Has The peak-to-average ratio problem of OFDM been solved?

Subject states the question. Any information is appreciated.
-- 
%  Randy Yates                  % "And all that I can do
%% Fuquay-Varina, NC            %  is say I'm sorry, 
%%% 919-577-9882                %  that's the way it goes..."
%%%% <yates@ieee.org>           % Getting To The Point', *Balance of Power*, ELO
http://home.earthlink.net/~yatescr

Randy Yates wrote:
> Subject states the question. Any information is appreciated.
> --
> %  Randy Yates                  % "And all that I can do
> %% Fuquay-Varina, NC            %  is say I'm sorry,
> %%% 919-577-9882                %  that's the way it goes..."
> %%%% <yates@ieee.org>           % Getting To The Point', *Balance of Power*, ELO
> http://home.earthlink.net/~yatescr

Randy,

It depends on what you mean by solved. If you mean that the PAR can be
reduced to 0 dB or even 3 dB then no, it hasn't been solved. If you can
live with 6 dB then I'd say yes.

There are a bunch of papers on this, but IMO the foremost authority is
a guy named Jose Tellado, formerly of Stanford. He has written a book
on PAR reduction, which is hard to find and expensive but worth it. The
technique that Tellado advocates is called Tone Reservation. 

John

sampson164@gmail.com writes:

> Randy Yates wrote:
>> Subject states the question. Any information is appreciated.
>> --
>> %  Randy Yates                  % "And all that I can do
>> %% Fuquay-Varina, NC            %  is say I'm sorry,
>> %%% 919-577-9882                %  that's the way it goes..."
>> %%%% <yates@ieee.org>           % Getting To The Point', *Balance of Power*, ELO
>> http://home.earthlink.net/~yatescr
>
> Randy,
>
> It depends on what you mean by solved. If you mean that the PAR can be
> reduced to 0 dB or even 3 dB then no, it hasn't been solved. If you can
> live with 6 dB then I'd say yes.
>
> There are a bunch of papers on this, but IMO the foremost authority is
> a guy named Jose Tellado, formerly of Stanford. He has written a book
> on PAR reduction, which is hard to find and expensive but worth it. The
> technique that Tellado advocates is called Tone Reservation. 

Thanks for the info, John. 

Now I'm wondering just exactly how this is measured. When they say
"peak,," do they really mean the instantaneous peak power? Or is
it an average power over some relatively short interval?

What is the PAR of a single-carrier system (say, BPSK) with a 
white input stream?
-- 
%  Randy Yates                  % "The dreamer, the unwoken fool - 
%% Fuquay-Varina, NC            %  in dreams, no pain will kiss the brow..."
%%% 919-577-9882                %  
%%%% <yates@ieee.org>           % 'Eldorado Overture', *Eldorado*, ELO
http://home.earthlink.net/~yatescr

Randy Yates wrote:
> sampson164@gmail.com writes:
> 
>> Randy Yates wrote:
>>> Subject states the question. Any information is appreciated.
>>> --
>>> %  Randy Yates                  % "And all that I can do
>>> %% Fuquay-Varina, NC            %  is say I'm sorry,
>>> %%% 919-577-9882                %  that's the way it goes..."
>>> %%%% <yates@ieee.org>           % Getting To The Point', *Balance of Power*, ELO
>>> http://home.earthlink.net/~yatescr
>> Randy,
>>
>> It depends on what you mean by solved. If you mean that the PAR can be
>> reduced to 0 dB or even 3 dB then no, it hasn't been solved. If you can
>> live with 6 dB then I'd say yes.
>>
>> There are a bunch of papers on this, but IMO the foremost authority is
>> a guy named Jose Tellado, formerly of Stanford. He has written a book
>> on PAR reduction, which is hard to find and expensive but worth it. The
>> technique that Tellado advocates is called Tone Reservation. 
> 
> Thanks for the info, John. 
> 
> Now I'm wondering just exactly how this is measured. When they say
> "peak,," do they really mean the instantaneous peak power? Or is
> it an average power over some relatively short interval?
> 
> What is the PAR of a single-carrier system (say, BPSK) with a 
> white input stream?

Instantaneous. PAR is usually defined in the literature over one OFDM 
symbol (IFFT) as 20*log10(max(abs(x))/mean(abs(x))). This is difficult 
to measure in a lab though. Analyzers look at a sample stream of 
concatenated symbols without regard to boundaries and measure the ratio 
of each sample magnitude to the mean without looking for peaks. In 
either case the results are presented on a semilog CCDF plot indicating 
probability on the y-axis vs PAR on the x-axis.

The PAR of an ideal BPSK signal with instantaneous transitions would be 
0 dB, just like an unmodulated carrier.

John

Randy Yates wrote:

> Subject states the question. Any information is appreciated.

The problem is insolvable in the general. However there is a number of 
tricks that can reduce the PAR to acceptable level or alleviate the 
effects of clipping on the signal. The approaches fall into two 
categories (or a combination of two):

1. Using dummy carriers modulated in the way to reduce PAR. To be 
efficient, the tradeoff has to be as much as 20~30% of the available 
bandwidth.

2. Using a FEC scheme which is designed for clipping distortion.

The main problem is that the overhead required to reduce PAR also 
reduces the energy efficiency, and in most practical cases there is very 
little gain or no gain at all. So the systems that I know of are 
designed to operate at the compromise PAR ~ 12..14dB with no explicit 
attempts to reduce it.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

<snipped>
> Instantaneous. PAR is usually defined in the literature over one OFDM
> symbol (IFFT) as 20*log10(max(abs(x))/mean(abs(x))). This is difficult
> to measure in a lab though. Analyzers look at a sample stream of
> concatenated symbols without regard to boundaries and measure the ratio
> of each sample magnitude to the mean without looking for peaks. In
> either case the results are presented on a semilog CCDF plot indicating
> probability on the y-axis vs PAR on the x-axis.
>
> The PAR of an ideal BPSK signal with instantaneous transitions would be
> 0 dB, just like an unmodulated carrier.
>

John, I have to disagree with the last statement.  It surely depends on
the response of the bandlimiting filter does it not?  I know you say
instantaneous transitions, but the signal doesn't flip from +/- 1 in a
real system and when we're talking about PAPR (PAR) then you're really
getting into the nuts and bolts of the transmitter.  

col

Randy Yates wrote:


> Now I'm wondering just exactly how this is measured. When they say
> "peak,," do they really mean the instantaneous peak power?

Exactly. This is a maximum instantaneous peak power in the baseband.


> 
> What is the PAR of a single-carrier system (say, BPSK) with a 
> white input stream?

Good question. If the BPSK is not band limited, then PAR = 1. If it is 
bandlimited, then PAR depends on the how much of bandlimiting do you 
have. The interesting thing is that more narrow is the bandwidth, more 
Gaussian is the PDF of the signal.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

cb135@hotmail.com wrote:
> <snipped>
> > Instantaneous. PAR is usually defined in the literature over one OFDM
> > symbol (IFFT) as 20*log10(max(abs(x))/mean(abs(x))). This is difficult
> > to measure in a lab though. Analyzers look at a sample stream of
> > concatenated symbols without regard to boundaries and measure the ratio
> > of each sample magnitude to the mean without looking for peaks. In
> > either case the results are presented on a semilog CCDF plot indicating
> > probability on the y-axis vs PAR on the x-axis.
> >
> > The PAR of an ideal BPSK signal with instantaneous transitions would be
> > 0 dB, just like an unmodulated carrier.
> >
>
> John, I have to disagree with the last statement.  It surely depends on
> the response of the bandlimiting filter does it not?  I know you say
> instantaneous transitions, but the signal doesn't flip from +/- 1 in a
> real system and when we're talking about PAPR (PAR) then you're really
> getting into the nuts and bolts of the transmitter.
>
> col

I said *ideal*. You are right that the statement isn't true for *real*
signals.

John

sampson164@gmail.com writes:

> cb135@hotmail.com wrote:
>> <snipped>
>> > Instantaneous. PAR is usually defined in the literature over one OFDM
>> > symbol (IFFT) as 20*log10(max(abs(x))/mean(abs(x))). This is difficult
>> > to measure in a lab though. Analyzers look at a sample stream of
>> > concatenated symbols without regard to boundaries and measure the ratio
>> > of each sample magnitude to the mean without looking for peaks. In
>> > either case the results are presented on a semilog CCDF plot indicating
>> > probability on the y-axis vs PAR on the x-axis.
>> >
>> > The PAR of an ideal BPSK signal with instantaneous transitions would be
>> > 0 dB, just like an unmodulated carrier.
>> >
>>
>> John, I have to disagree with the last statement.  It surely depends on
>> the response of the bandlimiting filter does it not?  I know you say
>> instantaneous transitions, but the signal doesn't flip from +/- 1 in a
>> real system and when we're talking about PAPR (PAR) then you're really
>> getting into the nuts and bolts of the transmitter.
>>
>> col
>
> I said *ideal*. You are right that the statement isn't true for *real*
> signals.

By the way, John, that's how I took it. I assumed you were referring
to the theoretical ideal of a rectangular pulse-shape, and that a real
system would have a PAR that was dependent on (20*log of) the ratio of
the peak to the RMS of the actual pulse shape.
-- 
%  Randy Yates                  % "She has an IQ of 1001, she has a jumpsuit
%% Fuquay-Varina, NC            %            on, and she's also a telephone."
%%% 919-577-9882                % 
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://home.earthlink.net/~yatescr

On Fri, 01 Dec 2006 04:15:52 GMT, Randy Yates <yates@ieee.org> wrote:

>Subject states the question. Any information is appreciated.

To add a tiny bit to what's tranpired so far (dang, you guys move
quickly):

The problem has been "solved" to the extent that there are quite a few
practical OFDM systems in common use, so it's definitely workable.

My experience matches Vladimir's a bit in that for the most part
whitening alone goes a long, long way to PAPR reduction in OFDM, and
people just generally live with what's left.   Other than reasonably
simple linearizing or pre-distortion technique for the PAs many
systems don't rely on highly sophisticaed tricks to mitigate PAPR in
OFDM.

e.g., 802.11a/g uses OFDM with 48 subcarriers, and the PAPR management
techniques are pretty straightforward (whitening, etc).   It's not
really specified in the standard how to manage it, just that the
transmit mask and EVM have to meet certain specs, but herculean
efforts are not needed to get there.

FWIW, as the number of subcarriers goes up the problem stabilizes due
mostly to the central limit theorem (whitening gets easier).  Beyond
FFT sizes of 64-128 points the PAPR is increasing very slowly, so it's
not hard to bound the problem.

I did a short study a long time ago and made this comparison:  64-QAM
single-carrier with 20% RRC filtering gets a PAPR of about 5.5dB (at
about the 90% spot of the cdf).   OFDM with 48 subcarriers and _only
whitening applied to mitigate PAPR_ was about 7.5dB PAPR at 90% and
OFDM with 240 subcarriers (something I was proposing at the time) was
about 8.5dB.

So even for an OFDM system with a fair number of subcarriers (240) the
difference to a practical single-carrier system was 3dB, without doing
anything special to reduce PAPR in the OFDM system.   3dB can be a big
deal in the rf, but it's not at all insurmountable or impractical to
deal with.
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org