Hi Jim and the group,
I apologize for creating confusion in my earlier post about the Central Limit
Theorem. Let me try to clarify a few points that I glossed over. My example
considered an SDR transceiver that received two signals, each with
instantaneous RF voltage that varied from +3V to -3V, and for simplicity I
assumed each signal could have only seven values spanning this range. I didn't
make it clear that these are independent signals on different frequencies. Thus
every time the ADC in an SDR samples the voltage sum of the two signals at its
input, it will get a different result. For example, with one sample the SDR may
see a voltage of +1V, which comes from +2V from one signal and -1V from the
other signal. A later sample might produce a voltage of -2V, which could come
from +1V from one signal and -3V from the other. In other words, with each
sample, the SDR will measure a different voltage, because the signals have
different frequencies and are not in phase with each other.
Suppose now that we let the SDR sample the voltage a million times, one after
another. Then the Central Limit Theorem tells us how those million measurements
will be distributed, in other words how many times the SDR will measure 6V, 5V,
4V...0...-4V,-5V,and -6V. What the CLT tells us is that the distribution of
these measurements generally follow a bell-shaped curve, with the peak at 0V.
This means that most of the time, the SDR will measure approximately 0V at its
input. Only infrequently will it measure the large +6V and -6V voltages,
because those large voltages are at the extreme edges of the bell-shaped
distribution. If the SDR overloads at, say, +/-6V, then it will only overload
when the sample measures that extreme voltage, which is not very often. Note
that this doesn't have anything to do with the AGC action of the radio.
Now, here's where I treated things too glibly in my earlier post. I asserted
that with more independent signals, as one might find on the entire crowded HF
spectrum, the distribution of the instantaneous RF voltage from the entire
spectrum tends to peak sharply at zero volts, which means paradoxically that
the more signals the radio hears, the more immune to overload it becomes. (The
explanation of the paradox is that all these signals tend to cancel each other.
For every positive voltage from one signal there is a negative voltage from
some other signal.)
Having said that, here's the fly in the ointment. There are several assumptions
buried in the Central Limit Theorem, so its validity isn't as universal as I
was suggesting. One assumption is that all these signals have to have about the
same amplitude. If one signal is vastly stronger than the others, as Tom W8JI
finds in his contest station, then that will dominate the input of the SDR and
you won't get this cancellation effect. Similarly, if you have a really strong
AM broadcast station near your QTH, then that could still overload the ADC in
your SDR transceiver. Keep in mind that the Central Limit Theorem is a complex
mathematical statement whose validity is only as good as the validity of its
underlying assumptions. To me, the CLT provides a ballpark guess as to how an
SDR will perform, but it shouldn't be taken too literally. The real world has a
habit of not conforming to mathematical theorems!
As I've thought more about this issue, I think a key advantage of an SDR
actually comes, not just from the cancellation effect, but from the fact that
an SDR has no front-end RF amplifier or subsequent IF amplifiers. Basically the
HF spectrum goes directly into the SDR's analog-to-digital converter. I believe
(hope someone can verify this) that modern, fast ADCs can handle a volt or more
at their inputs without overloading, which gives them a tremendous advantage
over superhet radios which use high gain RF and IF amplfiers. Signals in the
millivolt range that fall outside the IF passband in conventional superhets
won't capture the receiver's AGC and can therefore overload or dessense the
front end. That won't be a problem with SDR radios that can handle a volt or
more without overloading their ADC.
73,
Jim W8ZR
> -----Original Message-----
> From: James Wolf [mailto:jbwolf@comcast.net]
> Sent: Monday, October 12, 2015 9:45 PM
> To: 'Jim Garland'
> Cc: topband@contesting.com
> Subject: RE: Topband: ADC Overload
>
> 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
>
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