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sandman Community Member Offline Posts: 73	Article relating ACPR and two-tone IM3 calculations Dec 10^th, 2010, 8:33am Hi all, I was wondering if anyone on this forum had access to the following article - "COMPACT FORMULAS TO RELATE ACPR AND NPR TO TWO-TONE IMR AND IP3" by Nuno Borges Carvalho and Jose Carlos Pedro, made in the Microwave Journal, December 1999, pp. 70-84. Thanks, if you have it and can share! cheers, sandman.
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RFICDUDE

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Re: Article relating ACPR and two-tone IM3 calculations
Reply #1 - Dec 11^th, 2010, 6:27am

What is it that you would like to do and what types of signals are interested in analyzing?

Weakly nonlinear (i.e. 3rd order only) relationships between IM3 and ACPR are easier to deal with rather than PA problems operating near compression where 5th order and higher relations start to influence the ACPR and IM results.

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sandman

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Re: Article relating ACPR and two-tone IM3 calculations
Reply #2 - Dec 12^th, 2010, 5:16am

RFICDUDE wrote on Dec 11^th, 2010, 6:27am:

What is it that you would like to do and what types of signals are interested in analyzing?

I am trying to design a multi-mode transmitter for GSM/EDGE, WCDMA and LTE signals. If I can connect IP3 of the small signal stages to ACLR or ACPR, it would make 'optimised' performance budgeting easier. To make things simpler, we can ignore what 'optimised' implies and only try to work out a relation!

RFICDUDE wrote on Dec 11^th, 2010, 6:27am:

Weakly nonlinear (i.e. 3rd order only) relationships between IM3 and ACPR are easier to deal with rather than PA problems operating near compression where 5th order and higher relations start to influence the ACPR and IM results.

There's a relationship that connects IM3 (two tones, with same total power) and ACLR (modulated signals). This should be easily valid for the 3dB:1dB (IM3, P_out) operating region. I've got some decent equations already, but I don't fully know how the equations were worked out. Perhaps this paper can give me some leads.

I've read an excerpt of this used in a book (Practical RF Circuit Design for Modern Wireless Systems: Active circuits and ... By Rowan Gilmore, Les Besser), where
ACLR > IM3_two_tone,
which cannot be true when the same power is used for two-tones and modulated signals, for obvious reasons. I'd like to see how this paper compares IM3 to ACLR...

Tying this to PA ('higher' into compression) behaviour, with and without memory effects would be a logical next step.

Do you have this paper or any other comments?

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RFICDUDE

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Re: Article relating ACPR and two-tone IM3 calculations
Reply #3 - Dec 12^th, 2010, 7:01pm

Unfortunately it is not easy to obtain a simple expression that is valid for such a diverse set of signals. The reason for this is that it is the amplitude variation characteristics of the signals which determine the differences in ACPR for any given nonlinear amplifier characteristic of interest.

However, it is generally true that if you make improvements in two-tone IM3 that the ACPR of other modulated signals will also be improved although the improvement may not be dB for dB. For instance, if there is a sharp notch in the IM3 two-tone performance the notch will not necessarily be as deep for a randomly modulated signal.

Most engineers I have worked with use IM3 as a guideline and follow up with either AM-AM AM-PM models for memoryless circuits or envelope simulation to verify the ACPR results for various signals of interest.

I will say that there are some cases where signals can adequately be modeled to help simplify ACPR analysis. OFDM signals and CDMA/WCDMA with multiple user codes tend to have characteristics similar to Gaussian signals that have know statistical properties. The distortion generated by these types of signals are analytical (or at least they are statistically defined). But signals such as QPSK/OQPSK require detailed signal modeling in a context that is analytical. It can be done, but it is not simple.

Here are a couple of good references.
Intermodulation Distortion in Microwave and Wireless Circuits
Jose Carlos Pedro and Nuno Borges Carvalho
ISBN 978-1-58053-356-0

Aparin, V.; , "Analysis of CDMA signal spectral regrowth and waveform quality," Microwave Theory and Techniques, IEEE Transactions on , vol.49, no.12, pp.2306-2314, Dec 2001.

I'm not sure if this is helpful, but if so then I may be able to provide a bit more guidance.

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sandman

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Re: Article relating ACPR and two-tone IM3 calculations
Reply #4 - Dec 12^th, 2010, 11:30pm

Thanks for your reply RFICDUDE.

RFICDUDE wrote on Dec 12^th, 2010, 7:01pm:

Unfortunately it is not easy to obtain a simple expression that is valid for such a diverse set of signals. The reason for this is that it is the amplitude variation characteristics of the signals which determine the differences in ACPR for any given nonlinear amplifier characteristic of interest.

I think by that you mean the PDF (or CCDF) of the Peak to Average Power of the envelope (?). That's true in this case because I would like to relate 'raw' / unmodified signal ACLR to IM3 coming from two-tone tests rather than 'processed' signals and perhaps develop from that, empirical correction factors for processed signals.
Because in a real transmitter that would change a little given the signals are generally 'compressed' (CFR), apart from other things! In a 'real' scenario it would not be as simple as that.

RFICDUDE wrote on Dec 12^th, 2010, 7:01pm:

However, it is generally true that if you make improvements in two-tone IM3 that the ACPR of other modulated signals will also be improved although the improvement may not be dB for dB. For instance, if there is a sharp notch in the IM3 two-tone performance the notch will not necessarily be as deep for a randomly modulated signal.

Most engineers I have worked with use IM3 as a guideline and follow up with either AM-AM AM-PM models for memoryless circuits or envelope simulation to verify the ACPR results for various signals of interest.

I see what you mean. It makes sense, only, my effort is to have a more analytical relationship for each type of signal (GSM/WCDMA/LTE).

RFICDUDE wrote on Dec 12^th, 2010, 7:01pm:

I will say that there are some cases where signals can adequately be modeled to help simplify ACPR analysis. OFDM signals and CDMA/WCDMA with multiple user codes tend to have characteristics similar to Gaussian signals that have know statistical properties. The distortion generated by these types of signals are analytical (or at least they are statistically defined). But signals such as QPSK/OQPSK require detailed signal modeling in a context that is analytical. It can be done, but it is not simple.

Here are a couple of good references.
Intermodulation Distortion in Microwave and Wireless Circuits
Jose Carlos Pedro and Nuno Borges Carvalho
ISBN 978-1-58053-356-0

Aparin, V.; , "Analysis of CDMA signal spectral regrowth and waveform quality," Microwave Theory and Techniques, IEEE Transactions on , vol.49, no.12, pp.2306-2314, Dec 2001.

I'm not sure if this is helpful, but if so then I may be able to provide a bit more guidance.

I'll try to get my hands on these, thanks. Do any of these articles deal with connecting OFDM and CDMA modulation IM3 to two-tone-IM3 results?

But I think I'm still missing a link to the paper I had mentioned in my first comment above!

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RFICDUDE

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Re: Article relating ACPR and two-tone IM3 calculations
Reply #5 - Dec 15^th, 2010, 4:36am

People have developed semi-analytical relationships between OIP3 and ACPR/EVM for signals that have similar statistical characteristics (PDF, CCDF and moments) as Gaussian or complex Gaussian signals. Practical signals that fall into this category included WLAN/WiMAX/LTE OFDM and basestation CDMA/WCDMA. Signals that do not typically fall into this category are handset CDMA/WCDMA, EDGE, GSM and simple modulation such as QPSK.

A paper you may be interested in by Wu et. al. that relates OIP3 and OIP5 to ACPR for complex Gaussian-like signals is:
Q. Wu, H. Xiao and F. Li, "Linear RF power amplifier design for CDMA signals: A Spectrum Analysis Approach," Microwave Journal, Dec., 1998.

Search around and I think you maybe able to find it on the web.

If you want more general nonlinear models (not signal models) to run different signals through then I can provide references for that, but those models do not provide analytical signal models (you have to do that work yourself).

In designing transceiver transmitters, my experience always been that the signal which has the largest peak to average ratio tends to dominate the design since it dictates the worst case for achieving some average output power with a linearity constraint. This would be true if the peak of the peaky signal is at least as much in power as all your other signals. If max/peak powers are not similar then optimizing the design could be trickier since you would need to scale the design a bit to maintain optimum performance for different peak output power requirements.

Sounds like interesting and challenging work.

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sandman

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Re: Article relating ACPR and two-tone IM3 calculations
Reply #6 - Dec 15^th, 2010, 11:14am

Thanks again for your reply! Interesting comments.

RFICDUDE wrote on Dec 15^th, 2010, 4:36am:

People have developed semi-analytical relationships between OIP3 and ACPR/EVM for signals that have similar statistical characteristics (PDF, CCDF and moments) as Gaussian or complex Gaussian signals. Practical signals that fall into this category included WLAN/WiMAX/LTE OFDM and basestation CDMA/WCDMA. Signals that do not typically fall into this category are handset CDMA/WCDMA, EDGE, GSM and simple modulation such as QPSK.

I've found semi-analytical expressions (using empirical correction factors) to relate two tone 3rd order non-linearity (IP3) to modulated waveforms such as WCDMA. The reference you provide below is more tractable that the ones I've read, so, thanks

The trouble is the GSM/EDGE waveforms. For a simple amplifier without memory effects and a polynomial gain function (mclaurin series), none of the simulations match my calculations! Although the behaviour is closer to sinusoidal than the CDMA or OFDM family, the analysis or finding an expression has been much harder! If you have any papers or references relevant to multi-carrier GSM/EDGE non-linearity for base stations, that would be very interesting indeed!

RFICDUDE wrote on Dec 15^th, 2010, 4:36am:

A paper you may be interested in by Wu et. al. that relates OIP3 and OIP5 to ACPR for complex Gaussian-like signals is:
Q. Wu, H. Xiao and F. Li, "Linear RF power amplifier design for CDMA signals: A Spectrum Analysis Approach," Microwave Journal, Dec., 1998.

Search around and I think you maybe able to find it on the web.

I managed to find this paper. Thanks for the reference.

RFICDUDE wrote on Dec 15^th, 2010, 4:36am:

If you want more general nonlinear models (not signal models) to run different signals through then I can provide references for that, but those models do not provide analytical signal models (you have to do that work yourself).

I have already a set of time domain multi-standard signals that I can use. What sort of models do you refer to? Behavioural models of non-linear devices?

RFICDUDE wrote on Dec 15^th, 2010, 4:36am:

In designing transceiver transmitters, my experience always been that the signal which has the largest peak to average ratio tends to dominate the design since it dictates the worst case for achieving some average output power with a linearity constraint. This would be true if the peak of the peaky signal is at least as much in power as all your other signals. If max/peak powers are not similar then optimizing the design could be trickier since you would need to scale the design a bit to maintain optimum performance for different peak output power requirements.

Sounds like interesting and challenging work.

Challenging indeed!
I think I see what you mean. My assumptions are equal carrier power distribution for all types of carriers in my composite signal, so what you say holds for my case. I hope that makes sense.

I can imagine that for a device that is adequately backed-off, a signal with higher PAR will result in higher non-linearity on the output spectrum. However, I'm not able to connect the two, because the typical PAR on the CCDF curve considered for design is 10E-2% which is a rather low probability and the Spectral Mask requirements for all standards are 'ensemble and time' AVERAGE measurements (not PEAK-HOLD measurements), made over sevaral thousands of sample periods. I mean to say that the 'peaking' will occur so rarely within the observed time period, that, logically, it should not be a factor at all in the resulting non-linear distortion products (IM3). Do you have any comments here?

-sandman.

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totowo

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SH, PRC

Re: Article relating ACPR and two-tone IM3 calculations
Reply #7 - May 5^th, 2011, 8:35am

Hi，sandman,

I think this paper is what you want, the same author as you mentioned, Pedro, J.C.; De Carvalho, N.B.
<On the use of multitone techniques for assessing RF components' intermodulation distortion>.
This paper appears in: Microwave Theory and Techniques, IEEE Transactions on
Issue Date: Dec 1999
Volume: 47 Issue:12
On page(s): 2393 - 2402

You can easily get it by http://scholar.google.com

Good luck Cheesy

sandman wrote on Dec 12^th, 2010, 5:16am:

RFICDUDE wrote on Dec 11^th, 2010, 6:27am:

What is it that you would like to do and what types of signals are interested in analyzing?

I am trying to design a multi-mode transmitter for GSM/EDGE, WCDMA and LTE signals. If I can connect IP3 of the small signal stages to ACLR or ACPR, it would make 'optimised' performance budgeting easier. To make things simpler, we can ignore what 'optimised' implies and only try to work out a relation!

RFICDUDE wrote on Dec 11^th, 2010, 6:27am:

Weakly nonlinear (i.e. 3rd order only) relationships between IM3 and ACPR are easier to deal with rather than PA problems operating near compression where 5th order and higher relations start to influence the ACPR and IM results.

There's a relationship that connects IM3 (two tones, with same total power) and ACLR (modulated signals). This should be easily valid for the 3dB:1dB (IM3, P_out) operating region. I've got some decent equations already, but I don't fully know how the equations were worked out. Perhaps this paper can give me some leads.

I've read an excerpt of this used in a book (Practical RF Circuit Design for Modern Wireless Systems: Active circuits and ... By Rowan Gilmore, Les Besser), where
ACLR > IM3_two_tone,
which cannot be true when the same power is used for two-tones and modulated signals, for obvious reasons. I'd like to see how this paper compares IM3 to ACLR...

Tying this to PA ('higher' into compression) behaviour, with and without memory effects would be a logical next step.

Do you have this paper or any other comments?

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