Deep Learning-Aided Faster-Than-Nyquist Rate Optical Spatial Pulse Position Modulation

Yue Zhang; Xiangwen Ye; Minghua Cao; Huiqin Wang

doi:10.3788/AOS231709

Journals >Acta Optica Sinica >Volume 44 >Issue 5 >Page 0506003 > Article

Acta Optica Sinica
Vol. 44, Issue 5, 0506003 (2024)

Deep Learning-Aided Faster-Than-Nyquist Rate Optical Spatial Pulse Position Modulation

Yue Zhang, Xiangwen Ye, Minghua Cao^*, and Huiqin Wang

Author Affiliations

School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, Gansu , China

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DOI: 10.3788/AOS231709 Cite this Article Set citation alerts

Yue Zhang, Xiangwen Ye, Minghua Cao, Huiqin Wang. Deep Learning-Aided Faster-Than-Nyquist Rate Optical Spatial Pulse Position Modulation[J]. Acta Optica Sinica, 2024, 44(5): 0506003 Copy Citation Text

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Fig. 1. OSPPM-FTN system model

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Fig. 2. MNN decoder block diagram

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Fig. 3. Comparison of theoretical upper bound and simulation performance of BER in OSPPM-FTN system

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Fig. 4. BER performance of OSPPM-FTN system with different parameters

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Fig. 5. Performance comparison of OSPPM and OSPPM-FTN systems. (a) BER performance of OSPPM and OSPPM-FTN systems with different

τ

; (b) transmission rate and spectral efficiency of OSPPM and OSPPM-FTN systems with different

τ

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Fig. 6. Relationship between loss and training rounds of MNN decoder

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Fig. 7. Comparison of computational complexity of different decoders

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Fig. 8. BER performance of ML and MNN decoders under different turbulence

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Input bits	LD index	4-PPM signal	4PPM-FTN signal
0000	$x_{s} = {[1 0 0 0]}^{T}$	$x_{p p m} = [P_{1} 0 0 0]$	$x_{m} = [ο_{1} \dots P_{1} + ο_{9} \dots 0 + ο_{q} \dots 0 + ο_{27} \dots 0 + ο_{B}]$
0001	$x_{s} = {[1 0 0 0]}^{T}$	$x_{p p m} = [0 P_{1} 0 0]$	$x_{m} = [ο_{1} \dots 0 + ο_{9} \dots P_{1} + ο_{q} \dots 0 + ο_{27} \dots 0 + ο_{B}]$
0010	$x_{s} = {[1 0 0 0]}^{T}$	$x_{p p m} = [0 0 P_{1} 0]$	$x_{m} = [ο_{1} \dots 0 + ο_{9} \dots 0 + ο_{q} \dots P_{1} + ο_{27} \dots 0 + ο_{B}]$
0011	$x_{s} = {[1 0 0 0]}^{T}$	$x_{p p m} = [0 0 0 P_{1}]$	$x_{m} = [ο_{1} \dots 0 + ο_{9} \dots 0 + ο_{q} \dots 0 + ο_{27} \dots P_{1} + ο_{B}]$
$⋮$	$⋮$	$⋮$	$⋮$
1110	$x_{s} = {[0 0 0 1]}^{T}$	$x_{p p m} = [0 0 P_{1} 0]$	$x_{m} = [ο_{1} \dots 0 + ο_{9} \dots 0 + ο_{q} \dots P_{1} + ο_{27} \dots 0 + ο_{B}]$
1111	$x_{s} = {[0 0 0 1]}^{T}$	$x_{p p m} = [0 0 0 P_{1}]$	$x_{m} = [ο_{1} \dots 0 + ο_{9} \dots 0 + ο_{q} \dots 0 + ο_{27} \dots P_{1} + ο_{B}]$

Table 1. Mapping table of OSPPM-FTN system

Parameter	$C_{n}^{2}$ / $m^{- 2 / 3}$
Strong turbulence	$2.5 \times 10^{- 11}$
Middle turbulence	$6.0 \times 10^{- 13}$
Weak turbulence	$9.0 \times 10^{- 16}$

Table 2. Turbulence model parameters

Modulation	Spectral efficiency /（bit · s^-1· Hz^-1）	Transmission rate /（bit/channel）
OSPPM	$(l o g_{2} N_{t} D) / D$	$l o g_{2} N_{t} + l o g_{2} D$
OSPPM-FTN	$[l o g_{2} N_{t} + (l o g_{2} D) / τ] / (τ D)$	$l o g_{2} N_{t} + (l o g_{2} D) / τ$

Table 3. Spectral efficiency and transmission rate of different schemes

Parameter	Content
Hidden layer activation	ReLU
Output layer activation	Sigmoid
Loss function	Cross entropy loss
Optimizer	SGD
Epoch	30
Learning rate	0.001
Number of training set	$6 \times 10^{6}$
Number of validation set	$1 \times 10^{6}$
Hidden nodes	16, 24, 16

Table 4. Parameters of MNN decoder

Hidden layer number	Accuracy /%
2	99.930015
3	99.978038
4	99.953223
5	99.821631

Table 5. Relationship between hidden layer number and decoding accuracy

Learning rate	Accuracy /%
0.01000	99.640017
0.00100	99.996005
0.00010	99.987218
0.00001	99.705215

Table 6. Relationship between learning rate and decoding accuracy

Decoder	Complexity /FLOPs
ML	$N_{r} D (2 N_{t} N_{r} D + 2 N_{r} D - 1)$
MNN	$2 N_{r} D G_{1} + 2 G_{1} G_{2} + 2 G_{2} G_{3} + 2 G_{3} N_{t} D + N_{t} D$

Table 7. Computational complexity of different decoders

Yue Zhang, Xiangwen Ye, Minghua Cao, Huiqin Wang. Deep Learning-Aided Faster-Than-Nyquist Rate Optical Spatial Pulse Position Modulation[J]. Acta Optica Sinica, 2024, 44(5): 0506003

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