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does the equalizer come before the matched filter or after?

Started by bharat pathak December 5, 2010
I have a basic doubt. Does the equalizer come before the matched
filter or after?


On 12/05/2010 11:16 AM, bharat pathak wrote:
> I have a basic doubt. Does the equalizer come before the matched > filter or after? > >
bharat, A matched filter can be thought of as a device that performs a time-domain correlation of the incoming signal with a known signal shape. If the channel filtering changes the shape of the filter, and the equalizer's purpose is to inverse-filter the channel filtering, what would the answer be? -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" mailto://yates@ieee.org % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
On 12/05/2010 02:19 PM, Randy Yates wrote:
 > [...]
> If the channel filtering changes the shape of the filter,
Correction: If the channel filtering changes the shape of the signal... -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" mailto://yates@ieee.org % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
On 12/05/2010 02:19 PM, Randy Yates wrote:
> On 12/05/2010 11:16 AM, bharat pathak wrote: >> I have a basic doubt. Does the equalizer come before the matched >> filter or after? >> >> > > bharat, > > A matched filter can be thought of as a device that performs a > time-domain correlation of the incoming signal with a known signal > shape. If the channel filtering changes the shape of the filter, > and the equalizer's purpose is to inverse-filter the channel > filtering, what would the answer be?
Although now that I think about it, if they're both linear you can swap the order... -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" mailto://yates@ieee.org % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Thanks Randy.

-Bharat
On Sun, 05 Dec 2010 16:26:58 -0500, Randy Yates <yates@ieee.org>
wrote:

>On 12/05/2010 02:19 PM, Randy Yates wrote: >> On 12/05/2010 11:16 AM, bharat pathak wrote: >>> I have a basic doubt. Does the equalizer come before the matched >>> filter or after? >>> >>> >> >> bharat, >> >> A matched filter can be thought of as a device that performs a >> time-domain correlation of the incoming signal with a known signal >> shape. If the channel filtering changes the shape of the filter, >> and the equalizer's purpose is to inverse-filter the channel >> filtering, what would the answer be? > >Although now that I think about it, if they're both linear you >can swap the order...
What if the equalizer is adaptive ie time-varying? In that case the equalizer also tries to synthesize the matched filter too but I am not entirely sure if having the known matched filter helps the equalizer adapt better. -- Muzaffer Kal DSPIA INC. ASIC/FPGA Design Services http://www.dspia.com
On Dec 6, 3:52&#2013266080;am, "bharat pathak" <bharat@n_o_s_p_a_m.arithos.com>
wrote:
> Thanks Randy. > > -Bharat
It's probably worth noting that the matched filter and the equalizer may not operate at the same sampling rate, e.g. root-raised-cosine matched filter running at a twice oversampled rate, decimation by 2, followed by a symbol-spaced equalizer. So, in the case where the matched filter is running at a higher sample rate then the system is certainly not linear in that case and the matched filter must come first. It is for this reason that I would be inclined just to say that the matched filter comes first. Frank

bharat pathak wrote:

> I have a basic doubt. Does the equalizer come before the matched > filter or after?
The order of applying equalizer and matched filter would be unimportant but the equalizer is usually executed at low sample rate (1 or 2 samples per symbol). So, filter first, equalizer after. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
On 12/06/2010 04:13 AM, Frank wrote:
 > On Dec 6, 3:52 am, "bharat pathak"<bharat@n_o_s_p_a_m.arithos.com>
 > wrote:
 >> Thanks Randy.
 >>
 >> -Bharat
 >
 >
 > It's probably worth noting that the matched filter and the equalizer
 > may not operate at the same sampling rate, e.g. root-raised-cosine
 > matched filter running at a twice oversampled rate, decimation by 2,
 > followed by a symbol-spaced equalizer. So, in the case where the
 > matched filter is running at a higher sample rate then the system is
 > certainly not linear in that case and the matched filter must come
 > first. It is for this reason that I would be inclined just to say that
 > the matched filter comes first.
 >
 > Frank

Hi Frank,

 From a processing perspective I see your point, but if the channel
has corrupted the waveshape, what good is a matched filter going to
do?
-- 
Randy Yates                      % "My Shangri-la has gone away, fading like
Digital Signal Labs              %  the Beatles on 'Hey Jude'"
mailto://yates@ieee.org          %
http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
On Mon, 06 Dec 2010 01:12:05 -0800, Muzaffer Kal <kal@dspia.com>
wrote:

>On Sun, 05 Dec 2010 16:26:58 -0500, Randy Yates <yates@ieee.org> >wrote: > >>On 12/05/2010 02:19 PM, Randy Yates wrote: >>> On 12/05/2010 11:16 AM, bharat pathak wrote: >>>> I have a basic doubt. Does the equalizer come before the matched >>>> filter or after? >>>> >>>> >>> >>> bharat, >>> >>> A matched filter can be thought of as a device that performs a >>> time-domain correlation of the incoming signal with a known signal >>> shape. If the channel filtering changes the shape of the filter, >>> and the equalizer's purpose is to inverse-filter the channel >>> filtering, what would the answer be? >> >>Although now that I think about it, if they're both linear you >>can swap the order... > >What if the equalizer is adaptive ie time-varying? In that case the >equalizer also tries to synthesize the matched filter too but I am not >entirely sure if having the known matched filter helps the equalizer >adapt better. >-- >Muzaffer Kal > >DSPIA INC. >ASIC/FPGA Design Services > >http://www.dspia.com
That's an important consideration. I know of systems that have been built with just a big, gnarly equalizer intended to sort out the channel AND the pulse shape in one operation. This means that the EQ has to be designed with enough degrees of freedom to do both tasks. If the pulse shape is known, then the EQ can be simplified by running the known, matched filter prior to it. This lets the EQ be used for what it is intended, i.e., correcting the channel effects. So when the pulse shape is known it is often less complex to implement the (often decimating) matched filter followed by the EQ. Letting the matched filter do the decimation also helps control the EQ complexity by letting it be T-spaced rather than some higher sampling rate. Strictly speaking the order is not consequential since, as Randy pointed out, the EQ and matched filter are both linear filters. The complexity can get pretty crazy if the EQ is first, though, and it still has to be trained with errors sliced after both filters. This probably does bad things to the error feedback latency from the slicer to the EQ. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com