>> often you can compute the magnitude of
>> the multiplicative noise, then model it as additive noise of that
>> magnitude.
>>
>>> and I even derived something that results in this relation in my
>>> original posting. Based on that, to first order it is additive (though
>>> not white).
>>
>> No, this does not mean it's additive noise even to a 0th order, it is
>> still multiplicative noise, and you would need to recompute it for each
>> signal magnitude; and if you have something like a dropout channel
>> changing dynamically, you cannot model it this way at all.
>
>You are right, it is multiplicative.
>
>Fortunately it seems it does not make much difference if I add or
>multiply it:
>
>s0 = pn_generator(); % generate PN without carrier
>
>% add carrier for multiplicative noise
>s1 = s0 + 1;
>
>% generate some random signal
>x = (randn(size(s))+1i*randn(size(s)))/sqrt(2);
>
>% calculate signal errors
>[ 20*log10(norm(x)/norm((x .* s1)-x)) , ...
> 20*log10(norm(x)/norm((s0+x)-x)) ]
>
>ans =
>
> 40.8796e+000 40.8714e+000
>
>This number also agrees pretty well from the one obtained via
>20*log(1/(2*pi*fc*sigma))
I am going to say that if the coherence time of the signal is
less than, or on the order of, the time constants within the
PLL or other element generating the phase noise, the attempt
to approximate the multiplicative noise as afdditive noise is
going to fail.
Steve
Reply by ●March 1, 20162016-03-01
I mentioned before that the carrier tracking loop in a receiver
Acts like a high pass filter to phase noise.
Mark
Reply by Peter Mairhofer●February 29, 20162016-02-29
On 2016-02-29 15:45, Eric Jacobsen wrote:
> On Mon, 29 Feb 2016 12:00:51 -0800, Peter Mairhofer <63832452@gmx.net>
> wrote:
>>> [...]
>>> Phase noise does not behave the same as additive noise.
>>
>> Why not? I read everywhere (and it was mentioned here) that phase noise
>> results in an SNR degradation (though it's not "real" noise).
>
> Because additive noise can add in both the I and Q dimensions to form
> an error vector with random phase and amplitude. Phase noise adds in
> ONLY the phase dimension.
>
> Here's a constellation diagram with phase noise. It looks very
> different than a constellation diagram with additive noise.
>
> http://i.cmpnet.com/analog-europe/2008/05/ADIclocksFig7.jpg
Cool, thanks.
>> [...]
>> Why not? Suppose I send a baseband signal x[n]=1 and it gets (ideally)
>> upconverted to RF, then the signal is x(t) = cos(wc t). Downconversion
>> with a non-ideal LO gives y(t).
>>
>> The PSD of y(t) (after removing the carrier and normalizing to 1Hz per
>> bin) gives the well known L(f) phase noise figure.
>>
>> Ideal sampling gives y[n] which contains the phase noise. The error is
>> the "SNR degradation due to phase noise":
>>
>> 20*log10(norm(y-x)/norm(x))
>>
>> Now looking at the spectruof y[n] it can be seen that the error is not
>> constant ("white") in the frequency domain: High amounts of error are
>> very close to 0 (where the carrier was).
>>
>> For a direct conversion receiver, this is where the actual signal lies,
>> hence it suffers from huge errors in this (small) frequency region.
>>
>> On the other hand, a het receiver has an LO which is offset from the
>> actual carrier. That means the region around 0 does NOT contain the
>> actual signal and can be filtered out.
>>
>> Similarly as with DC offets and 1/f noise.
>
> Write the equations for the mixing operation, both for real-valued
> signals (het-, super-het-), and complex (direct conversion). Note
> again that the noise is ONLY in the phase dimension, so it only
> affects the argument to the sin and cos mixers.
>
> Then note that the effect on the signal is the same, regardless of how
> it is mixed.
Ok, I think you are right. I think I mean something else. Assume my
signal is between fc-BW/2 and fc+BW/2.
With a direct conversion receiver, after mixing the signal the actual I
signal part will be between 0 and BW/2.
Now instead of mixing down with fc, let's mix down by (fc-fx). The
actual signal is now between fx and BW/2+fx (sampling the signal of
course requires an ADC of 2*(BW/2+fx) insead of BW ...)
The part between 0 and fx contains the major effective part of the phase
noise and a digital high pass filter with fcut=fx could filter this
stuff out. Afterwards, digital downconversion by -fx gives the actual
samples in digital domain with reduced phase noise.
fx could be something like 1 MHz to capture most of the low frequency
phase noise parts.
Clearly, this approach could be implemented in analog domain as well by
just using appropriately sized AC coupling caps between mixer and
baseband filters (requirements on ADC and digital downconversion by fx
would remain).
This is what I meant.
Any thoughts on this?
I have a reason to ask this: I know about a system with exceptional
performance (like a VSA or better) ... raw stated EVM (just on the
complex baseband signals) something like -50 to -60dB.
However, the PLL they are using (ADF4153) does not have an integrated
jitter significantly lower than 700fs RMS at the frequency of interest
which which would result in an EVM not more than -40dB (according to my
calculations and simulations).
Hence I am wondering what happens here and maybe high-pass filtering the
phase noise (similarly as I described) is something that's generally done?
Actually, while writing this, I realized that the assumption with most
of the noise around the carrier would only be valid for *additive*
noise. When I plot
plot(dB20(fft(x .* s1 - x)))
(s1 ... phase noise with carrier; x ... actual signal, random,
wideband), the error signal is not colored any more but appears white!
Then let me ask a different question: Why would I ever care about the
specific shape of L(f) instead of the integrated jitter ?
Peter
Reply by Eric Jacobsen●February 29, 20162016-02-29
On Mon, 29 Feb 2016 12:00:51 -0800, Peter Mairhofer <63832452@gmx.net>
wrote:
>On 2016-02-29 9:31, Eric Jacobsen wrote:
>> On Sun, 28 Feb 2016 19:29:40 -0800, Peter Mairhofer <63832452@gmx.net>
>> wrote:
>>> [...]
>>>
>>> x(t) = cos(2 pi f t + phi(t))
>>>
>>> y(t) = "downconvert x(t) to 0 Hz and remove images"
>>>
>>> Sample y(t) -> y[n]
>>>
>>> NMSE = 10*log10(var(y))
>>>
>>> Or using the quoted script from Markus [1]:
>>>
>>> srcPar.f_Hz = [ 0 10 100 1e3 10e3 100e3 1e6 10e6 100e6 9e9 ];
>>> srcPar.g_dBc1Hz = [ -90 -90 -107 -121 -131 -130 -140 -145 -145 -145 ];
>>> srcPar.includeCarrier = 0; % remove carrier, so just noise is left
>>> s = pn_generator();
>>> % actual signal is defined as 0dBc = 1
>>> NMSE = 10*log10(var(s))
>>> = -61.7993
>>>
>>> Is this correct so far?
>>>
>>> Is it also true then that this added "noise" is just colored noise on
>>> the signal? If so, it seems that the noise is strongest very close to
>>> the carrier and gets less farther apart.
>>
>> Phase noise does not behave the same as additive noise.
>
>Thanks, Eric.
>
>Why not? I read everywhere (and it was mentioned here) that phase noise
>results in an SNR degradation (though it's not "real" noise).
Because additive noise can add in both the I and Q dimensions to form
an error vector with random phase and amplitude. Phase noise adds in
ONLY the phase dimension.
Here's a constellation diagram with phase noise. It looks very
different than a constellation diagram with additive noise.
http://i.cmpnet.com/analog-europe/2008/05/ADIclocksFig7.jpg
>Apart from that: I can always define an error measure like the
>normalized mean square error above and express it in dB. I am just
>interested in the normalized difference in the error of my signal due to
>the phase noise.
As you can see in the diagram above, there will be a degradation due
to the phase noise, and it can be approximately modelled as an SNR
reduction that would yield the same degradation. It is, however,
only an approximation.
>>> Is my conclusion true that this is a big problem for a direct conversion
>>> receiver because most of the "noise" is close to the carrier (where an
>>> actual signal exists in a direct conversion receiver)?
>>
>> The architecture doesn't really have much affect on sensitivity to
>> phase noise. Whatever the net rms phase noise happens to be, it
>> won't matter whether it was het-. super-het-, or direct conversion.
>
>Why not? Suppose I send a baseband signal x[n]=1 and it gets (ideally)
>upconverted to RF, then the signal is x(t) = cos(wc t). Downconversion
>with a non-ideal LO gives y(t).
>
>The PSD of y(t) (after removing the carrier and normalizing to 1Hz per
>bin) gives the well known L(f) phase noise figure.
>
>Ideal sampling gives y[n] which contains the phase noise. The error is
>the "SNR degradation due to phase noise":
>
>20*log10(norm(y-x)/norm(x))
>
>Now looking at the spectruof y[n] it can be seen that the error is not
>constant ("white") in the frequency domain: High amounts of error are
>very close to 0 (where the carrier was).
>
>For a direct conversion receiver, this is where the actual signal lies,
>hence it suffers from huge errors in this (small) frequency region.
>
>On the other hand, a het receiver has an LO which is offset from the
>actual carrier. That means the region around 0 does NOT contain the
>actual signal and can be filtered out.
>
>Similarly as with DC offets and 1/f noise.
Write the equations for the mixing operation, both for real-valued
signals (het-, super-het-), and complex (direct conversion). Note
again that the noise is ONLY in the phase dimension, so it only
affects the argument to the sin and cos mixers.
Then note that the effect on the signal is the same, regardless of how
it is mixed.
>>>> The impact that noise will have on a receiver BER depends on the
>>>> Sensitivity of the modulation and how the carrier tracking loop
>>>> removes the phase noise. I'm not sure if you are dealing
>>>> with a digital receiver or what?
>>>
>>> It is not anything "conventional" and there is no modulation scheme used
>>> etc (except direct I/Q modulation). Think of it just as a VSA.
>>>
>>> Hence the way I want to think about it: Suppose I have an *arbitrary
>>> signal* between fc-BW/2 and fc+BW/2 and I downconvert this signal with a
>>> non-ideal oscillator to 0-BW and sample it to y[n] (ideal sampling),
>>> what is the impact in terms of NMSE (as defined above) ?
>>
>> As mentioned previously, it depends on the modulation. e.g., BPSK is
>> far less sensitive to phase noise than 8PSK.
>
>As mentioned, NO specific modulation or constellation is assumed except
>ordinary I/Q - same as for an oscilloscope/Signal Analyzer. You can call
>it 2^14-QAM or 2^16-QAM if you like.
>
>I am interested in the error between
>
>x_baseband_ideal(t) - x_baseband_with_pn(t)
>
>or after ideal sampling
>
>x_baseband_ideal[n] - x_baseband_with_pn[n]
>
>resp. the "integrated", normalized measure
>
>var(x_baseband_ideal - x_baseband_with_pn)/var(x_baseband_ideal)
>
>Peter
>
>
Reply by Peter Mairhofer●February 29, 20162016-02-29
On 2016-02-29 14:21, Steve Pope wrote:
> Peter Mairhofer <63832452@gmx.net> wrote:
>
>> On 2016-02-29 10:03, Steve Pope wrote:
>
>>> Peter Mairhofer <63832452@gmx.net> wrote:
>
>>>> On 2016-02-28 6:38, makolber@yahoo.com wrote:
>
>>>> Sure, it is not AWGN.
>
>>> Not only that, it is not additive noise of any sort. Both phase
>>> noise and jitter are forms of multiplicative noise.
>
>> But once again, there is tons of evidence in literature that it can be
>> trated as SNR degradation to first order, on of them given by Markus
>> (?): MT008:
>
>> SNR = 20*log(1/(2*pi*fc*sigma))
>
> Yes, as I wrote in this thread although perhaps not in the post
> you just replied to, often you can compute the magnitude of
> the multiplicative noise, then model it as additive noise of that
> magnitude.
>
>> and I even derived something that results in this relation in my
>> original posting. Based on that, to first order it is additive (though
>> not white).
>
> No, this does not mean it's additive noise even to a 0th order, it is
> still multiplicative noise, and you would need to recompute it for each
> signal magnitude; and if you have something like a dropout channel
> changing dynamically, you cannot model it this way at all.
You are right, it is multiplicative.
Fortunately it seems it does not make much difference if I add or
multiply it:
s0 = pn_generator(); % generate PN without carrier
% add carrier for multiplicative noise
s1 = s0 + 1;
% generate some random signal
x = (randn(size(s))+1i*randn(size(s)))/sqrt(2);
% calculate signal errors
[ 20*log10(norm(x)/norm((x .* s1)-x)) , ...
20*log10(norm(x)/norm((s0+x)-x)) ]
ans =
40.8796e+000 40.8714e+000
This number also agrees pretty well from the one obtained via
20*log(1/(2*pi*fc*sigma))
Peter
Reply by Steve Pope●February 29, 20162016-02-29
Peter Mairhofer <63832452@gmx.net> wrote:
>On 2016-02-29 10:03, Steve Pope wrote:
>> Peter Mairhofer <63832452@gmx.net> wrote:
>>> On 2016-02-28 6:38, makolber@yahoo.com wrote:
>>> Sure, it is not AWGN.
>> Not only that, it is not additive noise of any sort. Both phase
>> noise and jitter are forms of multiplicative noise.
>But once again, there is tons of evidence in literature that it can be
>trated as SNR degradation to first order, on of them given by Markus
>(?): MT008:
>SNR = 20*log(1/(2*pi*fc*sigma))
Yes, as I wrote in this thread although perhaps not in the post
you just replied to, often you can compute the magnitude of
the multiplicative noise, then model it as additive noise of that
magnitude.
>and I even derived something that results in this relation in my
>original posting. Based on that, to first order it is additive (though
>not white).
No, this does not mean it's additive noise even to a 0th order, it is
still multiplicative noise, and you would need to recompute it for each
signal magnitude; and if you have something like a dropout channel
changing dynamically, you cannot model it this way at all.
Tangentially, in mathematics an operation can be bilinear without
being linear, and this is closely related to that.
Steve
Reply by Peter Mairhofer●February 29, 20162016-02-29
On 2016-02-29 10:03, Steve Pope wrote:
> Peter Mairhofer <63832452@gmx.net> wrote:
>
>> On 2016-02-28 6:38, makolber@yahoo.com wrote:
>
>>> The SNR will be due to the noise integrated over your bandwidth.
>>> I prefer to call it MER or EVM when it is due to phase instead of
>>> Awgn.
>
>> Sure, it is not AWGN.
>
> Not only that, it is not additive noise of any sort. Both phase
> noise and jitter are forms of multiplicative noise.
But once again, there is tons of evidence in literature that it can be
trated as SNR degradation to first order, on of them given by Markus
(?): MT008:
SNR = 20*log(1/(2*pi*fc*sigma))
and I even derived something that results in this relation in my
original posting. Based on that, to first order it is additive (though
not white).
Peter
Reply by Peter Mairhofer●February 29, 20162016-02-29
On 2016-02-29 9:31, Eric Jacobsen wrote:
> On Sun, 28 Feb 2016 19:29:40 -0800, Peter Mairhofer <63832452@gmx.net>
> wrote:
>> [...]
>>
>> x(t) = cos(2 pi f t + phi(t))
>>
>> y(t) = "downconvert x(t) to 0 Hz and remove images"
>>
>> Sample y(t) -> y[n]
>>
>> NMSE = 10*log10(var(y))
>>
>> Or using the quoted script from Markus [1]:
>>
>> srcPar.f_Hz = [ 0 10 100 1e3 10e3 100e3 1e6 10e6 100e6 9e9 ];
>> srcPar.g_dBc1Hz = [ -90 -90 -107 -121 -131 -130 -140 -145 -145 -145 ];
>> srcPar.includeCarrier = 0; % remove carrier, so just noise is left
>> s = pn_generator();
>> % actual signal is defined as 0dBc = 1
>> NMSE = 10*log10(var(s))
>> = -61.7993
>>
>> Is this correct so far?
>>
>> Is it also true then that this added "noise" is just colored noise on
>> the signal? If so, it seems that the noise is strongest very close to
>> the carrier and gets less farther apart.
>
> Phase noise does not behave the same as additive noise.
Thanks, Eric.
Why not? I read everywhere (and it was mentioned here) that phase noise
results in an SNR degradation (though it's not "real" noise).
Apart from that: I can always define an error measure like the
normalized mean square error above and express it in dB. I am just
interested in the normalized difference in the error of my signal due to
the phase noise.
>> Is my conclusion true that this is a big problem for a direct conversion
>> receiver because most of the "noise" is close to the carrier (where an
>> actual signal exists in a direct conversion receiver)?
>
> The architecture doesn't really have much affect on sensitivity to
> phase noise. Whatever the net rms phase noise happens to be, it
> won't matter whether it was het-. super-het-, or direct conversion.
Why not? Suppose I send a baseband signal x[n]=1 and it gets (ideally)
upconverted to RF, then the signal is x(t) = cos(wc t). Downconversion
with a non-ideal LO gives y(t).
The PSD of y(t) (after removing the carrier and normalizing to 1Hz per
bin) gives the well known L(f) phase noise figure.
Ideal sampling gives y[n] which contains the phase noise. The error is
the "SNR degradation due to phase noise":
20*log10(norm(y-x)/norm(x))
Now looking at the spectruof y[n] it can be seen that the error is not
constant ("white") in the frequency domain: High amounts of error are
very close to 0 (where the carrier was).
For a direct conversion receiver, this is where the actual signal lies,
hence it suffers from huge errors in this (small) frequency region.
On the other hand, a het receiver has an LO which is offset from the
actual carrier. That means the region around 0 does NOT contain the
actual signal and can be filtered out.
Similarly as with DC offets and 1/f noise.
>>> The impact that noise will have on a receiver BER depends on the
>>> Sensitivity of the modulation and how the carrier tracking loop
>>> removes the phase noise. I'm not sure if you are dealing
>>> with a digital receiver or what?
>>
>> It is not anything "conventional" and there is no modulation scheme used
>> etc (except direct I/Q modulation). Think of it just as a VSA.
>>
>> Hence the way I want to think about it: Suppose I have an *arbitrary
>> signal* between fc-BW/2 and fc+BW/2 and I downconvert this signal with a
>> non-ideal oscillator to 0-BW and sample it to y[n] (ideal sampling),
>> what is the impact in terms of NMSE (as defined above) ?
>
> As mentioned previously, it depends on the modulation. e.g., BPSK is
> far less sensitive to phase noise than 8PSK.
As mentioned, NO specific modulation or constellation is assumed except
ordinary I/Q - same as for an oscilloscope/Signal Analyzer. You can call
it 2^14-QAM or 2^16-QAM if you like.
I am interested in the error between
x_baseband_ideal(t) - x_baseband_with_pn(t)
or after ideal sampling
x_baseband_ideal[n] - x_baseband_with_pn[n]
resp. the "integrated", normalized measure
var(x_baseband_ideal - x_baseband_with_pn)/var(x_baseband_ideal)
Peter
Reply by Steve Pope●February 29, 20162016-02-29
<makolber@yahoo.com> wrote:
>On Monday, February 29, 2016 at 1:03:26 PM UTC-5, Steve Pope wrote:
>> Peter Mairhofer <63832452@gmx.net> wrote:
[ phase noise
>> >Sure, it is not AWGN.
>> Not only that, it is not additive noise of any sort. Both phase
>> noise and jitter are forms of multiplicative noise.
>> (I'm not familiar with the acronym MER but maybe the M mean
>> multiplicative.)
>Modulation Error Ratio usually expressed in dB
>popular in the CATV biz
Thanks.
These metrics are fine for transmitters, but the effect of phase
noise in a receiver is more complicated. In low levels, it degrades
sensitivity; in medium levels, it causes an error floor and in
high levels it can eliminate all reception nomatter how good the
SNR.
But it's often usually sufficient to calculate that phase noise (once
you determine its magnitude) will combine in an RMS fashion with
other unrelated noise sources. Son long as the phase noise is
not in an extreme, performance-killing region. son in that sense
you can treat the RX not much differently than the EVM in a TX.
Steve
Reply by ●February 29, 20162016-02-29
On Monday, February 29, 2016 at 1:03:26 PM UTC-5, Steve Pope wrote:
> Peter Mairhofer <63832452@gmx.net> wrote:
>
> >On 2016-02-28 6:38, makolber@yahoo.com wrote:
>
> >> The SNR will be due to the noise integrated over your bandwidth.
> >> I prefer to call it MER or EVM when it is due to phase instead of
> >> Awgn.
>
> >Sure, it is not AWGN.
>
> Not only that, it is not additive noise of any sort. Both phase
> noise and jitter are forms of multiplicative noise.
>
> (I'm not familiar with the acronym MER but maybe the M mean
> multiplicative.)
>
> Steve
Modulation Error Ratio usually expressed in dB
popular in the CATV biz
very similar to EVM usually expressed in %
M