EDFA#

class sionna.phy.channel.EDFA(g: float = 4.0, f: float = 7.0, f_c: float = 193550000000000.0, dt: float = 1e-12, with_dual_polarization: bool = False, precision: str | None = None, device: str | None = None, **kwargs)[source]#

Bases: sionna.phy.block.Block

Block implementing a model of an Erbium-Doped Fiber Amplifier

Amplifies the optical input signal by a given gain and adds amplified spontaneous emission (ASE) noise.

The noise figure including the noise due to beating of signal and spontaneous emission is \(F_\mathrm{ASE,shot} =\frac{\mathrm{SNR} _\mathrm{in}}{\mathrm{SNR}_\mathrm{out}}\), where ideally the detector is limited by shot noise only, and \(\text{SNR}\) is the signal-to-noise-ratio. Shot noise is neglected here but is required to derive the noise power of the amplifier, as otherwise the input SNR is infinitely large. Hence, for the input SNR, it follows [A2012] that \(\mathrm{SNR}_\mathrm{in}=\frac{P}{2hf_cW}\), where \(h\) denotes Planck’s constant, \(P\) is the signal power, and \(W\) the considered bandwidth. The output SNR is decreased by ASE noise induced by the amplification. Note that shot noise is applied after the amplifier and is hence not amplified. It results that \(\mathrm{SNR}_\mathrm{out}=\frac{GP}{\left (4\rho_\mathrm{ASE}+2hf_c\right)W}\), where \(G\) is the parametrized gain. Hence, one can write the former equation as \(F_\mathrm{ASE,shot} = 2 n_\mathrm{sp} \left(1-G^{-1}\right) + G^{-1}\). Dropping shot noise again results in \(F = 2 n_\mathrm{sp} \left(1-G^ {-1}\right)=2 n_\mathrm{sp} \frac{G-1}{G}\).

For a transparent link, e.g., the required gain per span is \(G = \exp\left(\alpha \ell \right)\). The spontaneous emission factor is \(n_\mathrm{sp}=\frac{F} {2}\frac{G}{G-1}\). According to [A2012] and [EKWFG2010] combined with [BGT2000] and [GD1991], the noise power spectral density of the EDFA per state of polarization is obtained as \(\rho_\mathrm{ASE}^{(1)} = n_\mathrm{sp}\left (G-1\right) h f_c=\frac{1}{2}G F h f_c\). At simulation frequency \(f_\mathrm{sim}\), the noise has a power of \(P_\mathrm{ASE}^{(1)}=\sigma_\mathrm{n,ASE}^2=2\rho_\mathrm{ASE}^{(1)} \cdot f_\mathrm{sim}\), where the factor \(2\) accounts for the unpolarized noise (for dual polarization the factor is \(1\) per polarization). Here, the notation \(()^{(1)}\) means that this is the noise introduced by a single EDFA.

Parameters:

  • g (float) – Amplifier gain (linear domain). Defaults to 4.0.

  • f (float) – Noise figure (linear domain). Defaults to 7.0.

  • f_c (float) – Carrier frequency \(f_\mathrm{c}\) in \((\text{Hz})\). Defaults to 193.55e12.

  • dt (float) – Time step \(\Delta_t\) in \((\text{s})\). Defaults to 1e-12.

  • with_dual_polarization (bool) – If True, considers axis [-2] as x- and y-polarization and applies the noise per polarization. Defaults to False.

  • precision (str | None) – Precision used for internal calculations and outputs. If set to None, precision is used.

  • device (str | None) – Device for computation. If None, device is used.

Inputs:

x – Tensor, torch.complex. Optical input signal.

Outputs:

y – Tensor (same shape as x), torch.complex. Amplifier output.

Examples

import torch
from sionna.phy.channel.optical import EDFA

edfa = EDFA(
    g=4.0,
    f=2.0,
    f_c=193.55e12,
    dt=1.0e-12,
    with_dual_polarization=False)

# x is the optical input signal
x = torch.randn(10, 100, dtype=torch.complex64)
y = edfa(x)
print(y.shape)
# torch.Size([10, 100])
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