Reply by Steve Pope March 1, 20162016-03-01
Peter Mairhofer  <63832452@gmx.net> wrote:

>On 2016-02-29 14:21, Steve Pope wrote:
>> 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 > >
Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
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