.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/optical/plot_02_launch_power_dbp.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_optical_plot_02_launch_power_dbp.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_optical_plot_02_launch_power_dbp.py:


Nonlinear fibre propagation and digital back-propagation
========================================================

The classical launch-power sweep of a long-haul optical link: 16-QAM at 32 GBd over
10 spans of 80 km of standard single-mode fibre with an EDFA (noise figure 4.5 dB)
after every span, simulated by the split-step Fourier method (1 km steps). At low
power the amplified spontaneous emission limits the SNR, which grows by 1 dB per dB of
launch power; at high power the Kerr nonlinearity
(:math:`\gamma = 1.3` /(W·km)) takes over and the SNR falls. The optimum is the
maximum of this "bell".

Dispersion compensation alone (``cdc``) undoes the linear part of the channel only.
Digital back-propagation solves the propagation equation backwards with the
coefficients negated (:meth:`comnum.Ssfm.backpropagate`): with enough steps per span it
removes the deterministic nonlinear distortion of a single channel, and the optimum
moves to a higher power and a higher SNR (Ip & Kahn, *J. Lightw. Technol.* 26(20),
2008).

.. GENERATED FROM PYTHON SOURCE LINES 20-56

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import comnum
    from comnum.plot import BACKGROUND, MUTED

    RS, SPS, N = 32e9, 4, 4096
    FS = RS * SPS
    fiber = comnum.FiberParams(n_spans=10)
    link = comnum.Ssfm(fiber, step_km=1.0)
    c = comnum.Constellation("qam", 16).normalized()
    h = comnum.pulse_shape("rrc", SPS, n_taps=4 * 256 + 1, rolloff=0.1)
    powers = np.arange(-6.0, 10.1, 2.0)
    receivers = {"CDC": None, "DBP, 1 step/span": 1, "DBP, 20 steps/span": 20}


    def snr_db(r, x):
        z = comnum.pnorm(comnum.downsample(comnum.fir_filter(h, r), SPS))
        return comnum.fast_ber_calc(z[256:-256], x[256:-256], c)[2]


    snr = {name: [] for name in receivers}
    for i, p in enumerate(powers):
        rng = comnum.Rng.stream(11, "launch-power", i, 0)
        _, x = comnum.symbols(c, N, rng)
        tx = comnum.pnorm(comnum.fir_filter(h, comnum.upsample(x, SPS))) * np.sqrt(comnum.dbm2w(p))
        y = link.propagate(tx, FS, rng=rng)
        for name, steps in receivers.items():
            r = (
                comnum.cdc(y, fiber, fiber.total_km, FS)
                if steps is None
                else link.backpropagate(y, FS, steps_per_span=steps)
            )
            snr[name].append(snr_db(r, x))








.. GENERATED FROM PYTHON SOURCE LINES 57-80

.. code-block:: Python

    fig, ax = plt.subplots()
    for (name, values), marker in zip(snr.items(), ["o", "s", "D"], strict=True):
        ax.plot(powers, values, marker=marker, markeredgecolor=BACKGROUND, label=name)
        if name != "DBP, 1 step/span":  # its optimum sits on top of the CDC one
            k = int(np.argmax(values))
            below = name == "CDC"
            ax.annotate(
                f"{values[k]:.1f} dB",
                (powers[k], values[k]),
                textcoords="offset points",
                xytext=(0, -15 if below else 8),
                ha="center",
                fontsize=8,
                color=MUTED,
            )
    ax.set(
        xlabel="launch power (dBm)",
        ylabel="effective SNR (dB)",
        title="16-QAM, 32 GBd, 10 × 80 km SSMF",
    )
    ax.legend(loc="lower center")
    fig.tight_layout()




.. image-sg:: /auto_examples/optical/images/sphx_glr_plot_02_launch_power_dbp_001.png
   :alt: 16-QAM, 32 GBd, 10 × 80 km SSMF
   :srcset: /auto_examples/optical/images/sphx_glr_plot_02_launch_power_dbp_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 81-84

.. code-block:: Python

    for name, values in snr.items():
        k = int(np.argmax(values))
        print(f"{name:<20} optimum {powers[k]:+.0f} dBm, SNR {values[k]:.1f} dB")




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    CDC                  optimum -2 dBm, SNR 21.8 dB
    DBP, 1 step/span     optimum -2 dBm, SNR 22.3 dB
    DBP, 20 steps/span   optimum +8 dBm, SNR 32.5 dB





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 2.193 seconds)


.. _sphx_glr_download_auto_examples_optical_plot_02_launch_power_dbp.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_launch_power_dbp.ipynb <plot_02_launch_power_dbp.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_launch_power_dbp.py <plot_02_launch_power_dbp.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_launch_power_dbp.zip <plot_02_launch_power_dbp.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_