1 Introduction
2 Mathematical model
2.1 Uniform and apodized FBG
Type | Apodization function |
---|---|
Gaussian | \(A\left( z \right) = \exp \left( { - \log_{2} \left( {\frac{{2\left( {z - \frac{l}{2}} \right)}}{0.5l}} \right)^{2} } \right)\) |
Hamming | \(A\left( z \right) = 0.54 - 0.4\cos \left( {2\pi z/l} \right)\) |
Tanh | \(A\left( z \right) = \tanh \left( {4z/l} \right)\tanh \left( {4\left( {z - 1} \right)/l} \right)\) |
Raised sine | \(A\left( z \right) = \left( {\sin \left( {z/l} \right)} \right)^{2}\) |
Sinc | \(A\left( z \right) = \sin c\left( {2\pi \left( {z - l/2} \right)/l} \right)\) |
Raised cosine | \(A\left( z \right) = \left( {\cos \left( {2z/l - 1} \right)} \right)^{8}\) |
2.2 Dispersion compensation with UFBG
2.3 MTDM transmission technique
3 The proposed model
3.1 Case one: simulation without the proposed model
3.1.1 Transmitter
3.1.2 Optical fiber
3.1.3 Receiver
UFBG parameters | |
Grating length (mm), lg | 2 |
Wavelength (nm), λ | 1553.6 |
Effective refractive index, neff | 1.45 |
Induced refractive index, Δn | 10–4 |
SSMF | |
Reference wavelength (nm), λ | 1553.6 |
Length (km), L | 70 |
Attenuation (dB/km), α | 0.2 |
Dispersion parameter (ps/nm km), Dt | 17 |
WDM link | |
Input power (dBm), Pi | 0 |
Bit rate (Gbps), Br | 10 |
EDFA gain (dB), G | 30 |
EDFA noise figure(dB) | 4 |
PIN photodetector responsivity, R (A/W) | 1 |
PIN photodetector dark current, I0 (nA) | 30 |
Bessel filter cutoff frequency, fc | 0.75 × bit rate |
3.2 Case two: simulation of pre-compensation scheme
3.3 Case three: simulation of post-compensation scheme
3.4 Case four: symmetrical-compensation scheme
4 Results and discussion
4.1 Case one: simulation results without the proposed model
4.2 Case two: Simulation results of pre-compensation scheme
Apodization function | Q-factor | BER |
---|---|---|
Tanh | 9.13 | 3.4 × 10–20 |
Gaussian | 8.42 | 1.92 × 10–17 |
Hamming | 8.16 | 2.96 × 10–16 |
Raised cosine | 8.15 | 1.8 × 10–16 |
Raised sine | 8.2 | 1.7 × 10–16 |
Sinc | 8.2 | 1.7 × 10–16 |
4.3 Case three: results of simulation of post-compensation scheme
Apodization function | Q-factor | BER |
---|---|---|
Tanh | 9.2 | 3.25 × 10–20 |
Gaussian | 8.5 | 1.15 × 10–17 |
Hamming | 8.17 | 1.74 × 10–16 |
Raised cosine | 8.15 | 1.8 × 10–16 |
Raised sine | 8.16 | 1.7 × 10–16 |
Sinc | 8.16 | 1.7 × 10–16 |
4.4 Case four: simulation results of symmetrical-compensation scheme
Apodization function | Q-factor | BER |
---|---|---|
Tanh | 8.8 | 8.22 × 10–19 |
Gaussian | 6.5 | 4.16 × 10–11 |
Hamming | 7.78 | 2.96 × 10–15 |
Raised cosine | 7.8 | 3.0 × 10–15 |
Raised sine | 7.82 | 2.56 × 10–15 |
Sinc | 7.81 | 2.94 × 10–15 |
4.5 Summary of Q-factor and BER for all cases
4.5.1 Q-factor
Apodization | Pre | Post | Symmetrical |
---|---|---|---|
Q-Factor | Q-Factor | Q-Factor | |
tanh | 9.13 | 9.2 | 8.8 |
Gaussian | 6.5 | 8.5 | 6.5 |
Hamming | 7.78 | 8.17 | 7.78 |
Raised cosine | 7.8 | 8.15 | 7.8 |
Raised sine | 7.82 | 8.16 | 7.82 |
Sinc | 7.81 | 8.16 | 7.81 |
Without model | 8.53 |
4.5.2 BER
Apodization | Pre | Post | Symmetrical |
---|---|---|---|
BER | BER | BER | |
tanh | 3.4 × 10–20 | 3.25 × 10–20 | 8.22 × 10–19 |
Gaussian | 1.92 × 10–17 | 1.15 × 10–17 | 4.16 × 10–11 |
Hamming | 2.96 × 10–16 | 1.74 × 10–16 | 2.96 × 10–15 |
Raised cosine | 1.8 × 10–16 | 1.8 × 10–16 | 3.0 × 10–15 |
Raised sine | 1.7 × 10–16 | 1.7 × 10–16 | 2.56 × 10–15 |
Sinc | 1.7 × 10–16 | 1.7 × 10–16 | 2.94 × 10–15 |
Without the model | 7.15 × 10–18 |
4.5.3 Comparison with related work
References | Apodization function | Br (Gbps) | Q-factor | BER | % superiority of our model |
---|---|---|---|---|---|
Hamming | 10 | 8.27 | 6.46 × 10–17 | 68 | |
Sayed et al. (2021) | Cauchy | 10 | 6.135 | 4.24 × 10–10 | 99 |
Hussein et al. (2019) | tanh | 10 | 7.106 | 5.47 × 10–13 | 99 |
The best proposed model (present work) | ||||
---|---|---|---|---|
Proposed model | Apodization function | Br (Gbps) | Q-factor | BER |
Case 3 | tanh | 10 | 9.2 | 3.25 × 10–20 |