Hi all,

A silly question, but as far as I'm aware of it, the two definitions are as follows:

Peak-to-Average-Power-Ratio = (Peak absolute amplitude power / Time averaged RMS power) of the waveform.

i.e. PAPR of x(t) = [(|x|max)^2] / E[(|x|rms)^ 2]

and Crest factor of x(t) is: √(PAPR)

Are these correct definitions for all types of waveforms?

Further, I understand PAPR increases by a factor of 10log(Nc) where Nc is the number of similarly modulated carriers added to the system. I've heard that this doesn't apply to WCDMA waveforms (probably because of the spreading), but I can't seem to confirm this either way (right or wrong). Could anyone comment?

Thanks and cheers.

Thanks for the reply, pancho_hideboo.

Well, I found the same webpage you sent from Wikipedia, but I've read few articles that differentiate the two, without explaining how.

My understanding is :

for a complex signal x(t),

PAPR = max(x(t).x*(t))/E(x(t).x*(t))

As an example, if x(t)= sin(2.pi.f.t) - a real valued signal, PAPR=2 (linear)  - doing the math!

The 'E' is the expected value function. http://en.wikipedia.org/wiki/Expected_value

And going by the same wikipedia page, crest factor of x(t)= sin(2.pi.f.t) is √2. i.e. crest factor = √papr.

Maybe crest factor deals with voltages and papr deals with power, because in the dB scale, they're both 3.01dB for a sine wave. I just need someone to clarify it with details!

Regarding multi-carrier PAPR, I read the same about 10log(Nc) not being applicable for WCDMA (multi-carrier), but without any explanation. Would you know why?

If it is due to the spread spectrum, how is different from OFDM-LTE? Because, beyond a certain number of carriers, OFDM has the same treatment as gaussian noise.

I find an alarming number of articles that use terms like 'carrier' (as opposed to modulated carrier or subcarrier) and 'crest factor' (as opposed to PAPR), very loosely, hence my confusion.

-sandman.

pancho_hideboo wrote on Nov 12^th, 2009, 6:14am:

Can you explain this further?

pancho_hideboo wrote on Nov 12^th, 2009, 6:14am:

What did you mean by 'multiple WCDMA wave of a single carrier'?

pancho_hideboo wrote on Nov 12^th, 2009, 6:14am:

I'm keen on knowing why, because I'm aware of this assumption being made. Does anyone out here know why exactly the WCDMA (multiple carrier) doesn't follow the 10log(Nc) principle?

Further I've read that with addition of WCDMA carriers, the PAPR is affected and not so much, the crest factor. I seek explanations! Anyone?

Thanks pancho_hideboo

pancho_hideboo wrote on Nov 12^th, 2009, 7:23am:


Still unclear. What do you mean by WCDMA 'wave' ?
What is multiple WCDMA ? Do you imply 'multi-code' transmission on a single carrier? Decresting via clipping is done among other forms for multi-code transmissions. Still, perhaps they have the same logic explaning the 10logNc non-compliance?

It would interest me to know in further detail what you meant by 'crest factor is differently defined for a bandpass signal' - in terms of it's envelope, how?

pancho_hideboo wrote on Nov 12^th, 2009, 6:14am:
I'm keen on knowing why, because I'm aware of this assumption being made. Does anyone out here know why exactly the WCDMA (multiple carrier) doesn't follow the 10log(Nc) principle? [/quote]My opinion is based on actual measurements using actual instruments not EDA Tool Play.

Multiple WCDMA and Multi Carrier are different.
But crest factors are surely increased for both cases compared to each of non multiple WCDMA and single Carrier.
[/quote]

Tool play or not, that still doesn't explain why. Hopefully someone will have analysis data to share.

Regarding the specific question of whether or not a multicarrier WCDMA signal crest factor grows as 10*LOG(Nc) ...

No, the crest factor of a sum of randomly modulated carriers does not grow as fast as 10*LOG(Nc). This relationship is only true for a sum of unmodulated carriers where the initial phase for all carriers is fixed. In this case the average power of carriers adds in power, but somewhere, during the period of the beat frequency, the voltages all add together to define the peak of the waveform.

You can play with this in the lab, but it starts to get difficult after 20 or more carriers because the crest factor is so high that the amplitude leveling amplifiers have a hard time trying to raise the average level of the baseband signal high enough to produce the desired average RF output power (this is the "UNLEVELED" indicator on the Agilent sig gens).

With random phase multicarriers the peaks don't all line up at the same time so the peak of the crest is not as large as it could be.

This one reason why a 54 carrier WLAN signal  doesn't have a 20dB crest factor.

EDA Tool Play (EDAToP) is OK if you then take it to the lab, measure what you expect, and figure out why the two are different.

But I do agree that just because you simulate something doesn't mean it is real. It is only real if you first expect something (through careful engineering) and verify it through simulation (taking into account the accuracy/validity of the models) and finally validating it through measurement and reconciliation.

Designers who think "I simulated it, therefore it must be" are in for a rude and humbling experience if they are forced to go to the lab to back up their faith in EDA tools and models.

My 2 cents ...