## BER performance for matched filter detection (cont) |
In-depth

#### The statistics of the integrated noise at the output of the integrate and dump detector are such that the probability density of the noise samples follows a Gaussian distribution as shown here. The probability of making a decision error is thus the probability of the noise sample being more negative than -V·T/2 volts. |

#### The probability of symbol error Ps (see in-depth section) is therefore given by the expression: #### Ps (symbol error probability) = (0.5·erfc)(0.25·Es/N0)1/2 #### where Es is the energy in the logic 1 symbol, and N0 is the noise power density.

#### If the symbol to be detected were a logic 0 (that is, 0 volts) rather than a logic 1, then exactly the same reasoning can be applied, except we need to evaluate the probability that the noise sample produces a positive value greater than +V·T/2 volts for an error to occur. Owing to the symmetry of the Gaussian distribution about 0 volts, this probability of error is identical to that for the logic 1 case.