LTE, FFT, OFDM

>Use the number of populated subcarriers from the link above, and take
>the next largest power-of-two N for the FFT size.  e.g., for the 5MHz
>BW case there are 301 subcarriers.   Use NQ2, populate the 301
>subcarriers around DC, and leave the remaining 211 subcarriers as
>zeros for guard band.

Dear Eric, All,

I have a follow-up question on the FFT used in OFDM.
A typical OFDM scheme shows, taking N complex inputs and then multiplying
each input with a specific sub-carrier frequency. Since LTE works with
either 15 KHz or 7.5 KHz sub-carriers, does the FFT need to be designed
specifically for these sub-carrier frequencies? if not, how exactly is the
sub-carrier frequency taken care?
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>>Use the number of populated subcarriers from the link above, and take
>>the next largest power-of-two N for the FFT size.  e.g., for the 5MHz
>>BW case there are 301 subcarriers.   Use NQ2, populate the 301
>>subcarriers around DC, and leave the remaining 211 subcarriers as
>>zeros for guard band.
>
>Dear Eric, All,
>
>I have a follow-up question on the FFT used in OFDM.
>A typical OFDM scheme shows, taking N complex inputs and then
multiplying
>each input with a specific sub-carrier frequency. Since LTE works with
>either 15 KHz or 7.5 KHz sub-carriers, does the FFT need to be designed
>specifically for these sub-carrier frequencies? if not, how exactly is
the
>sub-carrier frequency taken care?
>---------------------------------------
>Posted through http://www.DSPRelated.com

15KHz comes from 7.68MHz/512 (for lte 5MHz as example)

if there is 7.5KHz (and I don't know about this) then either reduce
sampling rate by half or increase ifft to 1024

Kaz
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On Tue, 24 Nov 2015 07:45:45 -0600, "Sharan123" <99077@DSPRelated>
wrote:

>>Use the number of populated subcarriers from the link above, and take
>>the next largest power-of-two N for the FFT size.  e.g., for the 5MHz
>>BW case there are 301 subcarriers.   Use NQ2, populate the 301
>>subcarriers around DC, and leave the remaining 211 subcarriers as
>>zeros for guard band.
>
>Dear Eric, All,
>
>I have a follow-up question on the FFT used in OFDM.
>A typical OFDM scheme shows, taking N complex inputs and then multiplying
>each input with a specific sub-carrier frequency. Since LTE works with
>either 15 KHz or 7.5 KHz sub-carriers, does the FFT need to be designed
>specifically for these sub-carrier frequencies? if not, how exactly is the
>sub-carrier frequency taken care?

Not sure what you mean by "multiplying each input with a specific
sub-carrier frequency".   The FFT does that for you.


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

>15KHz comes from 7.68MHz/512 (for lte 5MHz as example)
>
>if there is 7.5KHz (and I don't know about this) then either reduce
>sampling rate by half or increase ifft to 1024

Dear Kaz,

Probably a basic question. I assume that, specifically referring to
LTE/OFDM, when we refer to sub-carrier spacing of 15 KHz, we also mean
that sub-carriers themselves are 15 KHz wide. Is this correct?


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On Fri, 27 Nov 2015 09:23:12 -0600, "Sharan123" <99077@DSPRelated>
wrote:

>>15KHz comes from 7.68MHz/512 (for lte 5MHz as example)
>>
>>if there is 7.5KHz (and I don't know about this) then either reduce
>>sampling rate by half or increase ifft to 1024
>
>Dear Kaz,
>
>Probably a basic question. I assume that, specifically referring to
>LTE/OFDM, when we refer to sub-carrier spacing of 15 KHz, we also mean
>that sub-carriers themselves are 15 KHz wide. Is this correct?

They're generated with an FFT, so it is the effective bin spacing in
the FFT.


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

On Fri, 27 Nov 2015 09:23:12 -0600, "Sharan123" <99077@DSPRelated>

> I assume that, specifically referring to LTE/OFDM, when
> we refer to sub-carrier spacing of 15 KHz, we also mean that
> sub-carriers themselves are 15 KHz wide. Is this correct?

Depends what you mean by "width".

If each subcarrier is modulated using QAM (as is typical), then
the details of this modulation define the width of the subcarrier.
(Given that an unmodulated subcarrier has zero bandwidth...)
Typically the baud length is slightly longer than the inverse of
the subcarrier spacing due to the so-called cyclic prefix.
And a mild window (such as a trapezoidal window) is usually applied
to each baud.

You could define width however you like, but the inverse of the
baud length is one possible defintion.  The 20 dB bandwidth is
another possible definition.  Probably (but not certainly) you
end up with a value slightly less than the subcarrier spacing.

Steve

On Fri, 27 Nov 2015 21:10:11 +0000 (UTC), spope33@speedymail.org
(Steve Pope) wrote:

>On Fri, 27 Nov 2015 09:23:12 -0600, "Sharan123" <99077@DSPRelated>
>
>> I assume that, specifically referring to LTE/OFDM, when
>> we refer to sub-carrier spacing of 15 KHz, we also mean that
>> sub-carriers themselves are 15 KHz wide. Is this correct?
>
>Depends what you mean by "width".
>
>If each subcarrier is modulated using QAM (as is typical), then
>the details of this modulation define the width of the subcarrier.
>(Given that an unmodulated subcarrier has zero bandwidth...)
>Typically the baud length is slightly longer than the inverse of
>the subcarrier spacing due to the so-called cyclic prefix.
>And a mild window (such as a trapezoidal window) is usually applied
>to each baud.
>
>You could define width however you like, but the inverse of the
>baud length is one possible defintion.  The 20 dB bandwidth is
>another possible definition.  Probably (but not certainly) you
>end up with a value slightly less than the subcarrier spacing.
>
>Steve

It doesn't matter how the subcarriers are modulated because their
values are static for the duration of the symbol (and therefore the
DFT length).   The output is just the DFT of an array of arbitrary
input values, so the output subcarriers have the same characteristics
as the bins of any DFT.


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

Eric Jacobsen <eric.jacobsen@ieee.org> wrote:

>On Fri, 27 Nov 2015 21:10:11 +0000 (UTC), spope33@speedymail.org

>>On Fri, 27 Nov 2015 09:23:12 -0600, "Sharan123" <99077@DSPRelated>

>>> I assume that, specifically referring to LTE/OFDM, when
>>> we refer to sub-carrier spacing of 15 KHz, we also mean that
>>> sub-carriers themselves are 15 KHz wide. Is this correct?

>>Depends what you mean by "width".

>>If each subcarrier is modulated using QAM (as is typical), then
>>the details of this modulation define the width of the subcarrier.
>>(Given that an unmodulated subcarrier has zero bandwidth...)
>>Typically the baud length is slightly longer than the inverse of
>>the subcarrier spacing due to the so-called cyclic prefix.
>>And a mild window (such as a trapezoidal window) is usually applied
>>to each baud.

>>You could define width however you like, but the inverse of the
>>baud length is one possible defintion.  The 20 dB bandwidth is
>>another possible definition.  Probably (but not certainly) you
>>end up with a value slightly less than the subcarrier spacing.

>It doesn't matter how the subcarriers are modulated because their
>values are static for the duration of the symbol (and therefore the
>DFT length).   The output is just the DFT of an array of arbitrary
>input values, so the output subcarriers have the same characteristics
>as the bins of any DFT.

I agree it doesn't matter, however, the OP asked what is the "width"
of the subcarrier.  The answer to this is that the "width" (however
defined) is the same as that of any carrier modulated in the same
manner.

Steve

On Sat, 28 Nov 2015 00:12:03 +0000 (UTC), spope33@speedymail.org
(Steve Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote:
>
>>On Fri, 27 Nov 2015 21:10:11 +0000 (UTC), spope33@speedymail.org
>
>>>On Fri, 27 Nov 2015 09:23:12 -0600, "Sharan123" <99077@DSPRelated>
>
>>>> I assume that, specifically referring to LTE/OFDM, when
>>>> we refer to sub-carrier spacing of 15 KHz, we also mean that
>>>> sub-carriers themselves are 15 KHz wide. Is this correct?
>
>>>Depends what you mean by "width".
>
>>>If each subcarrier is modulated using QAM (as is typical), then
>>>the details of this modulation define the width of the subcarrier.
>>>(Given that an unmodulated subcarrier has zero bandwidth...)
>>>Typically the baud length is slightly longer than the inverse of
>>>the subcarrier spacing due to the so-called cyclic prefix.
>>>And a mild window (such as a trapezoidal window) is usually applied
>>>to each baud.
>
>>>You could define width however you like, but the inverse of the
>>>baud length is one possible defintion.  The 20 dB bandwidth is
>>>another possible definition.  Probably (but not certainly) you
>>>end up with a value slightly less than the subcarrier spacing.
>
>>It doesn't matter how the subcarriers are modulated because their
>>values are static for the duration of the symbol (and therefore the
>>DFT length).   The output is just the DFT of an array of arbitrary
>>input values, so the output subcarriers have the same characteristics
>>as the bins of any DFT.
>
>I agree it doesn't matter, however, the OP asked what is the "width"
>of the subcarrier.  The answer to this is that the "width" (however
>defined) is the same as that of any carrier modulated in the same
>manner.

The modulation type doesn't matter.   The subcarrier width is
determined solely by the FFT size and sample rate, which determines
the bin width.

Does a subcarrier width shrink if it's a constant (CW)?  If it updates
at half, or some other fraction, of the OFDM symbol rate?  Ans:  no.

That being said, the subcarrier sinx/x spectrum is consistent with an
NRZ signal at a symbol period equal to the FFT length (in time), so
from that perspective there is consistency.   The realized width is
only proportional to the FFT transmit time, though, not including the
cyclic prefix, so from that perspective the subcarrier is actually a
little wider than an NRZ signal with a symbol rate equal to the OFDM
symbol rate.   So from that perspective there is not consistency, and
the width will not be the same as another carrier modulated in the
same manner.

The subcarrier width is entirely independent of the subcarrier
modulation type.


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

>The modulation type doesn't matter.   The subcarrier width is
>determined solely by the FFT size and sample rate, which determines
>the bin width.
>
>Does a subcarrier width shrink if it's a constant (CW)?  If it updates
>at half, or some other fraction, of the OFDM symbol rate?  Ans:  no.

Dear Eric, Steve,

Thanks for the comments. I have one question, especially pertaining to
LTE.

In case of OFDM, there are multiple sub-carriers and spacing between
consecutive sub-carriers is (say) 15 KHz. Hence isn't bandwidth of each
sub-carrier 15 KHz?



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