def _calcTheoreticalSingleCarrierErrorRate(self, SNR):
"""
Calculates the theoretical (approximation) error rate of a single
carrier in the QAM system (QAM has two carriers).
Parameters
----------
SNR : float | np.ndarray
Signal-to-noise-value (in dB).
Returns
-------
Psc : float | np.ndarray
The theoretical single carrier error rate.
Notes
-----
This method is used in the :meth:`calcTheoreticalSER`
implementation.
See also
--------
calcTheoreticalSER
"""
snr = dB2Linear(SNR)
# Probability of error of each carrier in a square QAM
# $P_{sc} = 2\left(1 - \frac{1}{\sqrt M}\right)Q\left(\sqrt{\frac{3}{M-1}\frac{E_s}{N_0}}\right)$
sqrtM = np.sqrt(self._M)
Psc = (2. * (1. - (1. / sqrtM)) *
qfunc(np.sqrt(snr * 3. / (self._M - 1.))))
return Psc
def _calcTheoreticalSingleCarrierErrorRate(self, SNR):
"""
Calculates the theoretical (approximation) error rate of a single
carrier in the QAM system (QAM has two carriers).
Parameters
----------
SNR : float | np.ndarray
Signal-to-noise-value (in dB).
Returns
-------
Psc : float | np.ndarray
The theoretical single carrier error rate.
Notes
-----
This method is used in the :meth:`calcTheoreticalSER`
implementation.
See also
--------
calcTheoreticalSER
"""
snr = dB2Linear(SNR)
# Probability of error of each carrier in a square QAM
# $P_{sc} = 2\left(1 - \frac{1}{\sqrt M}\right)Q\left(\sqrt{\frac{3}{M-1}\frac{E_s}{N_0}}\right)$
sqrtM = np.sqrt(self._M)
Psc = (2. * (1. - (1. / sqrtM)) *
qfunc(np.sqrt(snr * 3. / (self._M - 1.))))
return Psc
def calcTheoreticalSER(self, SNR):
"""Calculates the theoretical (approximation) symbol error rate for
the BPSK scheme.
Parameters
----------
SNR : float or array like
Signal-to-noise-value (in dB).
Returns
-------
SER : float or array like
The theoretical symbol error rate.
"""
snr = dB2Linear(SNR)
# $P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right)$
# Alternative formula (same result)
# $P_b = \frac{1}{2}erfc \left ( \sqrt{\frac{E_b}{N_0}} \right )$
ser = qfunc(np.sqrt(2 * snr))
return ser
def calcTheoreticalSER(self, SNR):
"""
Calculates the theoretical (approximation) symbol error rate for
the BPSK scheme.
Parameters
----------
SNR : float | np.ndarray
Signal-to-noise-value (in dB).
Returns
-------
SER : float | np.ndarray
The theoretical symbol error rate.
"""
snr = dB2Linear(SNR)
# $P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right)$
# Alternative formula (same result)
# $P_b = \frac{1}{2}erfc \left ( \sqrt{\frac{E_b}{N_0}} \right )$
ser = qfunc(np.sqrt(2 * snr))
return ser
def calcTheoreticalSER(self, SNR):
"""Calculates the theoretical (approximation for high M and high
SNR) symbol error rate for the M-PSK scheme.
Parameters
----------
SNR : float | np.ndarray
Signal-to-noise-value (in dB).
Returns
-------
SER : float | np.ndarray
The theoretical symbol error rate.
"""
snr = dB2Linear(SNR)
# $P_s \approx 2Q\left(\sqrt{2\gamma_s}\sin\frac{\pi}{M}\right)$
# Alternative formula (same result)
# $P_s = erfc \left ( \sqrt{\gamma_s} \sin(\frac{\pi}{M}) \right )$
ser = 2. * qfunc(np.sqrt(2. * snr) * math.sin(PI / self._M))
return ser
def calcTheoreticalSER(self, SNR):
"""Calculates the theoretical (approximation for high M and high
SNR) symbol error rate for the M-PSK scheme.
Parameters
----------
SNR : float | np.ndarray
Signal-to-noise-value (in dB).
Returns
-------
SER : float | np.ndarray
The theoretical symbol error rate.
"""
snr = dB2Linear(SNR)
# $P_s \approx 2Q\left(\sqrt{2\gamma_s}\sin\frac{\pi}{M}\right)$
# Alternative formula (same result)
# $P_s = erfc \left ( \sqrt{\gamma_s} \sin(\frac{\pi}{M}) \right )$
ser = 2. * qfunc(np.sqrt(2. * snr) * math.sin(PI / self._M))
return ser
def test_qfunc(self):
self.assertAlmostEqual(misc.qfunc(0.0), 0.5)
self.assertAlmostEqual(misc.qfunc(1.0), 0.158655254, 9)
self.assertAlmostEqual(misc.qfunc(3.0), 0.001349898, 9)
def test_qfunc(self):
self.assertAlmostEqual(misc.qfunc(0.0), 0.5)
self.assertAlmostEqual(misc.qfunc(1.0), 0.158655254, 9)
self.assertAlmostEqual(misc.qfunc(3.0), 0.001349898, 9)
