On Thu, 21 Feb 2008 02:12:55 -0800 (PST), Rune Allnor
<[email protected]> wrote:

>On 21 Feb, 06:05, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
>
>> He's talking about a communication system where the "matched filter"
>> is the pulse shaping filter. * Root Raised Cosine is a very common
>> matched filter that is applied to both the transmit and recieve pulses
>> to get a Raised Cosine frequency response.
>>
>> The "rectangular" reference means unfiltered NRZ pulses, i.e.,
>> rectangular symbols.
>
>Does 'matched filter' mean something else in this application
>than I think it does? If you have a 'raw' symbol and apply a
>window function to it, a 'classical' matched filter which
>looks for the 'raw' symbol will not preform very well at all.

The meaning is the same, but I think the terminology has resulted in
some confusion.

In the communications case Raised Cosine describes the frequency
response of the aggregate filter, not any windowing function that is
applied anywhere. The "match" part of the filtering is so that the
point where the receiver is sampling the symbol has no InterSymbol
Interference from adjacent symbols. This is the classical sense of
"matched filtering" in that the filter is matched to the symbol
response shape at that sample point. i.e., the energy sampled at
that point is maximizing the energy related to that symbol and
minimizing energy from other, adjacent symbols, or anything not
correlated with that pulse shape.

Generally, in order to limit the transmit spectrum to something
reasonable to minimize the occupied channel bandwidth, the transmit
filter shapes the spectrum to something with a reasonably flat top and
reasonably steep sides. Matching the receiving filter to the
spectral shape of the transmitted energy maximizes the received energy
while rejecting adjacent channel energy or adjacent noise. Performing
both of those function AND the zero-InterSymbol Interference function
is very often done by making the composite of the transmit and receive
filters a Raised Cosine shape in the frequency domain, and then
factoring it into two Root Raised Cosine filters so that half is done
at transmit and half at recieve.

If the channel is dispersive or otherwise adds distortion, a channel
equalizer inverts only the channel response, so that the matched pulse
filters still produce zero-ISI. A few people have built architectures
where a stupendous equalizer automatically seeks a zero-ISI solution
regardless of what was transmitted and what the channel response was,
so that it "matches" the received pulse shape. IMHO that's a more
complicated system than it needs to be, but it does work.

So the "raw" symbol is "windowed by a roughly sinx/x shape that has,
typically, a Root Raised Cosine frequency response. If the NRZ
rectangular pulses are left unfiltered and transmitted, which wastes a
lot of bandwidth, an integrate-and-dump filter in the receiver is the
"matched" filter for that situation.

The function of a "matching" filter that results in zero-ISI is
typically referred to as a Nyquist filter. There are an infinite
number of Nyquist filter shapes or matched pairs.

>My experience with matched filters is with certain types
>of sonars, where the system has to be tuned to what will
>be *recieved*. Frequency-dependent scattering and absorption
>effects mess up broad-band pulses to the extent that the
>matched filters at the recievers miss the reflections
>altogether. When we see that happen, we need to adjust
>the bandwidth of the transotted pulse so as to minimize
>the degrading scattering and absorption effects.
>
>Rune

Yup. In a comm system the channel equalizer performs that function of
correcting for the static or dynamic channel effects. The nature and
complexity of the equalizer depends on the expected channel
characteristics, which differ widely between short range, long range,
fixed or mobile systems.

One might get away with no equalizer at all in a satellite comm
system, or need a really big, gnarly equalizer for a mobile broadband
system that needs to work in an urban environment.



Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org