Channel-induced ISI

Hi, guys:

  Please give me some help for the following question:
  What is the relationship between the channel-induced ISI (i.e.
fast-fading and frequency selective fading) and Nyquist criterion of
zero ISI?
  I know both of them, but I can't find any link between them.
  Channel-induced ISI is produced because the coherent bandwidth f0 is
narrowed than the signal symbol rate. But I remember the ISI emerges
when Nyquist criterion can't be satisfied, namely the symbol rate is
higher than double limited bandwidth. It doesn't mention about
coherenet bandwidth...
 Any one can give me a tips for this question? THX a lot.

                                               Adi

Consider the communications channel to be a time varying filter H (e.g.
h(tau,t)) and the transmitter and receiver to have filters S and R,
respectively.

Fast fading / slow fading is a qualitative description of how the
channel filter varies with time (the "t" term).  One could characterize
the channel filter in the time domain by the correlation time of the
channel, or in the frequency domain by the Doppler power spectrum.  By
itself, the fade rate doesn't introduce meaningful intersymbol
interference - just signal attenuation/amplification and phase
rotation.  A reasonable definition of fast fading is the correlation
time of the channel is less than a symbol (or chip) time.

Frequency selective fading / frequency flat fading is a qualitative
description of how the channel filter varies in the "tau" term, e.g.
how much spreading/smearing occurs for an impulse into the channel.
One could characterize the channel filter in the time delay domain by
the delay spread of the channel, or in the frequency domain by the
coherence bandwidth of the channel.  This is the portion thats adding
the meaningful intersymbol interference.  A reasonable definition of
frequency selective fading is the delay spread of the channel is larger
than a symbol (or chip) time.

I wouldn't say that channel-induced ISI is produced only when the
coherence bandwidth is narrower than the symbol rate -- channel induced
ISI is produced whenever the delay spread is non-zero.

The book "Digital Communications" by Proakis has a good discussion of
this.

But back to your original question - how to consider the Nyquist ISI
criterion.  Instead of just looking at the system transfer function as
SR, look at it as SHR.  If the transmitter  knows what the channel
response is, then the transmitter could use the filter S/H and the
receiver could use the filter R.  If only the receiver knows what the
channel response is, the transmitter would still use the filter S but
the reciever could use the filter (1/H)R.  (depends on how well behaved
H is, of course)

Tim


shellte@hotmail.com wrote:
> Hi, guys:
>
>   Please give me some help for the following question:
>   What is the relationship between the channel-induced ISI (i.e.
> fast-fading and frequency selective fading) and Nyquist criterion of
> zero ISI?
>   I know both of them, but I can't find any link between them.
>   Channel-induced ISI is produced because the coherent bandwidth f0 is
> narrowed than the signal symbol rate. But I remember the ISI emerges
> when Nyquist criterion can't be satisfied, namely the symbol rate is
> higher than double limited bandwidth. It doesn't mention about
> coherenet bandwidth...
>  Any one can give me a tips for this question? THX a lot.
> 
>                                                Adi

shellte@hotmail.com wrote:
> Hi, guys:
>
>   Please give me some help for the following question:
>   What is the relationship between the channel-induced ISI (i.e.
> fast-fading and frequency selective fading) and Nyquist criterion of
> zero ISI?
>   I know both of them, but I can't find any link between them.
>   Channel-induced ISI is produced because the coherent bandwidth f0 is
> narrowed than the signal symbol rate. But I remember the ISI emerges
> when Nyquist criterion can't be satisfied, namely the symbol rate is
> higher than double limited bandwidth. It doesn't mention about
> coherenet bandwidth...
>  Any one can give me a tips for this question? THX a lot.
>
>                                                Adi


But I remember the ISI emerges
> when Nyquist criterion can't be satisfied, namely the symbol rate is
> higher than double limited bandwidth.


that is your problem.,,,,

in this context, the Nyquist criterion for no ISI is not simply the
channel BW but that the channel have a specific response, namely Root
Raised Cosine....

Mark

Mark wrote:
> shellte@hotmail.com wrote:
>> Hi, guys:
>>
>>   Please give me some help for the following question:
>>   What is the relationship between the channel-induced ISI (i.e.
>> fast-fading and frequency selective fading) and Nyquist criterion of
>> zero ISI?
>>   I know both of them, but I can't find any link between them.
>>   Channel-induced ISI is produced because the coherent bandwidth f0 is
>> narrowed than the signal symbol rate. But I remember the ISI emerges
>> when Nyquist criterion can't be satisfied, namely the symbol rate is
>> higher than double limited bandwidth. It doesn't mention about
>> coherenet bandwidth...
>>  Any one can give me a tips for this question? THX a lot.
>>
>>                                                Adi
> 
> 
> But I remember the ISI emerges
>> when Nyquist criterion can't be satisfied, namely the symbol rate is
>> higher than double limited bandwidth.
> 
> 
> that is your problem.,,,,
> 
> in this context, the Nyquist criterion for no ISI is not simply the
> channel BW but that the channel have a specific response, namely Root
> Raised Cosine....

Raised cosine is only one of many response shapes that suppress ISI. The 
requirement is that the impulse response place zeros at the center of 
all symbols but the current one.

Root raised cosine doesn't accomplish that; raised cosine does. Using 
root raised cosine at the transmitter to control bandwidth and again at 
the receiver to suppress noise simultaneously gives an overall root 
raised cosine response and the SNR advantage of matched filters.

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

On Sat, 02 Sep 2006 14:51:38 -0400, Jerry Avins <jya@ieee.org> wrote:

>Mark wrote:
>> shellte@hotmail.com wrote:
>>> Hi, guys:
>>>
>>>   Please give me some help for the following question:
>>>   What is the relationship between the channel-induced ISI (i.e.
>>> fast-fading and frequency selective fading) and Nyquist criterion of
>>> zero ISI?
>>>   I know both of them, but I can't find any link between them.
>>>   Channel-induced ISI is produced because the coherent bandwidth f0 is
>>> narrowed than the signal symbol rate. But I remember the ISI emerges
>>> when Nyquist criterion can't be satisfied, namely the symbol rate is
>>> higher than double limited bandwidth. It doesn't mention about
>>> coherenet bandwidth...
>>>  Any one can give me a tips for this question? THX a lot.
>>>
>>>                                                Adi
>> 
>> 
>> But I remember the ISI emerges
>>> when Nyquist criterion can't be satisfied, namely the symbol rate is
>>> higher than double limited bandwidth.
>> 
>> 
>> that is your problem.,,,,
>> 
>> in this context, the Nyquist criterion for no ISI is not simply the
>> channel BW but that the channel have a specific response, namely Root
>> Raised Cosine....
>
>Raised cosine is only one of many response shapes that suppress ISI. The 
>requirement is that the impulse response place zeros at the center of 
>all symbols but the current one.
>
>Root raised cosine doesn't accomplish that; raised cosine does. Using 
>root raised cosine at the transmitter to control bandwidth and again at 
>the receiver to suppress noise simultaneously gives an overall root 
>raised cosine response and the SNR advantage of matched filters.
>
>Jerry

 Wow.  We'll make a comm engineer out of you yet, Jerry.  ;)

As Jerry has stated, there are essentially an infinite number of
possible filter responses that will produce zero ISI and therefore
qualify as a "Nyquist" filter.

Also as Jerry has already stated, the requirement for zero ISI is just
that the trasmit, channel, and receive filter response are zero at the
sampling point of all the symbols within the response aperture except
the current (output) symbol.  So it can easily be seen from this that
a lot of things, not just coherence bandwidth, can affect ISI.   Any
channel memory (i.e., delay spread) can potentially cause ISI.  Pretty
much anything that affects the net impulse response so that it is no
longer zero at the sampling points of the adjacent symbols is, by
definition, causing ISI.   That's pretty easy to do.   It is, of
course, actually fairly difficult to keep that from happening in many
systems.
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Eric Jacobsen wrote:

   ...

>  Wow.  We'll make a comm engineer out of you yet, Jerry.  ;)

Ignorance is often remediable. :^)

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

> >Root raised cosine doesn't accomplish that; raised cosine does.

Yes thank you.... my error...  raised cosine is of course correct.
Mark

Thx for all your instruction. They really give me a lot of help.

That means: Channel-induce ISI is just channel's problem, but actually
ISI emerges because of the whole system (transmitter, channel and
receiver). H(f)=Ht(f)Hc(f)Hr(f).

Therefore in order to eliminate the ISI, we should consider impulse
response of all of them and not just focus on the coherent bandwidth.

THX.

                                                                     Adi