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Ever since I found out that coding gain allows you to receive a signal that is well below the noise floor I have been fascinated with the idea of covert radio signals (low probability of detection). You could imagine a clandestine scenario with spies or political dissidents where not only the content of the radio message must be kept secret, but the mere existence of the communication must also be kept secret. Using spread-spectrum you can keep the power spectral density of your signal well bellow the noise floor, which would perhaps make the signal impossible to spot with a simple glance at a spectrum analyzer...

My questions are the following:

  1. How likely would someone be to detect such a signal by accident?
  2. Assuming your adversary did not know any details about the signal (its bandwidth, center frequency, modulation, etc.) but merely suspected the existence of covert signals with ultra-low PSD below the noise floor, how easy would it be to detect and locate?
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  • $\begingroup$ this is far too wide. 1. Any sensibly designed system would make the accidental detection probability as low as possible – that'd be the whole point of the signal design. 2. "easy" is really: far too unspecific. Sorry! Nobody who'd be looking for unknown signals would restrict themselves to a spectrum analyzer. $\endgroup$ Dec 16, 2021 at 12:01
  • $\begingroup$ anyway, "you could imagine" implies you're not aware of this being totally normal technology. You might want to read up on the history of FHSS, or what UWB communication is. There's also a very solid amount of literature on the theory of detecting unknown signals (not the least of which was written during the Cold War), but I'll be honest, even giving an introduction to things like autocorrelation-based blind signal detectors, or statistical moment analysis methods, would (at least for me) lead to an answer that would be far too long (and high in effort) for a question here. $\endgroup$ Dec 16, 2021 at 12:07
  • $\begingroup$ @MarcusMüller I have a vivid imagination, but I have not found any good information on actual implementations of "low probability of detection", so I have no clue how "low" low is or how you would go about detecting them. As far as FHSS goes I think that's a bad example. FHSS is actually very easy to spot on a spectrum analyzer. At least all of the incarnations I've seen before. $\endgroup$
    – Chris_F
    Dec 16, 2021 at 12:10
  • $\begingroup$ Chris: was actually about the history of FHSS, which was invented due to a need for covert communications, like a lot of such systems. A low-power FHSS signal is relatively hard to spot on a spectrum analyzer, due to its low probability to fall within the time/spectral observation window. As said, research that and UWB. $\endgroup$ Dec 16, 2021 at 12:16
  • $\begingroup$ @MarcusMüller Reading about FHSS was my first introduction to the concept of spread-spectrum. My comment about FHSS being "easy" to detect has to do with the fact that FHSS has a narrow instantaneous bandwidth. At any given instance the entirety of the transmitter's output power is concentrated in a very narrow bandwidth which produces the kind of PSD that stands out from the noise floor. Good for anti-jamming and immunity from narrowband interference, less so for low probability of detection. DSSS by contrast seems better suited. $\endgroup$
    – Chris_F
    Dec 19, 2021 at 0:24

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People in the SIGINT community spend their careers answering these sort of questions. Governments and their defense organizations are always working to be less detectable and their adversaries are always working to be able to detect them more. To answer directly:

  1. I don't see how you'd ever accidently detect a RF signal. As you say, you'd have to at least switch on a spectrum analyzer and even then any signal designed to be covert shouldn't show up just by looking at the energy.

  2. This is the one where people spend entire careers on these things and so I'm not sure any attempt to answer would do it justice, but I'd suggest going to Google Scholar and searching terms like: blind signal detection, LPD/LPI, spread spectrum

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  • $\begingroup$ I'll definitely give it another try. I have a feeling though that information on this subject probably doesn't tend to be freely published as much for obvious reasons. $\endgroup$
    – Chris_F
    Dec 19, 2021 at 0:26
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    $\begingroup$ @Chris_F no, this is really just basics of signal detection, and standard transmission techniques. Nothing secretive about that, you're overestimating the "youngness" of your topic. $\endgroup$ Dec 19, 2021 at 11:18
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I guess it depends on the channel. If you can occupy a large relative bandwidth and use really long spread sequences without fear of fading or doppler making the signal unreadable, then you can go very deep into the noise floor. Using the right key it is then trivial to dig the signal out of the noise floor. Most practical applications are unlike a simple Matlab simulation, and other factors than noise might be a problem.

If you use the same key over and over, naiively modulated by +1 or -1, I think that correlation techniques would be able to exploit the repetiveness to spot a pattern. How to break up that pattern in such a way that you can still decode efficiently given the key, I dont know.

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  • $\begingroup$ Well, it also depends on how much effort is OK for the receiver to have to go through per bit. Say, you do DSSS, with a high spreading factor and a long code – basically, you get a cryptographically secure PRNG to output random bits and use that as spreading sequence. Correllating that out of noise will be hell – you'd need to go through all combinations of hypotheses from sampling rate offsets and frequency offsets, to then get tentative data that you put through a loooong interleaver, a low-rate channel (de)code(r) and a checksum, and if that works out, you got your bits: that'd be $\endgroup$ Dec 19, 2021 at 11:11
  • $\begingroup$ relatively hard to spot, since the random bits don't autocorrelate, and if your receiver doesn't rely on correlation statistics / spectral properties of the pulse shape, you can pretty much work with randomizing every single DSSS chip's shape to the point where your receiver barely works due to ISI and the periodic symbol timing doesn't lead to suspicious PSD. As everywhere, this is just a tradeoff of mutual information between Alice and Bob (the covert sender and intended receiver) and Alice and Eve (the eavesdropper trying to detect Alice's presence/data). $\endgroup$ Dec 19, 2021 at 11:15
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Just spreading the spectrum either with Direct Sequence Spread Spectrum (DSSS) or Frequency Hopping Spread Spectrum (FHSS) is not enough to ensure undetectability with over the air communications. We can always simply point a high gain antenna at the transmitter (or move closer to it) to the point where the signal power is higher than the noise (we can easily see DSSS or FHSS on a spectrum analyzer whenever the power is strong enough). To reduce this possibility, high gain directional antennas in the intentional communications link can help to minimize detecting in other spatial directions but we are always fighting pass loss vs spatial location in that ultimately a higher power signal will be available (negative SNR signals are not transmitted, but received).

That said, what can be considered in message hiding- instead of trying to bury signals in the "noise", bury them in other signals that would be there for other reasons. Make the signal look like something benign and normally expected for other reasons that it isn't.

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    $\begingroup$ Yep, fake a multipath component (or multiple) in something that is expected to contain multipath either way. The intended receiver knows statistic properties of the fake component if present, and hence gets a non-zero channel capacity. $\endgroup$ Dec 19, 2021 at 0:32
  • $\begingroup$ @MarcusMüller Would you not possibly be raising more attention by causing targeted interference with a specific signal? $\endgroup$
    – Chris_F
    Dec 19, 2021 at 1:06
  • $\begingroup$ no, as said, that'd be a signal that is expected to have a multipath component – so you're not interfering, you're um, augmenting the channel – actually, you might even make reception a bit better that way, on average, if the original system's receiver works well. It looks like you added a reflecting mountan, building or metal part somewhere far away, in addition to all these that are already there in the propagation environment. $\endgroup$ Dec 19, 2021 at 1:13
  • $\begingroup$ The truth is of course a clever receiver could figure that out, because multipath components have specific behaviour and development over time, and of course there's imperfections in hardware that you couldn't "fake away". But the amount of certainty about the covert transmitters presence, or position, or especially its message, can be very low. Physical Layer Security is a by now pretty large area of research, and such things fall under it. $\endgroup$ Dec 19, 2021 at 1:18
  • $\begingroup$ Introducing a fake reflection would be «plausible» for an eaves dropper, but might convey information for someone who knows what to look for. You are dependent on someone else actually transmitting something to be able to latch on. $\endgroup$
    – Knut Inge
    Dec 19, 2021 at 12:55

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