cyclic prefix in OFDM and precursor ISI

Cyclic prefix at the head of ea symbol, will prevent ISI, but what about
the tail end of the symbol.Isn't that going to subjected to precursor ISI
and be distorted too.How then does cyclic prefix combat precursor ISI

"Zeph80" <surabhi_talwar@hotmail.com> wrote in message
news:rs2dnVMzo9lMu5LZRVn-sQ@giganews.com...
> Cyclic prefix at the head of ea symbol, will prevent ISI, but what about
> the tail end of the symbol.Isn't that going to subjected to precursor ISI
> and be distorted too.How then does cyclic prefix combat precursor ISI

I thought the point of the cyclic prefix was to make the time waveform
circularly symmetric so that when the FFT is taken over the middle portion
all of the echos add constructively to the FFT result. It shouldn't matter
whether the echo is early or late so long as the ends meet on the portion
that falls in the FFT window.

-Clark

Well, the cylic prefix exists to combat ISI and the contents itself(tail of
the symbol) lends itself to making the channel look like a circular
convolution.So it really has a dual purpose, and my question is not the
contents of the cylic prefix, but how its existence will remove ISI


>"Zeph80" <surabhi_talwar@hotmail.com> wrote in message
>news:rs2dnVMzo9lMu5LZRVn-sQ@giganews.com...
>> Cyclic prefix at the head of ea symbol, will prevent ISI, but what
about
>> the tail end of the symbol.Isn't that going to subjected to precursor
ISI
>> and be distorted too.How then does cyclic prefix combat precursor ISI
>
>I thought the point of the cyclic prefix was to make the time waveform
>circularly symmetric so that when the FFT is taken over the middle
portion
>all of the echos add constructively to the FFT result. It shouldn't
matter
>whether the echo is early or late so long as the ends meet on the
portion
>that falls in the FFT window.
>
>-Clark
>
>
>

Due to multi-path channel effect, multiple copies of the signal reaches
the receiver with different delayes which causes ISI.
Normaly the subcarriers in OFDM symbol are orthogonal or ( they have
exactly an integer number of cycles in the OFDM symbol period T).

Due to multi-path the orthogonality is lost--> ISI..
Using CP would allow us to always have an integer number of cycles in
the FFT interval even when multiple received symbols are delayed.


Thanks
Hany

Zeph80 said the following on 09/03/2006 03:51:
> Well, the cylic prefix exists to combat ISI and the contents itself(tail of
> the symbol) lends itself to making the channel look like a circular
> convolution.So it really has a dual purpose, and my question is not the
> contents of the cylic prefix, but how its existence will remove ISI
> 
> 

To eliminate ISI, you need a time-domain guard interval in-between 
blocks, which is longer than the length of the channel response.

i.e.

TX SIGNAL:

      Block 1               Block 2
    +---------+           +---------+
    |         |           |         |
    |         |           |         |
---+         +-----------+         +----------  -> t


RX SIGNAL: (Convolved with channel response)

      Block 1               Block 2
    +---------+           +---------+
    |          \__        |          \__
    |             \_____  |             \_____
---+                   \-+                   \  -> t
                         ^
                         ^
             Blocks do not overlap.



The CP serves this purpose.


-- 
Oli

"Oli Filth" <catch@olifilth.co.uk> wrote in message
news:ZbUPf.75351$m13.19901@newsfe5-gui.ntli.net...
> Zeph80 said the following on 09/03/2006 03:51:
> > Well, the cylic prefix exists to combat ISI and the contents itself(tail
of
> > the symbol) lends itself to making the channel look like a circular
> > convolution.So it really has a dual purpose, and my question is not the
> > contents of the cylic prefix, but how its existence will remove ISI
> >
> >
>
> To eliminate ISI, you need a time-domain guard interval in-between
> blocks, which is longer than the length of the channel response.
>
> i.e.
>
> TX SIGNAL:
>
>       Block 1               Block 2
>     +---------+           +---------+
>     |         |           |         |
>     |         |           |         |
> ---+         +-----------+         +----------  -> t
>
>
> RX SIGNAL: (Convolved with channel response)
>
>       Block 1               Block 2
>     +---------+           +---------+
>     |          \__        |          \__
>     |             \_____  |             \_____
> ---+                   \-+                   \  -> t
>                          ^
>                          ^
>              Blocks do not overlap.
>
>
>
> The CP serves this purpose.
>
>
> -- 
> Oli

Right and the key is the operation of an FFT. When one takes an FFT of a
signal they are not taking it over 256 time samples, for example, they are
taking it over an infinitely long signal that is the same 256 samples
repeated in each direction. Since the signal is conceptually infinite it
doesn't matter that the echoes from ISI are delayed relative to one another,
as far as the FFT is concerned they are still the same signal and thus the
FFT results from each echo add constrcutively in the final result. I guess
this is analagous to a perfect rake receiver. And all it costs is 20% (or
so) of your bandwidth because you're not transmitting information when the
CP is sent and a significant chunk of hardware to implement the FFT
operation.

-Clark

Anonymous wrote:
> "Oli Filth" <catch@olifilth.co.uk> wrote in message
> news:ZbUPf.75351$m13.19901@newsfe5-gui.ntli.net...
> > Zeph80 said the following on 09/03/2006 03:51:
> > > Well, the cylic prefix exists to combat ISI and the contents itself(tail
> of
> > > the symbol) lends itself to making the channel look like a circular
> > > convolution.So it really has a dual purpose, and my question is not the
> > > contents of the cylic prefix, but how its existence will remove ISI
> >
> > To eliminate ISI, you need a time-domain guard interval in-between
> > blocks, which is longer than the length of the channel response.
> >
> > The CP serves this purpose.
>
> Right and the key is the operation of an FFT. When one takes an FFT of a
> signal they are not taking it over 256 time samples, for example, they are
> taking it over an infinitely long signal that is the same 256 samples
> repeated in each direction. Since the signal is conceptually infinite it
> doesn't matter that the echoes from ISI are delayed relative to one another,
> as far as the FFT is concerned they are still the same signal and thus the
> FFT results from each echo add constrcutively in the final result.

Not exactly...

The echoes are from *multipath*, not ISI.  This causes two separate
issues in an OFDM system:
 * ISI - i.e. one block interfering with the next.
 * Frequency-selective fading on a per-block basis.

Use of any time-domain guard interval resolves the ISI problem, even an
all-zeros guard interval.

Using a CP as the guard interval resolves the second problem (well,
makes it easier to deal with) by making the linear convolution of the
channel appear as cyclic convolution of the DFT operation, which is
what you were alluding to above.

Simply put, it allows the fading on each sub-carrier to be
(approximately) corrected post-DFT with a coefficient of the form
r.exp(j*phi).

-- 
Oli

Maybe I'm not framing my question right.Everywhere I read, they mention how
the head of the symbol(first n samples) is affected due to previous symbols
and so how discarding the CP solves that.(the distortion occurs only in
head).What about the tail of the OFDM symbol,wont that be affected by the
future symbols as much as the head would be by prevoius symbols.Why no
guard interval at the end too?

>Anonymous wrote:
>> "Oli Filth" <catch@olifilth.co.uk> wrote in message
>> news:ZbUPf.75351$m13.19901@newsfe5-gui.ntli.net...
>> > Zeph80 said the following on 09/03/2006 03:51:
>> > > Well, the cylic prefix exists to combat ISI and the contents
itself(tail
>> of
>> > > the symbol) lends itself to making the channel look like a
circular
>> > > convolution.So it really has a dual purpose, and my question is not
the
>> > > contents of the cylic prefix, but how its existence will remove
ISI
>> >
>> > To eliminate ISI, you need a time-domain guard interval in-between
>> > blocks, which is longer than the length of the channel response.
>> >
>> > The CP serves this purpose.
>>
>> Right and the key is the operation of an FFT. When one takes an FFT of
a
>> signal they are not taking it over 256 time samples, for example, they
are
>> taking it over an infinitely long signal that is the same 256 samples
>> repeated in each direction. Since the signal is conceptually infinite
it
>> doesn't matter that the echoes from ISI are delayed relative to one
another,
>> as far as the FFT is concerned they are still the same signal and thus
the
>> FFT results from each echo add constrcutively in the final result.
>
>Not exactly...
>
>The echoes are from *multipath*, not ISI.  This causes two separate
>issues in an OFDM system:
> * ISI - i.e. one block interfering with the next.
> * Frequency-selective fading on a per-block basis.
>
>Use of any time-domain guard interval resolves the ISI problem, even an
>all-zeros guard interval.
>
>Using a CP as the guard interval resolves the second problem (well,
>makes it easier to deal with) by making the linear convolution of the
>channel appear as cyclic convolution of the DFT operation, which is
>what you were alluding to above.
>
>Simply put, it allows the fading on each sub-carrier to be
>(approximately) corrected post-DFT with a coefficient of the form
>r.exp(j*phi).
>
>-- 
>Oli
>
>

Maybe I'm not framing my question right.Everywhere I read, they mention how
the head of the symbol(first n samples) is affected due to previous symbols
and so how discarding the CP solves that.(the distortion occurs only in
head).What about the tail of the OFDM symbol,wont that be affected by the
future symbols as much as the head would be by prevoius symbols.Why no
guard interval at the end too?

Zeph80 said the following on 09/03/2006 18:53:
> Maybe I'm not framing my question right.Everywhere I read, they mention how
> the head of the symbol(first n samples) is affected due to previous symbols
> and so how discarding the CP solves that.(the distortion occurs only in
> head).What about the tail of the OFDM symbol,wont that be affected by the
> future symbols as much as the head would be by prevoius symbols.

Technically, no.  By definition, any realisable channel response must be 
causal - something at time t = 1 can't possibly affect something that 
happened at t = 0.

However, the question of whether so-called precursor rays are an issue 
depends on your frame of reference.  If your timing algorithm is 
designed with t = 0 defined as the strongest incoming ray, rather than 
the first incoming ray, then it will appear that precursors are 
affecting previous symbols.  But in actual fact, its the fact that 
you're windowing blocks too late that's causing the interference.

If you design your timing recovery algorithm to sync to the first 
incoming ray, then there will be no "precursors".


> Why no guard interval at the end too?

There is nothing to stop you utilise a cyclic postfix as well, the maths 
is identical.

Be aware though, a lot of standard OFDM synchronisation algorithms in 
the literature rely on the correlation statistics of the standard cyclic 
prefix structure.  Adding a postfix will probably require quite a bit of 
re-working of these algorithms.



-- 
Oli