A Novel Underwater Wireless Optical Communication Optical Receiver Decision Unit Strategy Based on a Convolutional Neural Network
Abstract
:1. Introduction
2. Related Studies—A Brief Review
3. UWOC System Model
3.1. The Transmitter Unit
3.2. UWOC Propagation Channel
3.3. The Receiver Unit
3.4. Digital Signal Evaluation Cycle from Optical to Electronic—A Mathematical Viewpoint
4. BER Computational Strategies for Decision Unit—Background Tutorial
4.1. BER Estimation Schemes—A Brief Review
4.2. Monte Carlo (MC) Method Simulation
4.3. Importance Sampling Scheme
4.4. Tail Extrapolation Scheme
4.5. The Method of Quasi-analytical Estimation
- One handles the transmitted signal rf(t) in Equation (4);
- The other handles the noise component rth(t).
4.6. Estimating BER Based on the Log-Likelihood Ratio
- The first estimate of BER given by Equation (12a) may not be as efficient as the second BER estimate given by Equation (12b) since gA(y) is usually Gaussian and smooth.
- The second estimator is extra complicated to execute because an estimate of gA(y) ought to be computed (for instance, utilising a histogram) prior to the integral.
- Both methods are sensitive to channel noise variance as the LLR distribution vigorously relies upon the accuracy of the SNR estimate. We should note that the earlier estimators implicitly presume that the SNR is well-known to the decoder.
5. CNN Model Solution Framework Foundations
5.1. Receiver Performance Indicators
5.2. Test Data
- DGFs with distances of 5.47 m and 45.45 m for harbour and coastal waters, respectively, and (20°, 180°) field of view (FOV).
- WDGFs and CEAPFs with distances of 10.93 m and 45.45 m for harbour and coastal waters, respectively, and 20° FOV.
- BP with 5 m and 10 m distances for harbour and coastal waters, respectively, and 180° FOV.
- Loading the images’ names and SNRs from the database.
- Converting the data into a ‘pandas’ data frame.
- Shuffling the data frame.
- Using TensorFlow library on Python, we conducted the following:
- Loaded the eye diagram images based on their names and normalised them using max normalisation (dividing each pixel by 255).
- Split the dataset into training (70%) and validation (30%).
- Converted the colour mode from RGB into grayscale.
- Used the images’ original size instead of resizing them to keep the resolution high.
5.3. Machine Learning—Neural Networks (NNs)
6. CNN Model Architecture, Design, and Implementation
6.1. Model Solution Architecture and Design
6.2. Model Dataset
6.3. CNN Algorithm
- The dimensions of the input eye diagram images are 2366 × 3125 pixels, with a resolution of 600 dpi.
- The network includes convolutional layers with a filter size of 10 and a stride of 1. The filters range from 16 to 64, increasing by four at each step. There is no activation function applied.
- There are three non-overlapping max-pooling layers with a size and stride 3.
- Flattened values refer to the input values that will be fed into the NN.
- This study refers to the hidden layer as FC and uses the ReLU activation function to reduce the CNN calculations by setting negative values to zero.
- The ultimate output of the CNN is the prediction of the signal-to-noise ratio (SNR) using a linear activation function, which is appropriate for regression tasks.
6.4. SNR Prediction
7. Results and Discussion
8. Conclusions
9. Future Studies
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Ref. | Year | Type of Modulation | Data Rate | Optical Fibre/UWOC | Distance | ML Tec. | Sim./Exp. | Train: Test | Input | Hidden Layers | Hidden Neurons | SNR Range (dB) | BER | Performance |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[25] | 2017 | PDM-64QAM | 32 Gbaud | Fibre | 250 km | NN, regression | Exp. To generate an eye diagram | 1664:832 | variance from the eye diagram | 1 | 3 | 4–30 | ------- | mean estimation error range from 0.2–1.2 dB |
[58] | 2009 | NRZ-OOK RZ-DPSK | 10 Gb/s 40 Gb/s | Fibre | --------- | ANN | Sim. | --------------- | Q-factor, closure, jitter, crossing-amplitude from eye diagram | 1 | 12 | 16–32 | ------- | correlation coefficient = 0.91 (@10G) correlation coefficient = 0.96 (@40G) |
[26] | 2009 | RZ-OOK RZ-DPSK | 40 Gb/s | Fibre | --------- | ANN | Sim. | 135:32 | Q-factor, closure, jitter, Crosspoint, mean, standard deviation from eye diagram | 1 | 12 | 16–32 | ------- | |
[116] | 2021 | NRZ-OOK | 10 Gb/s | Fibre | 100 km | ANN | Sim | 145: 41 | factor, noise power, eye amplitude, eye height, eye closure, eye-opening factor, extinction ratio at min BER, and RMS jitter | 1 | 5 | 15–30 | ------- | |
[8] | 2009 | NRZ- DPSK | 40 Gb/s | Fibre | 50 km | NO | ------------- | 500–1500 for training | six features | ------- | ------- | 25, 35 | ------- | ------------------ |
[68] | ------ | NRZ-OOK | 1.25 Gbps | UWOC | 1.5–6 m | NO | Exp | --------------- | --------------- | ------- | ------- | ----------- | 1 × 10−7 | ------------------ |
[59] | 2012 | NRZ, RZ and QPSK | 40 Gb/s | Fibre | --------- | ANN | Sim | --------------- | 24 features from the Eye diagram | 1 | 10 | 10–30 | ------- | |
Our study | 2024 | NRZ-OOK | 2 Gb/s | UWOC | 12 m | CNN | Sim | 404:172 | Eye diagram | 1 | 80–320 | (−2.42–9.11) | 0.0022–0.2247 | MAE = 0.291 RMSE = 0.387 |
Ref. | [24,60] | [61] | Our Work |
---|---|---|---|
ML technique | CNN | CNN | CNN |
Input data | Eye diagrams | Eye-opening, height, width, closure. | Eye diagrams |
Images format | jpg | No | jpg |
Approach | Classification | classification | Regression |
No. of convolutional and pooling layers | 2 | 3 | 5 |
No. of filters | C1 = 6 C2 = 12 | C1 = 60 C2 = 80 C3 = 180 | Unified for all convolutional layers, and it ranges from 16 to 64 |
Filter size | 5 | 3 | 10 |
Pooling size | 2 | 2 | 3 |
activation functions | Sigmoid in the whole CNN | ReLU for each convolutional layer and soft-max | ReLU for hidden layer Linear for output layer |
No. of hidden layers | 0 | 2 | 1 |
No. of elements of the fully connected feature map | 192 | FC1=360 FC2 =120 | Range from 80 to 320 According to no. of filters |
Dropout | No | yes | 45% |
Backpropagation | Yes | Yes | Yes |
No. of output nodes | 20 | No | 1 |
Output | 4 modulation formats 16 SNR | modulation formats, OSNR, ROF, and IQ skew | SNR |
No. of epochs | 35 | No | 250 |
Modulation format | RZ-OOK, NRZ-OOK, RZ-DPSK, and 4PAM | QAM and QPSK | NRZ-OOK |
Data rate | 25Gbaud | 32 Gbaud | 2 Gb/s |
Collecting eye diagrams way | Simulating signals and displaying eye diagrams using the oscilloscope | Experimental | Simulating everything using Python |
Colour mode | Coloured converted into grayscale | Coloured | Black and white in RGB convert to grayscale |
Original image size | 900 × 1200 | 224 × 224 | 2366 × 3125 |
Resized image | 28 × 28 | No | No |
Resolution | Low | Low | High (600 dpi) |
No. of models | 1 | 2 | 13 |
Prediction time | 0.46 s | No | Range from 0.17 to 0.20 s |
SNR range | (10–25) dB | (15 to 40) dB | (−2.42–9.11) dB |
BER range | No | No | 0.0022–0.2247 |
Total no. of images | 6400 | 1170 | 576 |
Performance | 100% accuracy | 99.57% accuracy | MAE = 0.29–0.52 RMSE = 0.39–0.73 |
Learning curves existence | No | No | Yes |
UWOC/ Fibre | Fibre | Fibre | UWOC |
Year | 2017 | 2019 | 2024 |
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Model Name | The Equation of the Model | Ref. |
---|---|---|
DGF | The closed-form expression of the double gamma functions (DGFs) is given as follows: | [74] |
WDGF | The weighted double gamma functions (WDGFs) model is given as follows: | [75] |
CEAPE | A combination of exponential and arbitrary power functions (CEAPEs) is given as follows: | [76] |
BP | Beta Prime (BP) distribution is given as follows: | [77] |
Metadata | Values |
---|---|
Water types | Harbour and coastal waters |
Channel models | DGF, WDGF, CEAPF, and BP |
Pulse shapes | Gaussian and Rectangular |
Pulse widths | 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95 |
Centre positions on the eye diagrams | 0/1 |
Min | Max | Mean | |
---|---|---|---|
Training Time (h) | 8.33 | 10.99 | 9.6915 |
Predicting Time (s) | 0.1732 | 0.2098 | 0.1855 |
Loss | 0.2911 | 0.5190 | 0.3739 |
Validation Loss | 0.3605 | 0.6113 | 0.4730 |
RMSE | 0.3869 | 0.7253 | 0.5070 |
Validation RMSE | 0.5178 | 0.8686 | 0.6779 |
Loss Ratio | 0.0297 | 0.3381 | 0.2107 |
RMSE Ratio | 0.0183 | 0.4153 | 0.2551 |
Number of Filters | 16 | 64 | 40 |
Number of Parameters | 516,881 | 2,267,201 | 1,369,161 |
Standard Hyperparameters | Values |
---|---|
Colour mode | Grayscale |
Eye diagram image size (height × width) | 2366 × 3125 |
Model | Functional API |
Optimizer | Adam |
Loss function | MAE |
Metric | RMSE |
Batch size | 15 |
No. of convolutional layers | 5 |
No. of max pooling layers | 5 |
Filters size | 10 |
Filters stride | 1 |
Pooling size | 3 |
Pooling stride | 3 |
No. of hidden layers | 1 |
Activation function in the hidden layer | ReLU |
Activation function in the output layer | linear |
Learning rate | 10−5 |
Epochs | 250 |
Dropout rate | 0.45 |
Training Time (h) | Predicting Time (s) | Loss | Validation Loss | RMSE | Validation RMSE | Loss Ratio | RMSE Ratio | No. of Filters | No. of Parameters |
---|---|---|---|---|---|---|---|---|---|
9.82 | 0.18551209 | 0.519 | 0.6113 | 0.7253 | 0.8686 | 0.8490 | 0.8350 | 16 | 516,881 |
10.12 | 0.18702742 | 0.481 | 0.4956 | 0.673 | 0.6605 | 0.9703 | 1.0183 | 20 | 651,301 |
8.84 | 0.18525898 | 0.446 | 0.4907 | 0.592 | 0.7047 | 0.9097 | 0.8404 | 24 | 787,801 |
9.86 | 0.18294497 | 0.443 | 0.5089 | 0.575 | 0.7332 | 0.8701 | 0.7848 | 28 | 926,381 |
8.96 | 0.18577732 | 0.363 | 0.475 | 0.502 | 0.6566 | 0.7634 | 0.7638 | 32 | 1,067,041 |
10.19 | 0.18203078 | 0.326 | 0.4659 | 0.434 | 0.6689 | 0.7004 | 0.6493 | 36 | 1,209,781 |
9.97 | 0.18092463 | 0.355 | 0.4582 | 0.495 | 0.6766 | 0.7737 | 0.7317 | 40 | 1,354,601 |
10.62 | 0.18176481 | 0.361 | 0.5051 | 0.486 | 0.7251 | 0.7137 | 0.6707 | 44 | 1,501,501 |
10.09 | 0.19424853 | 0.339 | 0.5122 | 0.462 | 0.7133 | 0.6619 | 0.6476 | 48 | 1,650,481 |
10.99 | 0.18315452 | 0.314 | 0.4202 | 0.412 | 0.6336 | 0.7475 | 0.6509 | 52 | 1,801,541 |
9.08 | 0.18004519 | 0.291 | 0.4383 | 0.387 | 0.6617 | 0.6642 | 0.5847 | 56 | 1,954,681 |
9.12 | 0.17316376 | 0.331 | 0.3605 | 0.458 | 0.5178 | 0.9190 | 0.8839 | 60 | 2,109,901 |
8.33 | 0.20982659 | 0.293 | 0.4075 | 0.39 | 0.5916 | 0.7183 | 0.6589 | 64 | 2,267,201 |
No. of Parameters | Interpretation | |
---|---|---|
Loss | −0.8977 | Strong linear inverse correlation |
Val. loss | −0.7891 | Strong linear inverse correlation |
RMSE | −0.8863 | Strong linear inverse correlation |
Val. RMSE | −0.7029 | Strong linear inverse correlation |
No. of filters | 0.9997 | Very strong linear direct correlation |
No. of Filters | Interpretation | |
---|---|---|
Training Time | −0.1923 | Very weak linear inverse correlation |
Predicting Time | 0.1793 | Very weak linear direct correlation |
Loss | −0.9053 | Very strong linear inverse correlation |
Validation Loss | −0.7897 | Strong linear inverse correlation |
RMSE | −0.8429 | Strong linear inverse correlation |
Validation RMSE | −0.6416 | Moderate linear inverse correlation |
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El Ramley, I.F.; Bedaiwi, N.M.; Al-Hadeethi, Y.; Barasheed, A.Z.; Al-Zhrani, S.; Chen, M. A Novel Underwater Wireless Optical Communication Optical Receiver Decision Unit Strategy Based on a Convolutional Neural Network. Mathematics 2024, 12, 2805. https://doi.org/10.3390/math12182805
El Ramley IF, Bedaiwi NM, Al-Hadeethi Y, Barasheed AZ, Al-Zhrani S, Chen M. A Novel Underwater Wireless Optical Communication Optical Receiver Decision Unit Strategy Based on a Convolutional Neural Network. Mathematics. 2024; 12(18):2805. https://doi.org/10.3390/math12182805
Chicago/Turabian StyleEl Ramley, Intesar F., Nada M. Bedaiwi, Yas Al-Hadeethi, Abeer Z. Barasheed, Saleha Al-Zhrani, and Mingguang Chen. 2024. "A Novel Underwater Wireless Optical Communication Optical Receiver Decision Unit Strategy Based on a Convolutional Neural Network" Mathematics 12, no. 18: 2805. https://doi.org/10.3390/math12182805