On Thu, 30 Apr 2015 04:15:39 -0500, "runinrainy" <100271@DSPRelated>
wrote:

>>On Tuesday, May 27, 2014 4:24:45 PM UTC+5:30, runinrainy wrote:
>>> Could someone please explain me in details how we select the FFT
>>window
>>> 
>>> size at the receiver of the OFDM system?
>>> 
>>> 
>>> 
>>> Does it include both the size of N parallel sub carriers and the
>>Cyclic
>>> 
>>> Prefix length?
>>> 
>>> 
>>> 
>>> Thanks!
>>> 
>>> 
>>> 
>>> 	 
>>> 
>>> 
>>> 
>>> _____________________________		
>>> 
>>> Posted through www.DSPRelated.com
>>
>>Hello Eric/mnentweg,
>>Thanks for correcting the '512 unique freq sine waves are generated'
>>statement of mine made earlier. That was a grave mistake on my part.
>Infact
>>that helped me figure out one reason why no more than N/2 unique
>frequencies
>>are not possible. Eg: If IFFT generates a sine wave of (N/2 + x)
>repitions
>>per N samples, that would violate Nyquist Theorem! 
>>However, I still cant comprehend completely how a say, 513 pt dft would
>>yield me carriers at exactly the frequencies generated by a 512 pt IDFT,
>>even after considering the same time window and upsampling the signal in
>the
>>time window by (513/512). Will work/contemplate on it more and see where
>it
>>takes me. Thanks a lot for the insightful feedback.
>
>
>=====================
>
>Thanks all for your comments on this topic!
>
>Could you also please explain me the synchronization of the OFDM symbol? I
>am also trying to understand how to decide the OFDM symbol start/end time
>at the receiver just before going into FFT process.
>
>So far I understand that there two methods  for time synchronization which
>are data-aided and non-data aided methods, and in the data-aided methods
>the training subcarriers are included in OFDM symbol and they are
>correlated with the known training subcarriers at the receiver and the
>time of the peak of the auto-correlation is the time delay (tao)of the
>channel and this means the OFDM symbol reaches the receiver after this tao
>delay.
>
>My questions here are;
>
>1-For time synchronization, if the data-aided method is used, should the
>one complete OFDM symbol contain all training subcarriers and then all are
>correlated with the known trainings one by one at the receiver?
>
>2-Or the OFDM symbol contains a few training subcarriers and when they are
>received by the receiver each of the trainings is correlated by the known
>pilots?

You can use whatever pilots are there, and that will depend on the
system you're working on.

You can also correlate the CP with the end of the symbol (from which
it was copied) and get time synchronization that way.   This is very
commonly done.



Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

>On Tuesday, May 27, 2014 4:24:45 PM UTC+5:30, runinrainy wrote:
>> Could someone please explain me in details how we select the FFT
>window
>> 
>> size at the receiver of the OFDM system?
>> 
>> 
>> 
>> Does it include both the size of N parallel sub carriers and the
>Cyclic
>> 
>> Prefix length?
>> 
>> 
>> 
>> Thanks!
>> 
>> 
>> 
>> 	 
>> 
>> 
>> 
>> _____________________________		
>> 
>> Posted through www.DSPRelated.com
>
>Hello Eric/mnentweg,
>Thanks for correcting the '512 unique freq sine waves are generated'
>statement of mine made earlier. That was a grave mistake on my part.
Infact
>that helped me figure out one reason why no more than N/2 unique
frequencies
>are not possible. Eg: If IFFT generates a sine wave of (N/2 + x)
repitions
>per N samples, that would violate Nyquist Theorem! 
>However, I still cant comprehend completely how a say, 513 pt dft would
>yield me carriers at exactly the frequencies generated by a 512 pt IDFT,
>even after considering the same time window and upsampling the signal in
the
>time window by (513/512). Will work/contemplate on it more and see where
it
>takes me. Thanks a lot for the insightful feedback.

=====================

Thanks all for your comments on this topic!

Could you also please explain me the synchronization of the OFDM symbol? I
am also trying to understand how to decide the OFDM symbol start/end time
at the receiver just before going into FFT process.

So far I understand that there two methods  for time synchronization which
are data-aided and non-data aided methods, and in the data-aided methods
the training subcarriers are included in OFDM symbol and they are
correlated with the known training subcarriers at the receiver and the
time of the peak of the auto-correlation is the time delay (tao)of the
channel and this means the OFDM symbol reaches the receiver after this tao
delay.

My questions here are;

1-For time synchronization, if the data-aided method is used, should the
one complete OFDM symbol contain all training subcarriers and then all are
correlated with the known trainings one by one at the receiver?

2-Or the OFDM symbol contains a few training subcarriers and when they are
received by the receiver each of the trainings is correlated by the known
pilots?

Thanks!

---------------------------------------
Posted through http://www.DSPRelated.com

On Tuesday, May 27, 2014 4:24:45 PM UTC+5:30, runinrainy wrote:
> Could someone please explain me in details how we select the FFT window
> 
> size at the receiver of the OFDM system?
> 
> 
> 
> Does it include both the size of N parallel sub carriers and the Cyclic
> 
> Prefix length?
> 
> 
> 
> Thanks!
> 
> 
> 
> 	 
> 
> 
> 
> _____________________________		
> 
> Posted through www.DSPRelated.com

Hello Eric/mnentweg,
Thanks for correcting the '512 unique freq sine waves are generated' statement of mine made earlier. That was a grave mistake on my part. Infact that helped me figure out one reason why no more than N/2 unique frequencies are not possible. Eg: If IFFT generates a sine wave of (N/2 + x) repitions per N samples, that would violate Nyquist Theorem! 
However, I still cant comprehend completely how a say, 513 pt dft would yield me carriers at exactly the frequencies generated by a 512 pt IDFT, even after considering the same time window and upsampling the signal in the time window by (513/512). Will work/contemplate on it more and see where it takes me. Thanks a lot for the insightful feedback.

On Wed, 25 Jun 2014 10:50:14 -0700 (PDT), Rakesh Joshi
<rakesh@saankhyalabs.com> wrote:

>Lets say ifft size used @ the tx is 512.now this creates 512 orthogonal fre=
>quencies within the channel bw. Data is modulated using sine waves of these=
> 512 frequencies. At the rx, i need to precisely generate these sine waves =
>to correlate with the time domain signal. Can i generate these 512 unique f=
>requency sine waves using 513,123456789 pt fft? Whereas with 512,1024,1536,=
>2048 etc pt dft, one is sure to generate the required sine waves precisely =
>for correlation.

As was previously mentioned, as long as the FFT window is exactly the
time length of the FFT portion of the OFDM symbol (i.e., the symbol
period less the CP), it doesn't matter how many points are in the FFT.

Remember what the indices in the FFT/DFT mean, numbering the bins from
-N/2, 0, N/2-1, bin 1 contains the energy for signals with 1 cycle/N
samples, bin 2 contains the energy for signals with 2 cycles/N
samples, etc., etc.   Bins -1 and -2 have the energy for 1 and 2
cycles/N, respectively, with the opposite rotation.

That is always true, regardless of N.

So if you have subcarriers -52 to +52, they will occupy bins -52 to
+52 regardless of N, but you'll have to adjust the sample rate if N
changes, keeping the time length of the N samples constant.

So using the minimum N minimizes computation complexity in a number of
ways, by keeping the FFT size minimized and keeping the sample rate
minimized, which affects complexity elsewhere.

But it is not strictly necessary to use the minimum FFT size in either
the modulator or demodulator, and they don't even have to match, it
just makes things a bit harder in general.

Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

Lets say ifft size used @ the tx is 512.now this creates 512 orthogonal frequencies within the channel bw. Data is modulated using sine waves of these 512 frequencies. At the rx, i need to precisely generate these sine waves to correlate with the time domain signal. Can i generate these 512 unique frequency sine waves using 513,123456789 pt fft? Whereas with 512,1024,1536,2048 etc pt dft, one is sure to generate the required sine waves precisely for correlation.

>> Else one will potentially end up losing the transmitted carriers in the
fractional frequency space

I'm sorry, but it seems I failed to make my point:
The length of the OFDM symbol in seconds is the same, regardless of the FFT
size I use for reception (how should it know).
The subcarrier spacing is the inverse of the symbol length and does not
change with FFT size. 
There is no "fractional frequency spacing" problem or the like. 
	 

_____________________________		
Posted through www.DSPRelated.com

@runinrainy : i confused your question regarding choosing fft size at the rx of ofdm systems. My point about dis/adv of choosing a smaller/bigger fft windows were related to the no. of carriers used to form an ofdm symbol at the transmitter. My apologies for the same. 

As far as the question of choosing an fft window at the rx for a given mode of symbol size(@ baseband rate) is concerned one can use the fft window size used in tx or an integral multiple of that size should provide you the required data carriers with respective up sampling in the freq domain. ANY FFT SIZE ISNT OK! Else one will potentially end up losing the transmitted carriers in the fractional frequency space. Also, as Eric rightly points out, cyclic prefix is supposed to be used to align the fft window such that there isn't any effect due to ISI. If one takes the CP also while doing fft, isi gets into the signal.

sorry, but again, "nope". 

Let's say I receive a 300 subcarrier signal with a 512-bin FFT. Assume the
signal is filtered, containing no energy outside the subcarrier range. 
There are 512-300 = 212 unused subcarriers / FFT bins, 106 on either side,
that don't correlate with the signal (because we assume it's filtered) and
give zero. In reality we put them there because using an oversized FFT is
easier than implementing a steeper filter.

Now I change the FFT size to 513, 1024 or 987654321 bins. It doesn't matter
- all I do is add subcarrier bins that are uncorrelated with the signal and
give a zero result. The receiver always picks the subcarriers where it
expects the signal and doesn't care about the unused ones. 

What is maybe not obvious is that changing the FFT size scales the sampling
rate, if the "numerology" of the signal (from the radio standard), i.e.
symbol length, number of SCs etc remains unchanged.
For example, in LTE, 5 MHz mode with a 512 bin FFT, the correct sampling
rate is 7.68 MSPS. If I chose - for whatever reasons - to use a 2048 bin
FFT, the correct sampling rate would be 30.72 MSPS. 

Looking the other way, it means that an FFT can resample a cyclic (that's
the catch!) sampled signal to any integer number of samples. For example, I
take a 3-minute audio file, fft(), insert one sample, ifft(). The result is
exactly one sample longer. Try it, it really works.	 

_____________________________		
Posted through www.DSPRelated.com