#
# SPDX-FileCopyrightText: Copyright (c) 2021-2024 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: Apache-2.0
#
"""
This module defines a model for an Erbium-Doped Fiber Amplifier.
"""
import tensorflow as tf
from tensorflow.keras.layers import Layer
import sionna
[docs]class EDFA(Layer):
# pylint: disable=line-too-long
r"""EDFA(g=4.0,f=7.0,f_c=193.55e12,dt=1e-12,with_dual_polarization=False,dtype=tf.complex64,**kwargs)
Layer 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 :math:`F_\mathrm{ASE,shot} =\frac{\mathrm{SNR}
_\mathrm{in}}{\mathrm{SNR}_\mathrm{out}}`,
where ideally the detector is limited by shot noise only, and
:math:`\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
:math:`\mathrm{SNR}_\mathrm{in}=\frac{P}{2hf_cW}`, where :math:`h` denotes
Planck's constant, :math:`P` is the signal power, and :math:`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 :math:`\mathrm{SNR}_\mathrm{out}=\frac{GP}{\left
(4\rho_\mathrm{ASE}+2hf_c\right)W}`, where :math:`G` is the
parametrized gain.
Hence, one can write the former equation as :math:`F_\mathrm{ASE,shot} = 2
n_\mathrm{sp} \left(1-G^{-1}\right) + G^{-1}`.
Dropping shot noise again results in :math:`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 :math:`G =
\exp\left(\alpha \ell \right)`.
The spontaneous emission factor is :math:`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 :math:`\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 :math:`f_\mathrm{sim}`, the noise has a power of
:math:`P_\mathrm{ASE}^{(1)}=\sigma_\mathrm{n,ASE}^2=2\rho_\mathrm{ASE}^{(1)}
\cdot f_\mathrm{sim}`,
where the factor :math:`2` accounts for the unpolarized noise (for dual
polarization the factor is :math:`1` per polarization).
Here, the notation :math:`()^{(1)}` means that this is the noise introduced by a
single EDFA.
This class inherits from the Keras `Layer` class and can be used as layer in
a Keras model.
Example
--------
Setting-up:
>>> edfa = EDFA(
>>> g=4.0,
>>> f=2.0,
>>> f_c=193.55e12,
>>> dt=1.0e-12,
>>> with_dual_polarization=False)
Running:
>>> # x is the optical input signal
>>> y = EDFA(x)
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 :math:`f_\mathrm{c}` in :math:`(\text{Hz})`.
Defaults to 193.55e12.
dt : float
Time step :math:`\Delta_t` in :math:`(\text{s})`.
Defaults to 1e-12.
with_dual_polarization : bool
Considers axis [-2] as x- and y-polarization and applies the noise
per polarization. Defaults to `False`.
dtype : tf.complex
Defines the datatype for internal calculations and the output
dtype. Defaults to `tf.complex64`.
Input
-----
x : Tensor, tf.complex
Optical input signal
Output
-------
y : Tensor with same shape as ``x``, ``dtype``
Amplifier output
"""
def __init__(
self,
g=4.0,
f=7.0,
f_c=193.55e12,
dt=1e-12,
with_dual_polarization=False,
dtype=tf.complex64,
**kwargs):
super().__init__(dtype=dtype, **kwargs)
self._dtype = dtype
self._cdtype = tf.as_dtype(dtype)
self._rdtype = tf.as_dtype(dtype).real_dtype
self._g = tf.cast(g, self._rdtype)
self._f = tf.cast(f, self._rdtype)
self._f_c = tf.cast(f_c, self._rdtype)
self._dt = tf.cast(dt, self._rdtype)
assert isinstance(with_dual_polarization, bool), \
"with_dual_polarization must be bool."
self._with_dual_polarization = with_dual_polarization
# Spontaneous emission factor
if self._g == 1.0:
self._n_sp = tf.cast(0.0, self._rdtype)
else:
self._n_sp = self._f / tf.cast(
2.0, self._rdtype) * self._g / (
self._g - tf.cast(1.0, self._rdtype))
self._rho_n_ase = tf.cast(
self._n_sp * (self._g - tf.cast(1.0, self._rdtype)) *
sionna.constants.H * self._f_c,
self._rdtype) # Noise density in (W/Hz)
self._p_n_ase = tf.cast(
2.0, self._rdtype) * self._rho_n_ase * tf.cast(
1.0, self._rdtype) / (self._dt) # Noise power in (W)
if self._with_dual_polarization:
self._p_n_ase = self._p_n_ase / tf.cast(2.0, self._rdtype)
def call(self, inputs):
if self._with_dual_polarization:
tf.assert_equal(tf.shape(inputs)[-2], 2)
x = tf.cast(inputs, self._cdtype)
# Calculate noise signal with given noise power
n = tf.complex(
tf.random.normal(
tf.shape(x),
tf.cast(0.0, self._rdtype),
tf.sqrt(self._p_n_ase / tf.cast(2.0, self._rdtype)),
self._rdtype),
tf.random.normal(
tf.shape(x),
tf.cast(0.0, self._rdtype),
tf.sqrt(self._p_n_ase / tf.cast(2.0, self._rdtype)),
self._rdtype))
# Amplify signal
x = x * tf.cast(tf.sqrt(self._g), self._cdtype)
# Add noise signal
y = x + n
return y