cyclotron wrote:
>>
>> cyclotron wrote:
>>
>>> I am trying to figure out why all treatments of MLSE receiver for ISI
>>> channels use the idea of a matched-filter followed by a noise whitening
>>> filter? 
>> Because this is simple and convenient concept.
>>
>>> Isn't the latter a simple inverse of the former?
>> No, it is not. Signal path != Noise path.
>>
>>
>> Vladimir Vassilevsky
>> DSP and Mixed Signal Design Consultant
>> http://www.abvolt.com
>>
> 
> I am not sure if I got your second comment. Here is a block diagram of the
> system taken from Proakis:
> 
> 
>         ______      ______                 ________   smplr   _____
>        |      |    |      |  h(t)         |        |    /    |     |
> I(k)---| g(t) |--->| c(t) |-------> + --->| h*(-t) |---/ --->| NWF |---->
>        |______|    |______|         |     |________|         |_____| 
>                                     |
>                                    n(t)
> 
> g(t)=transmit filter 
> c(t)=channel impulse response
> h(t)=received pulse with ISI
> h*(-t)=filter matched to the receive pulse h(t)
> n(t)=White Gaussian noise
> NWF=Noise Whitening Filter
> 
> Aren't both the noise (n(t)) and the "signal" (h(t)) going through the same
> path? 
> 
> To further elaborate my original post, if NWF simply "inverts" the matched
> filter h*(-t), then why do I need the last two blocks in my model? I could
> start out with the following:
> 
> 
>         ______      ______               smplr
>        |      |    |      |  h(t)         /
> I(k)---| g(t) |--->| c(t) |-------> + ---/  --->
>        |______|    |______|         |      
>                                     |
>                                    n(t)
> 
> 
> in which case the noise n(t) at the output is already white, and the 
> T-spaced samples of the non-Nyquist pulse h(t) give me the taps of the
> Equivalent Discrete-time White Noise Filter model, and I am done without
> having to invoke a matched filter followed by a whitening filter.
> 
> I am sure I'm missing something here ....
> 
The signal I(k) and the noise n(t) are going through different paths.

D'zat help?

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

>
>
>cyclotron wrote:
>
>> I am trying to figure out why all treatments of MLSE receiver for ISI
>> channels use the idea of a matched-filter followed by a noise whitening
>> filter? 
>
>Because this is simple and convenient concept.
>
>> Isn't the latter a simple inverse of the former?
>
>No, it is not. Signal path != Noise path.
>
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>

I am not sure if I got your second comment. Here is a block diagram of the
system taken from Proakis:


        ______      ______                 ________   smplr   _____
       |      |    |      |  h(t)         |        |    /    |     |
I(k)---| g(t) |--->| c(t) |-------> + --->| h*(-t) |---/ --->| NWF |---->
       |______|    |______|         |     |________|         |_____| 
                                    |
                                   n(t)

g(t)=transmit filter 
c(t)=channel impulse response
h(t)=received pulse with ISI
h*(-t)=filter matched to the receive pulse h(t)
n(t)=White Gaussian noise
NWF=Noise Whitening Filter

Aren't both the noise (n(t)) and the "signal" (h(t)) going through the same
path? 

To further elaborate my original post, if NWF simply "inverts" the matched
filter h*(-t), then why do I need the last two blocks in my model? I could
start out with the following:


        ______      ______               smplr
       |      |    |      |  h(t)         /
I(k)---| g(t) |--->| c(t) |-------> + ---/  --->
       |______|    |______|         |      
                                    |
                                   n(t)


in which case the noise n(t) at the output is already white, and the 
T-spaced samples of the non-Nyquist pulse h(t) give me the taps of the
Equivalent Discrete-time White Noise Filter model, and I am done without
having to invoke a matched filter followed by a whitening filter.

I am sure I'm missing something here ....

cyclotron wrote:

> I am trying to figure out why all treatments of MLSE receiver for ISI
> channels use the idea of a matched-filter followed by a noise whitening
> filter? 

Because this is simple and convenient concept.

> Isn't the latter a simple inverse of the former?

No, it is not. Signal path != Noise path.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

I am trying to figure out why all treatments of MLSE receiver for ISI
channels use the idea of a matched-filter followed by a noise whitening
filter? Isn't the latter a simple inverse of the former? In fact if we
simply don't go into the matched-filter/whitening-filter duo, we can still
derive what Proakis refers to as the "Equivalent Discrete-time White Noise
Filter Model" for an ISI channel (and it is this model that leads into all
those sub-optimal channel equalization techniques).

To quote from Andrea Goldsmith's Wireless Communication, 

"It might seem odd at first to introduce the matched filter g*(-t) at the
receive front-end only to cancel its effect in the equalizer." 

Can any of the gurus on this forum help me _understand_ the raison d'etre
for this seeming oddity?

Thanks!