LTE, FFT, OFDM

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

>On Sat, 28 Nov 2015 21:18:45 +0000 (UTC), spope33@speedymail.org

>(Steve Pope) wrote:

>>Back to OFDM, if for instances one had an unusually very long cyclic
>>prefix, one could look at the signal with a spectrum analyzer
>>and observe that the modulated subcarriers are not filling the
>>entire space between the subcarriers...

>How do such fractionally-narrowed subcarriers maintain orthogonality
>in the receiver?   

This seems to (again?) be conflating signal characteristics with 
receiver algorithms.

The OP asked what the "width" (which I take to mean "bandwidth")
of the subcarriers is.  Taken literally, this has nothing to do
with the processing within the receiver, and only has to do with
the transmitted signal characteristics.

> The receiver depends on each subcarrier's sidelobes
> being spaced exactly such that they will be orthogonal wrt to the
> other subcarriers via the basis functions in the receiver FFT (i.e.,
> each subcarrier sits in the nulls of the other subcarrier's
> sidelobes).   If they've narrowed, how can the orthogonality be
> maintained?

I think we both know the answer is that a receiver can, if
it wishes, time-slice the signal into intervals over which the 
subcarriers are then orthogonal.  After said time-slicing, the
subcarrier bandwidth has changed (become greater).  But this
change occurs inside the chain of algorithms in the receiver.
It is not part of the transmitted signal.

The correct answer to OP's question is that no, the subcarrier
bandwidth is not tautologically equal to the subcarrier spacing,
so long as we are looking at the signal being transmitted,
and not some other derived signal.

Steve

On Sat, 28 Nov 2015 22:44:59 +0000 (UTC), spope33@speedymail.org
(Steve Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote:
>
>>On Sat, 28 Nov 2015 21:18:45 +0000 (UTC), spope33@speedymail.org
>
>>(Steve Pope) wrote:
>
>>>Back to OFDM, if for instances one had an unusually very long cyclic
>>>prefix, one could look at the signal with a spectrum analyzer
>>>and observe that the modulated subcarriers are not filling the
>>>entire space between the subcarriers...
>
>>How do such fractionally-narrowed subcarriers maintain orthogonality
>>in the receiver?   
>
>This seems to (again?) be conflating signal characteristics with 
>receiver algorithms.

Not at all, just trying to demonstrate that the "answer" is relative
to what's important, and the semantics matter (because they're not
clear).   To the receiver, which determines the performance of the
system, the "bandwidth", or whatever you want to call it, of the
subcarrier is constant, regardless of the modulation or whether it's
unmodulated or not.

>The OP asked what the "width" (which I take to mean "bandwidth")
>of the subcarriers is.  Taken literally, this has nothing to do
>with the processing within the receiver, and only has to do with
>the transmitted signal characteristics.

Only taken literally, which isn't always the best way to take things,
especially when talking about practical systems.

>> The receiver depends on each subcarrier's sidelobes
>> being spaced exactly such that they will be orthogonal wrt to the
>> other subcarriers via the basis functions in the receiver FFT (i.e.,
>> each subcarrier sits in the nulls of the other subcarrier's
>> sidelobes).   If they've narrowed, how can the orthogonality be
>> maintained?
>
>I think we both know the answer is that a receiver can, if
>it wishes, time-slice the signal into intervals over which the 
>subcarriers are then orthogonal.  After said time-slicing, the
>subcarrier bandwidth has changed (become greater).  But this
>change occurs inside the chain of algorithms in the receiver.
>It is not part of the transmitted signal.

Yes, and interpretation of statements and events happens inside one's
own head, and very often observers of the same event have very
different interpretations.   What is more important, the
statement/event, or the interpretation?   Which interpretation?  The
"signal" was the same to all observers.

I could go on, but the idea is that there are multiple perspectives,
and what happens in the receiver can be very important in
understanding a system, especially one like OFDM.

>The correct answer to OP's question is that no, the subcarrier
>bandwidth is not tautologically equal to the subcarrier spacing,
>so long as we are looking at the signal being transmitted,
>and not some other derived signal.

That's "an" answer, correct from one, lmited academic perspective in
the context of the question.   I would dispute that it is the only
"correct" one.   I would suggest that mine is more correct from the
point of view of understanding how OFDM systems work overall,
especially in the receiver, especially wrt synchronization, ICI, etc.,
etc.   I think your answer adds more confusion than clarity.




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

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

>On Sat, 28 Nov 2015 22:44:59 +0000 (UTC), spope33@speedymail.org

>>This seems to (again?) be conflating signal characteristics with 
>>receiver algorithms.

>Not at all, just trying to demonstrate that the "answer" is relative
>to what's important, and the semantics matter (because they're not
>clear).   

Obviously it is important to you to talk about the internals
of receiver algorithms.

Which is fine, but this does not mean the OP does not deserve a
direct answer to his question, which I provided.

>I could go on, 

I know

>>The correct answer to OP's question is that no, the subcarrier
>>bandwidth is not tautologically equal to the subcarrier spacing,
>>so long as we are looking at the signal being transmitted,
>>and not some other derived signal.

>That's "an" answer, correct from one, lmited academic perspective in
>the context of the question.   

B.S. 


Steve

All,

I have some follow-up questions related to LTE itself. All questions are
related to 20 MHz bandwidth.

1) There are a total of 1200 sub-carriers. Does it mean that the input to
the iFFT in the downlink path (at the transmitted) is only 1200 IQ
samples?

2) The sampling rate is 2048*1500 = 30.72 MSPS. if only 1200 sub-carriers
are really used then actual user data is roughly 50% of 30.72 MSPS. Is
this correct?

3) The output of iFFT after OFDM is 2048 samples. When and how are these
samples added into a single signal before transmission?

4) Considering the used sub-carriers of 1200, the used bandwidth is turns
out to be - 1200*1500 = 18 MHz. But in any case 2048 sub-carriers are
present (though not used). Hence the bandwidth is really - 2048*1500 = 30
MHz.

Why is bandwidth indicated as 20 MHz when above calculation turns out to
be 30 MHz?

Thanks once again ...

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

>All,
>
>I have some follow-up questions related to LTE itself. All questions are
>related to 20 MHz bandwidth.
>
>1) There are a total of 1200 sub-carriers. Does it mean that the input
to
>the iFFT in the downlink path (at the transmitted) is only 1200 IQ
>samples?
>

input is 2048 samples, 1200 carriers, rest zeros.

>2) The sampling rate is 2048*1500 = 30.72 MSPS. if only 1200
sub-carriers
>are really used then actual user data is roughly 50% of 30.72 MSPS. Is
>this correct?
>

per frame data is 1200/2048

>3) The output of iFFT after OFDM is 2048 samples. When and how are these
>samples added into a single signal before transmission?
>

output of ifft is 2048 + cP and this makes one frame, other frames follow
one by one.

>4) Considering the used sub-carriers of 1200, the used bandwidth is
turns
>out to be - 1200*1500 = 18 MHz. But in any case 2048 sub-carriers are
>present (though not used). Hence the bandwidth is really - 2048*1500 =
30
>MHz.
>
>Why is bandwidth indicated as 20 MHz when above calculation turns out to
>be 30 MHz?
>


it is 18MHz. 1200/2048 ratio is occupied, rest is zeros.
1200/2048 * 30.72 = 18MHz


and that is efficient since if it was not ofdm (if it was fdm) you will
need 30.72 MHz bandwidth for an input rate of 30.72Msps

>Thanks once again ...
>

no problem but I don't expect anyone to learn from forums but rather get
more confused as opinions are thrown freely.

I suggest you improve your background before jumping into ofdm.

Kaz

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

On Sun, 29 Nov 2015 02:17:43 +0000 (UTC), spope33@speedymail.org
(Steve Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote:
>
>>On Sat, 28 Nov 2015 22:44:59 +0000 (UTC), spope33@speedymail.org
>
>>>This seems to (again?) be conflating signal characteristics with 
>>>receiver algorithms.
>
>>Not at all, just trying to demonstrate that the "answer" is relative
>>to what's important, and the semantics matter (because they're not
>>clear).   
>
>Obviously it is important to you to talk about the internals
>of receiver algorithms.
>
>Which is fine, but this does not mean the OP does not deserve a
>direct answer to his question, which I provided.

The question, even as clarified, is specifically about OFDM.   I think
answers in that context are the most useful.

>>I could go on, 
>
>I know
>
>>>The correct answer to OP's question is that no, the subcarrier
>>>bandwidth is not tautologically equal to the subcarrier spacing,
>>>so long as we are looking at the signal being transmitted,
>>>and not some other derived signal.
>
>>That's "an" answer, correct from one, lmited academic perspective in
>>the context of the question.   
>
>B.S. 

There's that perspective thing again.   ;)


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

On Sun, 29 Nov 2015 11:55:05 -0600, "Sharan123" <99077@DSPRelated>
wrote:

>All,
>
>I have some follow-up questions related to LTE itself. All questions are
>related to 20 MHz bandwidth.
>
>1) There are a total of 1200 sub-carriers. Does it mean that the input to
>the iFFT in the downlink path (at the transmitted) is only 1200 IQ
>samples?

Plus zeros to fill out the rest of the 2048 input samples.

>2) The sampling rate is 2048*1500 = 30.72 MSPS. if only 1200 sub-carriers
>are really used then actual user data is roughly 50% of 30.72 MSPS. Is
>this correct?

1200/(2048 + CP samples), so, yes, roughly.

>3) The output of iFFT after OFDM is 2048 samples. When and how are these
>samples added into a single signal before transmission?

Those are the transmitted samples, plus the Cyclic Prefix, which is
part of the FFT output repeated again.

>4) Considering the used sub-carriers of 1200, the used bandwidth is turns
>out to be - 1200*1500 = 18 MHz. But in any case 2048 sub-carriers are
>present (though not used). Hence the bandwidth is really - 2048*1500 = 30
>MHz.

Those "guard band" samples are zero, so no energy comes out at those
frequencies other than the sidelobe leakage from the populated
subcarriers.   The system is designed so that by the edge of the
channel that energy is low enough, and/or can be suppressed by an IF
filter, so that it is not an issue for the adjacent channels.

>Why is bandwidth indicated as 20 MHz when above calculation turns out to
>be 30 MHz?

As you sorted out, the populated subcarriers only occupy 15k * 1200 =
18MHz.   That gives 1MHz on either side for "guard band" to the
adjacent channel.   That is used for IF filter rolloff as well as the
natural attenuation of the subcarrier sidelobes.   For a 15kHz-wide
subcarrier, the sidelobes are going to be WAY down at 1MHz away, so
the guard band is mostly for IF filter rolloff and other effects.   So
it doesn't matter that there are zeros out all the way to +/- 15MHz,
or 5MHz past the edge of the "channel".   That just makes it simpler
for the implementation.


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

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

>On Sun, 29 Nov 2015 02:17:43 +0000 (UTC), spope33@speedymail.org

>(Steve Pope) wrote:

>>>On Sat, 28 Nov 2015 22:44:59 +0000 (UTC), spope33@speedymail.org

>>>>The correct answer to OP's question is that no, the subcarrier
>>>>bandwidth is not tautologically equal to the subcarrier spacing,
>>>>so long as we are looking at the signal being transmitted,
>>>>and not some other derived signal.

>>>That's "an" answer, correct from one, lmited academic perspective in
>>>the context of the question.   

>>B.S. 

>There's that perspective thing again.   ;)

No idea where you're getting "limited academic perspective" from.

Especially when the cyclic prefix is there for a reason, and
it is only after a certain amount of receiver processing --
that uses the entire signal format, including the cyclic prefix,
to compensate for impairments -- that the signal can then be time-sliced, 
and becomes orthogonal.  

Your "doesn't matter" answer seems to gloss over this important part 
of the system.  In my experience.

Steve

On Sun, 29 Nov 2015 19:02:01 +0000 (UTC), spope33@speedymail.org
(Steve Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote:
>
>>On Sun, 29 Nov 2015 02:17:43 +0000 (UTC), spope33@speedymail.org
>
>>(Steve Pope) wrote:
>
>>>>On Sat, 28 Nov 2015 22:44:59 +0000 (UTC), spope33@speedymail.org
>
>>>>>The correct answer to OP's question is that no, the subcarrier
>>>>>bandwidth is not tautologically equal to the subcarrier spacing,
>>>>>so long as we are looking at the signal being transmitted,
>>>>>and not some other derived signal.
>
>>>>That's "an" answer, correct from one, lmited academic perspective in
>>>>the context of the question.   
>
>>>B.S. 
>
>>There's that perspective thing again.   ;)
>
>No idea where you're getting "limited academic perspective" from.

It's my opinion.

>Especially when the cyclic prefix is there for a reason, and
>it is only after a certain amount of receiver processing --
>that uses the entire signal format, including the cyclic prefix,
>to compensate for impairments -- that the signal can then be time-sliced, 
>and becomes orthogonal.  

The nice thing about the CP is that you don't really have to do any
processing with it in the receiver.   You can just throw it away.
It's done it's job just by being there when the signal went through
the channel.

You just need synchronization to get the subcarrier orthogonality
back, and there are a variety of ways to do that.  Some common
synchronization methods use the CP, but it isn't necessary to do so.
Regardless, once synchronization is achieved, which can be done with
or without the CP, the only time-slicing is to take the synchronized
samples from the symbol and put them in the FFT (or iFFT, whichever
doesn't match the modulator). 

>Your "doesn't matter" answer seems to gloss over this important part 
>of the system.  In my experience.

Not sure which "doesn't matter" you're talking about since you didn't
include any relevant context with that statement.

The question hasn't been about synchronization, so I think it would be
counterproductive to muddy up an answer with that when it isn't
relevant to the question.    Assuming perfect synchronization is a
very typical thing in comm when talking about other parts of the
system.   That's very appropriate here.


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

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

>On Sun, 29 Nov 2015 19:02:01 +0000 (UTC), spope33@speedymail.org

>>the cyclic prefix is there for a reason, and
>>it is only after a certain amount of receiver processing --
>>that uses the entire signal format, including the cyclic prefix,
>>to compensate for impairments -- that the signal can then be time-sliced, 
>>and becomes orthogonal.  

>The nice thing about the CP is that you don't really have to do any
>processing with it in the receiver.   You can just throw it away.
>It's done it's job just by being there when the signal went through
>the channel.

>You just need synchronization to get the subcarrier orthogonality
>back, and there are a variety of ways to do that.  Some common
>synchronization methods use the CP, but it isn't necessary to do so.
>Regardless, once synchronization is achieved, which can be done with
>or without the CP, the only time-slicing is to take the synchronized
>samples from the symbol and put them in the FFT (or iFFT, whichever
>doesn't match the modulator). 

>The question hasn't been about synchronization, so I think it would be
>counterproductive to muddy up an answer with that when it isn't
>relevant to the question.    Assuming perfect synchronization is a
>very typical thing in comm when talking about other parts of the
>system.   That's very appropriate here.

It's certainly appropriate -- in fact necessary, in a tutorial sense --
to talk about toy OFDM systems in which the cyclic prefix and its 
processing can be either left out entirely, or ignored.

However, it is better to make clear this is what you're doing 
from the outset.  Otherwise you find yourself arguing against true
statements... 

Steve