Topband: ADC Overload

[James Wolf]

Jim,

I sense a flaw in the CLT argument, which is likely a lack of understanding on my part.  What you are describing sounds more like AGC action.  In-other-words, moving the minimum detector level up the bell curve such that we have now lost any capability of listening down into a hole between strong stations and copying the weak station (which is really what we are talking about).  That scenario now sounds like a corner case. 
Other wise, what happened to the two +3V stations that add up to +6V.   Do they still show up on the bell curve, and if they no longer add up to +6V, why not?

Thanks for the insight,

Jim - KR9U

-----Original Message-----
From: Topband [mailto:topband-bounces at contesting.com] On Behalf Of Jim Garland
Sent: Monday, October 12, 2015 2:35 PM
To: steve at flexradio.com; topband at contesting.com
Cc: 'K1JD John'; 'Phillip Townsend Lontz'
Subject: Re: Topband: ADC Overload

Interesting comments, Steve, and to me quite on the mark. (In an ealier life, I was a physics prof, though I've forgotten most of what I once knew).

Re the comment by another list member that "there are various distractions such as the Central Limit Theorem...that don't add much to the discussion":  On the contrary, I believe the CLT is actually crucial to this discussion. Here's my attempt at an intuitive explanation of the CLT using a _very_ simplified example. I hope this contributes to this interesting discussion.

Suppose we have an SDR radio that hears two identical signals, and that the ADC in the receiver overloads when the instantaneous antenna voltage at the receiver input is greater than +/- 5V. Now let's assume that each of our identical signals has a maximum instantaneous RF voltage of +/- 3V, so that the receiver will overload when both signals add up to give either +6V or -6V. The question that the Central Limit Theorem addresses is how frequently this overload condition will occur. Here's how it works.

We'll keep things simple by assuming each of our two signals can take on only seven values of voltage: +3V, +2V,+1V, 0V, -1V, -2V, and -3V. (In reality of course, for a CW signal, the signals are sine waves varying continuously from +3V to -3V.) Every time the SDR samples these signals, it sees the instantaneous sum of their voltages. Since each signal has seven possible values, the sum of the voltages can have 7x7=49 possible values, which range from +6V down to -6V. 

If you make a list of all possible combinations of these two signals, you'll find that of the 49 possibilities, 0V comes up seven times, 1V comes up six times, 2V comes up 5 times and so forth, until you get to 6V (when the maximum value of signal adds up exactly). The reason 0V comes up seven times is because there are seven ways to get 0 by adding the voltages from the two signals, i.e., 0V plus 0V, +1V plus -1V, -1V plus +1V, +2V plus -2V, -2V plus +2V, +3V plus -3V, and -3V plus +3V. By contrast, there is only one way to get +6V, which is +3V plus +3V, and similarly for --6V.

Now if the ADC in the receiver overloads at any voltage greater than  +/- 5V, as we have assumed, then it will overload only two times in every 49 samples, once when the voltage is +6V and once when the voltage is -6V. If you draw a graph of all the possible combinations of voltages, plotting the numbers of times each combination of voltages comes up, you'll see that the graph resembles a bell-shaped curve, (called a "normal" distribution) peaked at zero. The maximum values of +6V and -6V are at the tail ends of the distribution.

So in this simplified example, our SDR radio will overload 2 out of every 49 samples, or about four percent of the time. That's not terrible, but not wonderful either. It means that we'd hear a pop in our receiver about four percent of the time. But suppose we let our two signals take on a continuous range of values between +3V and -3V. instead of only seven possible values. Unforunately, things don't get much better. The data points on our bell-shaped curve would smooth out, but we'd still overload roughly four percent of the time. The general shape of the curve doesn't change.

But...here's the interesting thing. Suppose instead of only two signals, we have thousands of signals appearing at our antenna terminals, and we'll continue to assume each of our thousands of signals varies from +/- 3V. Now when we add up the voltages of each of these signals, we find something remarkable. The sums of the voltages of all these signals is still a bell-shaped curve peaked at zero volts and extending from +6V down to -6V, but with one significant change. The bell-shaped curve narrows in, becoming very sharply peaked at 0V. The extremes of the curve, which would overload our receiver, almost never happens. This peaking of the curve is what the Central Limit Theorem tells us, and basically it is the reason SDR radios are in most cases nearly immune from overload. The more signals we're hearing with our receiver, the closer those voltages add up to zero. One can dress up this example with sophisticated math, which is what the CLT does, but the concept is actually very simple.

To me, this immunity to overload is the huge advantage SDR radios have over their superhet counterparts. In a conventional superhet receiver, with roofing filters and IF crystal filters, the averaging of signal voltages takes place only within the passband of the receiver. That's why a guy with a S9+60db signal who is 1 kHz away from the weak DX station you're trying to copy can wipe out your receiver: the RF voltage from his signal overloads the front end and IF amplifiers in the receiver. In an SDR, by contrast his RF voltage gets averaged out by all the other signals in the entire spectrum. Once the spectrum is digitized, which the DAC does immediately at the antenna input terminals, there are no more amplifiers to overload! 

As you can probably tell, I'm pretty solidly in the SDR camp. I use a Flex 6300 (though for contesting I've only used the radio in single-operator contests.) I can do A-B comparisons in my station between my Flex 6300, Elecraft K3, and Yaesu FTDX5000, and just in terms of raw performance (setting aside the display advantages of the Flex) I prefer the Flex 6300 to the other rigs, especially on 160m. I've never experienced overload problems of any sort. 

However, recall I said that "in most cases" SDR radios are superior to conventional superhets. In thinking about Tom W8JI's experience in his multi-multi contest environment, I think I can reconcile his SDR overload problems with my contrasting favorable experience in my station. In a multi-multi contest, the voltage at the input of nearby receivers will be dominated by a small number of very strong signals from the nearby QRO transmitters, often by only one signal. The favorable SDR averaging doesn't apply when the RF voltage at the receiver input is dominated by one huge signal, and if that signal exceeds the capability of the ADC in the radio, overload can definitely occur. So, although I believe that nearly all manufacturers will soon migrate to superior SDR technology, the "big gun" multi-multi contesters may want to hang onto their old Yaesu/ Icom/Kenwood transceivers (or else use bandpass filters on the inputs of their SDR rigs)!
73,
Jim W8ZR

> -----Original Message-----
> From: Topband [mailto:topband-bounces at contesting.com] On Behalf Of 
> Stephen Hicks, N5AC
> Sent: Sunday, October 11, 2015 9:24 AM
> To: topband at contesting.com
> Subject: Topband: ADC Overload
> 
> Rick,
> 
> I hope it's not an issue for me to post here directly.  I am posting 
> here because I believe that amateur radio has a huge educational 
> component and ultimately incorrect information services no one.  I got 
> started when I was
> 12 and really knew very little about the hobby.  My journey, like most 
> hams, has been a long, exciting educational process.  Still, there are 
> so many that know so much more than I do.  I am constantly amazed at 
> the breadth and depth of the hobby and the people in it.  My points 
> below are to clarify what I have observed, calculated and believe to 
> be true and are presented in the interest of mutual education:
> 
> On Sun, Oct 11, 2015 at 6:17 AM, wrote:
> 
> >
> > I have no experience with Flex Radio equipment, (it might be great 
> > stuff for all I know), so I will confine my comments to the theory 
> > discussed in the "ADC overload myths debunked"
> > paper.  A lot of what I read didn't make a lot of sense to me, or 
> > seemed irrelevant.
> >
> > To begin with, I'm not sure as to the exact nature of the "myth".
> 
> 
> Recently, a post was made to a reflector that definitively stated that 
> direct sampling receivers simply did not function -- that they would 
> overload with a minimal number of signals and/or signals of relatively 
> small magnitude.
> 
> 
> > Initally,
> > the myth is supposed to be that hams think average power of an 
> > ensemble of uncorrelated signals is the sum of the power of the 
> > components.  This is not a myth, it is true.  Then it is suggested 
> > that hams believe peak voltages add up, as in a 6 dB increase for 
> > two signals.  Supposedly, hams don't realize that the high peaks 
> > only occur rarely.  I'm not aware of any ham lore exhibiting this 
> > misunderstanding.
> 
> 
> > The discussion of crest factor obscures the fact that average power 
> > still adds.  100 signals at S9 still has a power of 20 dB over S9, 
> > on the average.
> > Once in a while it looks like 40 dB over S9.  The rest of the time, 
> > the combined power of all the signals still tests the dynamic range 
> > of the receiver.  It's not like a bunch of S9 signals is no worse 
> > than a single
> > S9 signal.
> >
> 
> The misunderstanding centers around a belief that an ADC reacts 
> negatively to a large average power.  There are two primary beliefs 
> rolled into this
> one: (1) That by taking the sum of any number of known signals in the 
> power domain we can reach a total, that when compared with the 
> overload point of the ADC, will definitively predict an overload of 
> the ADC, and (2) That the overload of an ADC  is a singular and 
> complete event -- when it occurs the ADC no longer functions.
> 
> Addressing each of these individually and getting more specific, the 
> first
> (1) belief is that if we have an ADC that overloads at +10dBm, that I 
> can take 100 -10dBm signals and completely overload the ADC to a point 
> of non-functioning.  This really seems like common sense to most.  We 
> all fully expect to be able to take 100 disparate signal generators, 
> feed them through a lossless combiner, read a power meter and see 
> +10dBm and then stick that in the ADC and overload it.  But this is not how it works.
> 
> To understand what actually happens, we have to look at how a discrete 
> sampled system works.  The ADCs we use are oversampled and run at 
> somewhere between 100-300MHz.  Each sample period, the ADC essentially 
> takes a voltage reading on the antenna and records this value, 
> transmitting it to to the computing element in an SDR.  The 
> instantaneous voltage of any RF signal varies with the sine wave that 
> defines the RF carrier so it varies from the bias point of the ADC to 
> the bias plus the voltage amplitude of the signal, back through the 
> bias point, down to the the bias minus the amplitude of the signal and 
> back to the bias point each cycle of the RF signal.  It is a sine wave 
> of given voltage amplitude centered around the bias point of the ADC.
> 
> If I add a second signal of equal amplitude, the second signal will 
> add to the first and I will get an instantaneous voltage that is the 
> sum of the two signals. But the voltage is not simply 2x the voltage 
> of the first -- this is only the case if the two signals are on 
> exactly the same frequency, phase and amplitude.  What actually 
> happens is a beat-note between the two signals who's envelope 
> oscillates in time at the frequency of the beat note (difference in 
> frequency of the two signals).  Periodically, the peaks of the two 
> signals will be exactly aligned and we will get a doubling of the 
> voltage.  For two signals this happens fairly frequently.  Similar to 
> the two signals adding, they will also subtract to result in a voltage 
> magnitude (absolute value) lower than either of the two signals would 
> have by themselves.  For example, one signal might be at +1V while the 
> other is at -0.66V.  The resulting voltage measured in the converter, due to linear superposition, is +0.33V.
> 
> Assuming for a moment that the two signals are large compared to the 
> overload of the ADC, say they are at +7dBm compared to the +10dBm 
> overload of the converter, they will overload the converter, but only periodically.
> If we assume for a moment that the two signals are 2kHz apart, there 
> will be a beat-note that runs at a 2kHz rate.  At the "nulls" of this 
> envelope, the signals will consistently add to very close to zero 
> because the signals are precisely 180-degrees out of phase: when one 
> signal is at it's peak voltage, the other will be at it's peak negative voltage.  At the "peaks"
> of the 2kHz beat-note, both signals will be in-phase and they will 
> look like two signals added in a power combiner -- providing a 6dB PEP 
> for a brief period.  THIS will overload the converter, but only 
> periodically as the signal exceeds +3dB of it's average power.  In 
> fact, to avoid any point where the two signals will add to exceed the 
> voltage limits of the ADC, we must subtract 6dB from each signal and 
> run them at +4dBm (again assuming a
> +10dBm overload).
> 
> This case, two very strong signals, just below the overload of the 
> ADC, is the worst case situation.  If I now go from two signals to 100 
> signals, each at -10dBm (20dB below the converter overload), the 
> probability of the signals adding like the two-signal case is 
> significantly decreased.  This is simply the reduced probability that 
> all the signals will add together at their peaks.  And because the 
> signals, even at S9+63dB, the overloads are infrequent (something like 
> one sample for every few hundred samples).  If I reduce the level of 
> the signals to 100 S9+53 signals, the overload becomes all but a statistical improbability.
> 
> This gets me to point number two (2) where the belief that an overload 
> is a enduring event.  In fact, as the number of signals are increased 
> (real
> world) and the amplitude becomes realistic -- most folks will not see 
> 100
> S9+50 signals -- the overload events as a percentage of time grow
> exceedingly small. These events "corrupt" a single datapoint in the 
> converter.  But for any given receiver in the FLEX-6000 radios over 
> 100 million samples are processed per second.  Losing a few of these 
> samples will not cause ANY perceptible degradation in the signal.  I 
> used the noise blanker as an example because most modern receivers 
> just "toss" samples that are perceived to be noise when the NB is on 
> and this has the same impact on the resulting output signal.
> 
> The net-net here is that a large number of mid-level signals (say 
> S9+30 to
> S9+50) are not going to cause an overload in a direct sampling receiver.
> This is a myth -- based on reasonable experiences and perceptions, but 
> a myth nonetheless.
> 
> 
> >
> > Then there is this statement:
> >
> > "The individual data points that make up a signal
> >   you are listening to are almost never going
> >   to fall in the same time as the overload, statistically."
> >
> > I have no idea what this means in terms of Nyquist sampling theory.
> 
> 
> The instantaneous voltage read in the converter for any given time 
> period is the superposition of the instantaneous voltage of all 
> signals passing through the Nyquist filter of the radio and into the 
> ADC.  Statistically speaking, the corruption of a small number of 
> samples will have little to no impact on the end voltage produced in a 
> narrow-band receiver derived from those samples.  Said another way, 
> each sample fed through a speaker in your receiver will be composed of 
> 10,240 samples received off the air.  The voltage change represented 
> by a a sample read in the converter as +1V instead of +1.05V will have 
> such a minuscule impact on the receiver as to be completely 
> imperceptible.  The decimation process in the direct sampling SDR 
> converts 10,240 samples at 245.75Msps to one sample at 24ksps, extending the number of bits of precision in the process.
> 
> The
> > paper goes on to
> > say:
> >
> > "With a noise blanker, we remove thousands of samples
> >   with no negative effects to the signal being
> >   monitored and a momentary overload from the
> >   addition of many signals summing up will have a
> >   much lower effect"
> >
> > I don't know whether this means Flex (IE "we") has invented some 
> > sort of magic digital noise blanker that removes samples corrupted 
> > by overload (I'm
> > skeptical) or whether it means that a noise blanking effect just 
> > happens as part of the sampling process (in which case, I'm still skeptical).
> >
> 
> Noise that is removed by a noise blanker essentially corrupts the 
> samples we want to use for our receiver because the characteristics of 
> the noise contain frequency components that overlap with our signal of interest.
> Once you've "peed in the pool" it's hard to separate out the pee.  So 
> modern noise blankers understand that removing samples by substituting 
> a 0V value or some other value will often not impact the receiver 
> negatively because there are so many samples containing the 
> information we need to play the audio for your receiver.  So modern 
> noise blankers do just this -- they remove the samples.  This is 
> generally a safe thing to do although there can be some side effects 
> that are detrimental, especially when the NB runs at a relatively low 
> sampling rate.  The most common issue is when the periodicity of the 
> noise causes the blanker to act like a mixer at the repetition 
> frequency of the noise.  The random nature of an overload due to the 
> addition of a large number of signals will not exhibit this problem.
> 
> My comment is about all noise blankers and not about a specific one we 
> created.  I figured a certain percentage of people reading what I 
> wrote would know how noise bankers worked and would hear this 
> explanation and say to themselves "oh yes, this makes complete sense 
> -- the overload removes far fewer samples than a NB would and so the impact will be less."
> 
> 
> > Then the subject shifts to decimation and "processing gain", which 
> > are simply references to digital filters.
> > These techniques are all based on linearity.  Adding digital 
> > filtering after a nonlinear front end cannot repair the damage 
> > caused by nonlinearity.
> > Just
> > like adding crystal filters to the IF in an analog receiver won't 
> > overcome front end overload caused by enabling the receiver's built in preamp.
> >
> 
> Absolutely true.  Once we have an overload event, nothing down the 
> line can fix it because the true value of that sample is lost forever.  
> But we still have people that believe that an 20-bit converter at 
> audio is superior to a 16-bit converter at RF because they do not understand processing gain.
> Again, this is myth that we have to stamp out through education.  It 
> is not directly related to the overload problem, but I figured while I 
> was stomping out myths, I would be an equal-opportunity stomper ;-)
> 
> >
> > There is an assertion that the large amount of "noise" added by 
> > hundreds of signals results in "linearization", which I believe is 
> > referring to what is usually called "dithering".  This is a complete 
> > misunderstanding of dithering, which uses small amounts of noise and 
> > does not involve clipping in the ADC.  High quality ADC's have 
> > dithering and similar randomization processes built in and don't need help from external noise anyway.
> >
> 
> The periodicity of alignment of a signal with the voltage bins of the 
> converter causes quantization noise due to what are effectively 
> rounding error.  The fewer signals there are to randomize how any one 
> signal will fall into which bins in the converter, the more 
> quantization noise will be evident in the resulting derived signal.  
> Anything that adds randomization to this process lessens quantization 
> noise.  Dither is used to do this, but on-air signals have the same 
> effect -- in fact large on-air signals are best because they cross 
> more bins.  A direct sampling converter should always perform better on-air than in a lab environment because of this.
> This is unrelated to clipping, as you say.
> 
> 
> >
> > The paper then changes the subject to phase noise.
> > This has nothing to do with ADC overload.  I will note that digital 
> > radios are much more sensitive to clock jitter (IE phase noise) than 
> > analog radios.
> > If anything, the phase noise issue is an argument against digital.
> >
> 
> You are correct -- a good phase noise oscillator is much more 
> important in a direct sampling receiver because the phase noise is 
> imparted in the signal at the point of sampling.  Because this 
> generally happens at a higher frequency (oversampling) in a direct 
> sampling system, it says the designer must have a better oscillator 
> than one that would be used in a superhet radio.  The LO in a superhet 
> radio is generally divided down, producing better phase noise on the 
> low bands (good news for top band aficionados) and worse phase noise 
> on the high bands.  For the oscillator designer, it's easier to get 
> better phase noise at a fixed frequency (sampling clock) than in a synthesizer, generally.
> 
> Of course a superhet has more LOs and care much be taken with each 
> oscillator to prevent phase noise.  In the end, the receivers RMDR is 
> a tell-all on how the designer did so the radio purchaser just needs 
> to look at RMDR for the answer, not look at the phase noise of individual LOs.
> 
> 
> >
> > There are various distractions such as the Central Limit Theorem and 
> > the Jupiter effect that don't add much to the discussion.
> >
> 
> It's hard to explain complex material in a way that will resonate and 
> impart a intuition in the reader's head.  The CLT is definitely at 
> play as can be seen in the random addition of a lot of carriers.  The 
> Jupiter discussion was to show that there is a common misconception 
> about the ease of alignment of a number of random objects that are 
> oscillating and the impact of that alignment.  This speaks to both 
> parts of the myth and, again, I was looking for ways to give the 
> reader an intuitive feel for the problem in the physical world.
> 
> 
> >
> > The dubious argument is made that the existence of 1000's of 
> > receivers in the field without complaints from their owners "proves" 
> > that overload problems do not exist.  Until last month, we could 
> > make a similar statement about the millions of satisfied Diesel 
> > Volkswagen owners.
> >
> 
> Haha yes good point.  It is not proof, of course.  But I can tell you 
> from personal experience that when things go wrong, hams call us to 
> tell us about them.  I do feel it is fair to say that the lack of 
> these types of complaints speaks to the lack of a problem, but it is not proof!
> 
> 
> >
> > The concluding statement is quite a stretch:
> >
> > " it is simply mathematically true.  FlexRadio Systems
> >   makes the best amateur transceivers available."
> >
> > Mathematically true?  Maybe it's that new Common Core math.
> >
> 
> I apologize for not showing more math.  I tend not to go there first 
> when explaining to large groups because a large percentage of the 
> folks will tune out the discussion quickly.
> 
> 
> >
> > Rick N6RK
> >
> >
> >
> ​All of your arguments and concerns are fair and I appreciate you 
> continuing the conversation.  Direct sampling is relatively new in the 
> amateur world.  I think it is here to stay because of the tremendous 
> benefits it offers.  But no one knows fully all of the benefits and 
> pitfalls that a new technology like this will bring.  It's my wish 
> that we will all learn them together for the benefit of ham radio.​
> 
> 
> ​Vy 73,
> Steve​
> 
> 
> Stephen Hicks, N5AC
> VP Engineering
> FlexRadio Systems™
> 4616 W Howard Ln Ste 1-150
> Austin, TX 78728
> Phone: 512-535-4713 x205
> Email: steve at flexradio.com
> Web: www.flexradio.com
> Click Here for PGP Public Key
> <https://sites.google.com/a/flex-radio.com/pgp-public-keys/n5ac>
> 
> 
> 
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