.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/foundations/plot_03_ber_psk.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_foundations_plot_03_ber_psk.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_foundations_plot_03_ber_psk.py:


M-PSK over AWGN with the Python runner
======================================

The bit error rate of Gray-mapped BPSK, QPSK, 8-PSK and 16-PSK, simulated with the
Monte Carlo runner of :mod:`comnum.sim`: the trial is a Python function, every point
runs until 200 bit errors (or 400 trials), and the result of every point is an error
rate with its Wilson interval. BPSK and QPSK share the same curve
:math:`Q(\sqrt{2 E_b/N_0})`; beyond four points, every doubling of the order costs
3.5 to 4.5 dB at a BER of :math:`10^{-5}`, since the points get closer on the circle:

.. math::

   P_b \approx \frac{2}{\log_2 M} Q\left(\sqrt{2 \log_2 M \frac{E_b}{N_0}}\sin\frac{\pi}{M}\right).

.. GENERATED FROM PYTHON SOURCE LINES 16-43

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import comnum
    from comnum import sim
    from comnum.plot import BACKGROUND, MUTED

    ORDERS = [2, 4, 8, 16]


    def trial(cond, rng, rec, c):
        k = c.bits_per_symbol
        bits = comnum.bits(k * 8192, rng)
        y = comnum.awgn_ebn0(c.map_bits(bits), cond["ebn0_db"], k, rng)
        rec.errors("ber", int((c.demap_bits(y) != bits).sum()), bits.size)


    results = sim.run(
        trial,
        sim.grid(m=ORDERS, ebn0_db=np.arange(0.0, 21.0, 2.0)),
        name="psk",
        seed=7,
        setup=lambda cond: comnum.Constellation("psk", cond["m"]).normalized(),
        stop=sim.Stop.min_errors("ber", 200) | sim.Stop.max_trials(400),
    )








.. GENERATED FROM PYTHON SOURCE LINES 44-78

.. code-block:: Python

    fig, ax = plt.subplots()
    eb = np.linspace(0, 20, 201)
    labels = {2: "BPSK", 4: "QPSK", 8: "8-PSK", 16: "16-PSK"}
    for m in ORDERS:
        pts = [r for r in results if r.condition["m"] == m and r.metrics["ber"].value > 0]
        x = np.array([r.condition["ebn0_db"] for r in pts])
        p = np.array([r.metrics["ber"].value for r in pts])
        ci = np.array([r.metrics["ber"].interval(0.95) for r in pts])
        (line,) = ax.semilogy(
            eb,
            comnum.theory_ber(m, eb, "psk"),
            linewidth=1.4,
            linestyle="--" if m == 4 else "-",
        )
        ax.errorbar(
            x,
            p,
            yerr=[p - ci[:, 0], ci[:, 1] - p],
            fmt="o" if m != 4 else "s",
            color=line.get_color(),
            markeredgecolor=BACKGROUND,
            label=labels[m],
        )
    ax.plot([], [], color=MUTED, linewidth=1.4, label="theory")
    ax.set(
        ylim=(1e-6, 0.5),
        xlim=(0, 20),
        xlabel="$E_b/N_0$ (dB)",
        ylabel="bit error rate",
        title="Gray-mapped PSK over AWGN",
    )
    ax.legend()
    fig.tight_layout()




.. image-sg:: /auto_examples/foundations/images/sphx_glr_plot_03_ber_psk_001.png
   :alt: Gray-mapped PSK over AWGN
   :srcset: /auto_examples/foundations/images/sphx_glr_plot_03_ber_psk_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 79-81

Every point carries its own trial count: the high-SNR points need many more trials
to collect their errors.

.. GENERATED FROM PYTHON SOURCE LINES 81-87

.. code-block:: Python

    for r in results[:6]:
        lo, hi = r.metrics["ber"].interval(0.95)
        print(
            f"m={r.condition['m']:>2} Eb/N0={r.condition['ebn0_db']:4.1f} dB  BER={r.metrics['ber'].value:.3e}"
            f"  [{lo:.2e}, {hi:.2e}]  trials={r.trials}"
        )




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

 .. code-block:: none

    m= 2 Eb/N0= 0.0 dB  BER=7.877e-02  [7.77e-02, 7.98e-02]  trials=32
    m= 2 Eb/N0= 2.0 dB  BER=3.741e-02  [3.67e-02, 3.81e-02]  trials=32
    m= 2 Eb/N0= 4.0 dB  BER=1.236e-02  [1.19e-02, 1.28e-02]  trials=32
    m= 2 Eb/N0= 6.0 dB  BER=2.445e-03  [2.26e-03, 2.64e-03]  trials=32
    m= 2 Eb/N0= 8.0 dB  BER=1.694e-04  [1.49e-04, 1.93e-04]  trials=160
    m= 2 Eb/N0=10.0 dB  BER=4.272e-06  [2.55e-06, 7.17e-06]  trials=400





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

   **Total running time of the script:** (0 minutes 2.609 seconds)


.. _sphx_glr_download_auto_examples_foundations_plot_03_ber_psk.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_ber_psk.ipynb <plot_03_ber_psk.ipynb>`

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

      :download:`Download Python source code: plot_03_ber_psk.py <plot_03_ber_psk.py>`

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

      :download:`Download zipped: plot_03_ber_psk.zip <plot_03_ber_psk.zip>`


.. only:: html

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

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