[time-nuts] power spectrum of hard limiter output

jimlux jimlux at earthlink.net
Wed Jan 26 03:32:38 UTC 2011

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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