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I am trying to build a bit error rate simulation for a digital baseband signal (specifically using Manchester coding). The simulator generates a digital waveform from random symbols at a sample rate of at least $f_s = 2/T_l$, where $T_l$ is the chip duration (the duration of the "on" time).

The transmitted signal is mixed with AWGN, based on the desired S/N ratio. The detector correlates each symbol period from the received signal with an ideal 0 waveform or 1 waveform, and chooses the best. Either "ideal" is 1V during the on time, and 0V during the off time. These ideal waveforms are sampled at the same rate as the input.

What I am seeing is that the BER improves when the sampling rate is increased, for a given SNR (see plot). This was unexpected, since I believed that the error rate would be independent of the sampling rate.

enter image description here

Am I missing something in this BER simulation? Shouldn't the error rate be independent of the sampling rate?

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Another hypothesis: as you increase the sample rate you also increase the bandwidth. Depending on how you generate the noise, this probably means that the spectral density of your noise decreases. If the spectral content of your signal stays constant, that means that the in-band SNR goes up.

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  • $\begingroup$ Yes this makes complete sense; since the noise is being simulated, not sampled-- following the similar logic in that the total noise density for noise that is independent sample to sample is spread over a wider bandwidth $\endgroup$ – Dan Boschen Jun 3 '20 at 19:37
  • $\begingroup$ @Hilmar Thanks, It looks like this explains it. By scaling the noise power up with the sampling rate, the noise spectral density is restored, giving the same rate of error for any sampling rate. $\endgroup$ – achatief Jun 3 '20 at 23:31
  • $\begingroup$ Hilmar - It makes sense if you work only with noise. But on the other hand bandwidth of the signal expands too. Or am I wrong? I tried this type of simulation with similar result as @achatief. The thing is, that SNR, or Eb/N0 did not change when changing f_s, because the power of signal changes proportionally to power of noise (according to my simulation). I probably didn't understand what you mean by scaling the noise power up with the sampling rate... :/ How do you generate the AWGN according to sampling frequency? $\endgroup$ – Adrian Mar 21 at 17:19

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