Question on single tone Peak power/ mean power ratio

Started by kaz 3 years ago6 replieslatest reply 3 years ago404 views

With reference to this paper regarding celluar IoT:

The Prach signal it is referring to is that used in LTE UE attachment to base station. It is deemed having too much PAPR for cellular IoT applications.

Therefore a new Prach signal (NBIoT Prach) is used. This signal is just a single tone that hops across sets of 5 ofdm symbols. 

The paper states that: 

[The PRACH signal after upsampling and filtering has a peak-to-average power ratio (PAPR) in the range of 2 to 7 decibels. The higher the PAPR, the more the required power amplifier backoff. Power amplifier backoff also gives rise to degraded power amplifier efficiency, and thus has a negative impact on device batterylife time.

A new single tone PRACH signal with frequency hopping has been designed for NPRACH in NB-IoT.

This new PRACH signal has extremely low PAPR and thus significantly reduces the need for power amplifier backoff]

The paper gives useful analysis but raises the question as why PAPR of this signal is seen as extremely low yet we know that for a single tone (in air) PAPR is 3dB

Any thoughts  Thanks

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Reply by SlartibartfastDecember 20, 2019

This may sound weird, but the PAPR of a complex-valued tone is 0dB.  That's usually the reference point for optimizing PAPR.  Class C amps can be useful in applications like this since they can be run in full saturation without excessive signal distortion or undesirable effects like excessive spectral regrowth (of sidelobes). This requires a signal with low- to no-PAPR, though, hence the design tradeoffs.

OFDM is generally a high-PAPR signal, but if you restrict the system to transmitting only one tone at a time, it becomes essentially frequency-hopping CW, which is low-PAPR.

I hope that helps a little.  There are many subtleties that can come into play in this.   I'm assuming the motivation is to be able to use Class C transmit amps to reduce power consumption.

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Reply by kazDecember 25, 2019

Hi Slartibartfast,

Thanks for the reply but you actually did not answer my question, here it is again:


The paper gives useful analysis but raises the question as why PAPR of this signal is seen as extremely low yet we know that for a single tone (in air) PAPR is 3dB


The signal is single tone (real only I assume input to PA is not complex, or is it?) therefore the PAPR is 3 dB which is higher than 2 dB the paper refers to as being high

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Reply by SlartibartfastDecember 25, 2019

The paper may be referring to a complex tone, which has a PAPR of 0dB as I mentioned.   From that reference, 2dB is a higher PAPR.

When a PA transmits a fully saturated signal, like a Class C PA, it will have 0dB PAPR, as I previously mentioned.  ;)

Happy Holidays!

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Reply by SlartibartfastDecember 27, 2019

Well, dangit, I had made another, long clarifying post, but it appears to have disappeared into the ether.

FWIW, Class-C amp appears to mean something to many people other than what I had intended, i.e., an amplifier operating in saturation.  What it comes down to is that PAs designed to operate in saturation can be much more power efficient than linear PAs, and so are useful for applications where power consumption or power efficiency are critical.  So for the case in point I suspect in order to extend battery life a modulation type is used that has very low PAPR that is designed to be used with such an amplifier, e.g., MSK, CPSK, OQPSK, etc.   These modulation types are constant-envelope (OdB PAPR) or nearly so, so that the signal can still be recovered after transmission through a saturated amplifier.

So the constant-envelope complex sinusoid with 0dB PAPR is the suitable reference point for such things, and is a practical reference when constant-envelope complex modulations, e.g., MSK, are used, or the hopping CW mentioned in the article.

From that perspective the real-valued, linear amplified sinusoid does have a higher PAPR.   So I suspect that this is what may have been in mind in the cited article.

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Reply by kazDecember 27, 2019

Hi Slartibartfast,

Thanks for the extended post. I am not RF engineer and I don't deal with PA stage but it is just to consolidate my understanding... the crucial point that I am after is this:

is the input to PA(any PA that sends signal to air) ever complex? I assumed it is real only and if it is real only then the PA will see 3dB PAPR for a single tone, not 0dB

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Reply by SlartibartfastDecember 27, 2019

When mixing a complex signal up to an IF for transmission, it effectively becomes a real-valued signal, or, more specifically, one transmits the real part of the complex spectrum.   If the bandwidth is preserved, no information is lost.   The trick is that if the complex signal had no amplitude modulation, i.e., has constant envelope, then transmitting that signal through a saturated amplifier with constant output amplitude won't lose any information.

There are spectral issues, i.e., a square wave has a different spectrum than a tone, and this is where it starts getting complicated.

So there's not a single answer to your question.   Generally you don't want to transmit a constant-envelope signal with more linearity than necessary because a Class-A amplifier is much less power efficient than a power amplifier that is designed to be run in saturation.   So modulation types and power amplifiers are often selected together, and the modulation type described in the article has no amplitude modulation and only single tones, so can be treated as a constant-envelope, i.e., 0dB PAPR, signal.  A benefit to doing this would be the improved power efficiency for battery life.

If you want to focus on the real-valued sinusoid and preserve its shape through a linear amplifier, then, yes, it has a PAPR of 3dB. 

There are a lot of tricky details that go on here, like input backoff, output backoff, filtering for control of spectral sidelobes due to clipping, etc., etc., so don't feel bad if it doesn't all make sense.  ;)