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QAM BER for AWGN channel

In this experiment the bit error rate (BER) vs ${E}_{b}/{N}_{0}$  of M-QAM over an AWGN channel is analyzed.

Start

The simulation starts with 4-QAM and $\frac{{E}_{b}}{{N}_{0}}=0dB$ - see marked cell in table below.

Measured BER approximates the analytical bit error probability ${p}_{b}$

$\frac{{E}_{b}}{{N}_{0}}$

[dB]

4 QAM

${p}_{b}$

16QAM

${p}_{b}$

64QAM

${p}_{b}$

256QAM

${p}_{b}$

-2 1,306E-01 1,873E-01 2,464E-01 2,909E-01
0 7,865E-02 1,410E-01 2,002E-01 2,561E-01
2 3,751E-02 9,774E-02 1,570E-01 2,178E-01
4 1,250E-02 5,862E-02 1,185E-01 1,786E-01
6 2,388E-03 2,787E-02 8,382E-02 1,412E-01
8 1,909E-04 9,247E-03 5,233E-02 1,079E-01
10 3,872E-06 1,754E-03 2,653E-02 7,860E-02
Analytical bit error probability ${p}_{b}$ for M-QAM considering ${2}^{nd}$ bit errors

Experiment

Adjust ${E}_{b}/{N}_{0}$ and M. Measure the corresponding BER and compare it to the analytical bit error probability.

Simulation - Settings (F11)

Simulation - Setup (F12): Set M, the size of the modulation constellation.

Note

• This BER simulation is quite slow as it implements quadrature modulation and pulse shaping.
To boost simulation speed switch to modem none in Simulation - Setup (F12)
• Adjusting ${E}_{b}/{N}_{0}$ adapts the noise power spectral density. These settings are not modified:  Transmitting power $1{V}^{2}$ Bit duration ${T}_{bit}$ $1\mu s$ Energy per bit ${E}_{b}$ $1\mu V{s}^{2}$

Next steps

• The analytical bit error probability ${p}_{b}$ considering ${2}^{nd}$ bit errors is a much better approximation in cases of low signal quality. For instance, ${E}_{b}/{N}_{0}=-2\text{\hspace{0.17em}}dB$ and 16-QAM: ${p}_{b}=0,1873$
However, the assumption of two bit errors in the case of non-adjacent symbol errors is an approximation as well. In the case of three points further there might be one or three bit errors. Simulation suggests that this bit error probability is an upper limit?