matched filters and interpolation

Hi,
I'm back on a project which I've been working on at times. The piece I
am working on right now is digital clock recovery which works ok but
I'd like to see if I can improve the performance. The current
implementation is a feed-forward timing detector and an interpolator
for data recovery with a farrow type interpolator. The piece I am
trying to add is a matched filter. I only have two samples per symbol
generated by an ADC triggered by a free-running clock. The channel has
significant frequency dependent loss and ISI. The difficulty is that
the transmit filter is not something which is suitable to DSP. It is a
very crude slew control filter which is basically a trapezoid with
0.5T rise time and 0.5T fall time instead of a square pulse. So an
isolated pulse looks like this. The symbol ends when the pulse starts
to fall so if there are multiple symbols of value 1 you get a
trapezoid with a longer top.
  _             _____
_/ \_        __/     \____


Is a matched filter still applicable in this situation ? How would one
design a digital matched filter with only two samples per symbol ? I
am considering merging the matched filter into the interpolator but
that makes testing the matched filter impossible.

Any suggestions are welcome.

Thanks,

Muzaffer Kal

http://www.dspia.com
ASIC/FPGA design/verification consulting specializing in DSP algorithm implementations

On Sun, 18 Jan 2004 23:13:53 GMT, Muzaffer Kal <kal@dspia.com> wrote:

>Hi,
>I'm back on a project which I've been working on at times. The piece I
>am working on right now is digital clock recovery which works ok but
>I'd like to see if I can improve the performance. The current
>implementation is a feed-forward timing detector and an interpolator
>for data recovery with a farrow type interpolator. The piece I am
>trying to add is a matched filter. I only have two samples per symbol
>generated by an ADC triggered by a free-running clock. The channel has
>significant frequency dependent loss and ISI. The difficulty is that
>the transmit filter is not something which is suitable to DSP. It is a
>very crude slew control filter which is basically a trapezoid with
>0.5T rise time and 0.5T fall time instead of a square pulse. So an
>isolated pulse looks like this. The symbol ends when the pulse starts
>to fall so if there are multiple symbols of value 1 you get a
>trapezoid with a longer top.
>  _             _____
>_/ \_        __/     \____
>
>
>Is a matched filter still applicable in this situation ?

Yes, and this is its impulse response (in continuous time):
  _  
_/ \_

as this is just the time-inverse of the transmit filter impulse
response.  (And yes, it is equivalent to a linear filter, even though
it has been implemented using "non-linear"-type ops such as slew rate
limiting.)

> How would one
>design a digital matched filter with only two samples per symbol ?

With this impulse response:

1,1 or perhaps 0.5,1,0.5 (they're the same but with a phase shift)

Note that this doesn't look so good in the frequency domain, but at
least it's better than a pulse without slew rate limiting.

> I
>am considering merging the matched filter into the interpolator but
>that makes testing the matched filter impossible.

I commiserate.

BTW, It would probably be easier if you could lock your ADC clock to
the symbol rate OR if you could sample at 4x the symbol rate.

Regards,
Allan.