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As per my current understanding, the ADC datasheets for modern high speed ADCs give the noise level measurements in terms of Noise Spectral Density (NSD) in unit of dBFS/Hz. Now to convert that value to the noise floor first the dBFS/Hz value is converted to dBm/Hz by using the value of full scale power in dBm for the respective device. Then the resulting value is added to $10\log 10(\text{Bandwidth})$ to get the noise floor for SNR and Dynamic Range calculations. The values should correspond to what is measured when analyzing the noise using FFT.

  1. If there is anything wrong in these steps then correction is most welcome.

  2. When integrating the noise over the total bandwidth, how should that value be chosen? As we are taking about thermal noise, shouldn't the value of the ADC analog bandwidth be used rather than the bandwidth of the filter prior to the ADC, even if Nyquist or oversampling is used? (Considering the thermal noise in ADC circuitry)

  3. For the case of sub-sampling over multiple Nyquist zones and using IQ data, what bandwidth value should be considered?

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  1. The interpretation is correct but note these levels are typically provided relative to a full scale sine wave not at clipping but at the point where SNR is maximized (typically 1 to 3 dB below clipping) and they are given at an assumed input frequency and sampling rate. Typically as sampling rate is increased, there is an increase in SNR due to spreading the quantization noise over a wider bandwidth but there is also a decrease due to non-linearities, analog input bandwidth and possible degradations due to sampling jitter contributions. Thus with regards to sampling rate and SNR considerations alone, there will be an optimum range where SNR is maximized.

  2. In a properly designed receiver our goal is to minimize the additional SNR degradation of our received signal between antenna and decision (this would be the receiver Noise Figure), so the signal and noise at the antenna is amplified and filtered accordingly. Thus we see that the noise density relative to the signal at the antenna would lead to total noise relative to signal when we consider the occupied signal bandwidth. The bandwidth chosen is the pre-detection bandwidth just prior to decision (or soft-decision) in the receiver. This is ultimately the SNR we care about whereas bad decisions due to the noise effect the bit-error-rate. A properly designed receiver would provide enough gain in front of the ADC such that the received noise from the signal dominates the locally generated thermal noise floor and quantization noise of the ADC.

  3. Subsampling does not change the bandwidth that is chosen as given in 2 above. With regards to IQ data, typically we are concerned with the signal and noise over the range of $-f_s/2$ to $+f_s/2$ and then the occupied bandwidth of our signal within that. If the receiver was designed properly when undersampling from a higher Nyquist zone, bandpass filtering would be provided such that the noise from only one Nyquist zone where the signal originates passes through.

One additional comment since FFT was mentioned; the noise will be the same but pay attention to proper accounting for the resolution bandwidth of each FFT bin and associated windowing losses if windowing.

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  • $\begingroup$ Thank you for your detailed answer, I think I understand now why we don't use the ADC's analog bandwidth because we have amplified the noise well above the ADC's own noise floor and now are only concerned with our concerned bandwidth. For the case of IQ sampling over multiple Nyquist zones and if no band limiting filter is used, I can expect the entire noise up-to the ADC's analog bandwidth to fold into the -fs/2 to fs/2 region? $\endgroup$
    – malik12
    Aug 25, 2022 at 11:47
  • $\begingroup$ and for your last point regarding FFT, I add the FFT processing gain to the measured noise floor level to estimate the actual noise floor and also account for windowing effects $\endgroup$
    – malik12
    Aug 25, 2022 at 11:59
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    $\begingroup$ @malik12 yes to your last point about folding that is correct— if no other filtering is used then the ADC would be the filter and it would fold as you described. A good visual of this for me is a histogram of AWGN: no matter how fast or how slow you sample it, given enough samples with an independent sampling rate you will get the same histogram and therefore same standard deviation, and therefore same total noise (it all folds in. $\endgroup$ Aug 25, 2022 at 12:30
  • $\begingroup$ Got it, thank you. $\endgroup$
    – malik12
    Aug 25, 2022 at 13:08

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