Hi,

So I have a really simple question about matched filters in
communication systems that, quite frankly, I'm a bit embarressed about
asking. Here goes:

So I understand that the point of the matched filter in a
communications system is to maximise the frequency spectrum of the
channel when transmitting pulses. So, for example as described in
Proakis, instead of sending a unit impluse (which would require an
infinite spectrum to communicate), a sinc (or in practise a root-raised
cosine) pulse is used, since that translated into a rectangle (max
bandwidth efficiency) in the frequency domain. This is superior to the
square pulse in the time domain since, in the frequency domain, this
translates to a sinc pulse (which make inefficient use of the available
bandwidth) Simple.

What I don't understand is precisely how this fits into the bigger
picture. Where it falls apart for me is I transmit the binary sequence
1010001010101, according to proakis (or at least my understanding of
what he is saying) for every '1' in the stream I send a sinc-like
pulse, for every '0' I send nothing. (these pulses and non-pulses
overlap to produce an analog waveform that can then be efficiently
transmitted). Basically, I'm not too sure how this fits in with
modulation. If i'm using a 256-QAM modulation scheme, does this mean
that that each sample of this new "analog" waveform (assuming 8-bit
samping), maps to a specific location on the (is it constellation? I
can't remember). This doesn't sound very efficient to me: 1bit mapping
to, in this case, 8-bits? Also, what about spread spectrum? In this
case, as I understand it, each bit is mapped to n bits according to the
state of the LFSR even before the filter which is even more
inefficient.

Now, looking at it slightly different, if i took that binary bitstream
and instead mapped it into bytes, and then filtered the data stream
using the matched filter then that would make more sense (no data
expansion). But, in this case the logic of the loop filter doesn't make
any sense. Whereas in the impulse (single bit) case, I am filtering the
infinite spectrum of an impulse response into the "rectangle"
accomodating the bandwidth of the channel. In the byte case, however, I
am simple removing those components about the maximum frequency of the
channel (that couldn't been recieved anyway), and not really doing
anything useful with the portion of the spectrum that could be
received.

I know this sounds like pretty confused argument it does so to me also.
Please help me out?

Stephen