On 1/25/11 10:47 AM, Magnus Danielson wrote:
Jim,
On 25/01/11 14:53, jimlux wrote:
On 1/24/11 1:19 PM, Magnus Danielson wrote:
What are you *really* trying to achieve? 1-bit ADC at the end of a noisy
channel?
I have a GPS receiver front end (sampler) that normally one tests by
running GPS signals through it, acquiring and tracking the signals and
deriving SNR estimates, etc. , but we're in a situation where we don't
have either the back end processing or the GPS signals. We *do* have a
signal generator, so I was looking for some analytical expression(s)
that say, if you put in a tone with X SNR, this is what you should see
coming out of the sampler.
It's easy to do a sort of qualitative test (put in a big signal, see if
you get a square wave out), but it would be nice to be able to have a
way to make a quantitative measurement, particularly of the noise figure
& gain of the receiver. People have done a sort of ad hoc measurement
(hooking up a spectrum analyzer to the single bit digital output of the
sampler), but I was looking for something a bit more rigorous, but not
to the point where *I* wanted to grind out the pages of equations.. I
was hoping that someone else (e.g. Aronson) had gone through the
exercise.
The interesting thing is that there *is* a fair amount of analysis of
the bandlimited signal(s) and noise into a hard/soft limiter into a
filter. However, there's not much on systems where there is a sampling
process as well (which aliases all those harmonics down, of course). The
more recent literature I was able to find tends to be of a more
empirical nature (e.g. the modeling/simulation/experimental results).
And that's fine (after all, Aronson says that simple closed form
solutions probably don't exist). I can crank out models with the best of
them, but, philosophically, if there is a nice *simple* analytical
approximation, that's nicer.
What you can do... is try different amplitudes and different SNRs. By
monitoring the compression that the added noise provides for various
sine amplitudes you can derive the internal noise and hence noise factor.
yes.. in fact, I did some simulations this morning and figured it all
out. For what it's worth, it's sort of like trying to measure No by
working from measured BER to Eb/No, where you know Eb. You need to be
in a particular range of SNR to have it work well.. too high, and the
noise is so small that you need to run zillions of samples to get a
decent measurement precision. Too low and you can't see the sine wave
in the noise unless you integrate over many samples. So, for a given
number of "bits" out of the limiter, there's an optimum range of SNRs.
Interesting stuff.
I'm sure you can borrow a GPS simulator if you really need to. If you
only can record the bit-stream for post-processing, any of several
software GPS softwares would be able to decode the stream. Even my hack
would be able to do it. Maybe only doing FFT-based locking would suffice
for you.
Oh.. doing it with recorded bits and a software GPS processor is
straightforward (and actually how they usually test these things), but
we were looking for a way to use a RF signal generator and no GPS
signals. Those GPS simulators are a pretty pricey piece of gear,
especially if you want L1,L2, and L5.
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