FPGA Central

Cyclic prefix at the head of ea symbol, will prevent ISI, but what abou
the tail end of the symbol.Isn't that going to subjected to precursor IS
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 o
the symbol) lends itself to making the channel look like a circula
convolution.So it really has a dual purpose, and my question is not th
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 wha
about
>> the tail end of the symbol.Isn't that going to subjected to precurso
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 middl
portion
>all of the echos add constructively to the FFT result. It shouldn'
matter
>whether the echo is early or late so long as the ends meet on th
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 ho
the head of the symbol(first n samples) is affected due to previous symbol
and so how discarding the CP solves that.(the distortion occurs only i
head).What about the tail of the OFDM symbol,wont that be affected by th
future symbols as much as the head would be by prevoius symbols.Why n
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 content
itself(tail
>> of
>> > > the symbol) lends itself to making the channel look like
circular
>> > > convolution.So it really has a dual purpose, and my question is no
the
>> > > contents of the cylic prefix, but how its existence will remov
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 o
a
>> signal they are not taking it over 256 time samples, for example, the
are
>> taking it over an infinitely long signal that is the same 256 samples
>> repeated in each direction. Since the signal is conceptually infinit
it
>> doesn't matter that the echoes from ISI are delayed relative to on
another,
>> as far as the FFT is concerned they are still the same signal and thu
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 ho
the head of the symbol(first n samples) is affected due to previous symbol
and so how discarding the CP solves that.(the distortion occurs only i
head).What about the tail of the OFDM symbol,wont that be affected by th
future symbols as much as the head would be by prevoius symbols.Why n
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

Zeph80 wrote:
> 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?

"The evil that men do lives on after them ..." What has not yet happened
can do no harm. I.e., causality.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

>Zeph80 said the following on 09/03/2006 18:53:
>> Maybe I'm not framing my question right.Everywhere I read, they mentio
how
>> the head of the symbol(first n samples) is affected due to previou
symbols
>> and so how discarding the CP solves that.(the distortion occurs onl
in
>> head).What about the tail of the OFDM symbol,wont that be affected b
the
>> future symbols as much as the head would be by prevoius symbols.
>
>Technically, no. By definition, any realisable channel response must b

>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 math

>is identical.
>
>Be aware though, a lot of standard OFDM synchronisation algorithms in
>the literature rely on the correlation statistics of the standard cycli

>prefix structure. Adding a postfix will probably require quite a bit o

>re-working of these algorithms.
>
>
>
>--
>Oli
>

Thank you, that makes a lot of sense.Though the cause for my confusio
stems, from the fact that while studying equalization they always conside
future symbols (at least in Sc systems).I realize the system is causal, s
is establishing a timning reference more difficult in these cases, or i
that the delay spread happens to be longer that the symbol time,and henc
precursor considered in Sc systems.

Thank you, that makes a lot of sense.Though the cause for my confusion
stems, from the fact that while studying equalization they alway
consider
future symbols (at least in Sc systems).I realize the system is causal
so
is establishing a timning reference more difficult in these cases, or is
that the delay spread happens to be longer that the symbol time,and hence
precursor considered in Sc systems.

Thank you, that makes a lot of sense.Though the cause for my confusion
stems, from the fact that while studying equalization they alway
consider
future symbols (at least in Sc systems).I realize the system is causal
so
is establishing a timning reference more difficult in these cases, or is
that the delay spread happens to be longer that the symbol time,and hence
precursor considered in Sc systems.