[time-nuts] power spectrum of hard limiter output

[Magnus Danielson]

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.

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.

Cheers,
Magnus