"if you have perfect phase recovery, zero 
doppler and you are only looking at one satellite" <--- NICE!

The difference between going from one to two bits has shown through
processing real GPS signals through my system an improvement of ~5ft.  In
most cases this is probably negligable but it some maybe not.  

I have a reference that quotes similar values to the ones you posted so
nice job on the simulations.  

On another note: would adding doppler or more satellites degrade your SNR?
 I could possibly see that adding more satellites MAY technically degrade
your SNR but adding doppler (since you have to figure out what it is
closely anyways) does not seem to degrade SNR in my simulations. (i.e.
when I create multiple satellite signals all with a doppler shift and a
delay to the first bit transition my results remain tighly grouped).

>Sounds good Ryan ,
>I did a quick and dirty sim too : if you have perfect phase recovery,
zero 
>doppler and you are only looking at one satellite then just using the
sign 
>bit loses you not quite 2 dB of SNR (in AWGN) compared with using lots of

>perfect quantisation steps.
>If you go to 2 bit samples then you lose about 1 dB SNR (according to my

>rough model if you arrange things so that the S+N actually gives you +/-3
at 
>the ADC o/p a fair percentage of the time). Many people would say that
the 
>extra power needed for processing the second bit isn't worth it but the 
>increased tolerance to narrowband interference is.  Going to even more
bits 
>seems a complete waste of time until you want to do some really expensive

>anti-jamming.
>
>I'm sure that this has been documented in stacks of books and papers
before 
>now and they show, not only good mathematico-physical proofs but, in some

>cases, interesting tricks.
>
>Best of Luck - Mike
>
>
>

"effimofunk" <rfrankel@ufl.edu> wrote in message 
news:AIKdnXx_mJRIeu_eRVn-hg@giganews.com...
> For anyone who cares:
>  I tested the theories put in this discussion out and they seem to make
> sense.  First I plotted the Signal(GPS Signal created in MATLAB[another
> whole discussion could have gone into that]),  Noise, and Quantized 2-bit
> Signal+Noise.  From this graph it is hard to tell whether the correlation
> between Signal and Signal+Noise still exists.  So, to put some numbers on
> it, and considering the signals are aligned properly in time...
>
> If I correlate the noise vs. the noise I get a value of
> sum(real(noise(1:50).*real(noise(51:100))))) = -2.276863328559156e-009
>
> If I correlate the noise vs. the signal I get
> sum(real(noise(1:50).*real(noise(51:100)+Signal(1:50)))) =
> -2.292580903252614e-009
>
> And if I correlate the (signal + noise) vs. the signal I get
> sum(real(A.data(1:50)).*real(noise(51:100)+Signal(1:50))) =
> -1.156741657174452e-005
>
> So what does this show?  I believe this shows that the quantized
> Signal+Noise does indeed retain some properties of the original signal due
> to a correlation existing between the two.  I also believe that the
> correlation will get better over longer data lengths.
>
> Thanks to all that have posted in this thread as it has been very
> informative to me and hopefully you.
>
> If you would like the diagrams I have for this or have any comments about
> what I have discussed above please post as I would like to see this
> discussion through with some proof.
>
Sounds good Ryan ,
I did a quick and dirty sim too : if you have perfect phase recovery, zero 
doppler and you are only looking at one satellite then just using the sign 
bit loses you not quite 2 dB of SNR (in AWGN) compared with using lots of 
perfect quantisation steps.
If you go to 2 bit samples then you lose about 1 dB SNR (according to my 
rough model if you arrange things so that the S+N actually gives you +/-3 at 
the ADC o/p a fair percentage of the time). Many people would say that the 
extra power needed for processing the second bit isn't worth it but the 
increased tolerance to narrowband interference is.  Going to even more bits 
seems a complete waste of time until you want to do some really expensive 
anti-jamming.

I'm sure that this has been documented in stacks of books and papers before 
now and they show, not only good mathematico-physical proofs but, in some 
cases, interesting tricks.

Best of Luck - Mike

For anyone who cares:
  I tested the theories put in this discussion out and they seem to make
sense.  First I plotted the Signal(GPS Signal created in MATLAB[another
whole discussion could have gone into that]),  Noise, and Quantized 2-bit
Signal+Noise.  From this graph it is hard to tell whether the correlation
between Signal and Signal+Noise still exists.  So, to put some numbers on
it, and considering the signals are aligned properly in time...

If I correlate the noise vs. the noise I get a value of 
sum(real(noise(1:50).*real(noise(51:100))))) = -2.276863328559156e-009

If I correlate the noise vs. the signal I get 
sum(real(noise(1:50).*real(noise(51:100)+Signal(1:50)))) =
-2.292580903252614e-009

And if I correlate the (signal + noise) vs. the signal I get
sum(real(A.data(1:50)).*real(noise(51:100)+Signal(1:50))) =
-1.156741657174452e-005

So what does this show?  I believe this shows that the quantized
Signal+Noise does indeed retain some properties of the original signal due
to a correlation existing between the two.  I also believe that the
correlation will get better over longer data lengths.
  
Thanks to all that have posted in this thread as it has been very
informative to me and hopefully you.

If you would like the diagrams I have for this or have any comments about
what I have discussed above please post as I would like to see this
discussion through with some proof.

--Ryan

Thanks.  Actually I am doing the acquisition and tracking in the frequency
domain which ends up as a coherent integration.  I was just trying to
maybe put some numbers on things instead of just determining them
experimentally.  Thanks again.


>Hi Ryan
>          The defined range for the GPS signal is between -130 dbm to
>-110 dbm. But genrally you dont oberve a signal stronger than -114 dbm,
>even in open sky.
>If you are talking about integration time in carrier loop , low SNR will
>require large Integration time,assuming to be non-coherent integration.
>
>Infact you can go for adaptive integration time in carrier loop
depending
>upon the signal strength.
>
>Regards
>sandeep
>
>
>
>
>
>>OK.  I see what you are saying now.  Don't mind me I am a little slow. 
>Is
>>there any sort of way to work out the needed integration time based on
>the
>>SNR of the incoming signal?  I am assuming there must be.  Also, Do you
>>know what the range of the GPS signal recieved power is?  I have seen
>-130
>>as a spec for the minimum power but I have seen nothing about the
>maximum. 
>>Just wondering.  I appreciate all of your help as this has been
>bothering
>>me for a few days now.
>>
>>--Ryan
>>
>
>
>

Hi Ryan
          The defined range for the GPS signal is between -130 dbm to
-110 dbm. But genrally you dont oberve a signal stronger than -114 dbm,
even in open sky.
If you are talking about integration time in carrier loop , low SNR will
require large Integration time,assuming to be non-coherent integration.

Infact you can go for adaptive integration time in carrier loop depending
upon the signal strength.

Regards
sandeep





>OK.  I see what you are saying now.  Don't mind me I am a little slow. 
Is
>there any sort of way to work out the needed integration time based on
the
>SNR of the incoming signal?  I am assuming there must be.  Also, Do you
>know what the range of the GPS signal recieved power is?  I have seen
-130
>as a spec for the minimum power but I have seen nothing about the
maximum. 
>Just wondering.  I appreciate all of your help as this has been
bothering
>me for a few days now.
>
>--Ryan
>

OK.  I see what you are saying now.  Don't mind me I am a little slow.  Is
there any sort of way to work out the needed integration time based on the
SNR of the incoming signal?  I am assuming there must be.  Also, Do you
know what the range of the GPS signal recieved power is?  I have seen -130
as a spec for the minimum power but I have seen nothing about the maximum. 
Just wondering.  I appreciate all of your help as this has been bothering
me for a few days now.

--Ryan

>No.  If the noise is random, then the digitized noise+signal will be 
>slightly non-random.  When the amplitude of the noise just happens to be

>very small in a given sample instant, the sample will reflect the signal.

>Over a long enough time, the correlation between the digitized signal and

>the SS code will be significant enough to detect reliably.  It's like a 
>casino making reliable profits over time by skewing the odds of each bet
a 
>tiny bit in their favour.
>
>--
>Matt
>
>
>

"effimofunk" <rfrankel@ufl.edu> wrote in message 
news:xs2dnQCvMsY41OzenZ2dnUVZ_smdnZ2d@giganews.com...
>I see what are saying but I am still hung up on something.  If you have a
> signal that is three to four times smaller than the noise and then you
> digitize the full-scale swing to lets say one-bit isn't the resultant
> digital signal just the noise?

No.  If the noise is random, then the digitized noise+signal will be 
slightly non-random.  When the amplitude of the noise just happens to be 
very small in a given sample instant, the sample will reflect the signal. 
Over a long enough time, the correlation between the digitized signal and 
the SS code will be significant enough to detect reliably.  It's like a 
casino making reliable profits over time by skewing the odds of each bet a 
tiny bit in their favour.

--
Matt

effimofunk wrote:
> I see what are saying but I am still hung up on something.  If you have a
> signal that is three to four times smaller than the noise and then you
> digitize the full-scale swing to lets say one-bit isn't the resultant
> digital signal just the noise?  It seems just by intuition on my end that
> the signal will be lost and all you will see is the noise.  Granted the
> mean will be zero over time but you can no longer recover your signal. 
> That is where I am getting confused.  Thanks for your help.  I am sure I
> am asking the wrong questions or misunderstanding your responses.
> --Ryan

Thinking about the first question...
You seem to be implying that the signal will have no influence over the 
quantized signal.  Essentially you're writing the signal off simply 
because it's lower in amplitude to the noise.

At some points in time the noise will have lower amplitude than the 
signal, and hence only the signal will be received.  If you average the 
noise over a large time, then the average noise amplitude will be zero, 
however the signal amplitude will be some non zero finite value.

So again, I ask you...
What is the mean of the channel noise?
What is the mean of the quantization noise?

I see what are saying but I am still hung up on something.  If you have a
signal that is three to four times smaller than the noise and then you
digitize the full-scale swing to lets say one-bit isn't the resultant
digital signal just the noise?  It seems just by intuition on my end that
the signal will be lost and all you will see is the noise.  Granted the
mean will be zero over time but you can no longer recover your signal. 
That is where I am getting confused.  Thanks for your help.  I am sure I
am asking the wrong questions or misunderstanding your responses.
--Ryan


>Well, what kind of noise is the channel noise represented as?
>And what kind of noise is the quantization noise?
>What's the mean of both these noises?
>
>So if I apply 0.0001V to this noise at the input to the receiver and 
>average over billions of samples, what is the measured output?  (The 
>receiver is just the basic integrate and dump matched filter, ie 
>baseband transmission)
>
>Now imagine that instead of just applying that 0.0001V signal you now 
>make it toggle every second sample (thus it has 2 samples at 0.0001V and

>2 samples at -0.0001V).  You apply this to the input of the receiver, 
>but now the receiver matched filter also inverts it again, so that you 
>again have 0.001V as the input to the integrate and dump.  Will the 
>output be the same as in the first situation?
>
>The next logical step to reduce the effect of narrow band interferer's 
>is to provide an additional level of 'randomness' to the toggling of the

>signal.  This is done by using a known PRBS.
>
>There is still the issue of AGC and offsets, AGC isn't such a big issue,

>as large amounts of clipping can occur, the energy isn't the big swings,

>it's simply in the small offsets.  Offset correction is aided by the 
>PRBS having a very uniform distribution.  On average it has as many 1's 
>as it has 0's, so that over a large period of time it can be tuned to 
>eliminate the offset pre-decoding.
>

effimofunk wrote:
> I understand the spread spectrum part of it.  The Gold Code correlation
> used in the acquisition process is clear but what is not clear to me is
> how the signal is not lost after the path loss from the satellite and such
> a low quantization level.  If we have 2 bits we can only get about 12 dB of
> SNR and the signal is -19 dB below the noise.  The processing gain of the
> DSP section only helps if you retain the structure of the signal itself. 
> If you lose the signal due to low quantization all the correlation in the
> world wouldn't help you.  How bout does it really have to do with the zero
> crossings due to the phase modulated signal?  Thanks for your responses so
> far. 

Well, what kind of noise is the channel noise represented as?
And what kind of noise is the quantization noise?
What's the mean of both these noises?

So if I apply 0.0001V to this noise at the input to the receiver and 
average over billions of samples, what is the measured output?  (The 
receiver is just the basic integrate and dump matched filter, ie 
baseband transmission)

Now imagine that instead of just applying that 0.0001V signal you now 
make it toggle every second sample (thus it has 2 samples at 0.0001V and 
2 samples at -0.0001V).  You apply this to the input of the receiver, 
but now the receiver matched filter also inverts it again, so that you 
again have 0.001V as the input to the integrate and dump.  Will the 
output be the same as in the first situation?

The next logical step to reduce the effect of narrow band interferer's 
is to provide an additional level of 'randomness' to the toggling of the 
signal.  This is done by using a known PRBS.

There is still the issue of AGC and offsets, AGC isn't such a big issue, 
as large amounts of clipping can occur, the energy isn't the big swings, 
it's simply in the small offsets.  Offset correction is aided by the 
PRBS having a very uniform distribution.  On average it has as many 1's 
as it has 0's, so that over a large period of time it can be tuned to 
eliminate the offset pre-decoding.