Modem Performance
=================

.. attention:: Add figures, include performance data for non-linear types

As discussed in [section-fec-performance],
the performance of an error-correction scheme is typically measured in
the bit error rate (BER)|the average error probability for a bit to be
in error in the presence of additive white Gauss noise (AWGN) [#f1]_ .

The bit error rate (BER) performance of the different available
modulation schemes can be seen in
Figures [fig-modem-M2]--[ref-fig-modem-M256], relative to the ratio
of energy per bit to noise power (:math:`E_b/N_0`).
The raw data can be found in the `doc/data/modem-ber/`
subdirectory.

.. figure [fig-modem-M2] doc/modem/modem_ber_ebn0_M2.png

.. qplot:: ber test/ber_qam16.dat
    :width: 65%
    :name: modem-ber-M2
    :caption: Bit error rates vs. :math:`E_b/N_0` for :math:`M=2`.


.. table:: :math:`M=2` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    BPSK, 2-ASK     9.59              9.59
    DBPSK          10.46             10.46
    OOK            12.61             12.61
    ============== ================= ===============

.. figure [fig-modem-M4] doc/modem/modem_ber_ebn0_M4.png
  Bit error rates vs. :math:`E_b/N_0` for :math:`M=4`.

.. table:: :math:`M=4` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    QPSK, 4-QAM      12.59            9.59
    4-APSK           14.76           11.75
    DQPSK            14.93           11.92
    4-ASK            16.59           13.58
    ============== ================= ===============

.. figure [fig-modem-M8] doc/modem/modem_ber_ebn0_M8.png
   Bit error rates vs. :math:`E_b/N_0` for :math:`M=8`.

.. table:: :math:`M=8` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    8-APSK           16.12           11.35
    8-QAM            17.28           12.51
    8-PSK            17.84           13.07
    8-DPSK           20.62           15.85
    8-ASK            22.61           17.84
    ============== ================= ===============

.. figure [fig-modem-M16] doc/modem/modem_ber_ebn0_M16.png
   Bit error rates vs. :math:`E_b/N_0` for :math:`M=16`.

.. table:: :math:`M=16` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    ARB-16-OPT       19.15           13.13
    16-QAM           19.57           13.55
    16-APSK          19.92           13.90
    V.29             20.48           14.45
    16-PSK           23.43           17.41
    16-DPSK          26.43           20.41
    16-ASK           28.54           22.52
    ============== ================= ===============

.. figure [fig-modem-M32] doc/modem/modem_ber_ebn0_M32.png
    Bit error rates vs. :math:`E_b/N_0` for :math:`M=32`.

.. table:: :math:`M=32` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    ARB-32-OPT       22.11           15.12
    32-SQAM          22.56           15.57
    32-APSK          23.43           16.44
    32-QAM           23.59           16.60
    32-PSK           29.38           22.38
    32-DPSK          32.38           25.39
    ============== ================= ===============

.. figure [fig-modem-M64] doc/modem/modem_ber_ebn0_M64.png
    Bit error rates vs. :math:`E_b/N_0` for :math:`M=64`.}

.. table:: :math:`M=64` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    ARB-64-OPT       25.22           17.44
    64-QAM           25.50           17.71
    64-APSK          27.06           19.28
    ARB-64-VT        31.67           23.89
    64-PSK           35.32           27.38
    64-DPSK          38.28           30.50
    ============== ================= ===============

.. figure [fig-modem-M128] doc/modem/modem_ber_ebn0_M128.png
    Bit error rates vs. :math:`E_b/N_0` for :math:`M=128`.}

.. table:: :math:`M=128` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    ARB-128-OPT      28.19           19.74
    128-SQAM         28.42           19.97
    128-QAM          29.60           21.15
    128-APSK         30.55           22.10
    ============== ================= ===============

.. figure [fig-modem-M256] doc/modem/modem_ber_ebn0_M256.png
    Bit error rates vs. :math:`E_b/N_0` for :math:`M=256`.

.. table:: :math:`M=256` BER performance, :math:`\hat{P}=10^{-5}`
    :width: 80%
    :widths: 50 25 25

    ============== ================= ===============
    Scheme         :math:`E_s/N_0`   :math:`E_b/N_0`
    ============== ================= ===============
    ARB-256-OPT      31.09           22.06
    256-QAM          31.56           22.53
    256-APSK         33.10           24.06
    ============== ================= ===============


.. rubric:: Footnotes

.. [#f1] assuming the modulated symbols are uncorrelated and identically distributed.