Peak Windowing for OFDM

Hi

I am trying to implement a program in Matlab in order to apply a window to
the peaks of the envelope of an OFDM signal. The window I am using is a
Gaussian window, with factor gamma (exp(-gamma*t^2))

I have already implemented it, but I do not know if the results obtained
are so satisfactory as they should be. My concern is on the proper choice
of the value gamma: I make it inversely proportional to the duration of the
peak above the threshold (that is, if there are 8 samples in a peak above
the decided threshold, the factor gamma is proportional to
1/(8*SamplingTime^2)), but this is a rough approach and I have not found
anything about the choice of this factor when appying peak windowing to
OFDM.

Is there anyone with experience in this topic who may suggest me anything,
please?

Thanks

Crisanquito <crisancost@hotmail.com> wrote:

>I am trying to implement a program in Matlab in order to apply a window to
>the peaks of the envelope of an OFDM signal. The window I am using is a
>Gaussian window, with factor gamma (exp(-gamma*t^2))

>I have already implemented it, but I do not know if the results obtained
>are so satisfactory as they should be. My concern is on the proper choice
>of the value gamma: I make it inversely proportional to the duration of the
>peak above the threshold (that is, if there are 8 samples in a peak above
>the decided threshold, the factor gamma is proportional to
>1/(8*SamplingTime^2)), but this is a rough approach and I have not found
>anything about the choice of this factor when appying peak windowing to
>OFDM.

I have no insight into why you need to do this.  (e.g. I don't
know whether this signal is in the transmitter or the receiver,
whether you are analyzing it or implementing some processing
upon it, etc.)

You need to enlighten us...

Steve

>Crisanquito <crisancost@hotmail.com> wrote:
>
>>I am trying to implement a program in Matlab in order to apply a window
to
>>the peaks of the envelope of an OFDM signal. The window I am using is a
>>Gaussian window, with factor gamma (exp(-gamma*t^2))
>
>>I have already implemented it, but I do not know if the results
obtained
>>are so satisfactory as they should be. My concern is on the proper
choice
>>of the value gamma: I make it inversely proportional to the duration of
the
>>peak above the threshold (that is, if there are 8 samples in a peak
above
>>the decided threshold, the factor gamma is proportional to
>>1/(8*SamplingTime^2)), but this is a rough approach and I have not
found
>>anything about the choice of this factor when appying peak windowing to
>>OFDM.
>
>I have no insight into why you need to do this.  (e.g. I don't
>know whether this signal is in the transmitter or the receiver,
>whether you are analyzing it or implementing some processing
>upon it, etc.)
>
>You need to enlighten us...
>
>Steve
>

I have an OFDM model in Matlab and in the transmitter I am using a device
with a limited "quasi-linear" region (it is an optical modulator). I just
want to limit the excursion of the signal amplitude, I do not want it to
get any value. I think this is a step into a more realistic model of a
communication system with OFDM. 

After the IFFT processing in the transmitter, I am trying to apply peak
windowing in order to limit its excurssion. Hard clipping is another
option, but I want also to try peak windowing to not ruin so much the
performance. 

I do not know which more details you need, but I will give you them 	
pleasantly if you can help me. 

Crisanquito <crisancost@hotmail.com> wrote:

>I have an OFDM model in Matlab and in the transmitter I am using a device
>with a limited "quasi-linear" region (it is an optical modulator). I just
>want to limit the excursion of the signal amplitude, I do not want it to
>get any value. I think this is a step into a more realistic model of a
>communication system with OFDM. 

I have had good luck with clipping the tx OFDM waveform at about
4x RMS.  Hope this helps.

Steve

Crisanquito wrote:
> Hi
> 
> I am trying to implement a program in Matlab   in order to apply a window to
> the peaks of the envelope of an OFDM signal. The window I am using is a
> Gaussian window, with factor gamma (exp(-gamma*t^2))

Yes, this is one of the methods for PAPR reduction; it is better then 
hardlimiting.

> I have already implemented it, but I do not know if the results obtained
> are so satisfactory as they should be.

I don't know what do you consider as "satisfactory". What is the goal of 
your exersize?

> My concern is on the proper choice
> of the value gamma: I make it inversely proportional to the duration of the
> peak above the threshold (that is, if there are 8 samples in a peak above
> the decided threshold, the factor gamma is proportional to
> 1/(8*SamplingTime^2)), but this is a rough approach and I have not found
> anything about the choice of this factor when appying peak windowing to
> OFDM.

Think of the impact of your window as if you are adding the noise to the 
OFDM signal. The goal is the optimum performance considering the 
resulting PAPR and SNR.

> Is there anyone with experience in this topic who may suggest me anything,
> please?

Textbook stuff.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>
>
>Crisanquito wrote:

>> I have already implemented it, but I do not know if the results
obtained
>> are so satisfactory as they should be.
>
>I don't know what do you consider as "satisfactory". What is the goal of

>your exersize?


Well, I have just seen the effects of the windowing process on the
envelope of the signal. What I see is the next: the maximum value of the
peak is effectively reduced, but the sample next to it (or maybe two
samples next to it), originally also above the threshold, is, once the
windowing process is performed, higher than the previous maximum. Example:

Threshold=3;
SamplesAboveThreshold=[3 4 5 4 3]
SamplesAfterWindowing=[2 3.25 3 3.25 2], so now the problem is with the
samples with value 3.25. 

The result depends of the factor gamma chosen, and I have not found any
reference with a systematic explanation which relates the value of the
factor with the duration of the peak, or something similar. 

>> Is there anyone with experience in this topic who may suggest me
anything,
>> please?
>
>Textbook stuff.

I have already checked some books and articles, but no any detailed
explanation, so if there is anyone who has programmed this before, can tell
me what approach to take?

Thanks for the answer

Crisanquito wrote:


> Well, I have just seen the effects of the windowing process on the
> envelope of the signal. What I see is the next: the maximum value of the
> peak is effectively reduced, but the sample next to it (or maybe two
> samples next to it), originally also above the threshold, is, once the
> windowing process is performed, higher than the previous maximum. Example:

You are looking at the problem from the entirely wrong perspective. 
Limiting the envelope is no-brainer, but the real question is how much 
of BER performance impairment would you take due to that limiting. This 
is a long question as it depends on the parameters of OFDM and the channel.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Crisanquito <crisancost@hotmail.com> wrote:

>Well, I have just seen the effects of the windowing process on the
>envelope of the signal. What I see is the next: the maximum value of the
>peak is effectively reduced, but the sample next to it (or maybe two
>samples next to it), originally also above the threshold, is, once the
>windowing process is performed, higher than the previous maximum. Example:
>
>Threshold=3;
>SamplesAboveThreshold=[3 4 5 4 3]
>SamplesAfterWindowing=[2 3.25 3 3.25 2], so now the problem is with the
>samples with value 3.25. 

Confirm that your peak algorithm operates on the magnitude,
rather than on the I/Q signal.

S.

>
>
>Crisanquito wrote:
>
>
>> Well, I have just seen the effects of the windowing process on the
>> envelope of the signal. What I see is the next: the maximum value of
the
>> peak is effectively reduced, but the sample next to it (or maybe two
>> samples next to it), originally also above the threshold, is, once the
>> windowing process is performed, higher than the previous maximum.
Example:
>
>You are looking at the problem from the entirely wrong perspective. 
>Limiting the envelope is no-brainer, but the real question is how much 
>of BER performance impairment would you take due to that limiting. This 
>is a long question as it depends on the parameters of OFDM and the
channel.

My objective is, or it was, to make peak windowing in the correct way,
after that I would be able to study the level of clipping, the value of the
threshold to be applied in order to find a trade off, as you comment. But
if I do not make it in the correct way, I will introduce unnecesary
performance impairment, if will distort the signal more than necessary.
And the distortion I introduce depends on the value of gamma
(window=exp(-gamma*t^2)). At this point, my doubts are:

-Should I take a value of gamma which depends on the duration of each peak
above the threshold, or should I take a fixed value? I mean, why to use the
same duration window with a peak with 9 samples above the threshold than
with a peak with just one sample above the threshold? 
-Then, if I take a value of gamma which depends on the duration of the
peak, which relationship should be in order to obtain a proper scaling of
the peak?

For sure it must be easier than I think.   


>Crisanquito <crisancost@hotmail.com> wrote:
>
>>Well, I have just seen the effects of the windowing process on the
>>envelope of the signal. What I see is the next: the maximum value of
the
>>peak is effectively reduced, but the sample next to it (or maybe two
>>samples next to it), originally also above the threshold, is, once the
>>windowing process is performed, higher than the previous maximum.
Example:
>>
>>Threshold=3;
>>SamplesAboveThreshold=[3 4 5 4 3]
>>SamplesAfterWindowing=[2 3.25 3 3.25 2], so now the problem is with the
>>samples with value 3.25. 
>
>Confirm that your peak algorithm operates on the magnitude,
>rather than on the I/Q signal.
>

My peak algorithm operates just after the IFFT processing, on the
magnitude of the digital samples.