J
jimlux
Mon, Jan 24, 2011 1:35 AM
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
Jim
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
Jim
S
shalimr9@gmail.com
Mon, Jan 24, 2011 3:34 AM
Jim,
You should be able to model it in Spice and do an FFT on the output.
Didier KO4BB
Sent from my Verizon Wireless BlackBerry
-----Original Message-----
From: jimlux jimlux@earthlink.net
Sender: time-nuts-bounces@febo.com
Date: Sun, 23 Jan 2011 17:35:38
To: Discussion of precise time and frequency measurementtime-nuts@febo.com
Reply-To: Discussion of precise time and frequency measurement
time-nuts@febo.com
Subject: [time-nuts] power spectrum of hard limiter output
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
Jim
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
Jim,
You should be able to model it in Spice and do an FFT on the output.
Didier KO4BB
Sent from my Verizon Wireless BlackBerry
-----Original Message-----
From: jimlux <jimlux@earthlink.net>
Sender: time-nuts-bounces@febo.com
Date: Sun, 23 Jan 2011 17:35:38
To: Discussion of precise time and frequency measurement<time-nuts@febo.com>
Reply-To: Discussion of precise time and frequency measurement
<time-nuts@febo.com>
Subject: [time-nuts] power spectrum of hard limiter output
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
Jim
_______________________________________________
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
MD
Magnus Danielson
Mon, Jan 24, 2011 6:01 AM
Jim,
On 24/01/11 02:35, jimlux wrote:
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for those
conditions as you get a more stable property.
Another approach of understanding is to consider that when the gaussian
noise is sufficiently high it will start interpolate on the slope of the
sine and as you add more noise more and more of the sine would linearize
until you come to the point where it is linear. Soft-clipping will
indeed be similar.
I haven't seen a spectrum plot, but simulation in spice should be
trivial. Setting up a sine + noise, comparator and then a low-pass
filter should be a trivial SPICE setup. It does not take much
imagination to see that the spectrum will migrate from that of a square
over to that of a sine. It will loose power in those overtones.
Cheers,
Magnus
Jim,
On 24/01/11 02:35, jimlux wrote:
> I'm looking for a reference that gives the power spectrum of the output
> of a hard limiter (1 bit thresholder) with band limited noise and a
> single sinusoid.
>
> At high SNR, the output of the limiter is basically a square wave at at
> the input frequency, but as the SNR decreases, it starts to act like a
> soft limiter with a gaussian characteristic, so what is the power
> spectrum of the output?
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for those
conditions as you get a more stable property.
Another approach of understanding is to consider that when the gaussian
noise is sufficiently high it will start interpolate on the slope of the
sine and as you add more noise more and more of the sine would linearize
until you come to the point where it is linear. Soft-clipping will
indeed be similar.
I haven't seen a spectrum plot, but simulation in spice should be
trivial. Setting up a sine + noise, comparator and then a low-pass
filter should be a trivial SPICE setup. It does not take much
imagination to see that the spectrum will migrate from that of a square
over to that of a sine. It will loose power in those overtones.
Cheers,
Magnus
J
jimlux
Mon, Jan 24, 2011 6:21 AM
Jim,
You should be able to model it in Spice and do an FFT on the output.
Or in Matlab.. Simulation is easy for this one...
I was looking for a paper that looked at it analytically.. I figure it's
such a straightforward thing that someone back in the 60s or 70s slogged
through the stuff and did it. I found some papers from the late 70s
where they look at 2 or more tones in AWGN through a hard limiter.
I figure that Bessel functions enter into it somewhere (because when you
talk limiters, you're talking PM or FM, and Bessel functions always show
up)....
And I'm lazy enough to not do the derivation myself and throw myself on
on the kindness of strangers. (hmmm are timenuts strangers? they're
strange, that's to be sure...)
On 1/23/11 7:34 PM, shalimr9@gmail.com wrote:
> Jim,
>
> You should be able to model it in Spice and do an FFT on the output.
>
Or in Matlab.. Simulation is easy for this one...
I was looking for a paper that looked at it analytically.. I figure it's
such a straightforward thing that someone back in the 60s or 70s slogged
through the stuff and did it. I found some papers from the late 70s
where they look at 2 or more tones in AWGN through a hard limiter.
I figure that Bessel functions enter into it somewhere (because when you
talk limiters, you're talking PM or FM, and Bessel functions always show
up)....
And I'm lazy enough to not do the derivation myself and throw myself on
on the kindness of strangers. (hmmm are timenuts strangers? they're
strange, that's to be sure...)
J
jimlux
Mon, Jan 24, 2011 6:28 AM
On 1/23/11 10:01 PM, Magnus Danielson wrote:
Jim,
On 24/01/11 02:35, jimlux wrote:
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for those
conditions as you get a more stable property.
Another approach of understanding is to consider that when the gaussian
noise is sufficiently high it will start interpolate on the slope of the
sine and as you add more noise more and more of the sine would linearize
until you come to the point where it is linear. Soft-clipping will
indeed be similar.
I haven't seen a spectrum plot, but simulation in spice should be
trivial. Setting up a sine + noise, comparator and then a low-pass
filter should be a trivial SPICE setup. It does not take much
imagination to see that the spectrum will migrate from that of a square
over to that of a sine. It will loose power in those overtones.
oh, yes.. I did the simulation, and modeled the aliasing of the
overtones and all..
I was looking for a reference to cite (you know how it is.. measure it
yourself and it's something you did.. but cite someone who ground
through it before, and it's worth a lot more...)
On 1/23/11 10:01 PM, Magnus Danielson wrote:
> Jim,
>
> On 24/01/11 02:35, jimlux wrote:
>> I'm looking for a reference that gives the power spectrum of the output
>> of a hard limiter (1 bit thresholder) with band limited noise and a
>> single sinusoid.
>>
>> At high SNR, the output of the limiter is basically a square wave at at
>> the input frequency, but as the SNR decreases, it starts to act like a
>> soft limiter with a gaussian characteristic, so what is the power
>> spectrum of the output?
>
> It goes towards sine as I recall it. The gaussian noise rubs of
> overtones. Gardner describes this in his PLL book. Setting up a nice
> sawtooth detector is no good when seeing bad noise, as it will degrade
> into a sine-detector anyways, so using a multiplier is better for those
> conditions as you get a more stable property.
>
> Another approach of understanding is to consider that when the gaussian
> noise is sufficiently high it will start interpolate on the slope of the
> sine and as you add more noise more and more of the sine would linearize
> until you come to the point where it is linear. Soft-clipping will
> indeed be similar.
>
> I haven't seen a spectrum plot, but simulation in spice should be
> trivial. Setting up a sine + noise, comparator and then a low-pass
> filter should be a trivial SPICE setup. It does not take much
> imagination to see that the spectrum will migrate from that of a square
> over to that of a sine. It will loose power in those overtones.
>
oh, yes.. I did the simulation, and modeled the aliasing of the
overtones and all..
I was looking for a reference to cite (you know how it is.. measure it
yourself and it's something *you* did.. but cite someone who ground
through it before, and it's worth a lot more...)
BG
Bruce Griffiths
Mon, Jan 24, 2011 6:39 AM
On 1/23/11 10:01 PM, Magnus Danielson wrote:
Jim,
On 24/01/11 02:35, jimlux wrote:
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for those
conditions as you get a more stable property.
Another approach of understanding is to consider that when the gaussian
noise is sufficiently high it will start interpolate on the slope of the
sine and as you add more noise more and more of the sine would linearize
until you come to the point where it is linear. Soft-clipping will
indeed be similar.
I haven't seen a spectrum plot, but simulation in spice should be
trivial. Setting up a sine + noise, comparator and then a low-pass
filter should be a trivial SPICE setup. It does not take much
imagination to see that the spectrum will migrate from that of a square
over to that of a sine. It will loose power in those overtones.
oh, yes.. I did the simulation, and modeled the aliasing of the
overtones and all..
I was looking for a reference to cite (you know how it is.. measure it
yourself and it's something you did.. but cite someone who ground
through it before, and it's worth a lot more...)
jimlux wrote:
> On 1/23/11 10:01 PM, Magnus Danielson wrote:
>> Jim,
>>
>> On 24/01/11 02:35, jimlux wrote:
>>> I'm looking for a reference that gives the power spectrum of the output
>>> of a hard limiter (1 bit thresholder) with band limited noise and a
>>> single sinusoid.
>>>
>>> At high SNR, the output of the limiter is basically a square wave at at
>>> the input frequency, but as the SNR decreases, it starts to act like a
>>> soft limiter with a gaussian characteristic, so what is the power
>>> spectrum of the output?
>>
>> It goes towards sine as I recall it. The gaussian noise rubs of
>> overtones. Gardner describes this in his PLL book. Setting up a nice
>> sawtooth detector is no good when seeing bad noise, as it will degrade
>> into a sine-detector anyways, so using a multiplier is better for those
>> conditions as you get a more stable property.
>>
>> Another approach of understanding is to consider that when the gaussian
>> noise is sufficiently high it will start interpolate on the slope of the
>> sine and as you add more noise more and more of the sine would linearize
>> until you come to the point where it is linear. Soft-clipping will
>> indeed be similar.
>>
>> I haven't seen a spectrum plot, but simulation in spice should be
>> trivial. Setting up a sine + noise, comparator and then a low-pass
>> filter should be a trivial SPICE setup. It does not take much
>> imagination to see that the spectrum will migrate from that of a square
>> over to that of a sine. It will loose power in those overtones.
>>
>
> oh, yes.. I did the simulation, and modeled the aliasing of the
> overtones and all..
>
> I was looking for a reference to cite (you know how it is.. measure it
> yourself and it's something *you* did.. but cite someone who ground
> through it before, and it's worth a lot more...)
>
See:
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4101285
Bruce
MD
Magnus Danielson
Mon, Jan 24, 2011 7:44 PM
On 24/01/11 07:39, Bruce Griffiths wrote:
On 1/23/11 10:01 PM, Magnus Danielson wrote:
Jim,
On 24/01/11 02:35, jimlux wrote:
I'm looking for a reference that gives the power spectrum of the output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for those
conditions as you get a more stable property.
Another approach of understanding is to consider that when the gaussian
noise is sufficiently high it will start interpolate on the slope of the
sine and as you add more noise more and more of the sine would linearize
until you come to the point where it is linear. Soft-clipping will
indeed be similar.
I haven't seen a spectrum plot, but simulation in spice should be
trivial. Setting up a sine + noise, comparator and then a low-pass
filter should be a trivial SPICE setup. It does not take much
imagination to see that the spectrum will migrate from that of a square
over to that of a sine. It will loose power in those overtones.
oh, yes.. I did the simulation, and modeled the aliasing of the
overtones and all..
I was looking for a reference to cite (you know how it is.. measure it
yourself and it's something you did.. but cite someone who ground
through it before, and it's worth a lot more...)
On 24/01/11 07:39, Bruce Griffiths wrote:
> jimlux wrote:
>> On 1/23/11 10:01 PM, Magnus Danielson wrote:
>>> Jim,
>>>
>>> On 24/01/11 02:35, jimlux wrote:
>>>> I'm looking for a reference that gives the power spectrum of the output
>>>> of a hard limiter (1 bit thresholder) with band limited noise and a
>>>> single sinusoid.
>>>>
>>>> At high SNR, the output of the limiter is basically a square wave at at
>>>> the input frequency, but as the SNR decreases, it starts to act like a
>>>> soft limiter with a gaussian characteristic, so what is the power
>>>> spectrum of the output?
>>>
>>> It goes towards sine as I recall it. The gaussian noise rubs of
>>> overtones. Gardner describes this in his PLL book. Setting up a nice
>>> sawtooth detector is no good when seeing bad noise, as it will degrade
>>> into a sine-detector anyways, so using a multiplier is better for those
>>> conditions as you get a more stable property.
>>>
>>> Another approach of understanding is to consider that when the gaussian
>>> noise is sufficiently high it will start interpolate on the slope of the
>>> sine and as you add more noise more and more of the sine would linearize
>>> until you come to the point where it is linear. Soft-clipping will
>>> indeed be similar.
>>>
>>> I haven't seen a spectrum plot, but simulation in spice should be
>>> trivial. Setting up a sine + noise, comparator and then a low-pass
>>> filter should be a trivial SPICE setup. It does not take much
>>> imagination to see that the spectrum will migrate from that of a square
>>> over to that of a sine. It will loose power in those overtones.
>>>
>>
>> oh, yes.. I did the simulation, and modeled the aliasing of the
>> overtones and all..
>>
>> I was looking for a reference to cite (you know how it is.. measure it
>> yourself and it's something *you* did.. but cite someone who ground
>> through it before, and it's worth a lot more...)
>>
> See:
>
> http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4101285
http://archive.numdam.org/ARCHIVE/RSMUP/RSMUP_1969__42_/RSMUP_1969__42__1_0/RSMUP_1969__42__1_0.pdf
http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA425520
... found using "hard limiter autocorrelation sine" in Google.
Cheers,
Magnus
J
jimlux
Mon, Jan 24, 2011 8:32 PM
On 1/24/11 11:44 AM, Magnus Danielson wrote:
On 24/01/11 07:39, Bruce Griffiths wrote:
On 1/23/11 10:01 PM, Magnus Danielson wrote:
Jim,
On 24/01/11 02:35, jimlux wrote:
I'm looking for a reference that gives the power spectrum of the
output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave
at at
the input frequency, but as the SNR decreases, it starts to act like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for those
conditions as you get a more stable property.
Another approach of understanding is to consider that when the gaussian
noise is sufficiently high it will start interpolate on the slope of
the
sine and as you add more noise more and more of the sine would
linearize
until you come to the point where it is linear. Soft-clipping will
indeed be similar.
I haven't seen a spectrum plot, but simulation in spice should be
trivial. Setting up a sine + noise, comparator and then a low-pass
filter should be a trivial SPICE setup. It does not take much
imagination to see that the spectrum will migrate from that of a square
over to that of a sine. It will loose power in those overtones.
oh, yes.. I did the simulation, and modeled the aliasing of the
overtones and all..
I was looking for a reference to cite (you know how it is.. measure it
yourself and it's something you did.. but cite someone who ground
through it before, and it's worth a lot more...)
Excellent.. I had found the Aronson paper (wherein he effectively says
"there's no simple analytical expression".. that's nice and justifies
doing it by numerical modeling). ANd the Jain paper (DTIC), which deals
with multiple sines. I hadn't run across the one by Greenhall (who
still works at JPL)...
Thanks a bunch to the nuts..
Jim
On 1/24/11 11:44 AM, Magnus Danielson wrote:
> On 24/01/11 07:39, Bruce Griffiths wrote:
>> jimlux wrote:
>>> On 1/23/11 10:01 PM, Magnus Danielson wrote:
>>>> Jim,
>>>>
>>>> On 24/01/11 02:35, jimlux wrote:
>>>>> I'm looking for a reference that gives the power spectrum of the
>>>>> output
>>>>> of a hard limiter (1 bit thresholder) with band limited noise and a
>>>>> single sinusoid.
>>>>>
>>>>> At high SNR, the output of the limiter is basically a square wave
>>>>> at at
>>>>> the input frequency, but as the SNR decreases, it starts to act like a
>>>>> soft limiter with a gaussian characteristic, so what is the power
>>>>> spectrum of the output?
>>>>
>>>> It goes towards sine as I recall it. The gaussian noise rubs of
>>>> overtones. Gardner describes this in his PLL book. Setting up a nice
>>>> sawtooth detector is no good when seeing bad noise, as it will degrade
>>>> into a sine-detector anyways, so using a multiplier is better for those
>>>> conditions as you get a more stable property.
>>>>
>>>> Another approach of understanding is to consider that when the gaussian
>>>> noise is sufficiently high it will start interpolate on the slope of
>>>> the
>>>> sine and as you add more noise more and more of the sine would
>>>> linearize
>>>> until you come to the point where it is linear. Soft-clipping will
>>>> indeed be similar.
>>>>
>>>> I haven't seen a spectrum plot, but simulation in spice should be
>>>> trivial. Setting up a sine + noise, comparator and then a low-pass
>>>> filter should be a trivial SPICE setup. It does not take much
>>>> imagination to see that the spectrum will migrate from that of a square
>>>> over to that of a sine. It will loose power in those overtones.
>>>>
>>>
>>> oh, yes.. I did the simulation, and modeled the aliasing of the
>>> overtones and all..
>>>
>>> I was looking for a reference to cite (you know how it is.. measure it
>>> yourself and it's something *you* did.. but cite someone who ground
>>> through it before, and it's worth a lot more...)
>>>
>> See:
>>
>> http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4101285
>
> http://archive.numdam.org/ARCHIVE/RSMUP/RSMUP_1969__42_/RSMUP_1969__42__1_0/RSMUP_1969__42__1_0.pdf
>
>
> http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA425520
>
>
> ... found using "hard limiter autocorrelation sine" in Google.
>
Excellent.. I had found the Aronson paper (wherein he effectively says
"there's no simple analytical expression".. that's nice and justifies
doing it by numerical modeling). ANd the Jain paper (DTIC), which deals
with multiple sines. I hadn't run across the one by Greenhall (who
still works at JPL)...
Thanks a bunch to the nuts..
Jim
E
ehydra
Mon, Jan 24, 2011 8:34 PM
The classical approach is to heavily band-limit the input of an
following hard-limiter. But would it possible to merge both functions in
several stages of an IF-strip?
I think most individuals cannot follow much of this idea but time-nuts
have the same problem :-)
My main interest is a practical (reduced to standard parts to buy) CMOS
inverter IF-strip where the individual stages are ac-coupled.
So it is possible to integrate a high-pass filter via the coupling
capacitor and low-pass via the cross connected capacitor over the
inverters. I think the interstage capacitor also removes 1/f noise of
the signal from the individual pre-stage inverter. CMOS having more 1/f
noise than bipolar transistors under approx. 1 KHz but can be
comfortable from 100 KHz to 1 MHz. The nice thing with CMOS is cheapness
and simplicity.
So the questions are:
- maximum useful amplification
- depends on noise in first stage
- compression on MOSFET inverter gives spectral regrowth
- limiting of burst noise in rf signals
- trying to avoid any form of automatic gain control
- etc.
I played with SPICE models in LTspice and practical with SpectrumLab
using CD4007 inverters as IF-strip at 25 KHz.
I try to be practical and avoid heavy mathematicals.
It works fine if one think of the price of such simple parts! But I'm a
little over my edge how to optimize it further.
Any suggestions are welcome. I don't have access to IEEE papers.
This paper is interesting because it mentions main aspects but looses
itself in CDMA specific aspects:
www4.ncsu.edu/~kggard/kg_papers/MTT_05_FrontEnd_Distortion.pdf
regards -
Henry
(Sorry for bad english)
The classical approach is to heavily band-limit the input of an
following hard-limiter. But would it possible to merge both functions in
several stages of an IF-strip?
I think most individuals cannot follow much of this idea but time-nuts
have the same problem :-)
My main interest is a practical (reduced to standard parts to buy) CMOS
inverter IF-strip where the individual stages are ac-coupled.
So it is possible to integrate a high-pass filter via the coupling
capacitor and low-pass via the cross connected capacitor over the
inverters. I think the interstage capacitor also removes 1/f noise of
the signal from the individual pre-stage inverter. CMOS having more 1/f
noise than bipolar transistors under approx. 1 KHz but can be
comfortable from 100 KHz to 1 MHz. The nice thing with CMOS is cheapness
and simplicity.
So the questions are:
1. maximum useful amplification
2. depends on noise in first stage
3. compression on MOSFET inverter gives spectral regrowth
4. limiting of burst noise in rf signals
5. trying to avoid any form of automatic gain control
6. etc.
I played with SPICE models in LTspice and practical with SpectrumLab
using CD4007 inverters as IF-strip at 25 KHz.
I try to be practical and avoid heavy mathematicals.
It works fine if one think of the price of such simple parts! But I'm a
little over my edge how to optimize it further.
Any suggestions are welcome. I don't have access to IEEE papers.
This paper is interesting because it mentions main aspects but looses
itself in CDMA specific aspects:
www4.ncsu.edu/~kggard/kg_papers/MTT_05_FrontEnd_Distortion.pdf
regards -
Henry
(Sorry for bad english)
MD
Magnus Danielson
Mon, Jan 24, 2011 9:19 PM
On 24/01/11 21:32, jimlux wrote:
On 1/24/11 11:44 AM, Magnus Danielson wrote:
On 24/01/11 07:39, Bruce Griffiths wrote:
On 1/23/11 10:01 PM, Magnus Danielson wrote:
Jim,
On 24/01/11 02:35, jimlux wrote:
I'm looking for a reference that gives the power spectrum of the
output
of a hard limiter (1 bit thresholder) with band limited noise and a
single sinusoid.
At high SNR, the output of the limiter is basically a square wave
at at
the input frequency, but as the SNR decreases, it starts to act
like a
soft limiter with a gaussian characteristic, so what is the power
spectrum of the output?
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for
those
conditions as you get a more stable property.
Another approach of understanding is to consider that when the
gaussian
noise is sufficiently high it will start interpolate on the slope of
the
sine and as you add more noise more and more of the sine would
linearize
until you come to the point where it is linear. Soft-clipping will
indeed be similar.
I haven't seen a spectrum plot, but simulation in spice should be
trivial. Setting up a sine + noise, comparator and then a low-pass
filter should be a trivial SPICE setup. It does not take much
imagination to see that the spectrum will migrate from that of a
square
over to that of a sine. It will loose power in those overtones.
oh, yes.. I did the simulation, and modeled the aliasing of the
overtones and all..
I was looking for a reference to cite (you know how it is.. measure it
yourself and it's something you did.. but cite someone who ground
through it before, and it's worth a lot more...)
Excellent.. I had found the Aronson paper (wherein he effectively says
"there's no simple analytical expression".. that's nice and justifies
doing it by numerical modeling). ANd the Jain paper (DTIC), which deals
with multiple sines. I hadn't run across the one by Greenhall (who still
works at JPL)...
Thanks a bunch to the nuts..
Actually, if you think of it... for you to be able to even consider a
"waveform" you will need to do filtering, but then... the shape of that
filter will also have great influence on the overtone spectra... ruling
out analytic expressions. Noise degradation of hard limiter is analyzed
before, See chapter 6.5 Limiters in Gardner.
What are you really trying to achieve? 1-bit ADC at the end of a noisy
channel?
Cheers,
Magnus
On 24/01/11 21:32, jimlux wrote:
> On 1/24/11 11:44 AM, Magnus Danielson wrote:
>> On 24/01/11 07:39, Bruce Griffiths wrote:
>>> jimlux wrote:
>>>> On 1/23/11 10:01 PM, Magnus Danielson wrote:
>>>>> Jim,
>>>>>
>>>>> On 24/01/11 02:35, jimlux wrote:
>>>>>> I'm looking for a reference that gives the power spectrum of the
>>>>>> output
>>>>>> of a hard limiter (1 bit thresholder) with band limited noise and a
>>>>>> single sinusoid.
>>>>>>
>>>>>> At high SNR, the output of the limiter is basically a square wave
>>>>>> at at
>>>>>> the input frequency, but as the SNR decreases, it starts to act
>>>>>> like a
>>>>>> soft limiter with a gaussian characteristic, so what is the power
>>>>>> spectrum of the output?
>>>>>
>>>>> It goes towards sine as I recall it. The gaussian noise rubs of
>>>>> overtones. Gardner describes this in his PLL book. Setting up a nice
>>>>> sawtooth detector is no good when seeing bad noise, as it will degrade
>>>>> into a sine-detector anyways, so using a multiplier is better for
>>>>> those
>>>>> conditions as you get a more stable property.
>>>>>
>>>>> Another approach of understanding is to consider that when the
>>>>> gaussian
>>>>> noise is sufficiently high it will start interpolate on the slope of
>>>>> the
>>>>> sine and as you add more noise more and more of the sine would
>>>>> linearize
>>>>> until you come to the point where it is linear. Soft-clipping will
>>>>> indeed be similar.
>>>>>
>>>>> I haven't seen a spectrum plot, but simulation in spice should be
>>>>> trivial. Setting up a sine + noise, comparator and then a low-pass
>>>>> filter should be a trivial SPICE setup. It does not take much
>>>>> imagination to see that the spectrum will migrate from that of a
>>>>> square
>>>>> over to that of a sine. It will loose power in those overtones.
>>>>>
>>>>
>>>> oh, yes.. I did the simulation, and modeled the aliasing of the
>>>> overtones and all..
>>>>
>>>> I was looking for a reference to cite (you know how it is.. measure it
>>>> yourself and it's something *you* did.. but cite someone who ground
>>>> through it before, and it's worth a lot more...)
>>>>
>>> See:
>>>
>>> http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4101285
>>
>> http://archive.numdam.org/ARCHIVE/RSMUP/RSMUP_1969__42_/RSMUP_1969__42__1_0/RSMUP_1969__42__1_0.pdf
>>
>>
>>
>> http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA425520
>>
>>
>>
>> ... found using "hard limiter autocorrelation sine" in Google.
>>
>
> Excellent.. I had found the Aronson paper (wherein he effectively says
> "there's no simple analytical expression".. that's nice and justifies
> doing it by numerical modeling). ANd the Jain paper (DTIC), which deals
> with multiple sines. I hadn't run across the one by Greenhall (who still
> works at JPL)...
>
> Thanks a bunch to the nuts..
Actually, if you think of it... for you to be able to even consider a
"waveform" you will need to do filtering, but then... the shape of that
filter will also have great influence on the overtone spectra... ruling
out analytic expressions. Noise degradation of hard limiter is analyzed
before, See chapter 6.5 Limiters in Gardner.
What are you *really* trying to achieve? 1-bit ADC at the end of a noisy
channel?
Cheers,
Magnus
BC
Bob Camp
Mon, Jan 24, 2011 9:41 PM
Hi
Most communications systems also have constraints based on signals in
adjacent channels. That pretty much forces a solution of "lots of filter
before lots of gain". Distributing both gain and filtering across multiple
stages gets you into a variety of issues that map junk into the passband.
Once the junk is there, you can't get rid of it later.
Bob
-----Original Message-----
From: time-nuts-bounces@febo.com [mailto:time-nuts-bounces@febo.com] On
Behalf Of ehydra
Sent: Monday, January 24, 2011 3:35 PM
To: Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] power spectrum of hard limiter output
The classical approach is to heavily band-limit the input of an
following hard-limiter. But would it possible to merge both functions in
several stages of an IF-strip?
I think most individuals cannot follow much of this idea but time-nuts
have the same problem :-)
My main interest is a practical (reduced to standard parts to buy) CMOS
inverter IF-strip where the individual stages are ac-coupled.
So it is possible to integrate a high-pass filter via the coupling
capacitor and low-pass via the cross connected capacitor over the
inverters. I think the interstage capacitor also removes 1/f noise of
the signal from the individual pre-stage inverter. CMOS having more 1/f
noise than bipolar transistors under approx. 1 KHz but can be
comfortable from 100 KHz to 1 MHz. The nice thing with CMOS is cheapness
and simplicity.
So the questions are:
- maximum useful amplification
- depends on noise in first stage
- compression on MOSFET inverter gives spectral regrowth
- limiting of burst noise in rf signals
- trying to avoid any form of automatic gain control
- etc.
I played with SPICE models in LTspice and practical with SpectrumLab
using CD4007 inverters as IF-strip at 25 KHz.
I try to be practical and avoid heavy mathematicals.
It works fine if one think of the price of such simple parts! But I'm a
little over my edge how to optimize it further.
Any suggestions are welcome. I don't have access to IEEE papers.
This paper is interesting because it mentions main aspects but looses
itself in CDMA specific aspects:
www4.ncsu.edu/~kggard/kg_papers/MTT_05_FrontEnd_Distortion.pdf
regards -
Henry
(Sorry for bad english)
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to
https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
Hi
Most communications systems also have constraints based on signals in
adjacent channels. That pretty much forces a solution of "lots of filter
before lots of gain". Distributing both gain and filtering across multiple
stages gets you into a variety of issues that map junk into the passband.
Once the junk is there, you can't get rid of it later.
Bob
-----Original Message-----
From: time-nuts-bounces@febo.com [mailto:time-nuts-bounces@febo.com] On
Behalf Of ehydra
Sent: Monday, January 24, 2011 3:35 PM
To: Discussion of precise time and frequency measurement
Subject: Re: [time-nuts] power spectrum of hard limiter output
The classical approach is to heavily band-limit the input of an
following hard-limiter. But would it possible to merge both functions in
several stages of an IF-strip?
I think most individuals cannot follow much of this idea but time-nuts
have the same problem :-)
My main interest is a practical (reduced to standard parts to buy) CMOS
inverter IF-strip where the individual stages are ac-coupled.
So it is possible to integrate a high-pass filter via the coupling
capacitor and low-pass via the cross connected capacitor over the
inverters. I think the interstage capacitor also removes 1/f noise of
the signal from the individual pre-stage inverter. CMOS having more 1/f
noise than bipolar transistors under approx. 1 KHz but can be
comfortable from 100 KHz to 1 MHz. The nice thing with CMOS is cheapness
and simplicity.
So the questions are:
1. maximum useful amplification
2. depends on noise in first stage
3. compression on MOSFET inverter gives spectral regrowth
4. limiting of burst noise in rf signals
5. trying to avoid any form of automatic gain control
6. etc.
I played with SPICE models in LTspice and practical with SpectrumLab
using CD4007 inverters as IF-strip at 25 KHz.
I try to be practical and avoid heavy mathematicals.
It works fine if one think of the price of such simple parts! But I'm a
little over my edge how to optimize it further.
Any suggestions are welcome. I don't have access to IEEE papers.
This paper is interesting because it mentions main aspects but looses
itself in CDMA specific aspects:
www4.ncsu.edu/~kggard/kg_papers/MTT_05_FrontEnd_Distortion.pdf
regards -
Henry
(Sorry for bad english)
_______________________________________________
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to
https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
J
jimlux
Tue, Jan 25, 2011 1:53 PM
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.
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.
J
jimlux
Tue, Jan 25, 2011 1:56 PM
On 1/24/11 1:41 PM, Bob Camp wrote:
Hi
Most communications systems also have constraints based on signals in
adjacent channels. That pretty much forces a solution of "lots of filter
before lots of gain". Distributing both gain and filtering across multiple
stages gets you into a variety of issues that map junk into the passband.
Once the junk is there, you can't get rid of it later.
And GPS (and other CDMA systems in general) is an example of a system
where it's different.The "capture effect" of limiters is well known, and
it's fascinating that the system actually works worse if the SNR is too
high, because you need the noise to be able to receive ALL the signals
at once.
On 1/24/11 1:41 PM, Bob Camp wrote:
> Hi
>
> Most communications systems also have constraints based on signals in
> adjacent channels. That pretty much forces a solution of "lots of filter
> before lots of gain". Distributing both gain and filtering across multiple
> stages gets you into a variety of issues that map junk into the passband.
> Once the junk is there, you can't get rid of it later.
>
And GPS (and other CDMA systems in general) is an example of a system
where it's different.The "capture effect" of limiters is well known, and
it's fascinating that the system actually works worse if the SNR is too
high, because you need the noise to be able to receive ALL the signals
at once.
E
ehydra
Tue, Jan 25, 2011 2:45 PM
Yes, it depends. Sometimes noise lowers SNR, sometimes it improves.
A similar scheme exists to improve ADC performance. If I remember it
correctly, LTC owns a patent where they inject pseudo-noise with known
properties, then the signal runs thru the ADC, then 'a picture of' the
added input noise is removed (maybe in some form of the decimator).
Interesting and a little obscusing the brain.
I must add that I'm not running for ultimate precision (not really
cost-bounded) but for simplicity. My ultimate is to have parasitic
functionality converted in useful functions.
jimlux schrieb:
On 1/24/11 1:41 PM, Bob Camp wrote:
Hi
Most communications systems also have constraints based on signals in
adjacent channels. That pretty much forces a solution of "lots of filter
before lots of gain". Distributing both gain and filtering across
multiple
stages gets you into a variety of issues that map junk into the passband.
Once the junk is there, you can't get rid of it later.
And GPS (and other CDMA systems in general) is an example of a system
where it's different.The "capture effect" of limiters is well known, and
it's fascinating that the system actually works worse if the SNR is too
high, because you need the noise to be able to receive ALL the signals
at once.
Yes, it depends. Sometimes noise lowers SNR, sometimes it improves.
A similar scheme exists to improve ADC performance. If I remember it
correctly, LTC owns a patent where they inject pseudo-noise with known
properties, then the signal runs thru the ADC, then 'a picture of' the
added input noise is removed (maybe in some form of the decimator).
Interesting and a little obscusing the brain.
I must add that I'm not running for ultimate precision (not really
cost-bounded) but for simplicity. My ultimate is to have parasitic
functionality converted in useful functions.
- Henry
jimlux schrieb:
> On 1/24/11 1:41 PM, Bob Camp wrote:
>> Hi
>>
>> Most communications systems also have constraints based on signals in
>> adjacent channels. That pretty much forces a solution of "lots of filter
>> before lots of gain". Distributing both gain and filtering across
>> multiple
>> stages gets you into a variety of issues that map junk into the passband.
>> Once the junk is there, you can't get rid of it later.
>>
>
> And GPS (and other CDMA systems in general) is an example of a system
> where it's different.The "capture effect" of limiters is well known, and
> it's fascinating that the system actually works worse if the SNR is too
> high, because you need the noise to be able to receive ALL the signals
> at once.
MD
Magnus Danielson
Tue, Jan 25, 2011 6:47 PM
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
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
E
ehydra
Tue, Jan 25, 2011 11:32 PM
Hi Bob -
Yes. But coming back to the CMOS inverter multi-stage amplifier:
Because of the absolute momentum signal level the first stages
(=amplifier) sees it operates more linear than later more saturating stages.
As long as the single one stage works linear, this stage will not change
the spectrum!
Only a little noise is added (I think adding here to the linear domain,
but BEWARE: in later stages magnified adding into saturation regions...)
and the signal level is improved, say 15dB. All goes linear up by 15dB here.
So we can see that indeed it is possible to move the front 'brick-wall'
filter at least in part to following stages. How many parts??
I currently have a test-bed with three stages. All the same values. The
question is simply: Would changing parts values for every stage to
something individual different: would this improve the overall response
considerable? Or is it a useless academic exercise?
Bob Camp schrieb:
Hi
Most communications systems also have constraints based on signals in
adjacent channels. That pretty much forces a solution of "lots of filter
before lots of gain". Distributing both gain and filtering across multiple
stages gets you into a variety of issues that map junk into the passband.
Once the junk is there, you can't get rid of it later.
Hi Bob -
Yes. But coming back to the CMOS inverter multi-stage amplifier:
Because of the absolute momentum signal level the first stages
(=amplifier) sees it operates more linear than later more saturating stages.
As long as the single one stage works linear, this stage will not change
the spectrum!
Only a little noise is added (I think adding here to the linear domain,
but BEWARE: in later stages magnified adding into saturation regions...)
and the signal level is improved, say 15dB. All goes linear up by 15dB here.
So we can see that indeed it is possible to move the front 'brick-wall'
filter at least in part to following stages. How many parts??
I currently have a test-bed with three stages. All the same values. The
question is simply: Would changing parts values for every stage to
something individual different: would this improve the overall response
considerable? Or is it a useless academic exercise?
- Henry
Bob Camp schrieb:
> Hi
>
> Most communications systems also have constraints based on signals in
> adjacent channels. That pretty much forces a solution of "lots of filter
> before lots of gain". Distributing both gain and filtering across multiple
> stages gets you into a variety of issues that map junk into the passband.
> Once the junk is there, you can't get rid of it later.
E
ehydra
Tue, Jan 25, 2011 11:35 PM
Hi Magnus -
What book? This one maybe:
Gardner F M PHASELOCK TECHNIQUES Wiley & Sons 1966
Magnus Danielson schrieb:
It goes towards sine as I recall it. The gaussian noise rubs of
overtones. Gardner describes this in his PLL book. Setting up a nice
sawtooth detector is no good when seeing bad noise, as it will degrade
into a sine-detector anyways, so using a multiplier is better for those
conditions as you get a more stable property.
Hi Magnus -
What book? This one maybe:
Gardner F M PHASELOCK TECHNIQUES Wiley & Sons 1966
- Henry
Magnus Danielson schrieb:
> It goes towards sine as I recall it. The gaussian noise rubs of
> overtones. Gardner describes this in his PLL book. Setting up a nice
> sawtooth detector is no good when seeing bad noise, as it will degrade
> into a sine-detector anyways, so using a multiplier is better for those
> conditions as you get a more stable property.
>
J
jimlux
Wed, Jan 26, 2011 3:32 AM
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.
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.
>
MD
Magnus Danielson
Wed, Jan 26, 2011 5:34 AM
On 26/01/11 00:35, ehydra wrote:
Hi Magnus -
What book? This one maybe:
Gardner F M PHASELOCK TECHNIQUES Wiley & Sons 1966
Yes, but there is later revisions of it. A classic on PLLs.
Cheers,
Magnus
On 26/01/11 00:35, ehydra wrote:
> Hi Magnus -
>
> What book? This one maybe:
> Gardner F M PHASELOCK TECHNIQUES Wiley & Sons 1966
Yes, but there is later revisions of it. A classic on PLLs.
Cheers,
Magnus
MD
Magnus Danielson
Wed, Jan 26, 2011 5:44 AM
On 26/01/11 04:32, jimlux wrote:
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.
Indeed. It's just like No measurement and where I was inspired.
You need to be in the same range as your No with the added No since
that's when No+Ni changing Ni will give best sensitivity.
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.
True, but even the big guys get L1 simulators for their bulk testing.
You can get many test-cases with a simple L1 C/A instrument. Then you
can use the big iron test generator for those test which really requires it.
Cheers,
Magnus
On 26/01/11 04:32, jimlux wrote:
> 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.
Indeed. It's just like No measurement and where I was inspired.
You need to be in the same range as your No with the added No since
that's when No+Ni changing Ni will give best sensitivity.
>>
>> 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.
True, but even the big guys get L1 simulators for their bulk testing.
You can get many test-cases with a simple L1 C/A instrument. Then you
can use the big iron test generator for those test which really requires it.
Cheers,
Magnus
