BER performance for matched filter detection

Let us consider the BER performance for a rectangular baseband pulse using an integrate and dump filter for detection. (We know that this is a matched filter detector for this pulse shape and hence we can infer that this result will apply for all matched filter detectors regardless of the pulse shape.)





If we look at a single symbol s(t) of voltage V passing through the detector, with additive noise n(t), then the output of the integrator y(t) can be written as:

The contribution at the sampling instant due to the symbol is thus a voltage V·T volts. The symbol will be detected correctly if the contribution due to noise does not take the signal plus noise sample below the decision threshold (V·T/2 volts) which is halfway between 0 volts for the logic 0 case, and V·T volts for the logic 1 case.