QPSK BER for AWGN channel - labAlive experiment

Quadrature phase-shift keying (QPSK) transmission - bit error rate for AWGN channel

The bit error probability of QPSK over an AWGN channel is given by:

$p_{b} = \frac{1}{2} e r f c (\sqrt{\frac{E_{b}}{N_{0}}})$

$p_{b} = Q (\sqrt{\frac{2 E_{b}}{N_{0}}})$

\frac{E_{b}}{N_{0}}

[dB]

Bit error probability

$p_{b}$

6

2,388E-03

$\frac{E_{b}}{N_{0}}$	Energy per bit to noise power spectral density ratio
$N_{0}$	Noise power spectral density	$N_{0} = \frac{N}{B}$
$N$	Noise power
$B$	Bandwidth

In this experiment the bit error rate (BER) vs $E_{b} / N_{0}$ of QPSK over an AWGN channel is analyzed.

Quadrature phase-shift keying (QPSK) transmission - Monte Carlo simulation of bit error rate for AWGN channel

Start

The simulation starts with a setting of $E_{b} / N_{0} = 0 d B$ . This yields to this bit error probability:

p_{b} = \frac{1}{2} e r f c (\sqrt{\frac{E_{b}}{N_{0}}}) = \frac{1}{2} e r f c (1) = 7,865 E - 02

Measured BER approximates the analytical bit error probability

p_{b}

Analytical bit error probability

p_{b}

for QPSK

Now adjust $E_{b} / N_{0}$ . Measure the corresponding BER and compare it to the analytical bit error probability.

Simulation - Settings (F11)

Measured BER approximates the analytical bit error probability:

E_{b} / N_{0} = - 2, 2, 4 d B

Adjusting

E_{b} / N_{0}

adapts the noise power spectral density. These settings are not modified:

The initial noise power-spectral-density of $N_{0} = 1 μ V^{2} / H z$ results in:

\frac{E_{b}}{N_{0}} = \frac{1 μ V s^{2}}{1 μ V^{2} / H z} = 1 = 0 d B

This BER simulation is quite slow as it implements quadrature modulation and pulse shaping. To boost simulation speed you might change to QPSK BER - equivalent baseband without pulse shaping.

Vary the pulse shape. Note that the pulse shape has no effect on the BER but the transmit spectrum.

Simulation - Setup (F12)
Switch to equivalent baseband. Note that the modem doesn’t affect the BER performance but the shifts the transmit spectrum to the base band.
Switch to modem none. Note that the modem doesn’t affect the BER performance. There’s only one sample per symbol and no pulse shaping, so the simulation is much faster.

Adjust $E_{b} / N_{0}$ and measure the corresponding BER.

Simulation - Settings (F11)

Measured BER approximates the analytical bit error probability:

E_{b} / N_{0} = - 2, 2, 4 d B

Resize the BER-meter to see the number of bit errors and the total number of transferred bits