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```Hi all,
I'm studying OFDM from documents available from Internet for free
and I have some doubts.

I understand that guard interval was added to solve problems with
multipath-signal delayed. So, because symbol duration in OFDM is
long, a little fraction of it can guarantee immunity against
long-delayed multipath-signals.

So, if I have:

.....-------+-------------------------------+-----------....
.....       |GUARD|      Nth Symbol         |GUARD|
.....-------+-------------------------------+-----------....

.........-------+-------------------------------+-----------....
.........       |GUARD|      Nth Symbol         |GUARD|
.........-------+-------------------------------+-----------....
C   D     A                         B

In the demodulating interval (A-B) the signal is the sum of the same
symbol
(Nth) so we haven't intersymbol interference, right?
But delayed signal can sum with direct signal in constructive or
disruptive
way... it depends from the delay interval (C-D). The guard inteval don't
resolve this problem, right?

Sorry for the poor English, I hope you understand the things I wrote.

Thanks in advance for the answers.

```
 0
Reply pozz 8/29/2003 1:20:47 PM

```I think you have the basics of it.   The guard interval prevents ISI
(intersymbol interference) by allowing the multipath delayed signals
from the same symbol to overlap within the FFT window.

And you are also correct that this does not prevent frequency
selectivity in the channel, there will still be some subcarriers that
can be badly faded.

The basic idea, though, is that the fading in each subcarrier, taken
individually, is flat.  This means that each subcarrier needs only a
single equalizing coefficient, and this bounds the equalization
problem.

Hope that helps a bit.

Cheers,

Eric

On Fri, 29 Aug 2003 13:20:47 GMT, "pozz" <pozNOzuSPgnAMo@libero.it>
wrote:

>Hi all,
>I'm studying OFDM from documents available from Internet for free
>and I have some doubts.
>
>I understand that guard interval was added to solve problems with
>multipath-signal delayed. So, because symbol duration in OFDM is
>long, a little fraction of it can guarantee immunity against
>long-delayed multipath-signals.
>
>So, if I have:
>
>....-------+-------------------------------+-----------....
>....       |GUARD|      Nth Symbol         |GUARD|
>....-------+-------------------------------+-----------....
>
>........-------+-------------------------------+-----------....
>........       |GUARD|      Nth Symbol         |GUARD|
>........-------+-------------------------------+-----------....
>           C   D     A                         B
>
>In the demodulating interval (A-B) the signal is the sum of the same
>symbol
>(Nth) so we haven't intersymbol interference, right?
>But delayed signal can sum with direct signal in constructive or
>disruptive
>way... it depends from the delay interval (C-D). The guard inteval don't
>resolve this problem, right?
>
>Sorry for the poor English, I hope you understand the things I wrote.
>
>Thanks in advance for the answers.
>

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org
```
 0
Reply eric 8/30/2003 2:23:11 AM

```Pozz,

The effects of frequency selective fading are essentially orthogonal
to the effects of ISI.   ISI causes interference between adjacent
symbols, and frequency selective fading will fade some subcarriers
more than others.  The mechanisms of the effects are quite different.

I think you have the idea of the guard interval and how it is used to
prevent ISI down pretty well.

Cheers,

Eric

On Sat, 30 Aug 2003 12:18:31 GMT, "pozz" <pozNOzuSPgnAMo@libero.it>
wrote:

>"Eric Jacobsen" <eric.jacobsen@ieee.org> ha scritto nel messaggio
>news:3f5009a1.5835572@news.west.earthlink.net...
>[...]
>> The basic idea, though, is that the fading in each subcarrier, taken
>> individually, is flat.  This means that each subcarrier needs only a
>> single equalizing coefficient, and this bounds the equalization
>> problem.
>
>What is equalizing coefficient and the equalization problem?
>
>I'll do a simple example. Consider a single subcarrier at f0 (i.e.,
>100Mhz).
>The active symbol duration is Ts=1ms and every symbol carries only 1 bit
>(2-QAM, 0� or 180�). So I can transmit 1000 bit/sec.
>To prevent ISI (intersymbol interference) I add a guard interval Tg
>(i.e., 1/4Ts=250us). So I transmit a symbol for Ts+Tg=1.25ms and I can
>transmit only 1/1.25=800bit/sec, right? I degraded performance
>(data-rate)
>but I earn in immunity against multipath.
>
>In fact, if I receive a direct signal and a delayed signal and the delay
>Td is smaller than Tg (i.e., Td<Tg) I have no intersymbol interference
>because I demodulate the symbol only in the Ts period and in this
>interval
>I have the same symbol (the Nth one).
>
>           <-Tg-> <------- Ts ------------>
>....-------+-------------------------------+-----------....
>....       |GUARD|      Nth Symbol         |GUARD|
>....-------+-------------------------------+-----------....
>           <Td> <-Tg-> <--------- Ts ---------->
>........-------+-------------------------------+-----------....
>........       |GUARD|      Nth Symbol         |GUARD|
>........-------+-------------------------------+-----------....
>
>OK, if Nth symbol is associated to sin(2*PI*f0*t) I receive:
>    sr(t)=sin(2*PI*f0*t)+sin(2*PI*f0*(t-Td))
>Even if Td<Tg, Td can assume a particular value such that sr(t)=0
>(i.e., Td=1/4/f0). In other terms, even if I use guard interval
>I can't resolve frequency fading.
>
>So I added guard interval, decreased data-rate from 1kbit/sec to
>800bit/sec
>to resolve ISI problem but I didn't resolve frequency-selective fading.
>Isn't it better without guard-interval? Or the probability of ISI is
>grater
>than fading?
>

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org
```
 0
Reply eric 8/31/2003 10:34:50 PM

```eric.jacobsen@ieee.org (Eric Jacobsen) wrote in message news:<3f52777c.165056078@news.west.earthlink.net>...
> On Sat, 30 Aug 2003 12:18:31 GMT, "pozz" <pozNOzuSPgnAMo@libero.it>
> wrote:
>
> >"Eric Jacobsen" <eric.jacobsen@ieee.org> ha scritto nel messaggio
> >news:3f5009a1.5835572@news.west.earthlink.net...
> >[...]
> >> The basic idea, though, is that the fading in each subcarrier, taken
> >> individually, is flat.  This means that each subcarrier needs only a
> >> single equalizing coefficient, and this bounds the equalization
> >> problem.
> >
> >What is equalizing coefficient and the equalization problem?
> >

In my opinion, *a single tap equalizing coefficient* is not directly
related to OFDM systems but to the frequency domain equlizer systems
since the perfect OFDM systems never require any eqaulization
between frequency in the receiver, while it is only used for
the coherent demodulation processing in OFDM systems.

>
> Eric Jacobsen
> Minister of Algorithms, Intel Corp.
> My opinions may not be Intel's opinions.
> http://www.ericjacobsen.org

--
Regards,
===
James K. (txdiversity@hotmail.com)
- Private opinions: These are not the opinions from my affiliation.
```
 0
Reply txdiversity 9/1/2003 5:53:37 AM

```txdiversity@hotmail.com (Sung Jin Kim) wrote in message news:<a7769bac.0308312153.822257f@posting.google.com>...
> eric.jacobsen@ieee.org (Eric Jacobsen) wrote in message news:<3f52777c.165056078@news.west.earthlink.net>...
> > On Sat, 30 Aug 2003 12:18:31 GMT, "pozz" <pozNOzuSPgnAMo@libero.it>
> > wrote:
> >
> > >"Eric Jacobsen" <eric.jacobsen@ieee.org> ha scritto nel messaggio
> > >news:3f5009a1.5835572@news.west.earthlink.net...
> > >[...]
> > >> The basic idea, though, is that the fading in each subcarrier, taken
> > >> individually, is flat.  This means that each subcarrier needs only a
> > >> single equalizing coefficient, and this bounds the equalization
> > >> problem.
> > >
> > >What is equalizing coefficient and the equalization problem?
> > >
>
> In my opinion, *a single tap equalizing coefficient* is not directly
> related to OFDM systems but to the frequency domain equlizer systems
> since the perfect OFDM systems never require any eqaulization
> between frequency in the receiver, while it is only used for
> the coherent demodulation processing in OFDM systems.
>
> >
> > Eric Jacobsen
> > Minister of Algorithms, Intel Corp.
> > My opinions may not be Intel's opinions.
> > http://www.ericjacobsen.org

Hi Sung,

What do you mean by perfect OFDM system? I guess you meant perfect
synchronization - what about channel?
Regarding channel estimation I would say :
The need of channel estimation and tracking can be eliminated with
differntial demodulation(Non coherent) but at the expense of 3-4dB SNR
loss. An accurate channel estimation based on rank deficient SVD (an
efficient reduced complexity LMMSE) is discussed by J.J van de Beek et
al - the system as a set of  paralell Gaussian channels each channel
is described as one tap coeff. in frequency domain.The modulation is
chosen as coherent - it is standardized in WLAN systems now. The above
estimation is what you probably try to describe here -please correct
me if I am wrong. But this may not give good enough performance for
Multi user system like WLAN where Uplink synchronization is bit
diffcult and
can give rise to substantial ICI. Time domain filtering in cascade can
improve the performance further(See Li,Cimini IEEE Trans on
Com,July,1998).

I have seen some papers to utilize pilot sub-carriers for channel
tracking after preambles being used as initial LS based channel
estimate. It seems Kalman based channel tracking is one of the better
methods for multi user based OFDM systems.

Regards,
Santosh
```
 0
Reply santosh 9/1/2003 10:13:00 PM

```santosh.nath@ntlworld.com (santosh nath) wrote in message news:<6afd943a.0309011412.462e343e@posting.google.com>...

> What do you mean by perfect OFDM system? I guess you meant perfect
> synchronization - what about channel?

In there, perfect means no ISI in each subcarrier;
therefore an equlization processing to supress ISI is no needed
but coherent demodulation processing to detect a symbol without
a phase ambiguity is needed. Thus, I had insisted out that
the term of an equlization tap using above had not been well proper.

However, the imperfect synchronization also makes to use some
signal processing in the OFDM receiver as you pointed out so
we definetely need some pilot or preamble technique
to estimate a channel for such processing.

> Regarding channel estimation I would say :
> The need of channel estimation and tracking can be eliminated with
> differntial demodulation(Non coherent) but at the expense of 3-4dB SNR
> loss.

That's right. It is a very general fact but it should not still be
a reason why we need equlization processing for/between
each no ISI sub-carrier in OFDM system.

> An accurate channel estimation based on rank deficient SVD (an
> efficient reduced complexity LMMSE) is discussed by J.J van de Beek et
> al - the system as a set of  paralell Gaussian channels each channel
> is described as one tap coeff. in frequency domain.

As you noticed, the channel model can be realized with one tap coeff
per each sub-carrier in frequency domain while the taped delay line is
a channel realization in time domain. Furthermore,
each one tap coeff in frequecy domain may has some correlation
among adjacent carrier coeffs so SVD helps to estimate channel
more robustly on noise environment in this case.

> The modulation is
> chosen as coherent - it is standardized in WLAN systems now.

Based on long time wireless history, a coherent de-modulation is proved
more efficient approach than non-coherent one in spite of its loss
from pilot utilization, even in mobile system as well as
OFDM based system WLAN.

> The above
> estimation is what you probably try to describe here -please correct
> me if I am wrong.

No, I just mean no ISI in my perfect senario but no non-coherent one.

> But this may not give good enough performance for
> Multi user system like WLAN where Uplink synchronization is bit
> diffcult and
> can give rise to substantial ICI. Time domain filtering in cascade can
> improve the performance further(See Li,Cimini IEEE Trans on
> Com,July,1998).

ICI is supposed to be somewhat different problem to ISI,
since ICI is happened from time domain selectivity or impaiement;
hence, time domain processing mentioned by Li seems
much efficient way, as freq domain approach is more efficient way
for freq domain selectivity.

> I have seen some papers to utilize pilot sub-carriers for channel
> tracking after preambles being used as initial LS based channel
> estimate. It seems Kalman based channel tracking is one of the better
> methods for multi user based OFDM systems.

Is it for Broad-Cast channel (down link) or Multiple Access channel
(up link)?

Mnay pilots are always better than the other but it costs the spectral
efficiency. However, a good multiplexing between time domain pilot
(PREAMBLE) and freq. domain pilot (pilot sub-carrieres) seems a
proper way to enhance its efficiency in implementation point of view.

>
> Regards,
> Santosh

Many thanks for your comments.

--
Regards,
===
James K. (txdiversity@hotmail.com)
- Private opinions: These are not the opinions from my affiliation.
```
 0
Reply txdiversity 9/3/2003 2:26:57 PM

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