FPGA Central

Hello group,
It is my pleasure to be posting queries to this group again.

My understanding of the presence of the cyclic prefix (CP) in an OFDM
symbol is to:

1. Prevent inter-symbol interference in a FIR channel if the length of
the CP is larger than the delay spread of channel.
2. Makes linear convolution "appear" as circular convolution over the
duration of the useful period in the OFDM symbol, thereby simplifying
equalization at receiver.
3. My own advantage: Timing offset correction is simplified since any
timing offset results in a progressive phase rotation, with
sub-carriers closer to DC having much smaller phase rotation compared
to sub-carriers closer to the nyquist frequency.

My question is this: Advantage 3 holds only when the timing offset is
such that the FFT input window starts before the ideal OFDM FFT start
window i.e. the start of the FFT window includes a portion of the
cyclic prefix, followed by the "useful portion" of the OFDM symbol. In
such a case, the consequences outlined in (3) follow.

What happens if the FFT input window starts with the first sample
occuring AFTER the ideal FFT start window. In such a case, the last
sample into the FFT input will be drawn from the cyclic prefix of the
next OFDM symbol. In which case, the progressive phase rotation no
longer occurs as the input to the FFT block is no longer circularly
rotated.

Should'nt practical OFDM symbols therefore include a cyclic postfix
(drawn from the beginning of the OFDM symbol) to account for timing
recovery if the timing offset is past the ideal timing instant. For
example, the European DVB standard does not mention any cyclic
post-fixes in their description of the OFDM transmit frame...

Please clarify..

thank you
regards
Vikram

Sounds like you understand this well enough.

Most systems don't apply a post-fix although sometimes it can make
sense to do so if a window is applied to the symbols to control
spectral sidelobes. You're right that most standards don't say
anything about a post-fix, so it's important for a timing
synchronization system to get it right for the reasons you've
indicated.


On 11 Feb 2005 17:09:37 -0800, [email protected] wrote:

>Hello group,
>It is my pleasure to be posting queries to this group again.
>
>My understanding of the presence of the cyclic prefix (CP) in an OFDM
>symbol is to:
>
>1. Prevent inter-symbol interference in a FIR channel if the length of
>the CP is larger than the delay spread of channel.
>2. Makes linear convolution "appear" as circular convolution over the
>duration of the useful period in the OFDM symbol, thereby simplifying
>equalization at receiver.
>3. My own advantage: Timing offset correction is simplified since any
>timing offset results in a progressive phase rotation, with
>sub-carriers closer to DC having much smaller phase rotation compared
>to sub-carriers closer to the nyquist frequency.
>
>My question is this: Advantage 3 holds only when the timing offset is
>such that the FFT input window starts before the ideal OFDM FFT start
>window i.e. the start of the FFT window includes a portion of the
>cyclic prefix, followed by the "useful portion" of the OFDM symbol. In
>such a case, the consequences outlined in (3) follow.
>
>What happens if the FFT input window starts with the first sample
>occuring AFTER the ideal FFT start window. In such a case, the last
>sample into the FFT input will be drawn from the cyclic prefix of the
>next OFDM symbol. In which case, the progressive phase rotation no
>longer occurs as the input to the FFT block is no longer circularly
>rotated.
>
>Should'nt practical OFDM symbols therefore include a cyclic postfix
>(drawn from the beginning of the OFDM symbol) to account for timing
>recovery if the timing offset is past the ideal timing instant. For
>example, the European DVB standard does not mention any cyclic
>post-fixes in their description of the OFDM transmit frame...
>
>Please clarify..
>
>thank you
>regards
>Vikram
>

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

Vikram,

There are a couple of solutions to your problem. The first solution
(to ensure your timing is correct) is to repeat the first OFDM symbol
twice. This ensures that when you take the FFT over your window, you
will capture a linear shifted version of your signal and can thus
extract correct timing information. The second solution again
assuming a repitition of the first OFDM symbol in a frame, then
techniques are used to correlate the cyclic prefix to obtain a coarse
estimate and then use further signal processing techniques to hone in
on the correct timing.

Incidentally, you can perform a similar estimate of the FFT window by
extracting and correlating the scattered pilot symbols in a standard
like DVB. Actually, as I stir the pot of my memory on OFDM, there are
a number of techniques you can use to get the correct timing, because,
after all, without that you'll end up with garbage coming out.

Not sure if i answered your question because i'm not clear whether you
want a feeling for the problem or want a specific technique used in
the standards?

col


[email protected] wrote in message news:<[email protected] roups.com>...
> Hello group,
> It is my pleasure to be posting queries to this group again.
>
> My understanding of the presence of the cyclic prefix (CP) in an OFDM
> symbol is to:
>
> 1. Prevent inter-symbol interference in a FIR channel if the length of
> the CP is larger than the delay spread of channel.
> 2. Makes linear convolution "appear" as circular convolution over the
> duration of the useful period in the OFDM symbol, thereby simplifying
> equalization at receiver.
> 3. My own advantage: Timing offset correction is simplified since any
> timing offset results in a progressive phase rotation, with
> sub-carriers closer to DC having much smaller phase rotation compared
> to sub-carriers closer to the nyquist frequency.
>
> My question is this: Advantage 3 holds only when the timing offset is
> such that the FFT input window starts before the ideal OFDM FFT start
> window i.e. the start of the FFT window includes a portion of the
> cyclic prefix, followed by the "useful portion" of the OFDM symbol. In
> such a case, the consequences outlined in (3) follow.
>
> What happens if the FFT input window starts with the first sample
> occuring AFTER the ideal FFT start window. In such a case, the last
> sample into the FFT input will be drawn from the cyclic prefix of the
> next OFDM symbol. In which case, the progressive phase rotation no
> longer occurs as the input to the FFT block is no longer circularly
> rotated.
>
> Should'nt practical OFDM symbols therefore include a cyclic postfix
> (drawn from the beginning of the OFDM symbol) to account for timing
> recovery if the timing offset is past the ideal timing instant. For
> example, the European DVB standard does not mention any cyclic
> post-fixes in their description of the OFDM transmit frame...
>
> Please clarify..
>
> thank you
> regards
> Vikram

Col and Eric,

Thank you very much for your prompt replies.
Col, I liked your solution very much.
The idea of repeating the OFDM symbol (since it is phase continuous) is
a very appealing idea.
It sounds like an idea that is easily implementable in practice.

I am doing an design exploration of what it takes to build up a set of
features for a OFDM modulator/demodulator. Hence the question...

Regards
Vikram

Col Brown wrote:
> Vikram,
>
> There are a couple of solutions to your problem. The first solution
> (to ensure your timing is correct) is to repeat the first OFDM symbol
> twice. This ensures that when you take the FFT over your window, you
> will capture a linear shifted version of your signal and can thus
> extract correct timing information. The second solution again
> assuming a repitition of the first OFDM symbol in a frame, then
> techniques are used to correlate the cyclic prefix to obtain a coarse
> estimate and then use further signal processing techniques to hone in
> on the correct timing.
>
> Incidentally, you can perform a similar estimate of the FFT window by
> extracting and correlating the scattered pilot symbols in a standard
> like DVB. Actually, as I stir the pot of my memory on OFDM, there
are
> a number of techniques you can use to get the correct timing,
because,
> after all, without that you'll end up with garbage coming out.
>
> Not sure if i answered your question because i'm not clear whether
you
> want a feeling for the problem or want a specific technique used in
> the standards?
>
> col
>
>
> [email protected] wrote in message
news:<[email protected] roups.com>...
> > Hello group,
> > It is my pleasure to be posting queries to this group again.
> >
> > My understanding of the presence of the cyclic prefix (CP) in an
OFDM
> > symbol is to:
> >
> > 1. Prevent inter-symbol interference in a FIR channel if the length
of
> > the CP is larger than the delay spread of channel.
> > 2. Makes linear convolution "appear" as circular convolution over
the
> > duration of the useful period in the OFDM symbol, thereby
simplifying
> > equalization at receiver.
> > 3. My own advantage: Timing offset correction is simplified since
any
> > timing offset results in a progressive phase rotation, with
> > sub-carriers closer to DC having much smaller phase rotation
compared
> > to sub-carriers closer to the nyquist frequency.
> >
> > My question is this: Advantage 3 holds only when the timing offset
is
> > such that the FFT input window starts before the ideal OFDM FFT
start
> > window i.e. the start of the FFT window includes a portion of the
> > cyclic prefix, followed by the "useful portion" of the OFDM symbol.
In
> > such a case, the consequences outlined in (3) follow.
> >
> > What happens if the FFT input window starts with the first sample
> > occuring AFTER the ideal FFT start window. In such a case, the last
> > sample into the FFT input will be drawn from the cyclic prefix of
the
> > next OFDM symbol. In which case, the progressive phase rotation no
> > longer occurs as the input to the FFT block is no longer circularly
> > rotated.
> >
> > Should'nt practical OFDM symbols therefore include a cyclic postfix
> > (drawn from the beginning of the OFDM symbol) to account for timing
> > recovery if the timing offset is past the ideal timing instant. For
> > example, the European DVB standard does not mention any cyclic
> > post-fixes in their description of the OFDM transmit frame...
> >
> > Please clarify..
> >
> > thank you
> > regards
> > Vikram

Hi Eric, Vikram, & Col,

Are you aware of any technique by which one can achieve orthognality o
the subcarriers (zero ICI) in an OFDM symbol duration without employin
any cyclic prefix ?

The channel is frequency selective and assume that sufficient guar
interval is provided between adjacent OFDM symbols (zero ISI). Also
perfect time and frequency synchronization is assumed and is not an issu
at present.

I am exploring one such scheme and any reply from your side (whether yo
are aware of one or not) will be of great help to me.

Thanks,

John