.33	DM-HDCO	1.0247	$O (16)$	$O (12)$
1.33	HDCO-IM	0.8660	$O (16)$	$O (24)$
1.67	DM-HDCO	0.7969	$O (32)$	$O (18)$
1.67	HDCO-IM	0.4813	$O (32)$	$O (48)$
0.75	DM-HACO	0.7746	$O (64)$	$O (16)$
0.75	HACO-IM	0.3757	$O (64)$	$O (64)$
0.875	DM-HACO	0.6236	$O (128)$	$O (24)$
0.875	HACO-IM	0.2026	$O (128)$	$O (128)$

			Complexity of Detectors
Spectral Efficiency (bits/s/Hz)	DM-OFDM Schemes	Minimum Distance	ML	(S-)LLR /RC-ML
1.67	DM-HDCO	1.1456	$O (1024)$	$O (24)$
1.67	DM-DCO	0.8101	$O (1024)$	$O (48)$
2.17	DM-HDCO	0.8101	$O (8192)$	$O (36)$
2.17	DM-DCO	0.6047	$O (8192)$	$O (96)$
0.875	DM-HACO	0.8367	$O (16384)$	$O (32)$
0.875	DM-ACO	0.5916	$O (16384)$	$O (64)$
1.125	DM-HACO	0.5883	$O (262144)$	$O (48)$
1.125	DM-ACO	0.4243	$O (262144)$	$O (128)$

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Applied Optics