S/N Ratio and PSK31

Discussion in 'General Technical Questions and Answers' started by WB6LA, Jul 28, 2016.

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  1. WB6LA

    WB6LA Ham Member QRZ Page

    I've recently begun using both PSK31 and HRD's DM 780. This leads me to a puzzle.

    I read that PSK31 signals can be copied well below the noise level; that is, below 0 dB S/N. And, as a user of JT-65, I've often seen this sort of thing. But I notice that signals reported by DM 780 at even (positive) 20-25 dB S/N are often very badly copied. And I have yet to see a signal reported at less than 10 dB, let alone a signal below the noise level. Not only that, but signals only faintly discernible on the waterfall and hardly copyable at all often have S/N values of 20 or even 30 dB.

    It seems to me that I should be able to more or less accurately copy PSK31 signals at, say, 10 dB. Because PSK31 signals can be copied well below the noise level, 0 dB. But, as I mentioned, that's not the case.

    I suspect the apparently inconsistency lies with the definition of dB the programmers of DM 780 have followed. Certainly a variety of definitions does exist.

    But my hypothesis amounts to speculation. Can anyone shed definite light on this apparent inconsistency? Why does DM 780 report such high S/N levels for PSK31 signals? And why are PSK31 signals with pretty generous S/N levels not accurately copied by DM 780?
  2. WB3BEL

    WB3BEL Ham Member QRZ Page

    Actually PSK31 signals can NOT be copied reliably below the noise level in the matched filter bandwidth. These are BPSK signals with very weak error correction coding.

    Where the confusion comes in is that many people calculate the noise in a voice channel bandwidth of something between 2 and 3 KHz and the signal power in the signal bandwidth which is only ~50 Hz. This results in a negative signal to noise calculation and this kind of number is reported by many demodulator programs including JT65.

    The reason some strong signals do not decode well is that they can be distorted by many things and the noise component may be small but the distortion component is so big that the demodulator makes decision errors. This can be distortion of the transmitting station due to non-linearity or speech processing or filter adjustments like equalization or noise/hum on the audio path or frequency instability. It can be similar distortions in the receiver due to receiver settings or audio clipping levels in the baseband A to D converter. Or it can be distortion or interference caused on the propagation path due to ionospheric effects or interfering signals.
    -Harry WB3BEL
    N0SYA likes this.
  3. K0RGR

    K0RGR Premium Subscriber QRZ Page

    Distortion in the transmitted signal is fairly common due to ALC action. I'm working with a local ham who has a weak signal here, but it should be copiable. However, I am having a hard time with him. I think we're finally figuring out that his SWR is so high that it is causing the radio to go into SWR shutdown, and that involves the ALC circuit in his rig, hence, mucho distortion.

    If you want a mode that you can reliably work stations below the noise, try Olivia. Most Olivia modes have a great deal of error correction and work under absolutely horrendous conditions. My Olivia net is tonight at 8:00 Central on 3583.5 (USB dial - about 3584.7 on the waterfall) - we start out using Olivia 8/500. I typically run about 40 watts or less, and many of my 'regulars' check in with 5 watts. We get people from both coasts when the conditions are good. Tonight, we will have t-storms in the region, so noise levels will be high. Here's a list of common Olivia frequencies and modes - just because you don't hear a signal, don't give up!


    A friend of mine works Europe using Olivia 1000/32 on 20 meters quite often. No audible signals...

    Then, of course, there's JT65, JT9, and WSPR...
  4. WB6LA

    WB6LA Ham Member QRZ Page

    Harry, thanks for taking the time to respond. I believe that I entirely understand your points. I wish those who don't understand would improve the web's signal-to-noise ratio by spending less time writing web pages.

    If distortion is the cause of copy errors, as I do suppose it is, then it appears to me to be typical rather than atypical, which I would not have suspected. But I do see many, many PSK31 signals that seem to me to exceed their proper bandwidth. At least, I observe noise suppression for a wide swath of frequencies immediately above and below the actual signal. This somewhat frightens me as I think I need to develop some way of ascertaining the quality of my own signal before I transmit PSK31 other than experimentally. I mean, it doesn't seem like I can rely on the offered opinions of others as I naively supposed I could.

    K0RGR, I have a fair amount of experience with JT65, which is why I did not doubt claims that PSK31 signals below the noise level could often/generally be copied. Now, thanks to Harry, I have to reconsider that claim as well. Didn't Joe Taylor himself offer some figures showing negative signal-to-noise ratios for JT65A and friends? When you can't trust a two-time Nobel prize winning physicist life seems tough! Perhaps those figures are the work of others.

    I haven't used Olivia but I have attempted to copy almost every Olivia signal I've identified by means of an RSID header. I've also read descriptions and analyses of the protocol. What I have read generally concurs with what you wrote.

    But, of course, using some protocol is not so easy as merely choosing to use it--at least, unless one is content with few responses to CQs. Olivia use seems to me to be below what students of media call critical mass; that is, there aren't yet enough stations using Olivia for Olivia to be an especially reliable means of communication. (However, perhaps there are Olivia watering holes that I haven't found? I generally have found Olivia signals a few kHz above PSK31 signals.)

    I suppose we can agree that the best way to deal with lack of critical mass is to use Olivia rather than ignore Olivia. I will most definitely try Olivia out for an extended period of time before you hear me criticize it in any way. It's already on my short list of protocols that are better in some sense than run-of-the-mill protocols (CW, SSB, etc.), at least in principle.

    Thanks again for your time taken in responding. It's much appreciated notwithstanding all the little cognitive structures that I'm now pressed to reorganize by re-reading everything I've read on the signal-to-noise ratios of digital protocols. :)

  5. K4SAV

    K4SAV Ham Member QRZ Page

    On the same subject and hoping not to steal someone's thread, I am confused about how JT-65 calculates signal to noise ratio. I don't have a lot of experience with JT-65 but it seems to me that JT-65 reports a signal to noise ratio of about 45 dB higher than it should be. I can read the signal to noise ratio directly on my TS-990S bandscope and a signal that is 40 dB above the noise floor, JT-65 reports -5 dB. A signal that's 30 dB above the noise floor, JT-65 reports -15 dB. That means JT-65 would have to report something lower than -45 dB to be below the noise floor. The smallest signal I have ever seen reported so far was -29 dB.

    Any words of wisdom that would help me understand this would be appreciated.

    Oh, and I am using WSJT9.5.

    Jerry, K4SAV
  6. W8JX

    W8JX Ham Member QRZ Page

    Domino EX has error correction, Olivia does not. While Olivia uses a protocol and tone scheme that works better than PSK in weak signal and multi-path conditions, Domino EX has CRC error correction. It is also un-effected by drift. MFSK 8 and 16 while dated are very robust too but rarely used today as is Pactor that can produce a solid copy from a signal your ears cannot even reliably detect.
  7. WB6LA

    WB6LA Ham Member QRZ Page

    Jerry, your question is one I might have asked. I was merely trying to express my immediate question tightly.

    In re-reading from my collection of articles on SNR, the most helpful article I've found so far is found at http://www.pa3fwm.nl/technotes/tn09b.html. The article is titled "Signal/noise radio of digital amateur modes" and was written by Pieter-Tjerk de Boer.

    The author writes, "The Signal to Noise Ratio (SNR) quoted for amateur radio modes is traditionally based on a receiver bandwidth of 2500 Hz, because these modes are usually received with a normal SSB receiver, whose IF filter is about 2500 Hz wide." That, it seems to me is the interpretive key.

    The author goes on to describe a more consistent way of calculating a SNR that does take account of bandwidth, using a measure preferred by theoretical physicists that is called the "energy per bit to noise power spectral density ratio" or Eb/N0 (also known as "SNR per bit"). The following table selectively summarizes a few of the author's results. I apologize for the crude formatting. I tried using BB Code to display a table but it did not work on this forum.

    Power Based
    on 2500 Hz Eb/N0
    Protocol (dB) (dB)
    SSB +10 +31
    CW -18 +16
    PSK31 -10 +9
    JT65 -24 +5

    The Shannon limit, beyond which it is theoretically impossible to communicate without error would be -1.6 if expressed using Eb/N0. The author also discusses several limitations of the metric, making clear that it is not a perfect solution to the problem of calculating SNR, as well as several admittedly questionable assumptions underlying the table values. As the author puts it, the table numbers need to be taken with a grain of salt.

    I would like to be able to calculate. or at least estimate, Eb/N0 for other protocols. I would suppose that it would be possible to somehow adjust the 2500 Hz SNR using the known bandwidth. But it's not immediately obvious how to do this. Sadly, the details of the author's calculations of Eb/N0 are omitted and the article has no references whatsoever. Wikipedia has an article on the subject, available at https://en.wikipedia.org/wiki/Eb/N0, which provides a few references. However, the material appears to me to be written at a graduate engineering level and engineering is not my field. I'm currently pondering the explanations given at http://www.gaussianwaves.com/2008/11/relation-between-ebn0-and-snr-2/ and http://www.rowetel.com/blog/?p=4621.

    If someone could point me to some examples of fully expressed calculations of Eb/N0, I'd very much appreciate it.
  8. WB3BEL

    WB3BEL Ham Member QRZ Page

    I am quite sure that you can trust that Joe Taylor is not trying to confuse the issue of S/N. I think that he merely followed in the footsteps of amateurs before him and presented the SNR in SSB bandwidth like many did before him. You are correct that understanding the Eb/No provides more insight from an engineering perspective. But, without an understanding of the operating bit rate and associated bandwidth to allow people to evaluate the performance of a waveform and modem together it is impossible to compare different digital modes.

    So perhaps the problem is that most people will want to compare these digital modes to other things they know like CW. The ear/brain combination together provide a pretty good filter. In the presence of Gaussian noise many experienced CW operators can decode signals with perhaps a few dB of SNR in bandwidths of about one hundred to few hundred Hz. Some operators prefer a filter before the audio signal is applied to the ear and think it helps. Others like a bit wider filter and use the brain/ear to provide more filtering.

    But the real world is more complicated than a static Gaussian noise environment. Add complexity like QRN or QRM and the optimum filter for each operator and condition change. This is why adjustable controls are so vital in decoding weak CW signals in the presence of noise and interference.

    The coded symbol rate of JT65A is just a few Hz. Signals that can not be heard by ear can be decoded reliably by this digital mode. But instead of comparing to 2500 Hz bandwidth maybe it would make more logical sense to compare to a few hundred Hz bandwidth. But this is not how the earlier amateurs presented their demod statistics. JT65A can decode signals that are perhaps 10 or so dB weaker than CW. This is partly because the signalling rate is slower and partly due to the error correction.

    Anyway if you want to dig into the details Joe Taylor and Steven Franke have published it all here:


    Of particular interest to you might be the equations and summary contained in Appendix A.

    Hopefully this answers your questions.
    Best Regards,
    Harry WB3BEL
  9. KA5IPF

    KA5IPF Ham Member QRZ Page

    I would say by using the SSB bandwidth for all gives a basis for comparison between modes.
  10. W8JX

    W8JX Ham Member QRZ Page

    Not really valid because while your receiver bandwidth would be same for all modes, the AFSK transmitted signal will vary in bandwidth depending on mode. CW has a narrow bandwidth, multi-path tolerant and some error correction in human brain filling it lost characters. PSK is narrow with no error correction and very sensitive to multi-path Doppler shifts. Modes like JT65, MFSK and Pactor has CRC error correction. (Pactor is very robust because it will re-transmit packet until it gets confirmation, a ack, of a copy) Narrowing receiver bandwidth can help picking signal out of noise but it is the focus of that signal in a narrow bandwidth on transmit that gives it the best chance of success vs wider modes at same power level. To put it is simpler terms, compare it to a flashlight with a variable beam width. Like a radio the input power is a constant but as you narrow beam (use radio data modes of narrower bandwidth) it carries farther with greater strength than when wider at same distance

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