QPSK BER for AWGN channel - equivalent baseband

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

QPSK / 4-QAM transmission - Monte Carlo simulation of bit error rate for AWGN channel. For best simulation performance this equivalent baseband simulation applies no pulse shaping and uses one sample per symbol.

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

$p_{b}$

$\frac{E_{b}}{N_{0}}$ [dB]	Bit error probability $p_{b}$
-2	1,306E-01
0	7,865E-02
2	3,751E-02
4	1,250E-02
6	2,388E-03
8	1,909E-04
10	3,872E-06

Analytical bit error probability

$p_{b}$ for QPSK

Experiment

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

QPSK BER - equivalent baseband

Start

Experiment