# SNR wall definition

I want to ask you if my understanding of the definition of the so called "SNR wall" is correct and complete. The SNR wall phenomenon is described here and here. If one has further information that will help to improve the knowledge about the SNR wall, you are welcome!

My understanding:

To detect if there is a signal present or not, assuming you know nothing about the signal itself, you are left with energy detection.

If you use energy detection, the signal you are looking for has to be strong enough, such that you are able to detect the difference between noise and the signal.

But: If you can only observe a limited band and a station transmits a spread signal that covers the whole band, you will only see "noise". Since you do not know how the band looks without the spread signal, you can't tell for sure, that the signal is present (you are missing a reference level you can compare your level to).

As far as I know, that is called the "noise uncertainty", am I right?

The same applies if your narrow-band signal is very weak and you can't detect the signal-energy with a good SNR, right? (Your peak in the spectrum is "hidden" in the noise floor.)

In conclusion: I would define the SNR wall as the threshold SNR value that a detector has. Below that threshold, the detector can't reliably make a decision if a signal is present or not.

So my central question is: What exactly is the SNR wall / What is it's definition?

• Some radar false-alarms set the trip for about 1.5 dB SNR. – analogsystemsrf Aug 16 '18 at 5:51

I'll try to answer this, although I don't have much knowledge of the area beyond the first paper you linked to. This would be a better fit on https://dsp.stackexchange.com/.

If you use energy detection, the signal you are looking for has to be strong enough, such that you are able to detect the difference between noise and the signal.

Yes. An energy detector assumes a known value for the SNR, and then looks for a statistically significant deviation from this power level. The longer the observation period, the lower the variance in the estimate and the more confident you can be in the detector's output.

However, you can't know the noise power exactly. In a realistic system you have an estimate. The difference between the estimate and true value is related to the noise uncertainty. If there is no uncertainty, with a long enough observation time it would be possible to detect any signal, no matter how weak. With uncertainty, it's impossible to tell whether variation is due to your inexact knowledge of the noise power, or due to a weak signal being present. The paper you linked to is just putting quantifiable limits on this, in terms of uncertainty and the SNR wall.

The SNR wall is the point where a signal is weak enough that it can't be distinguished from noise, regardless of the number of observations used. This is a rather poor name, as it's determined more by the knowledge you have of system parameters (the noise level) than the SNR of a signal.

The same applies if your narrow-band signal is very weak and you can't detect the signal-energy with a good SNR, right? (Your peak in the spectrum is "hidden" in the noise floor.)

The difference here is you can always take more observations and get a better estimate. The SNR decreases as you average multiple estimates of the spectrum, and eventually the peak will come through. On the other hand, if your signal power is smaller than errors in the system model you can average all the estimates you want from an energy detector and you still won't know if you've detected a signal, or your model is wrong. The SNR wall arises from errors in the system, rather than properties of the signal being detected.

I would define the SNR wall as the threshold SNR value that a detector has. Below that threshold, the detector can't reliably make a decision if a signal is present or not.

The difference is that the detector threshold can be chosen. If you want a higher probability of detection increase the threshold. If you want fewer false positives, decrease it. You might have very poor performance if the SNR is low, but you have meaningful tradeoffs. If the signal power is less than the SNR wall the tradeoffs are no longer meaningful. Decreasing the threshold might improve false positives, or it might not.

So, the SNR wall is just a way to quantify when errors in your system model (estimates of noise power are primarily considered) will prevent signal detection. This paper is the first I've heard the term, although the concept seems rather obvious. The paper does seem to be cited primarily by works related to spectrum sensing for cognitive radios, rather than general theory of detection and estimation. This may already be a well known problem under another name in that field.

• SNR is signal/noise, there is a whole science dedicated to thresholds and SNR, it's called detection and estimation. – Voltage Spike Mar 13 '19 at 21:08
• @laptop2d Yes, that's what makes me rather suspicious of the whole "SNR wall" idea - most of the references to it come from papers outside the traditional "detection and estimation" field. But, as I said, it's not my area of expertise. I'd be curious what someone who's practiced in the area thinks. – user2699 Mar 13 '19 at 21:26
• @VoltageSpike a related concept is at en.wikipedia.org/wiki/Minimum_detectable_signal, for anyone interested. – user2699 Feb 6 '20 at 2:01