OFDM Cyclic prefix question

Hi,

This has been a very informative forum while i have been working on this
small simulation. I have a couple of questions now.

1) First I am simulating a simple uncoded 16-QAM OFDM system. I tried
evaluate the performance of such a system in an AWGN channel and the
results i have matches results of a single carrier system using 16 QAM in
a AWGN channel.

2) Now I would like to study the effects of cyclic prefix in an OFDM
system and do that i have made the necessary modifications to my
transmitter and receiver. Specifically, i add the cyclic prefix at the
transmitter pass it through a multipath channel, remove the cyclic prefix
at the receiver before the FFT operation at the receiver.

3) The multipath channel i consider have static paths ( No fading, No
Dopper ). 

My question is : For such an uncoded system what channel impulse response
can i consider whereby i can see the benefits of the cyclic prefix. 
A comparison of  channel impulse response vs prefix lengths ( greater and
less than impulse response length) is what i have in mind.

Also, I am not clear on what sort of compensation needs to be done at the
receiver for the channel. If we assume perfect knowledge of the channel at
the receiver an operation of the form FFT(Y)./FFT(h) would suffice ?, where
Y is the received signal before FFT operation and h is the impulse
response


Thanks

>Hi,
>
>This has been a very informative forum while i have been working on this
>small simulation. I have a couple of questions now.
>
>1) First I am simulating a simple uncoded 16-QAM OFDM system. I tried
>evaluate the performance of such a system in an AWGN channel and the
>results i have matches results of a single carrier system using 16 QAM
in
>a AWGN channel.
>
>2) Now I would like to study the effects of cyclic prefix in an OFDM
>system and do that i have made the necessary modifications to my
>transmitter and receiver. Specifically, i add the cyclic prefix at the
>transmitter pass it through a multipath channel, remove the cyclic
prefix
>at the receiver before the FFT operation at the receiver.
>
>3) The multipath channel i consider have static paths ( No fading, No
>Dopper ). 
>
>My question is : For such an uncoded system what channel impulse
response
>can i consider whereby i can see the benefits of the cyclic prefix. 
>A comparison of  channel impulse response vs prefix lengths ( greater
and
>less than impulse response length) is what i have in mind.
>
>Also, I am not clear on what sort of compensation needs to be done at
the
>receiver for the channel. If we assume perfect knowledge of the channel
at
>the receiver an operation of the form FFT(Y)./FFT(h) would suffice ?,
where
>Y is the received signal before FFT operation and h is the impulse
>response
>
>
>Thanks
>
>

Hi, As long as the delay spread of channel is less than CP length,
multipath won't affect performance. But you have to consider if the peak
does not appear at the very beginning, then there might still be some ISI
"leaking" from backwards. 

As long as the channel impulse response is less than the duration of
the cyclical prefix, there should be no inter-symbol interference. In
this case the receiver need only remove the cyclical prefix samples and
conduct an FFT for demodulation of the symbol.

Should this not be the case as is usually expected, the receiver needs
to compensate by creating a time-domain equalizer (TEQ) at the front
end. In truth, the purpose of the TEQ is to create an overall shortened
impulse response when placed in series with the actual channel that
ordinarily has a impuse response longer than the CP.

There are any number of methods of computing the TEQ, all with various
tradeoffs. 

Good luck.

-V

>As long as the channel impulse response is less than the duration of
>the cyclical prefix, there should be no inter-symbol interference. In
>this case the receiver need only remove the cyclical prefix samples and
>conduct an FFT for demodulation of the symbol.
>
>Should this not be the case as is usually expected, the receiver needs
>to compensate by creating a time-domain equalizer (TEQ) at the front
>end. In truth, the purpose of the TEQ is to create an overall shortened
>impulse response when placed in series with the actual channel that
>ordinarily has a impuse response longer than the CP.
>
>There are any number of methods of computing the TEQ, all with various
>tradeoffs. 
>
>Good luck.
>
>-V
>
>

Hi, 

Thank you for your replies. I don't think I made myself clear in my
earlier posting.

1) What I want to understand through simulation is the effect of cyclic
prefix length on performance in a multipath channel. 

For example consider that the channel impulse response is [0.7071 0 0 0 0
0 0 0 0 0.7071], which is a channel with impulse response length 10 (
static paths with no fading component).
Now if we consider four cases 
1)cp=0, 
2)cp=5, 
3) cp=11
4) cp =15

The first two cases, based on theory should result in ISI. My question is:
when i perform the simulations i do not see much of a difference. Will the
difference be seen only at high SNR's ?


2) Presently, I transmit a known OFDM symbol at the beginning of the
simulation, At the receiver after FFT operation I divide the output with
the known OFDM symbol values and store them as channel state information
for the remaining simulation. 
For all subsequent transmissions after the FFT operation i divide the
output with the stored channel state information ( Zero forcing in
frequency domain). 
My question is even for cyclic prefix lengths greater than the impulse
response, don't we still need to do equalization operation at the receiver
( something trivial as i am doing now). 
Also can anyone suggest me a reference to other frequency domain
equalization approaches. 

Thanks