## 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.