mohatta2015.pdf

38 MATCHED FILTERING
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- 4 - 3 - 2 - 1 0 1 2 3 4
decision variable values
Figure 2.3
BPSK received PDFs.
2.3.3 TDM
With TDM, the channel response for symbol s(m) is h(t — mT). Thus, the decision
variables z(m) are obtained by correlating to
fm(t) = /o(i - mT) = h(t - mT). (2.33)
We can interpret this as matched filtering using filter response g(t) = h*(—r) and
sampling the output every T seconds. Thus, to obtain z(m) for different m, we
filter with a common filter response and sample the result at different times.
2.3.4 Maximum SNR
Does MF maximize output SNR? We will show that it does. Thus, another way
to derive the matched filter is to find the linear receiver filter that maximizes the
output SNR. Also, we saw in the previous section that for MF, error performance
depends directly on the output SNR. This is true in general. Thus, maximizing
output SNR will allow us to minimize bit or symbol error rate.
Consider filtering the complex received signal r(t) to produce the real decision
variable for BPSK symbol s(0), denoted z r . Instead of working with a filter impulse
response and a convolutional integral, it is more convenient to work with a complex