ADC overload myths debunked

w8mqw

N5AC writes:

The variance of the algebraic sum of these signals will decrease with the square root of the number of signals present.  As more signals are added, there is a decreasingly small probability that these signals will add (precise alignment of the highest voltage peak of the signals) and the algebraic sum of the signals will degenerate into a quasi-Gaussian distribution.

This is faulty mathematics. The variance of a sum of uncorrelated random variables (signals) is the sum of the variances. You are stating the rule for the average of the signals, not the simple sum. By your reasoning, noise in a channel will decrease as you widen the bandwidth.

(Also the Central Limit Theorem involves dividing the sum of normalized random variables (signals) by sqrt(n) rather than n so as to maintain the identical standard deviations as this quotient approaches Gaussian.)

  This averaging idea is used in astrophotography, where multiple images (n > 50) are taken of the same object, then superimposed (averaged). In this case indeed the standard deviation (visual noise) decreases as 1/sqrt(n).

What you have to worry about with a ADC is the random variable

                         Y = max(X1 + X2 + X3 + ... + Xn),

whose s.d. increases with n.

Paul Bradbeer

I think I'm still on yesterday's crypto..... ;-)

Gerald-K5SDR

@W8MQW

A few months ago I decided to prove this to myself empirically by building a spreadsheet that calculates the vector sum voltage of 100 uncorrelated CW stations.  The spreadsheet creates a time domain pk-pk voltage plot as shown below based on the criteria shown on the left.  You can recalc to your heart's content and the maximum vector sum does not get worse that about 0.02 Vpk.  The horizontal lines represent the +/- soft overload limits of the ADC input voltage with the 20 dB preamp turned on.  

By soft overload I mean that it is not possible to drive the ADC to the point of where it destroys the signals of interest before reverse power detection kicks in.  I can combine a +18 dBm carrier with an antenna and still copy all of the signals on the band 24/7/365.  Further, the ADC never gets close overload even with one hundred CW stations of S9 to 40 over S9.  In fact, you can make it 100 continuous carriers at 40 over S9 and it does not overload.  The more continuous carriers I add at the same level, the more Gaussian the output looks.

Dan -- KC4GO

Couldn't get to -130 with a 50 Ohm terminator on the XVTR input. 
My 6500 must be broken. (NOT)  I just couldn't let it go....

Ken - NM9P

Hey Dan, is that with or without the preamp turned on? Ha ha! You might have a noisy resistor.

Walt - KZ1F

You could invite your neighbor to join you so he'd have the opportunity to defend himself.

w8mqw

Gerald:

  Very interesting simulation. I would have to examine the code to feel totally confident that this empirical evidence is correct. There are very subtle sampling statistical issues that I may have overlooked and would have to review before I would abandon the straightforward probability arguments I presented.

Chuck

Gerald-K5SDR

Happy to share it.  Send me an email request to gerald at flexradio dot com.  I would love your feedback.  

By the way, I asked K6tU to capture a contest in the SFO Bay Area.  Here is a screen shot of 15m during the CQ WW SSB contest in October 2015.  You can see the strongest signal on the band was K2YY at about -60 dBm.  He did see it peak once at about -42 dBm, which he said is unusually hot for the ham bands.



Stu also sent me shot below of the entire AM BCB spectrum on his 160m antenna.  Looks like the strongest carrier is around -7 dBm or so. This means that he is receiving DC to 71 MHz in one chunk with no overload on an efficient 160m antenna.

W9OY

I've spent the past 2 years trying to find a case where the ADC overloads on both the 6300 and the 6500.  I have 50KW AM ten miles away and 10KW AM 3 miles away on all the time.  I've seen SWBC as loud as -35 dBm (Radio Havana a few hundred miles from here, who has a monster array pointed at my QTH.).  The point being is I have spent considerable time surveying for worse cases and have not found a failure.   I can work the 630 M band with a whole band full of BCB stations including the 50KW and 10KW stations 60khz up the band.  I could not do this with the F5K and I also had issues on 160 with the F5K using the same location and antennas.  I have zero problems with the ADC radios regarding overload.   I work contests and pileups all over the place and have never seen the first sign of overload.  I've never seen anyone complain about this.  It would seem to me if this is such an issue there would be a lot of complaining.  The only thing I've ever seen are the analogue boys cooking up fairy tales about "issues".  

I was able to force an ADC overload by transmitting 900 W on a highly efficient 40M 1/2 wave vertical in my back yard and receiving on a 40M matched 3/8 wave vertical 175 ft away from my transmit antenna using the 6300.  The measured crunch point was +9 dBm, exactly as predicted by the 6300's specs.  I have run SO2R on a 6500 with about 500W using an automated band switching amp plus antenna switch to resonant antennas for TX and a wide band low noise receiving loop for RX on the RX port.  My RX antenna is about 100 ft from the TX antenna.  Except for exact harmonics the receiver on the pounce band could care less about the transmitter on the run band and vis versa.   I set this up for proof of concept and it worked fine.  

73  W9OY

Barry N1EU

Yeah, I think it's unfortunate that there's such a serious disconnect with those who deny what us direct sampling radio users are experiencing and what's technologically possible NOW.  The ham radio state of the art should be advancing faster.

KY6LA_Howard

I have a similar experience as Lee has except my local RF **** is much worse. 

I live on the side of a mountain that sports 23FM Stations and 18 TV stations PLUS the US Navy secret transmitters.  The FCC Data indicates about 5MW Power PLUS the undisclosed US Navy Power which is likely more than those combined   I am 2,900' horizontal and 300' down vertical from the towers.   Walking up to the towers bends my RF Field Strength meter....  The signals and intermod is splattered all over the HF Band.  It is pretty obvious where the towers are as I only need to point a beam in that direction to see the noise floor rise 30dB

That said, even in contests, I have never had an ADC overload..

For some contests, I schlep my 6700 up to NX6Twhere we have all sorts of radios, amps and beams running simultaneously... even working on the same band I have never experienced and ADC overload from any of the radios running even in the same room...

Personally my best theory is FOLLOW the MONEY.. Most of the Myth Makers have monetary interested in claiming alleged overloads where none exists.

ctate243

I have taken a 6500 and a 6700 to N6RO during major multi-op contests.  Never had an issue. I can see the 3rd order stuff but it doesn't overload anything or affect the perceptible noise floor.  Just means I need to buy more coax and make new stubs :-)  and even then it will be visible.   Whos gonna post this as a response to that guy on the elecraft reflector :-).

Steve-N5AC

@W8MQW You are correct -- I did use the wrong terms in two cases as you point out.  I don't work with statistical math everyday and I used the wrong terminology.  Thanks for pointing this out!  I hope you will agree that my sloppiness with the terminology in my post does not invalidate these assertions I'm trying to bring to light:

1. The "sum" of a group of uncorrelated signals reaches a voltage peak on a sharper and sharper and more infrequent peak that becomes sharper/peaks a shorter time with an increase in the number of signals
2. These peaks presented to an ADC reach overload at an increasingly infrequent amount of time the more signals are added, rather than the simplistic view that assumes that signals are a constant scalar power that is simply summed and the algebraic power sum continuously overloads an ADC (rather, the ADC is an instantaneous voltage device and you must consider the instantaneous voltage effects)
3. A brief overload of an ADC does little to impact the a receiver operating at a fraction of the ADC sampling rate.  This is because the non-linear alteration of a single or a few points digitized at many MHz has little end effect on a signal derived through decimation whose sampling rate is many dB lower than the ADC sampling rate (40dB in our case)
4. The noise produced by the correlation of a signal and the sampling rate of the ADC, caused by the moire pattern of ADC bit crossings at periodic intervals (quantization noise) reduces in frequency the more signals are present due to the randomization of temporal bit crossings.
5. The larger the total signal presented to an ADC, the more frequently smaller signals will cross ADC bits as they "ride" on larger signals.  This also contributes to randomization and thus a more linear digitization of the signals present.  The net effect is that a direct sampling receiver PREFERS more strong signals whereas a Superheterodyne receiver PREFERS few strong signals (because of the non-linearities they induce in the receiver).  
6. The ultimate irony is that the overload argument against direct sampling is actually arguing against the one of the strongest benefits of an ADC.  This is natural, though, as those arguing are living in a world where many strong signals are bad and this has been recited, discussed, and argued for years so it has become a "receiver fact" that surely must apply to all receivers (except that it doesn't).

The layman who has not studied this a little tends to believe that 1) overload is easy to achieve and 2) overload is a fairly non-transient event that is devastating.  The term overload is, itself, pejorative and those openly discussing its finer points appear to be mincing words because conventional wisdom says (2).  

My hope is that more hams will either (1) seek to understand how direct sampling works and see the immense benefits and the lack of merit in some of the discussions arguing against the technology or (2) view the mounting evidence that shows the benefits, advantages and successes in contesting of direct sampling and simply trust the mounting evidence proves the technology's benefits by proxy.

Jay Nation

But Steve ...
Regarding that last hope of yours 
I haven't ever seen much evidence, Hams are capable of doing either of those things. 
73, Jay - NO5J

Steve-N5AC

@NO5J - I don't know -- I have a pretty positive view of the ham community.  I watch what happens when a new antenna design hits the market and I am amazed: there will be folks that immediately go buy the antenna, put it on the air, A/B it with existing designs and report what they've found.  Another group will go simulate the antenna in NEC and report on why the design does/does not work.  Still others will put it in an anechoic chamber and measure the antenna patterns.  All that info will be assimilated over time and a consensus about the antenna will form and it will take its rightful place in the ranks of antennas.  The best designs will be adopted and often achieve commercial success from performance attributes.  

It really is no different with radios, but radios seem to be more of a personal decision than antennas are.   I'm just expressing that I hope that in time, hams will find time to read up and understand direct sampling since it is and will continue to sweep across all aspects the hobby.

w8mqw

Steve:

  I agree with your intuition. There may be other factors as well---the flash sampling itself is an averaging process, etc. I've got to think about it. 

  Is it true that the lower the frequency of interference, the more destructive to ADC headroom?

Chuck

DrTeeth

@ KY6LA

"Personally my best theory is FOLLOW the MONEY."

Spot on!

W9OY

Actually I think hams have tremendous potential to embrace the underlying concepts of direct sampling.  The key to understanding is education provided in the proper channels.  Back in the 60's hams didn't have the first clue about blocking dynamic range and 3rd order intercept, RMDR and all of the concepts that have been developed to describe a theoretical basis for thinking about receivers and comparing receivers in overload and near overload situations.  

In the 70's QST published some articles describing a standardized criteria and methodology by which to characterize receivers.  Many hams understood the topic, and many of those hams brought their understanding to their local ham clubs and helped others to understand the concepts.  So this narrow analogue understanding (prejudice) is the basis by which direct sampling is judged.  In addition there was an explosion of "direct conversion" receivers, mostly mediocre QRP rigs that occurred in the 70's.   The SDR-1000 was in some essence a direct conversion radio, and this I think has an effect as well.  Non-SDR Hams sometimes follow SDR development from a kind of arm chair perspective.  For example they may have read Gerald's QEX articles and understood SDR somehow was related to a direct conversion radio plus some kind of software/soundcard back end and promptly stopped learning at that point feeling they mastered SDR concept and it was somehow connected to those silly direct conversion radios.  The SDR-1000 in many respects is an analogue radio, so it would not be unreasonable to assume SDR's of that kind and therefore SDR's in general have the same front end vulnerabilities as a Kenwood or an Icom.  Even the KX3 (a so called SDR) is basically a digitized K1 with some kind of DSP soundcard like dongle hanging off the output of the receiver, and even the KX3 has a roofing filter.  So you can well expect the K3 crowd is going to assume the KX3 represents present day SDR thinking.  

If you want Hams to understand the power of direct sampling in today's SDR apart from the "direct conversion" of yesteryear, then you really should publish a primer, as in a QST article that introduces the average ham to direct sampling definitions and concepts and how they are different from the 1970's concepts of what constituted a "good" receiver.  

Demonstrated above in this thread are a theoretical basis/model to understand direct sampling from Steve further refined by W8MQW, an empirical model demonstrated by Gerald, and a successful experiential basis in real life situations by KY6LA, N6WM, K6TU, K9CT and others in environments which are challenging if not deadly to receiver performance.  N1DG wrote an interesting article in the SDR forum of eham describing how he characterizes the differences and KY6LA also developed a way to hierarchically understand SDR development, the problem is this stuff is not exposed to the ham community at large as would be the case in a QST article.  What you want to do is capture the interest of the ham who understands and then can bring that understanding to the local ham club.  

SDR is the future and that is clear.  Now is the time to begin to fix a correct understanding in the mind of the average ham.  If we don't do that someone else like Icom or Elecraft will.

73 W9OY

Mike W8MM

Excellent observation and idea for action!!!!

W9OY

N1DG should be N9DG in the above

Vlad Borisov

"As more signals are added, there is a decreasingly small probability that these signals will add ...  To get a fabled 6dB voltage rise, they would have to already be exactly the same voltage, frequency and phase ..."

"They would virtually never all add at the same time so they will not combine at just the point where the peak of all signals occurs.  It just doesn't ever happen.  As a mathematician friend of mine pointed out ..."

Congratulations! The critical problems of OFDM and CDMA have just been resolved!

Steve-N5AC

Which specific problems are your referring to?

Bob-N4HY

Boris doesn't understand the difference between overload of a power amplifier with the crest factor problem in a power amplifier in the sum of few hundred channels and the overload of a ADC on receive. It's a poor attempt at sarcasm that fails to know it is off the mark.

Bob-N4HY

Like my sideways picture

Tim - W4TME

YES!  Quadrature Bob.

Bob-N4HY

Joe is a well known ham (microHam).  Flex is a major threat to sales of lots of equipment by lots of different people.  It is a clear indication of how far behind we are in certain technology areas that things I was doing years ago, using commercial parts, is disruptive hardware technology.  Flex is a terrific software company and this is most of the disruptive technology.  The hardware is mostly just superbly engineered.

Joe will get over it soon enough since he has no choice.

Bob-N4HY

I was not going to claim his obvious conflict of interest but I agree with you completely now that you have said it.  

Greg - K5GJ

Dr. Bob has ALWAYS followed his own vector!

Bob-N4HY

What's your vector Victor?