Performance analysis and optimal detector of wireless optical space–time shift keying over the Gamma–Gamma turbulence channel

Yue Zhang; Huiqin Wang; Xuemei Ma; Li Zhao; Yicong Mao

doi:10.1364/AO.419484

Applied Optics
Vol. 60,
Issue 12,
pp. 3501-3509
(2021)
•https://doi.org/10.1364/AO.419484

Performance analysis and optimal detector of wireless optical space–time shift keying over the Gamma–Gamma turbulence channel

Yue Zhang, Huiqin Wang, Xuemei Ma, Li Zhao, and Yicong Mao

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Yue Zhang, Huiqin Wang, Xuemei Ma, Li Zhao, and Yicong Mao, "Performance analysis and optimal detector of wireless optical space–time shift keying over the Gamma–Gamma turbulence channel," Appl. Opt. 60, 3501-3509 (2021)

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Table of Contents Category
- Fiber Optics, Fiber Sensors, and Optical Communications
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About this Article
History
- Original Manuscript: January 13, 2021
- Revised Manuscript: March 22, 2021
- Manuscript Accepted: March 23, 2021
- Published: April 19, 2021

Abstract

In this paper, an optical space–time shift-keying (OSTSK) scheme based on the space–time dispersion matrix block of orthogonal design and laser selection technology is proposed to improve the transmission bits per symbol (TBS) and bit error rate (BER) performance of the traditional optical space shift keying (OSSK). The average BER of OSTSK is investigated over the Gamma–Gamma channel and simulated using the Monte Carlo method. The results show that the proposed scheme has the highest TBS and best BER performance compared with OSSK and optical generalized space shift keying. In addition, we propose a threshold judgment orthogonal matching pursuit (TJ-OMP)-decoding algorithm near-optimal detector for the OSTSK scheme to reduce the computational complexity of the system. For the OSTSK system with ${N_{t}} = 4$ and ${N_{r}} = 4$, when the reasonable threshold is selected as $\theta = 1.5$, the computational complexity of OSTSK-(TJ-OMP) is 74.3% lower than that of the OSTSK-maximum likelihood sequence detection (OSTSK-MLSD), while the signal-to-noise ratio of the OSTSK-(TJ-OMP) decreases by about 1.5 dB at ${\rm BER }=1 \times {10^{- 3}}$.

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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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Source Bits	$X$	Source Bits	$X$	Source Bits	$X$	Source Bits	$X$
0000	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}]$	0100	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array}]$	1000	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$	1100	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}]$
0001	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array}]$	0101	$[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1001	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{array}]$	1101	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \end{array}]$
0010	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$	0110	$[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$	1010	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1110	$[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$
0011	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}]$	0111	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1011	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1111	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$

Turbulence Intensity	$C_{n}^{2}$	$α$	$β$
Weak AT	$5 \times 10^{- 15}$	20.11	19.25
Moderate AT	$1 \times 10^{- 14}$	10.03	9.47
Strong AT	$1 \times 10^{- 13}$	9.09	3.04

Algorithm	Computational Complexity
MLSD	$2^{⌊ \log_{2} N_{t}! ⌋} (2 N_{r} N_{t}^{2} + 2 N_{r} N_{t} - 1)$
OMP	$N_{t} (2 N_{r} N_{t} + 4 N_{r} - N_{t})$
TJ-OMP	$2 N_{r} N_{t}^{2} - N_{t}^{2} + N_{r} N_{t} + (2 N_{r} N_{t}^{2} + 2 N_{r} N_{t} - 1) υ$

Algorithm	TBS (bpcu)	Spectrum Efficiency	Computational Complexity
OSSK-MLSD	$⌊ \log_{2} N_{t} ⌋$	$⌊ \log_{2} N_{t} ⌋$	$N_{t} (2 N_{r} N_{t} + 2 N_{r} - 1)$
OGSSK-MLSD	$⌊ \log_{2} (\begin{array}{l} N_{t} \\ N_{u} \end{array}) ⌋$	$⌊ \log_{2} (\begin{array}{l} N_{t} \\ N_{u} \end{array}) ⌋$	$2^{⌊ \log_{2} (\binom{N_{t}}{N_{u}}) ⌋} (2 N_{t} N_{r} + 2 N_{r} + N_{t} - 1)$
OSTSK-MLSD	$⌊ \log_{2} (N_{t}!) ⌋$	$⌊ \log_{2} (N_{t}!) ⌋ / N_{t}$	$2^{⌊ \log_{2} N_{t}! ⌋} (2 N_{r} N_{t}^{2} + 2 N_{r} N_{t} - 1)$
OSTSK-(TJ-OMP)	$⌊ \log_{2} (N_{t}!) ⌋$	$⌊ \log_{2} (N_{t}!) ⌋ / N_{t}$	$2 N_{r} N_{t}^{2} - N_{t}^{2} + N_{r} N_{t} + (2 N_{r} N_{t}^{2} + 2 N_{r} N_{t} - 1) υ$

Source Bits	$X$	Source Bits	$X$	Source Bits	$X$	Source Bits	$X$
0000	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}]$	0100	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array}]$	1000	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$	1100	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}]$
0001	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array}]$	0101	$[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1001	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{array}]$	1101	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \end{array}]$
0010	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$	0110	$[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$	1010	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1110	$[\begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$
0011	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{array}]$	0111	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1011	$[\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$	1111	$[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \end{array}]$

Abstract

Data availability

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Tables (5)

Equations (25)

Applied Optics