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For a radio receiver that digitizes over-the-air RF signals (such as an SDR), my assumption (as a DSP guy; pardon my hardware ignorance!) has been that thermal noise dominates total receiver noise, and quantization noise is a slightly distant second.

One reason for this is I assume you would put an LNA as close to the beginning of the signal chain as possible to reduce the effect of noise sources later in the receiver. Thus, SNR would largely be determined by thermal noise (probably mainly from the antenna). Is this accurate, or does it depend on the bit depth of the ADC?

Second question: Is quantization noise typically captured in the reported receiver noise figure, F, or does F only account for thermal noise?

Edit

Obviously the answer always "depends" on the designer's choices. But it seems likely there would be something typical, or a couple of standard cases.

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  • \$\begingroup\$ It depends on what it's a receiver of. And yes, it depends on the bit depth of the ADC. Usually you end up paying for just enough bits. \$\endgroup\$
    – hobbs
    May 13 at 3:48
  • \$\begingroup\$ Thanks for the comment @hobbs. I meant a radio receiver digitizing over the air radio signals. I'll clarify the question. \$\endgroup\$
    – Gillespie
    May 13 at 3:54

3 Answers 3

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It's a compromise.

You can easily make thermal noise dominate by adding an LNA stage with enough gain that the thermal noise exceeds the quantisation noise.

Then strong signals will exceed the ADC's input range and clip, even if the LNA is linear enough to keep intermodulation products from strong inputs below the quantisation noise (which is not always the case)

Or you can reduce the gain allowing good linearity for strong input signals; then quantisation noise will predominate.

Or you can use a higher resolution ADC; reducing the quantisation noise but adding cost.

Or you can add front end selectivity ahead of the ADC, to reduce the strength of signals outside the desired front end BW.

If this is ahead of the LNA it also guards against LNA non-linearity, but attenuates the input (thereby worsening thermal noise).

What you get is whatever compromise the designer chose, from their knowledge of the system requirements including response to unwanted interfering signals.

Second question : if the receiver includes an ADC, its noise figure ought to include not just the quantisation noise, but the ADC's own excess noise above that (from INL, DNL, sampling jitter or phase noise).

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  • \$\begingroup\$ Thanks for the reply @user_1818839. I'm sure you can make many different trade offs, but I guess my question is: What is more typical for a reasonably high-end RF receiver? Also, thanks for responding to the second question as well, but I'm slightly unclear on your answer. Are you saying the ADC noise (thermal, quantization, jitter, etc.) is typically included in the "receiver noise figure," or that the ADC has a separate noise figure that includes multiple effects? Do I need two noise figures to truly understand how much total noise will be in the digital signals? Thanks again. \$\endgroup\$
    – Gillespie
    May 13 at 18:00
  • \$\begingroup\$ As per answer, it depends on the parameters the designer optimised for. Now if you named a specific receiver and linked its datasheet you might get a better answer. As for the second Q : it is certainly possible to roll both thermal and ADC noise into a single figure. So some may do so, others may quote them separately. \$\endgroup\$ May 13 at 18:51
  • \$\begingroup\$ Of course it always depends on the designer's choices. You could say that about anything. But it seems like there would be a typical design choice. But perhaps I'm wrong. Is every receiver really so different from every other receiver that we can't say anything general about them? If so, please correct me. \$\endgroup\$
    – Gillespie
    May 16 at 13:30
  • \$\begingroup\$ For example, I found this answer that seems to say that it is typical to design for quantization noise to be low relative to thermal noise. Lots of detail is given to argue the case, and the author seems well informed. dsp.stackexchange.com/a/52647/55647 \$\endgroup\$
    – Gillespie
    May 16 at 13:33
  • \$\begingroup\$ Yes, that's a pretty good answer on the noise level aspects (actually the easy case) but doesn't touch much on strong signal performance, or the other end of the dynamic range problem. Whether that matters for your application I don't know; but understand that communications receivers for the "HF" bands (when "HF" was below 30MHz) could exceed 100dB dynamic range, done the old way ... using vacuum tubes. The "HF bands" were (are) a special case with very weak signals and strong interference on adjacent frequencies. \$\endgroup\$ May 16 at 15:08
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Thermal noise tends to dominate in an RF receiver. The bit-depth can be large enough so that the corresponding quantization noise becomes less significant w.r.t thermal noise. Quantization noise can be expressed as a noise figure and added to the noise figures of the other devices in cascade using Friis' formula.

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  • \$\begingroup\$ Thanks for your input @aganrock. Do you know roughly what bit-depth the switch from quantization noise dominance to thermal noise dominance happens at? \$\endgroup\$
    – Gillespie
    May 13 at 18:16
  • \$\begingroup\$ That depends on the system bandwidth and what you consider to be significant w.r.t. thermal noise. \$\endgroup\$
    – aganrock
    May 14 at 18:25
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I appreciate the other answers given, but I'm adding this answer to my own question because I think I found a more detailed answer here.

According to the author, it is typical to design for thermal noise to dominate rather than quantization noise. The main trade-off is dynamic range vs. noise figure degradation due to increased significance of quantization noise. If you place the quantization noise far below the input thermal noise, you give up dynamic range (I assume because to do this you have to boost your input signal power higher up in the range of the ADC).

This is all for a fixed ADC bit depth. If you increase the number of bits, quantization noise goes down, and/or dynamic range increases (my guess is you would typically use the extra bits to increase dynamic range and use an LNA to make sure the quantization noise doesn't dominate).

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  • \$\begingroup\$ That is a reasonable generalization for low to moderate frequencies where it is easy to make ADCs with high ENOB, but especially at higher sampling rates it can get quite hard to keep quantization noise 10dB below the noise floor. This is why digital cameras you still have an ISO (gain) setting that lets you adjust how much gain you provide to the ADC. This exists specifically because sensor dynamic range is higher than the ADC dynamic range, so the user may need to adjust the gain for bright or dim photography conditions to manage quantization noise. \$\endgroup\$ May 16 at 14:59
  • \$\begingroup\$ Thanks @user1850479. By low frequencies I assume you are referring to the bandwidth/sampling rate, not the carrier. I know there's no exact answer, but do you have a sense for roughly which BWs are "low or moderate?" Would 20 MHz be considered low to moderate? \$\endgroup\$
    – Gillespie
    May 16 at 15:08
  • \$\begingroup\$ The link you posted gives a good example. That ADC is a $100 in bulk (so fairly expensive), but of the 14 bits it specs less than 12 actually contain useable information at 105 MHz, so already at those frequencies you can see how ADCs are becoming expensive while quantization noise is creeping up. 20 MHz will be better, but your budget and specifications are going to determine what actually limits you. Below 1 MHz things are different, you'll rarely if ever be limited by the ADC at audio frequencies for example because you can get 18 or 20 bits for almost nothing. \$\endgroup\$ May 16 at 15:36

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