Well, good afternoon, everyone, and thanks for coming to the presentation this afternoon.
I am going to try to get or keep us on schedule. And let me go forward into the denser part
of my presentation. I have been struggling to take this somewhat lengthy and complicated
topic and make a good introduction to it, and that is what I will work on here today.
This information is going to be, actually there is another version available on a webcast
and we will have an application note on this to get to it to more detail. But I think I
can give you a good summary of the issues with respect to finding the signals that you
are trying to find, especially if those signals are hard to find. And that is especially important
these days because we are dealing with much more dense spectral environments and more
agile signals. And what that means in a lot of cases is that a very crowded spectrum means
that if your product have some sins, they will often be noticed, or that you may be
dealing with sins from someone else's product or emission. And some of these areas here,
let's talk directly more about the measurements themselves. The idea is to get a better understanding
of the way of how short of an event we can, intercept, the probability of intercept, or
how to trade off various factors that affect that. And that includes do you detect the
signals, how accurately can you measure them, what sort of power and frequency resolution
you get, and can you detect every event. Your individual situations are likely to be different,
so I will give you a general insight into the most important factors for that here today,
and then you can take that to make better measurements later. You are probably familiar
with swept spectrum analyzers. The problem is when you are sweeping at one frequency,
when your resolution bandwidth is at one frequency, you are missing something at other frequencies.
So, fixed LO schemes, where you digitize a certain bandwidth are the ways to get a well-defined
probability of intercept. These are typically in things like vector signal analyzers or
in FFT analyzers where we are not using a swept LO. It is sometimes called a basic mode,
but what it really means is that the digitizer is a not a baseband digitizer. It is an IF
digitizer. So instead of producing baseband samples like an oscilloscope, it produces
IQ samples with some implied LO frequency. So that is the IQ mode. That is the way typically
these FFT and vector signal analyzers are doing their sampling. Same thing with real-time
analyzers. So with real-time analyzers, I did some discussion of this in a paper yesterday
morning. For here, I will just note that the real-time analyzers do used this fixed IF
capability, this fixed IF digitizing, but they have a high-speed dedicated FFT processor,
a relatively inflexible processor, but very high speed; hundreds of thousands of FFTs
per second, which gives you consistent measurement speed and improves your chance of detecting
the signals you are looking for. And that does lead, in some cases, to specialized displays.
We will not really talk about those much today. And by the way, these are spectrum measurements,
where we are talking about probability of intercept in most cases. They are scalar measurements.
That is magnitude versus frequency. They are not vector measurements of time, domain, or
demodulation, but those can be done with the same hardware. I will talk about that at the
end of the presentation. There are two things here though that really give the core insights
in terms of probability of intercept and what is going on with FFT analyzers. And that is
typically, we have got a stream of samples coming past. And we are taking a block of
these, 1024, 512; it is typically powers of two. Sometimes it can be hundreds of thousands.
But we are taking a block of these samples, doing an FFT and creating a spectrum. And
then if we can do the calculations fast enough, then what that means is, we take another block
of samples or another FFT, even before the first FFT is done, even before a new time
record. So this is overlap processing, meaning each new FFT is done so fast that it can be
done before a new set of samples is done. So you take some of the samples, the last
samples from the previous FFT, and a new set of samples for the new FFT. But the other
thing that goes on, in almost all FFT processing, is some sort of windowing. The problem with
an FFT is that you do not get good results if the signal that you are measuring is not
periodic in the window. And of course, typically, signals are not periodic in your particular
window. I will show some examples of that as it comes up here. With respect to POI and
how it intersects with these issues of windows and sampling and overlap, we have a couple
of possible goals, sometimes a tradeoff between those. One of them is, are you trying to make
sure you never miss a signal, getting it 100% of the time. Or are you interested in an accurate
amplitude reading. And those are essentially competing goals. What is often happening if
you are dealing with optimizing probability of intercept is you are operating at the outer
envelope of measurement possibilities. If you improve one thing, say, you improve your
power measurement accuracy, it will cost you elsewhere. You might not have as good a probability
of catching the signal. On the other hand, if you want the maximum probability of capturing
a signal, you may have to give up some in terms of the accuracy of the measurement,
at least in a normal, real-time analyzer mode. So where that comes from has to do with the
windowing I mentioned a minute ago. If you do FFT of some time samples and if that signal
is periodic in your time record, you get very good resolution, very good accuracy. But if
the signal is not periodic in the time record, you do not have an even number of cycles of
your signal and the time record, if you move this off, you start to see much poorer signal-to-noise
ratio, and you start to see wider resolution bandwidths. That is an effect of non-periodicity
of the signal in the time record. And that is why in most cases you do weight the signal
and the time record by some sort of window. Meaning you maximum weight the signal at the
center of the window, and at the front -- at the beginning and the end of the time record,
you down-weight the signal, you attenuate the signal. What that does then, it trades
two things off. It gives you good dynamic range, as opposed to these signals here, but
it widens your resolution bandwidth. So you are trading away resolution bandwidth, or
resolution, for better dynamic range and for better amplitude accuracy. That is one of
the tradeoffs that is going on here. We are talking about a situation where any one thing
will trade off against others. That is shown here in a little bit different way. In this
case, here is a rectangular window, which is to say no window. We are weighting all
the data, all the samples in the time record the same, and if we move the signal around,
we notice the amplitude changes; the apparent bandwidth of the signal changes, and that
way, we get a very good result only if a signal is periodic in the window. On the other hand,
if we use other windows which trade off some of that resolution bandwidth, we get better
amplitude accuracy. We get better dynamic range. But we get poorer frequency resolution.
Some of the windows you will hear about, this is in FFT analyzers, things like, Kaiser,
Blackman-Harris, Hanning, Hamming, rectangular, uniform or Gaussian. Those are all different
shapes of weighting, but the rectangular or uniform window is essentially no window, no
weighting at all. That gives you the maximum resolution, but it hurts you in terms of dynamic
range and accuracy unless your signal is on bin, or periodic in the frequent -- in the
time record. The other thing that happens, for example, is in a shape of one window of
one FFT. These are the samples we are using. And here is the next FFT with some overlap
between the two FFTs, overlap in time. That way, some samples are FFT'ed in both FFTs.
If the signal is only on for much less than one window, or one time record length, then
we do not get accurate amplitude. We can detect this signal, but unfortunately, it only occupies
part of the time record so the amplitude does not look correct. So this is one of the tradeoffs
I mentioned earlier on. We can detect that the signal exists reliably, but we do not
get a good, accurate amplitude measurement of it. And that can be viewed as essentially
the area under the curve. That is one way to see what that amplitude de-rating would
be. Another way to look at that, is that the position of the burst; once again, we are
talking about a signal that is shorter than the time record, two different signals here;
the red one and the blue one. Both of them are the same length, but they occurred at
different times in the time record and we have got that window that we saw before. A
signal that occurs in the center of the time record will have a higher apparent power.
That same signal occurring at the beginning or the end of the time record will be windowed
off, and so the amplitude accuracy will be much poorer. And that is shown here, the difference
in this case, just by changing that location is about 25 dB. So again, we could detect
both of these, but we would not get as good as an amplitude accuracy, depending on where
this signal occurred in the window. And in many cases, unless you are making a triggered
measurement, you do not get to choose where it occurs in the window. Although that is
one of the bits of wisdom I will offer; if you are trying to get high probability of
intercept, then in things like the vector signal analyzers using a magnitude trigger,
which evaluates the signal magnitude on every single sample and synchronously triggers those
can ensure that you have the signal where you want it in the window. Plus, you can use
things like gated sweep. I will come back to that at the end of the presentation. Another
issue with this then is sampling rate. If you are trying to get high probability of
intercept over a really wide bandwidth, you are sampling very quickly, short time records.
It is harder with very little overlap to get 100% probability of intercept. If you are
analyzing over a narrower frequency span, then once again, this is an information theory
challenge; analyzing over a narrower frequency span means the samples come slower, but you
are FFT'ing fast at the same rate. So you have more overlap and more chance of getting
the signals. So if you are trying to get 100% probability of intercept, do not set your
span any wider than you absolutely need it. The narrower the span, the higher the probability
of intercept will be because you are overlapping these FFTs more and more extensively. But
another issue that comes up then is if you want maximum amplitude accuracy. So you are
probability of intercept means the probability that you are going to get 100% amplitude accuracy,
then you can change window size and change how much -- you can trade off some of the
resolution by going for a shorter window, and wider resolution bandwidth, for higher
accuracy. So you can make 100% accurate measurement, the same accuracy for a transient signal as
you would with a continuous signal using a narrower in window time or wider resolution,
and get full amplitude accuracy. So once again, we loop back to that issue of you are operating
at the maximum information envelope. If you want something more in one area, you are going
to want to trade something else -- trade something off in the other. And that is actually always
a good practice in engineering of these systems is to understand what it is that you want
the most. Is it just to detect the signal? Is it to get 100% accuracy? Is your signal
just one signal or is it a repeating signal? Is it alright if you just capture one once
in a while, that you do not capture everyone, but you capture one of them occasionally with
perfect accuracy? The other thing that interacts with this is detection with the real-time
analyzers or the vector signal analyzers in a frequency masked trigger mode because in
some cases, what you are looking for may not happen every second or every minute or every
hour or every day, so you may want to use something like a frequency masked trigger
function. And the same issues come into play. With overlap, we can determine how long the
signal has to be and how big it has to be. If the signal is very near the noise level,
then the signal will have to be longer in its duration before you can detect it. If
the signal is way, way above the noise level, you can detect it over a much shorter interval
because it stands out from the noise; its power is much different than the noise. Its
frequency behavior is much different than the noise. So in this case, we chose a 40
dB figure just as an example, and if we take what part of this signal occupies either of
these windows, in this case, the worst place to be is where both windows are intersecting
and there is minimal overlap, then the window shape actually determines whether we need
11 samples or 65 samples to see that signal with accuracy or to see that to detect that
signal 40 dB above. So I do not really have the time today to go into all of the tradeoffs
back and forth, but I did want to give you an idea; if you have signals that are shorter,
they are harder to detect. If you have signals that are closer to noise, they are harder
to detect. If you have signals that happen very rarely or only once, they are harder
to detect. Now, if the opposite of those things is true, then you can detect them more easily.
You can detect them with better amplitude accuracy. Just keep in mind that we have moved
out of the swept spectrum world where you could trade some things off without a problem
and we are now in a sort of an information theory limited world where if you are trying
to find things that are very elusive or very rare, use all the tools at your disposal.
Recognize if you want maximum accuracy. You are going to need something longer. You are
going to need better signal-to-noise. I mentioned earlier on about using narrower spans. Again,
if you -- one of the other tradeoffs is if you can sample slower and do more overlap,
meaning you sample slower at a narrower bandwidth, but your FFT'ing just as fast as before with
this fast FFT hardware. Then that means you can get more overlap and you can improve your
probability of intercept. You can find signals closer to the noise. If you trade off any
one of these, you will get benefits in the others. So in this case, for example, going
from 200 MHz to 100 MHz for the Blackman-Harris window, we needed 65 samples before. Now,
we can use only 8 samples and detect this signal at the same level above the noise.
So these are not all linear relationships, but you can find the ones that are most favorable
to you. So in this case, for example, it takes twice as long to get the samples, but they
are eight times better in terms of detecting the signal, eight times shorter signal; we
can detect it with the same probability. I will not talk about the real-time analyzers
and the displays. The other thing -- because I think you have seen that kind of material
before. The other thing I wanted to mention then is that if you are dealing with these
transient or very difficult to detect signals, the other technique that works really well
is to use the same sort of hardware, perhaps use a frequency masked trigger or a magnitude
trigger to trigger on the signal, but then use the vector signal analysis software. The
reason for that is that you can grab a large chunk of the data in real-time that is gap-free
and post process it. And by post process it, you can take the same data and look at it
again and again and again with a nearly infinite amount of overlap, even sample by sample overlap,
the equivalent of billions of FFTs per second. You can change the windows and change the
window shape and change the window size and use things like gating and trade all of these
things off one measurement after another after another to optimize for different uses. So
remember when I said earlier that the problem was that anytime you tried to make one thing
better, it cost you in some other aspect; accuracy versus dynamic range versus probability
of intercept versus resolution bandwidth. If you want all of those things, then the
VSA software, by capturing the signal and then allowing you to reprocess it and reprocess
it and reprocess it, just changing the settings, allows you to make successive measurements,
each one of which is better optimized for the things you want to see. So by three different
measurements, you might be able to optimize three different parameters that way. Plus,
you can do it all visibly. You have the signal. You have captured it all over whatever bandwidth.
You can change that bandwidth. You can change the center frequency you are at and look in
at specific signals among others. Often in engineering, if you find yourself operating
at the edge of the envelope, you are sort of looking for a trick or a way out or a special
approach. And what I would say in this case, the best bet that way is probably VSA software
time capture, whether you are triggering on the signal or just captured a big wad of time
and then find the signal you want, and then reanalyze over and over and over again. The
other advantage that has, I think that we have all experienced, is you go to make a
measurement on a transient repeating signal. You make a measurement. Then you switch the
analyzer settings around a little bit and you make another measurement and you get a
different answer. And you are not sure, "Well, did the signal change? Or was that a result
of the parameter change I made? Or is there some evil interaction going on there?" If
you have got a time capture, then you have got the same data over and over and over again.
You can make all the changes you want and you know that all of the changes you see in
measurement results are due to the change in the setting, not the change in the signal
because you've got the same signal over and over and over again. And of course, if the
signal only happens every minute or every hour then that allows you to grab it and keep
it and send it to someone else for analysis. So that is sort of the overview I wanted to
give you today. We are coming out with a new paper and an app note on probability of intercept
that goes through this in more detail and gives you the numbers and equations you need
if you need to actually quantify that. What I would say is if you are generally interested
in probability of intercept and you want to improve that, then things like real-time analysis,
frequency masked triggers, those can allow you to spot the things and then capture the
signal and do that reprocessing. That will allow you to get the maximum available in
a particular signal. So I am sorry to go through this so fast. I hope I gave you at least some
good guidance and directions to go to make more productive measurements that way. I will
be at the Agilent booth after this. I will be happy to talk with you at all or I can
give you a business card and we can talk offline. And thanks very much for coming today.