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The simulation starts with a setting of ${E}_{b}/{N}_{0}=0dB$ (see marked line in the table below). This yields to this bit error probability:

${p}_{b}=\frac{1}{2}erfc\left(\sqrt{\frac{{E}_{b}}{{N}_{0}}}\right)=\frac{1}{2}erfc\left(1\right)=\mathrm{7,865}E-02$ |

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

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

- 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 ${E}_{b}$ $1\mu V{s}^{2}$ The initial noise power-spectral-density of ${N}_{0}=1\mu {V}^{2}/Hz$ results in:

$\frac{{E}_{b}}{{N}_{0}}=\frac{1\mu V{s}^{2}}{1\mu {V}^{2}/Hz}=1=0dB$ - This BER simulation is quite slow as it implements quadrature modulation and pulse shaping. To boost simulation speed
*y*ou 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.
- 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.